### premio tesi di dottorato – 57 –

#### PREMIO TESI DI DOTTORATO

#### Commissione giudicatrice, anno 2015

Vincenzo Varano, *presidente della Commissione*

Tito Arecchi, *Area scientifica* Aldo Bompani, *Area Scienze Sociali* Franco Cambi, *Area Umanistica* Paolo Felli, *Area Tecnologica* Michele Arcangelo Feo, *Area Umanistica* Roberto Genesio, *Area Tecnologica* Mario Pio Marzocchi, *Area Scientifica* Adolfo Pazzagli, *Area Biomedica* Giuliano Pinto, *Area Umanistica* Salvatore Ruggieri, *Area Biomedica* Saulo Sirigatti, *Area Biomedica* Fiorenzo Cesare Ugolini, *Area Tecnologica* Graziella Vescovini, *Area Umanistica*

# **Imaging and engineering optical localized modes at the nanoscale**

Firenze University Press 2016

Imaging and engineering optical localized modes at the nanoscale / Niccolò Caselli. – Firenze : Firenze University Press, 2016.

(Premio Tesi di Dottorato; 57)

http://digital.casalini.it/9788864533513

ISBN 978-88-6453-350-6 (print) ISBN 978-88-6453-351-3 (online)

Front cover design: Alberto Pizarro Fernández, Pagina Maestra snc Front cover photo: Niccolò Caselli, Federico La China

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#### *Firenze University Press Editorial Board*

G. Nigro (Co-ordinator), M.T. Bartoli, M. Boddi, R. Casalbuoni, C. Ciappei, R. Del Punta, A. Dolfi, V. Fargion, S. Ferrone, M. Garzaniti, P. Guarnieri, A. Mariani, M. Marini, A. Novelli, M.C. Torricelli, M. Verga, A. Zorzi.

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### **Contents**

9

The work presented in this thesis concerns the optics research field that is commonly called micro or nano-photonics. The term "photonics" emerged at the end of last century to describe the fundamental study of light and its applications to technology, whose purpose is to accomplish functions traditionally undertaken by electronics, such as telecommunications, information processing, and so on. In fact, in the effort to further progress the high density transistor integration and thus the modern electronic system performances, scientists are now turning to photons instead of electrons as the information carriers in communication. Photons show several advantages. Light can carry a larger amount of information per second. In addiction, at the single photon level, quantum information networks and quantum cryptography scheme can be pursued. Furthermore, photons are not as strongly interacting as electrons, thus reducing energy losses. However, in spite of the numerous advantages of photons, all optical integrated circuits have yet to be commercially available on large scale due to the

Nowadays, the suited objects to advance this research field are made up of photonic crystal devices, because of their versatility and ability to control the propagation of light at the nanoscale. Since the introduction of the photonic crystals, a great deal of groundbreaking phenomena concerning light-matter interaction at optical frequencies have been theoretically predicted and experimentally verified. They led to large technological developments, especially giving rise to innovative optoelectronic and photovoltaic applications. For instance, microscopic light manipulation is achievable through photonic crystals that exhibit finite energy band-gap for light. In particular, two-dimensional photonic crystal cavities fabricated on semiconductor slab are the state of the art devices to strongly localize electromagnetic (e.m.) fields in volumes below a cubic optical wavelength of light, thus acting as nano-resonators. In fact, they provide an efficient mechanism for controlling and inhibiting spontaneous light emission, or for reducing almost to zero the light group velocity. A noteworthy advantage of two-dimensional photonic crystal cavities is that they can be included in all-optical integrated circuits fabrication. The high quality factors enable these systems to reach the strong coupling regime between photonic localized modes and two level quantum emitters. However, the fundamental request to maximize these effects is the accurate positioning of the light source in the spot where the localized mode is maximum. Moreover, when systems of interacting resonators are conceived, a basic condition to be satisfied is the precise control on the overlap between adjacent elements to induce an effective coupling. The sub-wavelength imaging of the (e.m.) fields localized in

difficulties in designing efficient optical components building blocks.

**Introduction**

### **Introduction**

The work presented in this thesis concerns the optics research field that is commonly called micro or nano-photonics. The term "photonics" emerged at the end of last century to describe the fundamental study of light and its applications to technology, whose purpose is to accomplish functions traditionally undertaken by electronics, such as telecommunications, information processing, and so on. In fact, in the effort to further progress the high density transistor integration and thus the modern electronic system performances, scientists are now turning to photons instead of electrons as the information carriers in communication. Photons show several advantages. Light can carry a larger amount of information per second. In addiction, at the single photon level, quantum information networks and quantum cryptography scheme can be pursued. Furthermore, photons are not as strongly interacting as electrons, thus reducing energy losses. However, in spite of the numerous advantages of photons, all optical integrated circuits have yet to be commercially available on large scale due to the difficulties in designing efficient optical components building blocks.

Nowadays, the suited objects to advance this research field are made up of photonic crystal devices, because of their versatility and ability to control the propagation of light at the nanoscale. Since the introduction of the photonic crystals, a great deal of groundbreaking phenomena concerning light-matter interaction at optical frequencies have been theoretically predicted and experimentally verified. They led to large technological developments, especially giving rise to innovative optoelectronic and photovoltaic applications. For instance, microscopic light manipulation is achievable through photonic crystals that exhibit finite energy band-gap for light. In particular, two-dimensional photonic crystal cavities fabricated on semiconductor slab are the state of the art devices to strongly localize electromagnetic (e.m.) fields in volumes below a cubic optical wavelength of light, thus acting as nano-resonators. In fact, they provide an efficient mechanism for controlling and inhibiting spontaneous light emission, or for reducing almost to zero the light group velocity. A noteworthy advantage of two-dimensional photonic crystal cavities is that they can be included in all-optical integrated circuits fabrication. The high quality factors enable these systems to reach the strong coupling regime between photonic localized modes and two level quantum emitters. However, the fundamental request to maximize these effects is the accurate positioning of the light source in the spot where the localized mode is maximum. Moreover, when systems of interacting resonators are conceived, a basic condition to be satisfied is the precise control on the overlap between adjacent elements to induce an effective coupling. The sub-wavelength imaging of the (e.m.) fields localized in

9

optical nano-resonators is therefore of the utmost relevance in the road map to integrate photonic nano-resonators in chipset architectures. In order to achieve this goal we need to overcome the resolution limitations that are imposed by light diffraction to any standard microscope.

In Chapter (1) we review the more commonly methods employed to achieve a subwavelength spatial resolution. In particular, we describe the principle of operation of the scanning near-field optical microscope.

In Chapter (2) we describe the basic properties of light confinement in photonic crystal nanocavities and also in optical nano-resonators based on disordered arrangements of light scatterers, where multiple scattering regime gives rise to randomly placed nanocavities. In particular, we illustrate how near-field techniques can experimentally probe the e.m. optical fields localized at the nanoscale and how finite elements numerical calculations can simulate the behavior of light in such nano-resonators.

In Chapter (3), by exploiting the scanning near-field probe perturbation imaging technique, we report the sub-wavelength mapping of the electric or magnetic localized field component of light using dielectric tapered probes or aperture metal coated probes, respectively. The advent of artificial metamaterials operating at optical frequencies, in which the magnetic interaction with light can be as relevant as the electric response, makes it straightforward to simultaneously detect both the e.m. field components. We develop a plasmonic-based near-field probe to strongly enhance the collection efficiency and, more interestingly, to achieve an ultra-bright and sub-wavelength simultaneous detection of both the resonant electric and magnetic fields.

Photoluminescence based imaging methods, however, require optically active samples with the constrain of spectral and spatial matching between photonic mode and the light emitters, which may suffer from bleaching or blinking. Therefore, a pure optical method that can be applied on any kind of high quality factor nano-resonators to retrieve the confined modes distributions is actually missing. In order to achieve this goal we investigate the localized nanophotonic modes by developing a different approach. The experimental method, presented in Chapter (4), combines scanning near-field optical microscopy with resonant scattering spectroscopy, and it is called Fano-imaging. This technique largely extends the investigation of nanoscale localized light states, since it is applicable to nano-resonators based on any kind of material, even where light sources cannot be embedded. Moreover, resonant scattering experiments exhibit spectral Fano resonances, which correspond to the interference between light directly scattered from the sample and light scattered after being resonantly coupled to the localized mode. From the detailed analysis of Fano lineshapes it is possible to retrieve a deep sub-wavelength imaging of both the electric field intensity and the electric field spatial phase distribution, polarization resolved. Thus, we obtain unprecedented local information about the resonant light states.

In Chapter (5) we deeply investigate, both theoretically and experimentally, systems composed by coupled nano-resonators, called "photonic molecules". In fact, light behavior in system based on multiple aligned photonic crystal nanocavities resembles the molecular interaction where the resulting normal modes exhibit energy splitting and spatial delocalization. This condition is achieved by an evanescent pho-

11

ton tunnelling. These structures represent a large research topic also for quantum optics. However, a fundamental requirement to create proper quantum-optics devices is the design and control of adjacent nanocavity modes at the target wavelengths, within an accuracy that is not experimentally obtainable due to the fabrication tolerances. The compensation of the fluctuations related to the structural disorder can lead to the control of the resonance wavelength of each resonator and of the tunnelling coefficient. In our analysis, we compare the interaction strength and the mode symmetry character of photonic molecules aligned along different lattice symmetry directions and composed by two or three photonic crystal nanocavities. Moreover, we theoretically evaluate the proper set of parameters to efficiently act on the coupling strength at the fabrication level or even with post-growing techniques. In particular, we develop a laser-assisted local oxidation of the dielectric environment in which the photonic cavities are fabricated. This oxidation induces a smooth and irreversible spectral shift of the resonant modes confined close to the laser spot. Therefore, the spatial selectivity of the post-fabrication technique is exploited not only to adjust the resonant wavelength of a given nano-resonator to a target value, but, more strikingly, to modify the coupling strength in photonic molecules. Finally, by comparing the case of two and three nano-resonators and next-nearest-neighbour coupling in array of photonic

The last part of the thesis deals with the engineering of light states localized in strongly scattering disordered media, as reported in Chapter (6). Light behavior in complex disordered systems attracts a lot of attention by fundamental physics as well as by technological applications involved in imaging through turbid media such as fog, clouds or living tissues. The occurrence of localized states in disordered media is a well-established phenomenon traced back to Anderson localization for electrons. However, the interaction between adjacent light sates driven by disorder has still to be completely understood. In Chapter (6) we demonstrate the possibility to engineer the confinement and the mutual interaction of modes in a two-dimensional disordered photonic structure. On one hand, the strong light confinement is achieved at the fabrication stage by an optimization of the design parameters. On the other hand, exploiting the local laser oxidation, we probe the interaction between overlapping localized modes, thereby paving the way for the creation of open transmission channels in

molecules.

strongly scattering media.

ton tunnelling. These structures represent a large research topic also for quantum optics. However, a fundamental requirement to create proper quantum-optics devices is the design and control of adjacent nanocavity modes at the target wavelengths, within an accuracy that is not experimentally obtainable due to the fabrication tolerances. The compensation of the fluctuations related to the structural disorder can lead to the control of the resonance wavelength of each resonator and of the tunnelling coefficient. In our analysis, we compare the interaction strength and the mode symmetry character of photonic molecules aligned along different lattice symmetry directions and composed by two or three photonic crystal nanocavities. Moreover, we theoretically evaluate the proper set of parameters to efficiently act on the coupling strength at the fabrication level or even with post-growing techniques. In particular, we develop a laser-assisted local oxidation of the dielectric environment in which the photonic cavities are fabricated. This oxidation induces a smooth and irreversible spectral shift of the resonant modes confined close to the laser spot. Therefore, the spatial selectivity of the post-fabrication technique is exploited not only to adjust the resonant wavelength of a given nano-resonator to a target value, but, more strikingly, to modify the coupling strength in photonic molecules. Finally, by comparing the case of two and three nano-resonators and next-nearest-neighbour coupling in array of photonic molecules.

The last part of the thesis deals with the engineering of light states localized in strongly scattering disordered media, as reported in Chapter (6). Light behavior in complex disordered systems attracts a lot of attention by fundamental physics as well as by technological applications involved in imaging through turbid media such as fog, clouds or living tissues. The occurrence of localized states in disordered media is a well-established phenomenon traced back to Anderson localization for electrons. However, the interaction between adjacent light sates driven by disorder has still to be completely understood. In Chapter (6) we demonstrate the possibility to engineer the confinement and the mutual interaction of modes in a two-dimensional disordered photonic structure. On one hand, the strong light confinement is achieved at the fabrication stage by an optimization of the design parameters. On the other hand, exploiting the local laser oxidation, we probe the interaction between overlapping localized modes, thereby paving the way for the creation of open transmission channels in strongly scattering media.

10

In Chapter (5) we deeply investigate, both theoretically and experimentally, systems composed by coupled nano-resonators, called "photonic molecules". In fact, light behavior in system based on multiple aligned photonic crystal nanocavities resembles the molecular interaction where the resulting normal modes exhibit energy splitting and spatial delocalization. This condition is achieved by an evanescent pho-

edented local information about the resonant light states.

optical nano-resonators is therefore of the utmost relevance in the road map to integrate photonic nano-resonators in chipset architectures. In order to achieve this goal we need to overcome the resolution limitations that are imposed by light diffraction

In Chapter (1) we review the more commonly methods employed to achieve a subwavelength spatial resolution. In particular, we describe the principle of operation of

In Chapter (2) we describe the basic properties of light confinement in photonic crystal nanocavities and also in optical nano-resonators based on disordered arrangements of light scatterers, where multiple scattering regime gives rise to randomly placed nanocavities. In particular, we illustrate how near-field techniques can experimentally probe the e.m. optical fields localized at the nanoscale and how finite elements numerical calculations can simulate the behavior of light in such nano-resona-

In Chapter (3), by exploiting the scanning near-field probe perturbation imaging technique, we report the sub-wavelength mapping of the electric or magnetic localized field component of light using dielectric tapered probes or aperture metal coated probes, respectively. The advent of artificial metamaterials operating at optical frequencies, in which the magnetic interaction with light can be as relevant as the electric response, makes it straightforward to simultaneously detect both the e.m. field components. We develop a plasmonic-based near-field probe to strongly enhance the collection efficiency and, more interestingly, to achieve an ultra-bright and sub-wavelength simultaneous detection of both the resonant electric and magnetic fields.

Photoluminescence based imaging methods, however, require optically active samples with the constrain of spectral and spatial matching between photonic mode and the light emitters, which may suffer from bleaching or blinking. Therefore, a pure optical method that can be applied on any kind of high quality factor nano-resonators to retrieve the confined modes distributions is actually missing. In order to achieve this goal we investigate the localized nanophotonic modes by developing a different approach. The experimental method, presented in Chapter (4), combines scanning near-field optical microscopy with resonant scattering spectroscopy, and it is called Fano-imaging. This technique largely extends the investigation of nanoscale localized light states, since it is applicable to nano-resonators based on any kind of material, even where light sources cannot be embedded. Moreover, resonant scattering experiments exhibit spectral Fano resonances, which correspond to the interference between light directly scattered from the sample and light scattered after being resonantly coupled to the localized mode. From the detailed analysis of Fano lineshapes it is possible to retrieve a deep sub-wavelength imaging of both the electric field intensity and the electric field spatial phase distribution, polarization resolved. Thus, we obtain unprec-

to any standard microscope.

tors.

the scanning near-field optical microscope.

12 13

**Chapter 1**

**Optics at the nanoscale**

used near-field probes.

**1.1 The diffraction limit**

with vacuum-wavelength equal to :

Until the second half of last century, the spatial resolution achievable by an optical microscope, even without any imperfections, was hampered to the diffraction limit. Only the development of new kinds of microscopes allowed for investigating object and light emitters down to a sub-wavelength scale. Here we report the basic principles of nanoscale optics. Firstly, by describing the limit imposed by light diffraction. Afterwards, by theoretically investigating and reviewing the methods largely employed to overcome this limitation and to achieve a sub-wavelength spatial resolution. We focus on detecting the optical near-field employing scanning microscopy, in particular we summarize the possible implementations and we introduce the most commonly

The time when humans began to exploit the optical properties of materials to enlarge the vision of small or distant objects is traced back to centuries ago. As the scientific method was developed, both optics fundamental laws and technical achievements quickly enlarged the understanding of natural phenomena together with the instrument assisted eye perception. Likewise, the first prototype of an optical microscope (1610) is attributed to Galileo Galilei, however, only since the pioneering development of van Leeuwenhoek (1671) it was possible to observe red blood cells and bacteria gaining a few m size resolution [1]. In the 1873 thanks to the advances of the theory of light waves Abbe, working at the Zeiss microscope factory, clarified that also an ideal microscope without any imperfections in the lenses or misalignments would not be able to overcome the physical resolution limit imposed by diffraction [2]. In particular, the Abbe's limit accounts for the smallest radial resolution (∆//) obtainable in the image plane by an optical system that collects monochromatic light

Min[∆//] <sup>≈</sup> 0.61

where is the refractive index of the medium between the source and the microscope, is the half-angle of the maximum light cone accepted by the lens, as reported in Fig. (1.1 a), and it is related to the numerical aperture of the optical system that is

(1.1)

# **Chapter 1 Optics at the nanoscale**

Until the second half of last century, the spatial resolution achievable by an optical microscope, even without any imperfections, was hampered to the diffraction limit. Only the development of new kinds of microscopes allowed for investigating object and light emitters down to a sub-wavelength scale. Here we report the basic principles of nanoscale optics. Firstly, by describing the limit imposed by light diffraction. Afterwards, by theoretically investigating and reviewing the methods largely employed to overcome this limitation and to achieve a sub-wavelength spatial resolution. We focus on detecting the optical near-field employing scanning microscopy, in particular we summarize the possible implementations and we introduce the most commonly used near-field probes.

### **1.1 The diffraction limit**

12 13

The time when humans began to exploit the optical properties of materials to enlarge the vision of small or distant objects is traced back to centuries ago. As the scientific method was developed, both optics fundamental laws and technical achievements quickly enlarged the understanding of natural phenomena together with the instrument assisted eye perception. Likewise, the first prototype of an optical microscope (1610) is attributed to Galileo Galilei, however, only since the pioneering development of van Leeuwenhoek (1671) it was possible to observe red blood cells and bacteria gaining a few m size resolution [1]. In the 1873 thanks to the advances of the theory of light waves Abbe, working at the Zeiss microscope factory, clarified that also an ideal microscope without any imperfections in the lenses or misalignments would not be able to overcome the physical resolution limit imposed by diffraction [2]. In particular, the Abbe's limit accounts for the smallest radial resolution (∆//) obtainable in the image plane by an optical system that collects monochromatic light with vacuum-wavelength equal to :

$$\text{Min}[\Delta r\_{//}] \approx \frac{0.61 \,\text{A}}{n \sin \theta} \tag{1.1}$$

where is the refractive index of the medium between the source and the microscope, is the half-angle of the maximum light cone accepted by the lens, as reported in Fig. (1.1 a), and it is related to the numerical aperture of the optical system that is

defined as = . The resolution of an optical microscope evaluated in Eq. (1.1) is defined as the shortest distance between two distinguishable points on a specimen that can still be observed as separate entities, following the Rayleigh criterion [3, 4]. In order to understand the basic imaging process let us consider the image formation of a point-like source (whose dimension are ≪ ), as schematically reported in Fig. (1.1 a). The incoming light is diffracted by the point-like specimen (S), as always happens when light encounters an obstacle, than it is once again diffracted by lens L, which mimics a generic microscopy objective. In the case of a finite size object, rays leaving with the same angle cross again exactly at the back focal plane Σ, and the finite object image appears in the conjugate plane Σ [5].

Abbe found by experimentation that a larger resulted in higher resolution, even though the apparent cone of incident light filled only a small portion of the lens. In fact, the entire size of L interacts with the diffracted light. Since can not be large enough to collect all the diffracted light ( < /2), the image recorded in Σ does not exactly correspond to the original object and it is blurred with the typical Airy disk intensity pattern shown in Fig. (1.1 b) [5]. The Airy disk is defined as the diffraction pattern created by a circular pupil of diameter , uniformly illuminated. It consists on a central disk of angular radius 1.22/, surrounded by many alternatively dark and bright rings [6]. Therefore, in any finite optical system that detects e.m. radiation the image of a point-like light source is not a delta-like function but it is broadened as an Airy disk, which thus represents the point spread function. Abbe used the Airy disk properties to retrieve the net imaging resolution stated in Eq. (1.1), that is valid for every detector even with the highest collection efficiency. Moreover, any finite specimen can be schematized by a collection of point-like sources whose size is smaller than , consequently every time we use standard microscopy systems to perform images of small objects we inevitably loose information.

Although modern oil or solid immersion microscopes can achieve large equivalent up to 2.0 in the visible spectral range [7], Eq. (1.1) does not allow resolving an optical image with a sub-wavelength resolution (Δ ≪ ), thus closely resembling and being related to the Heisenberg's uncertainty principle [8]. For instance, in the telecom window near-infrared spectral range the largest transparent is about 1.4 and gives a spatial resolution of Δ ≈ 700 nm.

### **1.1.1 Evanescent waves**

As Maxwell equations were derived (1861), they entirely described the e.m. field behavior. But it took almost a century to discover a peculiar optical phenomenon that has put fundamental limits to any image reconstruction: this is the existence of e.m. evanescent waves in any diffraction process [9–11].

Evanescent e.m. waves are exact solutions of Maxwell wave-equations that do not propagate in space but exhibit an exponential decay of the amplitude. When total internal reflection occurs, they commonly describes light behavior in the low refractive index medium, as reported in Fig. (1.2 a). Evanescent waves do not deliver a net energy transfer. Only if frustrated total internal reflection takes pace it is possible to

15

generate propagating waves in an high refractive index material close to the evanescent waves source (closely resembling the electrons tunnel effect), as shown in Fig. (1.2 b) [5]. Classical wave optics based on Huygens-Fresnel principle has a fundamental deficiency since it overlooks the role of evanescent waves in diffraction. In fact, the classical solution of diffraction problems are accurate in the radiation zone,

In order to analyze the reason why, by collecting only propagating radiation with any kind of microscope (even an ideal one with = /2), the image is always blurred, we exploit the argument based on the angular spectrum decomposition that is a noteworthy technique for describing optical fields in homogeneous media. Using this Fourier based characterization we can estimate the series expansion of an arbitrary field in terms of propagating and evanescent waves with variable amplitudes and directions. The description of the e.m. field radiated by a light source or scattered by an object, as shown in Fig. (1.3), evaluated by the angular spectrum representation in a

−∞ exp( <sup>+</sup> <sup>+</sup> <sup>−</sup> ) (1.2)

2, the e.m. fields described by Eq. (1.2) have different

⟹ ∈ ℝ (1.3)

⟹ ∈ ℂ (1.4)

where (, ) represents either the electric () or the magnetic () field and ̂ () its Fourier transform; while = 2 −1 is the angular frequency. Since the wave-

behaviors in two complementary regimes in which the wavenumber component is

Hence, for a purely dielectric medium with no losses, turns out that the factor exp() is either an oscillatory or an exponentially decaying function if Eq. (1.3) or Eq. (1.4) respectively holds. Therefore, the angular spectrum is a superposition of both plane and evanescent waves. Remarkably, only if all the spatial frequencies (, ) are collected it is possible to reconstruct without any distortions the field

On the other hand, if the imaging system is sufficiently separated from the object, the contribution of the evanescent waves is negligible and only the low spatial frequencies, which satisfy Eq. (1.3), have to be considered. In other words, the image collected is a low pass filtered representation of the original field. By filtering out the high in plane spatial frequencies described by Eq. (1.4) we loose information about the object smallest details. In fact, dealing only with propagating waves the largest detectable in plane wavenumber // = 2 −1 , where we consider also the practical limitation in collecting a given range of angles, as highlighted in Fig. (1.1 a).

but fails to reproduce what happens in close proximity to the light source.

arbitrary = . plane is [12]:

(, ) <sup>=</sup> <sup>∬</sup> ̂ (, , 0) <sup>∞</sup>

<sup>2</sup> +

<sup>2</sup> +

 <sup>2</sup> +

 <sup>2</sup> +

coming from the specimen by exploiting Eq. (1.2).

<sup>2</sup> ≤ ( 2 ) 2

<sup>2</sup> > ( 2 ) 2

number is = √

either real or imaginary.

generate propagating waves in an high refractive index material close to the evanescent waves source (closely resembling the electrons tunnel effect), as shown in Fig. (1.2 b) [5]. Classical wave optics based on Huygens-Fresnel principle has a fundamental deficiency since it overlooks the role of evanescent waves in diffraction. In fact, the classical solution of diffraction problems are accurate in the radiation zone, but fails to reproduce what happens in close proximity to the light source.

In order to analyze the reason why, by collecting only propagating radiation with any kind of microscope (even an ideal one with = /2), the image is always blurred, we exploit the argument based on the angular spectrum decomposition that is a noteworthy technique for describing optical fields in homogeneous media. Using this Fourier based characterization we can estimate the series expansion of an arbitrary field in terms of propagating and evanescent waves with variable amplitudes and directions. The description of the e.m. field radiated by a light source or scattered by an object, as shown in Fig. (1.3), evaluated by the angular spectrum representation in a arbitrary = . plane is [12]:

$$\mathbf{A}(\mathbf{r},t) = \iint\_{-\infty}^{\infty} \hat{\mathbf{A}}\left(\mathbf{k}\_x, \mathbf{k}\_y, \mathbf{0}\right) \exp\left(i\mathbf{k}\_z \mathbf{z} + i\mathbf{k}\_x \mathbf{x} + i\mathbf{k}\_y \mathbf{y} - i\omega t\right) d\mathbf{k}\_x d\mathbf{k}\_y \qquad (1.2)$$

where (, ) represents either the electric () or the magnetic () field and ̂ () its Fourier transform; while = 2 −1 is the angular frequency. Since the wavenumber is = √ <sup>2</sup> + <sup>2</sup> + 2, the e.m. fields described by Eq. (1.2) have different behaviors in two complementary regimes in which the wavenumber component is either real or imaginary.

$$k\_{\chi}^2 + k\_{\mathcal{Y}}^2 \le \left(\frac{2\pi n}{\lambda}\right)\_{\downarrow}^2 \implies \quad k\_{\mathcal{Z}} \in \mathbb{R} \tag{1.3}$$

$$k\_{\chi}^2 + k\_{\chi}^2 > \left(\frac{2\pi n}{\lambda}\right)^2 \implies \quad k\_{\mathbf{z}} \in \mathbb{C} \tag{1.4}$$

Hence, for a purely dielectric medium with no losses, turns out that the factor exp() is either an oscillatory or an exponentially decaying function if Eq. (1.3) or Eq. (1.4) respectively holds. Therefore, the angular spectrum is a superposition of both plane and evanescent waves. Remarkably, only if all the spatial frequencies (, ) are collected it is possible to reconstruct without any distortions the field coming from the specimen by exploiting Eq. (1.2).

On the other hand, if the imaging system is sufficiently separated from the object, the contribution of the evanescent waves is negligible and only the low spatial frequencies, which satisfy Eq. (1.3), have to be considered. In other words, the image collected is a low pass filtered representation of the original field. By filtering out the high in plane spatial frequencies described by Eq. (1.4) we loose information about the object smallest details. In fact, dealing only with propagating waves the largest detectable in plane wavenumber // = 2 −1 , where we consider also the practical limitation in collecting a given range of angles, as highlighted in Fig. (1.1 a).

14

defined as = . The resolution of an optical microscope evaluated in Eq. (1.1) is defined as the shortest distance between two distinguishable points on a specimen that can still be observed as separate entities, following the Rayleigh criterion [3, 4]. In order to understand the basic imaging process let us consider the image formation of a point-like source (whose dimension are ≪ ), as schematically reported in Fig. (1.1 a). The incoming light is diffracted by the point-like specimen (S), as always happens when light encounters an obstacle, than it is once again diffracted by lens L, which mimics a generic microscopy objective. In the case of a finite size object, rays leaving with the same angle cross again exactly at the back focal plane

Abbe found by experimentation that a larger resulted in higher resolution, even though the apparent cone of incident light filled only a small portion of the lens. In fact, the entire size of L interacts with the diffracted light. Since can not be large enough to collect all the diffracted light ( < /2), the image recorded in Σ does not exactly correspond to the original object and it is blurred with the typical Airy disk intensity pattern shown in Fig. (1.1 b) [5]. The Airy disk is defined as the diffraction pattern created by a circular pupil of diameter , uniformly illuminated. It consists on a central disk of angular radius 1.22/, surrounded by many alternatively dark and bright rings [6]. Therefore, in any finite optical system that detects e.m. radiation the image of a point-like light source is not a delta-like function but it is broadened as an Airy disk, which thus represents the point spread function. Abbe used the Airy disk properties to retrieve the net imaging resolution stated in Eq. (1.1), that is valid for every detector even with the highest collection efficiency. Moreover, any finite specimen can be schematized by a collection of point-like sources whose size is smaller than , consequently every time we use standard microscopy systems

Although modern oil or solid immersion microscopes can achieve large equivalent up to 2.0 in the visible spectral range [7], Eq. (1.1) does not allow resolving an optical image with a sub-wavelength resolution (Δ ≪ ), thus closely resembling and being related to the Heisenberg's uncertainty principle [8]. For instance, in the telecom window near-infrared spectral range the largest transparent is about 1.4

As Maxwell equations were derived (1861), they entirely described the e.m. field behavior. But it took almost a century to discover a peculiar optical phenomenon that has put fundamental limits to any image reconstruction: this is the existence of e.m.

Evanescent e.m. waves are exact solutions of Maxwell wave-equations that do not propagate in space but exhibit an exponential decay of the amplitude. When total internal reflection occurs, they commonly describes light behavior in the low refractive index medium, as reported in Fig. (1.2 a). Evanescent waves do not deliver a net energy transfer. Only if frustrated total internal reflection takes pace it is possible to

Σ, and the finite object image appears in the conjugate plane Σ [5].

to perform images of small objects we inevitably loose information.

and gives a spatial resolution of Δ ≈ 700 nm.

evanescent waves in any diffraction process [9–11].

**1.1.1 Evanescent waves**

Accordingly to the properties of conjugate variables of Fourier optics, which resembles the Heisenberg principle, the radial in plane uncertain ∆// = √()2 + ()2 and the field finite angular spectrum ∆// are related by:

$$
\Delta k\_{//} \Delta r\_{//} \ge 1 \tag{1.5}
$$

Hence, to achieve the minimum spatial uncertain the largest angular spectrum is needed, which corresponds to ∆// = 2−1, giving for the ideal resolution:

$$\text{Min}[\Delta r\_{//}] > \frac{\lambda}{2\pi NA} \tag{1.6}$$

Therefore, even if an objective may collect = /2 it would not be able to interact with the evanescent waves and the specimen image would consequently still be incomplete. This limit is almost four times better with respect to Abbe's prediction of Eq. (1.1). In fact, Abbe required the paraxial approximation (small ) and applied the arbitrary Rayleigh's criterion to the case of two parallel dipoles oriented perpendicular to the optical axis. Nevertheless, the two formulations must not be perceived as opposed but conveying the same straightforward result. Meaning that any standard microscope has a limited spatial resolution, which is about ∆// ≈ /2.

By performing and experiment in which also the evanescent waves are detected, an infinite bandwidth of spatial frequencies can, in principle, be achieved. But this kind of measurement requires to probe the e.m. fields in close proximity to the sample surface, where evanescent waves are not yet totally suppressed. From this analysis it is clear that two spatial regimes, which show very different light behaviors, are relevant for any imaging purpose:

where is the distance between the specimen and the probe that collects the e.m. fields. The intermediate-field ( ∼ ), also called "Fresnel-field", is the vaguely defined as the region in between the near-field and the far-field. In this region, near-field behavior ceases to be important and far-field effects become dominating.

The two extreme spatial regimes can be highlighted by studying the emission of a dipole, that is the smallest radiating e.m. unit source, which represents the first approximation of any antenna emission [13]. In the far-field the magnetic and the electric fields are, respectively:

$$\mathcal{B} = k^2 (\mathfrak{n} \wedge \mathfrak{p}) \frac{\exp(\imath k \cdot r)}{r} \tag{1.7}$$

$$E = \mathcal{B} \wedge \mathfrak{n} \tag{1.8}$$

17

decrease as the square of distance. As in every propagating light wave, both fields described by Eq. (1.7) and Eq. (1.8) are strongly connected since each of them is generated by a variation of the other. Moreover, any absorption of the radiation does not

Differently from the propagating regime, in the near-field region the electric and magnetic fields exist independently of each other, and one type of field can dominate the other. In particular, the magnetic induction is a factor smaller than the electric field. Moreover, the near-field components depend on the detailed properties of source. For instance, Eq. (1.10) coincides with the electrostatic dipole, and both decay very rapidly as a function of the distance. Consequently, in the since a finite emitter can be regarded as an ensemble of Hertzian dipoles, near-field components carry the information needed to determine the spatial distribution of any finite size emitter. In addiction, in the near-field region absorption of radiation does strongly affect the load on the emitter. For instance, the magnetic induction in a transformer can be seen as a

In conclusion, it is straightforward that every time light is emitted or finds an obstacle and scatters there is a loss of information on propagating from the near-field region to the far-field. Optical techniques that allow near-field probing could improve the imaging hallmarks, reaching a sub-wavelength spatial resolution. However, the higher the spatial frequencies of an evanescent wave are, the faster the field decay along will be. Therefore, unavoidable practical limitations always make the band-

Many fascinating and disruptive optical techniques have been proposed and developed through the last decades revolutionizing the field of optical microscopy by gaining a sub-wavelength spatial resolution. At first, we briefly review the most successful methods that exploit specific optical schemes by collecting only far-field radiation and afterwords we focus the attention on near-field detection that is the basic

Confocal microscopy was the first and simplest invention for increasing optical resolution and especially the signal-to-noise ratio [14]. It takes advantage of a spatial filtering performed by a pinhole placed in the conjugate plane of the specimen, so that light impinging the sample and light following the inverse path by passing through the pinhole have the same focus on the object plane as reported in Fig. (1.4 a). This geometry allows eliminating most of the out-of-focus light and prevents nearby scatterers from contributing to the detected signal. The confocal microscope must detect only light coming from one point at a time, therefore a scanning system is required for reconstructing two or three-dimensional images. The drawback is that the lateral resolution does not overcome the diffraction limit although in the vertical direction a

 = ( ∧ ) −2 (1.9) = [3( ⋅ ) − ] −3 (2.0)

feed back to the emitter. While in the near-field ( ≪ 1) they become:

simple model of near-field e.m. interaction.

width finite.

**1.2 Modern microscopy**

research topic discussed in this thesis.

where = (/) is the unit vector of real space and the electric dipole moment is represented by = ∫ ()3 with () being the charges density. In the farfield region we find propagating spherical waves where both field radiation intensities

decrease as the square of distance. As in every propagating light wave, both fields described by Eq. (1.7) and Eq. (1.8) are strongly connected since each of them is generated by a variation of the other. Moreover, any absorption of the radiation does not feed back to the emitter. While in the near-field ( ≪ 1) they become:

$$\mathbf{B} = \underset{\cdot}{ik} (\mathbf{n} \wedge \mathbf{p}) r^{-2} \underset{\cdot \quad \dots}{} \tag{1.9}$$

$$E = [3n(n \cdot p) - p]r^{-3} \tag{2.0}$$

Differently from the propagating regime, in the near-field region the electric and magnetic fields exist independently of each other, and one type of field can dominate the other. In particular, the magnetic induction is a factor smaller than the electric field. Moreover, the near-field components depend on the detailed properties of source. For instance, Eq. (1.10) coincides with the electrostatic dipole, and both decay very rapidly as a function of the distance. Consequently, in the since a finite emitter can be regarded as an ensemble of Hertzian dipoles, near-field components carry the information needed to determine the spatial distribution of any finite size emitter. In addiction, in the near-field region absorption of radiation does strongly affect the load on the emitter. For instance, the magnetic induction in a transformer can be seen as a simple model of near-field e.m. interaction.

In conclusion, it is straightforward that every time light is emitted or finds an obstacle and scatters there is a loss of information on propagating from the near-field region to the far-field. Optical techniques that allow near-field probing could improve the imaging hallmarks, reaching a sub-wavelength spatial resolution. However, the higher the spatial frequencies of an evanescent wave are, the faster the field decay along will be. Therefore, unavoidable practical limitations always make the bandwidth finite.

### **1.2 Modern microscopy**

16

Accordingly to the properties of conjugate variables of Fourier optics, which resembles the Heisenberg principle, the radial in plane uncertain ∆// = √()2 + ()2

Hence, to achieve the minimum spatial uncertain the largest angular spectrum is

needed, which corresponds to ∆// = 2−1, giving for the ideal resolution:

croscope has a limited spatial resolution, which is about ∆// ≈ /2.

vant for any imaging purpose:

tric fields are, respectively:

Min[∆//] <sup>&</sup>gt;

Therefore, even if an objective may collect = /2 it would not be able to interact with the evanescent waves and the specimen image would consequently still be incomplete. This limit is almost four times better with respect to Abbe's prediction of Eq. (1.1). In fact, Abbe required the paraxial approximation (small ) and applied the arbitrary Rayleigh's criterion to the case of two parallel dipoles oriented perpendicular to the optical axis. Nevertheless, the two formulations must not be perceived as opposed but conveying the same straightforward result. Meaning that any standard mi-

By performing and experiment in which also the evanescent waves are detected, an infinite bandwidth of spatial frequencies can, in principle, be achieved. But this kind of measurement requires to probe the e.m. fields in close proximity to the sample surface, where evanescent waves are not yet totally suppressed. From this analysis it is clear that two spatial regimes, which show very different light behaviors, are rele-

> Near-field ≪ Far-field <

where is the distance between the specimen and the probe that collects the e.m. fields. The intermediate-field ( ∼ ), also called "Fresnel-field", is the vaguely defined as the region in between the near-field and the far-field. In this region, near-field

The two extreme spatial regimes can be highlighted by studying the emission of a dipole, that is the smallest radiating e.m. unit source, which represents the first approximation of any antenna emission [13]. In the far-field the magnetic and the elec-

<sup>=</sup> 2( <sup>∧</sup> ) (⋅)

where = (/) is the unit vector of real space and the electric dipole moment is represented by = ∫ ()3 with () being the charges density. In the farfield region we find propagating spherical waves where both field radiation intensities

behavior ceases to be important and far-field effects become dominating.

∆//∆// ≥ 1 (1.5)

2 (1.6)

(1.7)

= ∧ (1.8)

and the field finite angular spectrum ∆// are related by:

Many fascinating and disruptive optical techniques have been proposed and developed through the last decades revolutionizing the field of optical microscopy by gaining a sub-wavelength spatial resolution. At first, we briefly review the most successful methods that exploit specific optical schemes by collecting only far-field radiation and afterwords we focus the attention on near-field detection that is the basic research topic discussed in this thesis.

Confocal microscopy was the first and simplest invention for increasing optical resolution and especially the signal-to-noise ratio [14]. It takes advantage of a spatial filtering performed by a pinhole placed in the conjugate plane of the specimen, so that light impinging the sample and light following the inverse path by passing through the pinhole have the same focus on the object plane as reported in Fig. (1.4 a). This geometry allows eliminating most of the out-of-focus light and prevents nearby scatterers from contributing to the detected signal. The confocal microscope must detect only light coming from one point at a time, therefore a scanning system is required for reconstructing two or three-dimensional images. The drawback is that the lateral resolution does not overcome the diffraction limit although in the vertical direction a

narrow depth of field is achieved with respect to standard microscopy [15]. Nevertheless, this non-invasive technique has gained popularity in biology, biophysics, semiconductor inspection and materials science, particularly for investigating thick specimens or buried samples [16].

On the other hand, the invention of pulsed laser radiation propelled the field of nonlinear optics enabling, for instance, the invention of multiphotons microscopy [17, 18]. With respect to confocal microscopy it offers the advantages of deeper penetration and less photodamage but has the disadvantage of requiring a non-linear medium and may damage the sample due to the high power laser excitation.

Recent advances in ultra-sensitive instrumentation have allowed for the detection, identification, and dynamic studies of single molecules in the condensed phase. This measurement capability provides a new set of tools to explore the frontiers in many scientific disciplines, such as chemistry, molecular biology, molecular medicine, and nanostructured materials. Optical detection of single molecules has been achieved by both frequency modulated absorption and laser-induced fluorescence. Since the latter exhibits lower background and higher signal-to-noise ratio, it is the more employed one [19, 20]. Highly fluorescent molecules have been synthesized that can be specifically attached to biological entities. This chemically specific labelling and the associated discrimination of different dyes based on their fluorescence emission allows scientists to visualize the interior of cells and study biochemical reactions in live environments.

Another noteworthy technique is the stimulated emission depletion (STED) microscopy, which provides super resolution by selectively deactivating fluorophores thus enhancing the imaging in a localized area [21, 22]. STED works by depleting specific regions of the sample while leaving a center focal spot active to emit fluorescence, leading to an improved resolution with respect to confocal microscopy as reported in Fig. (1.4 b). The focal area can be engineered by altering the properties of the pupil plane of the objective lens. In this content a sub diffraction method was also developed by using spatially structured illumination in a wide-field fluorescence microscope employing a series of different excitation light patterns [23].

Photoactivated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM) have also proved to be super resolution microscopy techniques allowing to image specific proteins down to few nanometers and trajectories of single molecules [24–26]. They are both based on collecting under a fluorescent microscope a large number of images as a function of time, each containing just a few isolated stochastically activated fluorophores, resulting in a promising approach to distinguish neighboring molecules by separating their fluorescent emission in time. All these results recently gave to Betzig, Hell and Moerner the honour to be jointly awarded with the 2014 Nobel Prize in Chemistry [27].

A completely different approach was recently brought to the realm of device engineering by Pendry in his seminal work [28]. He proposed the realization of a "superlens" based on a metamaterial slab. Metamaterials are artificial material with both negative dielectric permittivity and negative magnetic permeability. As if the refrac-

19

Therefore, all the described methods are complementary to those presented in this work, since, on one hand, PALM and STED are based on standard optical microscopy instrumentation and rely on fluorescent labeling of the sample, on the other hand, TEM and AFM provide a high-resolution topography but cannot probe the sample

spectral and dynamic properties of the sample.

optical response.

tive index was negative, these engineered materials allows optical properties unavailable in naturally occurring substances, such as negative refraction, inverted Snell's law and Cherenkov radiation and optical cloaking [29–34]. The superlens is, in principle, able to gain a perfect resolution by retrieving all the information carried by evanescent waves, since in the transmission process they emerge from the metamaterial enhanced in amplitude after being resonantly coupled to surface plasmons, as shown in Fig. (1.4 c). Note that there is not any violation of energy conservation, since evanescent waves transport no energy, but nevertheless it is a surprising result confirmed by experiments that in the visible spectral range show a resolution down to

Instead of photons, by using electrons techniques to magnify objects down to the nanometer range have been developed by exploiting the shorter De Broglie wavelength of electrons, such as scanning electron microscope (SEM) or transmission electron microscope (TEM) [37, 38]. They involve an electron beam that generates a characteristic response from the sample surface (cathodoluminescence, back-scattered or secondary electrons) or is transmitted through an ultra-thin specimen, respectively. Significant advances in instrumentation are pursued by the wide class of scanning probe microscopes, where a small probe tip is brought into intimate contact with the sample surface without damaging it. The presence of the specimen manifests itself as a tunnel current flowing between the tip and the sample in scanning tunneling microscopes (STM) or as a deflection in the tip-height during the scanning in atomic force microscopes (AFM) [39, 40]. Both techniques push the spatial resolution beyond the Nanoscale and retrieve the image of single atoms. The former case provides a topographic picture of the surface by keeping the tunnel current constant and monitoring displacements of the metal tip given by the voltages applied to piezoelectric drives. Unfortunately, electron microscopes have to be operated in vacuum, which limits their application in life sciences, and requires special sample preparation. The AFM is a higher sensitivity tool designed to investigate both conductors and insulators down to the atomic scale. The typical AFM setup reported in Fig. (1.5 a) shows that the cantilever deflection is measured using a laser spot reflected from the top surface of the cantilever into an array of photodiodes. With this microscope images are obtained by measuring the force on a sharp tip (insulating or not) created by the proximity to the surface such as van der Waals forces, capillary forces, chemical bonding, electrostatic forces, magnetic forces and so on. This force is kept small and at a constant level with a piezoelectric based feedback mechanism to adjust the tip-to-sample distance, so that when the tip is moved sideways it follows the surface contours as is highlighted by the trace B in Fig. (1.5 b). Although these scanning techniques achieve a deep subwavelength resolution in mapping any sample topography, they cannot investigate or detect the light behavior in the same media and consequently retrieve the noteworthy

/6 [35, 36].

tive index was negative, these engineered materials allows optical properties unavailable in naturally occurring substances, such as negative refraction, inverted Snell's law and Cherenkov radiation and optical cloaking [29–34]. The superlens is, in principle, able to gain a perfect resolution by retrieving all the information carried by evanescent waves, since in the transmission process they emerge from the metamaterial enhanced in amplitude after being resonantly coupled to surface plasmons, as shown in Fig. (1.4 c). Note that there is not any violation of energy conservation, since evanescent waves transport no energy, but nevertheless it is a surprising result confirmed by experiments that in the visible spectral range show a resolution down to /6 [35, 36].

Instead of photons, by using electrons techniques to magnify objects down to the nanometer range have been developed by exploiting the shorter De Broglie wavelength of electrons, such as scanning electron microscope (SEM) or transmission electron microscope (TEM) [37, 38]. They involve an electron beam that generates a characteristic response from the sample surface (cathodoluminescence, back-scattered or secondary electrons) or is transmitted through an ultra-thin specimen, respectively.

Significant advances in instrumentation are pursued by the wide class of scanning probe microscopes, where a small probe tip is brought into intimate contact with the sample surface without damaging it. The presence of the specimen manifests itself as a tunnel current flowing between the tip and the sample in scanning tunneling microscopes (STM) or as a deflection in the tip-height during the scanning in atomic force microscopes (AFM) [39, 40]. Both techniques push the spatial resolution beyond the Nanoscale and retrieve the image of single atoms. The former case provides a topographic picture of the surface by keeping the tunnel current constant and monitoring displacements of the metal tip given by the voltages applied to piezoelectric drives. Unfortunately, electron microscopes have to be operated in vacuum, which limits their application in life sciences, and requires special sample preparation. The AFM is a higher sensitivity tool designed to investigate both conductors and insulators down to the atomic scale. The typical AFM setup reported in Fig. (1.5 a) shows that the cantilever deflection is measured using a laser spot reflected from the top surface of the cantilever into an array of photodiodes. With this microscope images are obtained by measuring the force on a sharp tip (insulating or not) created by the proximity to the surface such as van der Waals forces, capillary forces, chemical bonding, electrostatic forces, magnetic forces and so on. This force is kept small and at a constant level with a piezoelectric based feedback mechanism to adjust the tip-to-sample distance, so that when the tip is moved sideways it follows the surface contours as is highlighted by the trace B in Fig. (1.5 b). Although these scanning techniques achieve a deep subwavelength resolution in mapping any sample topography, they cannot investigate or detect the light behavior in the same media and consequently retrieve the noteworthy spectral and dynamic properties of the sample.

Therefore, all the described methods are complementary to those presented in this work, since, on one hand, PALM and STED are based on standard optical microscopy instrumentation and rely on fluorescent labeling of the sample, on the other hand, TEM and AFM provide a high-resolution topography but cannot probe the sample optical response.

18

narrow depth of field is achieved with respect to standard microscopy [15]. Nevertheless, this non-invasive technique has gained popularity in biology, biophysics, semiconductor inspection and materials science, particularly for investigating thick speci-

and may damage the sample due to the high power laser excitation.

croscope employing a series of different excitation light patterns [23].

awarded with the 2014 Nobel Prize in Chemistry [27].

On the other hand, the invention of pulsed laser radiation propelled the field of nonlinear optics enabling, for instance, the invention of multiphotons microscopy [17, 18]. With respect to confocal microscopy it offers the advantages of deeper penetration and less photodamage but has the disadvantage of requiring a non-linear medium

Recent advances in ultra-sensitive instrumentation have allowed for the detection, identification, and dynamic studies of single molecules in the condensed phase. This measurement capability provides a new set of tools to explore the frontiers in many scientific disciplines, such as chemistry, molecular biology, molecular medicine, and nanostructured materials. Optical detection of single molecules has been achieved by both frequency modulated absorption and laser-induced fluorescence. Since the latter exhibits lower background and higher signal-to-noise ratio, it is the more employed one [19, 20]. Highly fluorescent molecules have been synthesized that can be specifically attached to biological entities. This chemically specific labelling and the associated discrimination of different dyes based on their fluorescence emission allows scientists to visualize the interior of cells and study biochemical reactions in live en-

Another noteworthy technique is the stimulated emission depletion (STED) microscopy, which provides super resolution by selectively deactivating fluorophores thus enhancing the imaging in a localized area [21, 22]. STED works by depleting specific regions of the sample while leaving a center focal spot active to emit fluorescence, leading to an improved resolution with respect to confocal microscopy as reported in Fig. (1.4 b). The focal area can be engineered by altering the properties of the pupil plane of the objective lens. In this content a sub diffraction method was also developed by using spatially structured illumination in a wide-field fluorescence mi-

Photoactivated localization microscopy (PALM) and stochastic optical reconstruction microscopy (STORM) have also proved to be super resolution microscopy techniques allowing to image specific proteins down to few nanometers and trajectories of single molecules [24–26]. They are both based on collecting under a fluorescent microscope a large number of images as a function of time, each containing just a few isolated stochastically activated fluorophores, resulting in a promising approach to distinguish neighboring molecules by separating their fluorescent emission in time. All these results recently gave to Betzig, Hell and Moerner the honour to be jointly

A completely different approach was recently brought to the realm of device engineering by Pendry in his seminal work [28]. He proposed the realization of a "superlens" based on a metamaterial slab. Metamaterials are artificial material with both negative dielectric permittivity and negative magnetic permeability. As if the refrac-

mens or buried samples [16].

vironments.

### **1.3 Scanning near-field optical microscopy**

If AFM shear-force probe microscopy is combined with optical detection huge advantages can be achieved in the characterization of light emitting nanostructures and fluorescent molecules. The most striking example is near-field scanning optical microscopy (SNOM), in which the apex of a tapered or pulled optical fiber acts like a AFM tip, thus providing both optical and topographical information of the sampling surface. This integrated microscope works in close proximity with the sample surface, thus being strongly interacting with optical near-field and evanescent waves. Subwavelength imaging based on SNOM was experimentally tested for the first time in the visible spectral range more than 30 years ago by Pohl et al. employing aperture probes [41]. The principle of SNOM imaging operation relies on the point-by-point investigation by raster-scanning the local probe over the sample surface and recording at every position the corresponding optical signature. The local probe acts as an optical antenna, converting localized e.m. fields into radiation, and vice versa. Therefore, SNOM detection gives ultra-sensitive optical measurement beyond the diffraction limit and provides light behavior at the nanoscale, together with the topographical capability of the AFM imaging. Although the morphological performance is not as good as in cantilever based AFM, SNOM proved to be the state of the art technique for investigating nanostructures such as quantum wells, quantum dots, nanoresonators or for single molecules since it combines the excellent spectroscopic and temporal selectivity of classical optical microscopy with the sub-wavelength spatial resolution [42–44].

The concept of near-field optical microscopy was originally proposed in by Synge 1928 in a prophetic article, where he proposed an apparatus similar to the actual SNOM implementations [45]. A sub-wavelength aperture in an opaque plate placed in close proximity to the sample surface creates an illumination spot not limited by diffraction. Scanning the source along the surface and recording the transmitted, or reflected, light produces an image with subwavelength resolution. In fact, the resolution of such an image should be limited only by the size of the aperture and not by diffraction, as was also pointed out years later by Bethe studying the diffraction by small holes [46]. Only after the invention of the STM an efficient positioning technology was available at the nanoscale. Therefore an optical microscope similar to Synge's proposal was realized, firstly in the microwave by Nicholls and Ash, then in the visible spectral range simultaneously by Pohl et al. and Lewis et al. due to the obviously different fabrications difficulties demonstrating a sub-wavelength imaging with a resolution of /60 and /20, respectively [41, 47, 48]. The key innovation was the fabrication of a sub-wavelength optical aperture at the apex of a sharply pointed transparent (quartz) probe tip whose sidewalls were coated by metal. Such sharp aperture replaces the Synge's opaque screen for experimental purposes. In addition, a feedback loop was implemented based on proper piezoelectric quartz tuning forks (later replaced by piezoelectric bimorph bender element) maintaining the tip-sample distance constant (at few nanometers) while raster scanning the sample surface [49]. SNOM technique was systematically advanced and extended over the years to various configurations that provide a sharp confined photon flux in the near-field region, as

21

summarized in Fig. (1.6 a-d). Aperture probes are used in near-field illumination or detection, as reported in Fig. (1.6 a-b), respectively, or in the case of a sufficiently strong signal they can be even employed in illumination/collection geometry, Fig. (1.6 c). The last one is the best suited for improving the spatial resolution, since it provides an almost background free illumination. These configurations are suited of employing aperture or dielectric probe which, by exploiting the frustrated total internal reflection that occurs at the fiber end, allow the conversion of evanescent waves with high spatial frequencies to e.m. fields propagating through the optical fiber and

In Fig. (1.6 d) SNOM setup is based on sharply pointed apertureless tip (a-SNOM) that locally enhances light scattering. Both illumination and collection are in the farfield, therefore a-SNOM requires a sophisticated method for filtering out the huge background. Moreover, in order to enhance light scattering apertureless probes are commonly fabricated on high refractive index material, such as silicon, that would drastically perturb strongly localized optical modes, which are the basic topic of the

In combination with time-resolved excitation and detection schemes, near-field microscopy has the potential to give direct access to processes on ultra-short time and length scales. Near-field microscopy has therefore all the advantages of conventional

The fundamental parameter of a SNOM setup is the near-field probe, as it defines the spatial resolution, the amount of detected signal and the induced perturbation on a given sample. In this section, we review the basic near-field probe designs, fabrication method and optical properties focusing on those that will be mentioned in the

In e.m. theory an antenna is a device used to create e.m. waves with a well-defined radiation pattern, or to receive e.m. waves from a remote source in order to extract some encoded information, by measuring changes in their intensity, or by exploiting the transmitted power [50]. So antennas main ability relies in establishing efficient coupling between the near-field and the far-field by enhancing and concentrating the incoming fields and simultaneously allowing to control the directional emission of light sources placed in the near-field zone [51, 52]. Moreover, optical antenna can enhance light absorption, leading to advantageously photodetection and to photovoltaics applications [53]. Although antenna theory has been developed for the radiofrequency and the microwave range it holds great promise for inspiring new concepts in the optical frequency range. Therefore, the local SNOM probe can be viewed acting as an optical antenna, converting the investigated near-field into propagating radiation and vice-versa (because of reciprocity), with a net energy transfer efficiency that defines the antenna throughput. Standard aperture probes need a trade-off between spatial resolution versus throughput, since the transmission through a metal screen with a sub-wavelength hole of radius a scales as (/)4, with the same wavelength de-

spectroscopy with a high spatial resolution solely defined by the probe size.

finally measured by a conventional far-field detector.

research presented in this thesis.

**1.3.1 Probes design and fabrication**

thesis concerning the experiments discussion.

pendence of the Rayleigh scattering [46, 54, 55].

summarized in Fig. (1.6 a-d). Aperture probes are used in near-field illumination or detection, as reported in Fig. (1.6 a-b), respectively, or in the case of a sufficiently strong signal they can be even employed in illumination/collection geometry, Fig. (1.6 c). The last one is the best suited for improving the spatial resolution, since it provides an almost background free illumination. These configurations are suited of employing aperture or dielectric probe which, by exploiting the frustrated total internal reflection that occurs at the fiber end, allow the conversion of evanescent waves with high spatial frequencies to e.m. fields propagating through the optical fiber and finally measured by a conventional far-field detector.

In Fig. (1.6 d) SNOM setup is based on sharply pointed apertureless tip (a-SNOM) that locally enhances light scattering. Both illumination and collection are in the farfield, therefore a-SNOM requires a sophisticated method for filtering out the huge background. Moreover, in order to enhance light scattering apertureless probes are commonly fabricated on high refractive index material, such as silicon, that would drastically perturb strongly localized optical modes, which are the basic topic of the research presented in this thesis.

In combination with time-resolved excitation and detection schemes, near-field microscopy has the potential to give direct access to processes on ultra-short time and length scales. Near-field microscopy has therefore all the advantages of conventional spectroscopy with a high spatial resolution solely defined by the probe size.

### **1.3.1 Probes design and fabrication**

20

**1.3 Scanning near-field optical microscopy**

[42–44].

If AFM shear-force probe microscopy is combined with optical detection huge advantages can be achieved in the characterization of light emitting nanostructures and fluorescent molecules. The most striking example is near-field scanning optical microscopy (SNOM), in which the apex of a tapered or pulled optical fiber acts like a AFM tip, thus providing both optical and topographical information of the sampling surface. This integrated microscope works in close proximity with the sample surface, thus being strongly interacting with optical near-field and evanescent waves. Subwavelength imaging based on SNOM was experimentally tested for the first time in the visible spectral range more than 30 years ago by Pohl et al. employing aperture probes [41]. The principle of SNOM imaging operation relies on the point-by-point investigation by raster-scanning the local probe over the sample surface and recording at every position the corresponding optical signature. The local probe acts as an optical antenna, converting localized e.m. fields into radiation, and vice versa. Therefore, SNOM detection gives ultra-sensitive optical measurement beyond the diffraction limit and provides light behavior at the nanoscale, together with the topographical capability of the AFM imaging. Although the morphological performance is not as good as in cantilever based AFM, SNOM proved to be the state of the art technique for investigating nanostructures such as quantum wells, quantum dots, nanoresonators or for single molecules since it combines the excellent spectroscopic and temporal selectivity of classical optical microscopy with the sub-wavelength spatial resolution

The concept of near-field optical microscopy was originally proposed in by Synge 1928 in a prophetic article, where he proposed an apparatus similar to the actual SNOM implementations [45]. A sub-wavelength aperture in an opaque plate placed in close proximity to the sample surface creates an illumination spot not limited by diffraction. Scanning the source along the surface and recording the transmitted, or reflected, light produces an image with subwavelength resolution. In fact, the resolution of such an image should be limited only by the size of the aperture and not by diffraction, as was also pointed out years later by Bethe studying the diffraction by small holes [46]. Only after the invention of the STM an efficient positioning technology was available at the nanoscale. Therefore an optical microscope similar to Synge's proposal was realized, firstly in the microwave by Nicholls and Ash, then in the visible spectral range simultaneously by Pohl et al. and Lewis et al. due to the obviously different fabrications difficulties demonstrating a sub-wavelength imaging with a resolution of /60 and /20, respectively [41, 47, 48]. The key innovation was the fabrication of a sub-wavelength optical aperture at the apex of a sharply pointed transparent (quartz) probe tip whose sidewalls were coated by metal. Such sharp aperture replaces the Synge's opaque screen for experimental purposes. In addition, a feedback loop was implemented based on proper piezoelectric quartz tuning forks (later replaced by piezoelectric bimorph bender element) maintaining the tip-sample distance constant (at few nanometers) while raster scanning the sample surface [49]. SNOM technique was systematically advanced and extended over the years to various configurations that provide a sharp confined photon flux in the near-field region, as

The fundamental parameter of a SNOM setup is the near-field probe, as it defines the spatial resolution, the amount of detected signal and the induced perturbation on a given sample. In this section, we review the basic near-field probe designs, fabrication method and optical properties focusing on those that will be mentioned in the thesis concerning the experiments discussion.

In e.m. theory an antenna is a device used to create e.m. waves with a well-defined radiation pattern, or to receive e.m. waves from a remote source in order to extract some encoded information, by measuring changes in their intensity, or by exploiting the transmitted power [50]. So antennas main ability relies in establishing efficient coupling between the near-field and the far-field by enhancing and concentrating the incoming fields and simultaneously allowing to control the directional emission of light sources placed in the near-field zone [51, 52]. Moreover, optical antenna can enhance light absorption, leading to advantageously photodetection and to photovoltaics applications [53]. Although antenna theory has been developed for the radiofrequency and the microwave range it holds great promise for inspiring new concepts in the optical frequency range. Therefore, the local SNOM probe can be viewed acting as an optical antenna, converting the investigated near-field into propagating radiation and vice-versa (because of reciprocity), with a net energy transfer efficiency that defines the antenna throughput. Standard aperture probes need a trade-off between spatial resolution versus throughput, since the transmission through a metal screen with a sub-wavelength hole of radius a scales as (/)4, with the same wavelength dependence of the Rayleigh scattering [46, 54, 55].

Many different near-field probe designs have been conceived and have been tested in the last decades. They can be grouped in four categories: *i)* dielectric, i.e. transparent, probes that are also called uncoated tips, *ii)* metal coated aperture probes, *iii)* pointed probes (used in a-SNOM setup), *iv)* probes functionalized by placing a nano emitter or a plasmonic nanoantenna at the tip apex.

#### **Dielectric probes**

Dielectric tips are the fundamental class of near-field optical probes since they represent the key components for the fabrication of more complex probes. Tapering of dielectric optical fibers can be done by chemical etching, or by local heating and subsequent pulling.

A well established method for fabricating smooth dielectric tapered probes is the tube etching method [56, 57]. We exploit this recipe to produce by ourselves the dielectric probes employed the SNOM experiments that will be described in the thesis. Glass tip formation occurs inside a cylindrical cavity formed by the polymercoating of an optical glass-core fiber which is not stripped away prior to etching in aqueous 48% hydrofluoric acid (*HF*). The two basic steps of the etching mechanism are reported in Fig. (1.7 a-b). In the first one, the acid largely corrodes the lateral side of the fiber core with respect to the central part since at the rim of the glass cylinder *HF* supply occurs out of a larger volume as compared to the central region. As soon as the preliminary taper is formed, step convection driven by concentrations gradients that are influenced by the etching process itself and the gravitational removal of the reaction products delivers *HF* to the upper cone region. After about 90 minutes of tube-etching the fiber is rinsed with ethanol and successively the jacket is removed without damaging the cone. The solution is covered by an organic overlayer (isooctane) to protect the fiber against acid vapor. Moreover, since the etching process takes places inside a hollow cylinder formed by the protective jacket, it is less sensitive to environmental influences such as vibrations or temperature drifts. The procedure gives tapered probes with large cone angles (about 30°) and small apex (less than 100 nm size), resulting in a strong decrease of the loss region with respect to pulled probes [58], and low sidewall surface roughness, since the meniscus formed by the acid along the fiber does not move during the etching. Dielectric tips with reproducible shapes and optical performance are formed in a high yield, as the one reported in the SEM image of Fig. (1.7 c). Since glass is almost transparent in the visible and near-infrared spectral range, these tapered dielectric probes show a high throughput (more than 50%), thus being suited for the high-contrast illumination-collection geometry.

However, the drawback is the low spatial resolution in the direct imaging. This feature can be simply explained if we consider how the fundamental mode of the optical fiber interacts with the tapered apex and it is focused in the near-field. The tapered, conical part of the probe can be represented as a series of glass disks with decreasing diameters and infinitesimal thicknesses. With each step part of the radiation is reflected, and the transmitted mode becomes less confined, since the field extends more and more into the surrounding medium (air) and exhibits increasing losses. By

23

Also by using narrow pointed apertureless probes, made of metal or high refractive index dielectric such as silicon, it is possible to retrieve optical information during the scan by exploiting the strong field enhancement in the proximity of the antenna that for gold tips is predicted to be very large, up to 50 [67]. Of course, the only available configuration is collecting in the far-field the scattered light tip-sample system that carries information about the near-field interaction, as shown in Fig. (1.6 d). The

spatial resolution since only the near-field is excited/detected [66].

reciprocity, it is clear that dielectric probes collect not only evanescent waves in the near-field by frustrated total internal reflection at the tip apex, but also a considerable amount of the propagating e.m. far-field injected through the upper part of the cone. Therefore, by collecting also large // high throughput but poor spatial resolution are expected for uncoated probes and the use of such a probe is not always convenient.

Tapered rather than pulled glass based tips, after metal coating in high vacuum evaporator by sputtering, can be modeled to result in small well-defined apertures at the apex, showing good homogeneity and negligible leakage of light along the cone [12]. Typically the metal is an aluminum or sometimes a gold layer of about 100 nm thickness, but the former is preferred for the smallest skin depth in the visible spectrum. The aperture is formed by metal shadowing evaporation (that is rotating the probe along the cone axis during the coating process) and it is typically between 100 nm and 200 nm diameter size for balancing high resolution and good throughput,

A more sophisticated fabrication technique allows for obtaining a well-defined flat circular aperture with controllable diameter size down to 20 nm, by milling the coating with a focused ion beam (FIB) [61]. FIB is the state of the art method to build high quality nanoscale structures; however, it is a rather expensive and inherently slow technique. Significantly less expensive and reproducible procedures have been put forward for the reliable fabrication of aperture probes as controlled electrolysis, aperture punching, selective resin coating or by integrating a waveguide into the AFM cantilever making the most of established silicon engineering techniques [62–65]. The lateral metal coating avoids the leakages in the outer space thus confining the e.m. fields at the aperture. In fact, by approaching the tapered tip apex light is progressively confined, but exceeding a transverse diameter size smaller than the wavelength of the modes propagating in the fiber, all the sustained modes are back reflected or absorbed and dissipated by the metal and cannot propagate any further. For this reason, the sub-wavelength aperture probes introduce a diameter-size dependent cutoff causing only evanescent waves to escape, as highlighted in Fig. (1.8 b) [12, 60]. Of course, this characteristic gives an experimental extremely small throughput with respect to dielectric probes (with a ratio of about 10−5) but allows to obtain high

**Coated aperture probes**

see Fig. (1.8 a) [59, 60].

**Apertureless probes**

reciprocity, it is clear that dielectric probes collect not only evanescent waves in the near-field by frustrated total internal reflection at the tip apex, but also a considerable amount of the propagating e.m. far-field injected through the upper part of the cone. Therefore, by collecting also large // high throughput but poor spatial resolution are expected for uncoated probes and the use of such a probe is not always convenient.

#### **Coated aperture probes**

Tapered rather than pulled glass based tips, after metal coating in high vacuum evaporator by sputtering, can be modeled to result in small well-defined apertures at the apex, showing good homogeneity and negligible leakage of light along the cone [12]. Typically the metal is an aluminum or sometimes a gold layer of about 100 nm thickness, but the former is preferred for the smallest skin depth in the visible spectrum. The aperture is formed by metal shadowing evaporation (that is rotating the probe along the cone axis during the coating process) and it is typically between 100 nm and 200 nm diameter size for balancing high resolution and good throughput, see Fig. (1.8 a) [59, 60].

A more sophisticated fabrication technique allows for obtaining a well-defined flat circular aperture with controllable diameter size down to 20 nm, by milling the coating with a focused ion beam (FIB) [61]. FIB is the state of the art method to build high quality nanoscale structures; however, it is a rather expensive and inherently slow technique. Significantly less expensive and reproducible procedures have been put forward for the reliable fabrication of aperture probes as controlled electrolysis, aperture punching, selective resin coating or by integrating a waveguide into the AFM cantilever making the most of established silicon engineering techniques [62–65].

The lateral metal coating avoids the leakages in the outer space thus confining the e.m. fields at the aperture. In fact, by approaching the tapered tip apex light is progressively confined, but exceeding a transverse diameter size smaller than the wavelength of the modes propagating in the fiber, all the sustained modes are back reflected or absorbed and dissipated by the metal and cannot propagate any further. For this reason, the sub-wavelength aperture probes introduce a diameter-size dependent cutoff causing only evanescent waves to escape, as highlighted in Fig. (1.8 b) [12, 60]. Of course, this characteristic gives an experimental extremely small throughput with respect to dielectric probes (with a ratio of about 10−5) but allows to obtain high spatial resolution since only the near-field is excited/detected [66].

#### **Apertureless probes**

22

However, the drawback is the low spatial resolution in the direct imaging. This feature can be simply explained if we consider how the fundamental mode of the optical fiber interacts with the tapered apex and it is focused in the near-field. The tapered, conical part of the probe can be represented as a series of glass disks with decreasing diameters and infinitesimal thicknesses. With each step part of the radiation is reflected, and the transmitted mode becomes less confined, since the field extends more and more into the surrounding medium (air) and exhibits increasing losses. By

Many different near-field probe designs have been conceived and have been tested in the last decades. They can be grouped in four categories: *i)* dielectric, i.e. transparent, probes that are also called uncoated tips, *ii)* metal coated aperture probes, *iii)* pointed probes (used in a-SNOM setup), *iv)* probes functionalized by placing a

Dielectric tips are the fundamental class of near-field optical probes since they represent the key components for the fabrication of more complex probes. Tapering of dielectric optical fibers can be done by chemical etching, or by local heating and

A well established method for fabricating smooth dielectric tapered probes is the tube etching method [56, 57]. We exploit this recipe to produce by ourselves the dielectric probes employed the SNOM experiments that will be described in the thesis. Glass tip formation occurs inside a cylindrical cavity formed by the polymercoating of an optical glass-core fiber which is not stripped away prior to etching in aqueous 48% hydrofluoric acid (*HF*). The two basic steps of the etching mechanism are reported in Fig. (1.7 a-b). In the first one, the acid largely corrodes the lateral side of the fiber core with respect to the central part since at the rim of the glass cylinder *HF* supply occurs out of a larger volume as compared to the central region. As soon as the preliminary taper is formed, step convection driven by concentrations gradients that are influenced by the etching process itself and the gravitational removal of the reaction products delivers *HF* to the upper cone region. After about 90 minutes of tube-etching the fiber is rinsed with ethanol and successively the jacket is removed without damaging the cone. The solution is covered by an organic overlayer (isooctane) to protect the fiber against acid vapor. Moreover, since the etching process takes places inside a hollow cylinder formed by the protective jacket, it is less sensitive to environmental influences such as vibrations or temperature drifts. The procedure gives tapered probes with large cone angles (about 30°) and small apex (less than 100 nm size), resulting in a strong decrease of the loss region with respect to pulled probes [58], and low sidewall surface roughness, since the meniscus formed by the acid along the fiber does not move during the etching. Dielectric tips with reproducible shapes and optical performance are formed in a high yield, as the one reported in the SEM image of Fig. (1.7 c). Since glass is almost transparent in the visible and near-infrared spectral range, these tapered dielectric probes show a high throughput (more than 50%), thus being suited for the high-contrast illumination-collection ge-

nano emitter or a plasmonic nanoantenna at the tip apex.

**Dielectric probes**

subsequent pulling.

ometry.

Also by using narrow pointed apertureless probes, made of metal or high refractive index dielectric such as silicon, it is possible to retrieve optical information during the scan by exploiting the strong field enhancement in the proximity of the antenna that for gold tips is predicted to be very large, up to 50 [67]. Of course, the only available configuration is collecting in the far-field the scattered light tip-sample system that carries information about the near-field interaction, as shown in Fig. (1.6 d). The

illumination can be provided by standard microscopes as well as by evanescent waves from total internal reflection [68]. The optical signal is measured by inducing a modulation in the tip oscillations and performing homodyne or heterodyne interferometric detection using lock-in techniques in order to demodulate the beat signal at higher harmonics of the tip vibration; therefore the far field part can be suppressed effectively to discriminate the small scattered signal from the tip apex against the diffraction limited background, leading to a few nanometers resolution in the infrared spectral range [69–71].

#### **Functionalized probes**

In order to manipulate and confine optical radiation at subwavelength scales a key improvement has been developed by integrating single light sources or nanostructured devices on the apex of standard probes. In this way a further nanoantenna is created on top of the near-field probe and a tremendous advancement in terms of spatial resolution, throughput and sensitivity is achieved.

On one hand, the modification of the spontaneous emission rate of an emitter placed in a nano-optical resonator device (Purcell effect [72]) can be monitored by grafting the light source at the end of a scanning probe, see Fig. (1.9 a), and then performing fluorescence lifetime measurements as a function of position [73, 74]. However, the disadvantage is that single nano-emitters may suffer of bleaching and/or blinking [75, 76].

On the other hand, thanks to high reliable nano-fabrication procedures which in most of the cases exploit FIB or electron-beam lithography, metal-based nano-antennas milled at the apex of standard probes are fabricated in order to achieve outstanding spatial resolution and bright near-field probes, thus overcoming the throughput constrain imposed by the aperture dimension, by squeezing the near-field by means of localized plasmons coupling [77].

It is a well known principle of microwave engineering that the most efficient way to couple far-field radiation to a device of dimension much smaller than the light wavelength is to connect the device to an antenna [50]. If we follow the parallelism with antenna theory, in the optical regime we need to introduce metal materials losses, however such losses may be compensated by collective electron resonances, i.e. surface plasmons [78]. In fact, the recent enormous advance in nano-imaging techniques coincided with the introduction of concepts from plasmonics, such as surface plasmon polaritons (SPPs) confinement along metal-dielectric interfaces, into the design of nearfield probes [79, 80]. SPPs are waves that propagate along the surface of a conductor. By altering the structure of a metal surface the SPP interaction with light can be tailored on demand, offering the potential for developing new types of photonic devices, making optical antennas particularly efficient at selected frequencies and broadening the perspectives of near-field optics. With respect to metallic coated probes, plasmonic functionalized tips exhibit either a better spatial resolution (at constant throughput) or larger throughput (at constant resolution). Several high-performance near-field probe geometries, in which plasmonic nanoantennas are included,

25

have been engineered and optimized both experimentally and theoretically with respect to size, shape and material in order to efficiently transform light from the farfield to the near-field and the other way round, and for increasing the radiation effi-

Although the design of optical antennas is likely to be inspired by radio-frequency or microwave regime working geometries, it can be expected that the presence of new physical phenomena will demand the exploration of new structures and material compositions. The first developed plasmonic geometry was the renowned bow-tie nanoantenna that is constituted of two metal triangles facing each, as shown in Fig. (1.9 b), and optimizes the impedance matching, thus delivering high throughput and local field enhancement [84–86]. The practical realization on top of a scanning probe is performed by FIB, creating a bow-tie nano-aperture at the apex of a coated probe [87]. Other realizations are, for instance, mini-tip on aperture, single metal nanoparticle, see Fig. (1.9 c), and diabolo (complementary to the bow-tie) antenna structures have been grown on the end faces of aperture-type near-field probes [88–92]. However, all the reported functionalized probes rely on resonant structures with a limited spectral bandwidth that impose the spectral matching between the field enhancement effect

In Chapter (3) we will discuss SNOM experiments performed with a recently developed next generation plasmonic nanoantenna, called "Campanile tip". This nearfield probe milled by FIB on top of a gold coated tip shows a broadband operation and allows us for mapping with unprecedented spatial resolution the influence on carrier recombination in local trap states within individual solid state emitters (quantum wires) as well as the simultaneous electric and magnetic field distributions confined

ciency of nano-optical emitters [81–83].

and wavelength operation of the investigated sample.

in nanoresonators.

have been engineered and optimized both experimentally and theoretically with respect to size, shape and material in order to efficiently transform light from the farfield to the near-field and the other way round, and for increasing the radiation efficiency of nano-optical emitters [81–83].

Although the design of optical antennas is likely to be inspired by radio-frequency or microwave regime working geometries, it can be expected that the presence of new physical phenomena will demand the exploration of new structures and material compositions. The first developed plasmonic geometry was the renowned bow-tie nanoantenna that is constituted of two metal triangles facing each, as shown in Fig. (1.9 b), and optimizes the impedance matching, thus delivering high throughput and local field enhancement [84–86]. The practical realization on top of a scanning probe is performed by FIB, creating a bow-tie nano-aperture at the apex of a coated probe [87]. Other realizations are, for instance, mini-tip on aperture, single metal nanoparticle, see Fig. (1.9 c), and diabolo (complementary to the bow-tie) antenna structures have been grown on the end faces of aperture-type near-field probes [88–92]. However, all the reported functionalized probes rely on resonant structures with a limited spectral bandwidth that impose the spectral matching between the field enhancement effect and wavelength operation of the investigated sample.

In Chapter (3) we will discuss SNOM experiments performed with a recently developed next generation plasmonic nanoantenna, called "Campanile tip". This nearfield probe milled by FIB on top of a gold coated tip shows a broadband operation and allows us for mapping with unprecedented spatial resolution the influence on carrier recombination in local trap states within individual solid state emitters (quantum wires) as well as the simultaneous electric and magnetic field distributions confined in nanoresonators.

24

illumination can be provided by standard microscopes as well as by evanescent waves from total internal reflection [68]. The optical signal is measured by inducing a modulation in the tip oscillations and performing homodyne or heterodyne interferometric detection using lock-in techniques in order to demodulate the beat signal at higher harmonics of the tip vibration; therefore the far field part can be suppressed effectively to discriminate the small scattered signal from the tip apex against the diffraction limited background, leading to a few nanometers resolution in the infrared spectral range

In order to manipulate and confine optical radiation at subwavelength scales a key improvement has been developed by integrating single light sources or nanostructured devices on the apex of standard probes. In this way a further nanoantenna is created on top of the near-field probe and a tremendous advancement in terms of spatial res-

On one hand, the modification of the spontaneous emission rate of an emitter placed in a nano-optical resonator device (Purcell effect [72]) can be monitored by grafting the light source at the end of a scanning probe, see Fig. (1.9 a), and then performing fluorescence lifetime measurements as a function of position [73, 74]. However, the disadvantage is that single nano-emitters may suffer of bleaching and/or

On the other hand, thanks to high reliable nano-fabrication procedures which in most of the cases exploit FIB or electron-beam lithography, metal-based nano-antennas milled at the apex of standard probes are fabricated in order to achieve outstanding spatial resolution and bright near-field probes, thus overcoming the throughput constrain imposed by the aperture dimension, by squeezing the near-field by means of

It is a well known principle of microwave engineering that the most efficient way to couple far-field radiation to a device of dimension much smaller than the light wavelength is to connect the device to an antenna [50]. If we follow the parallelism with antenna theory, in the optical regime we need to introduce metal materials losses, however such losses may be compensated by collective electron resonances, i.e. surface plasmons [78]. In fact, the recent enormous advance in nano-imaging techniques coincided with the introduction of concepts from plasmonics, such as surface plasmon polaritons (SPPs) confinement along metal-dielectric interfaces, into the design of nearfield probes [79, 80]. SPPs are waves that propagate along the surface of a conductor. By altering the structure of a metal surface the SPP interaction with light can be tailored on demand, offering the potential for developing new types of photonic devices, making optical antennas particularly efficient at selected frequencies and broadening the perspectives of near-field optics. With respect to metallic coated probes, plasmonic functionalized tips exhibit either a better spatial resolution (at constant throughput) or larger throughput (at constant resolution). Several high-performance near-field probe geometries, in which plasmonic nanoantennas are included,

[69–71].

blinking [75, 76].

**Functionalized probes**

localized plasmons coupling [77].

olution, throughput and sensitivity is achieved.

Figure 1.1: a) Schematics concerning the image formation on the plane Σof a pointlike object (S) illuminated by a monochromatic plane wave with wavevector performed by the optical system L (lens or objective). is the half-angle of the maximum light cone accepted by L and Σ is the back focal plane. Red curves describe the behavior of radiation field wave front. The blue curve represents a one-dimensional profile cut of the Airy disk in Σ. b) Typical three-dimensional Airy disk intensity pattern representing the image of the point-like source in Σ.

Figure 1.2: a) Total internal reflection at the interface between two media with 2 < 1 if 1 > arctan (2 /1). The displacement represents the Goos-Hänchen shift. The evanescent wave in 2 medium is schematically reported exhibiting a Poyniting vector parallel to the interface. b) Frustrated total internal reflection occurs in a successive 1 medium placed in close proximity to 2 if the evanescent wave is not completely decayed.

27

plane the initial evanescent wave amplitude is retrieved.

Figure 1.4: a) Principle of confocal microscopy: the pinhole in front of detector filters out the light that does not come from the focal spot. b) Comparison between normalized point spread function (PSF) of STED fluorescence microscope, confocal microscope and conventional scanning microscope reported by , and curves, respectively, as evaluated in [21]. c) Pendry's superlens principle of operation. Negative refraction occurs inside the negative refractive index media (−1) leading to a double focusing inside and outside the slab. The red curve describes the evanescent wave decay in 1 and its amplification inside the superlens, so that in the image

Figure 1.3: In the angular spectrum representation the e.m. fields are evaluated in a plane perpendicular to an arbitrarily chosen axis. In this case we evaluate the total

field + .

Figure 1.3: In the angular spectrum representation the e.m. fields are evaluated in a plane perpendicular to an arbitrarily chosen axis. In this case we evaluate the total field + .

Figure 1.4: a) Principle of confocal microscopy: the pinhole in front of detector filters out the light that does not come from the focal spot. b) Comparison between normalized point spread function (PSF) of STED fluorescence microscope, confocal microscope and conventional scanning microscope reported by , and curves, respectively, as evaluated in [21]. c) Pendry's superlens principle of operation. Negative refraction occurs inside the negative refractive index media (−1) leading to a double focusing inside and outside the slab. The red curve describes the evanescent wave decay in 1 and its amplification inside the superlens, so that in the image plane the initial evanescent wave amplitude is retrieved.

26

Figure 1.2: a) Total internal reflection at the interface between two media with 2 < 1 if 1 > arctan (2 /1). The displacement represents the Goos-Hänchen shift. The evanescent wave in 2 medium is schematically reported exhibiting a Poyniting vector parallel to the interface. b) Frustrated total internal reflection occurs in a successive 1 medium placed in close proximity to 2 if the evanescent

wave is not completely decayed.

Figure 1.1: a) Schematics concerning the image formation on the plane Σof a pointlike object (S) illuminated by a monochromatic plane wave with wavevector performed by the optical system L (lens or objective). is the half-angle of the maximum light cone accepted by L and Σ is the back focal plane. Red curves describe the behavior of radiation field wave front. The blue curve represents a one-dimensional profile cut of the Airy disk in Σ. b) Typical three-dimensional Airy disk in-

tensity pattern representing the image of the point-like source in Σ.

Figure 1.5: a) Principle of AFM microscopy: the tip attached to the cantilever scan the sample surface following the blue curve B reported in b), while the laser deflections are measured by a four-quadrant photodiode. The electronic feedback control assures a constant tip-sample distance. b) Zoom on the tip-sample gap that highlights the path scanned by the tip. Only the tip front atoms inyeract with the specimen [39].

Figure 1.6: Schematics of the four more widespread SNOM configurations. a) Incoming light illuminates the sample in the near-field by means of an aperture probe and the scattered light is detected in far-field by standard microscopes. b) Complementary regime with respect of a): far-field illumination and near-field detection. c) Illumination/collection geometry in which both the near-field illumination and collection occur through the tip. d) Apertureless probe enhances the scattering in the near-field, whose information are analyzed by far-field detection.

29

Figure 1.7: Dielectric tapered fiber etching process in aqueous hydrofluoric acid [56]. a) First etching step: diffusive motion of the *HF* solution. b) Second etching step: convective motion of the *HF* solution. c) SEM image of an etched dielectric ta-

Figure 1.8: a) SEM image of an aluminum coated probe with a nominal aperture of 200 nm crated by shadowing evaporation, which is commercially available by the company LovaLite. b) Aperture probe lateral view schematics. It is highlighted the cutoff of the propagating modes when they approach the tip apex with an aperture

size smaller than that allows only evanescent waves to escape.

pered fiber.

Figure 1.7: Dielectric tapered fiber etching process in aqueous hydrofluoric acid [56]. a) First etching step: diffusive motion of the *HF* solution. b) Second etching step: convective motion of the *HF* solution. c) SEM image of an etched dielectric tapered fiber.

Figure 1.8: a) SEM image of an aluminum coated probe with a nominal aperture of 200 nm crated by shadowing evaporation, which is commercially available by the company LovaLite. b) Aperture probe lateral view schematics. It is highlighted the cutoff of the propagating modes when they approach the tip apex with an aperture size smaller than that allows only evanescent waves to escape.

28

Figure 1.6: Schematics of the four more widespread SNOM configurations. a) Incoming light illuminates the sample in the near-field by means of an aperture probe and the scattered light is detected in far-field by standard microscopes. b) Complementary regime with respect of a): far-field illumination and near-field detection. c) Illumination/collection geometry in which both the near-field illumination and collection occur through the tip. d) Apertureless probe enhances the scattering in the

near-field, whose information are analyzed by far-field detection.

Figure 1.5: a) Principle of AFM microscopy: the tip attached to the cantilever scan the sample surface following the blue curve B reported in b), while the laser deflections are measured by a four-quadrant photodiode. The electronic feedback control assures a constant tip-sample distance. b) Zoom on the tip-sample gap that highlights the path scanned by the tip. Only the tip front atoms inyeract with the speci-

men [39].

Figure 1.9: Schematics of functionalized near-field probes. a) Single molecule light source grafted at the end of the tip. b) Bow-tie aperture at the apex of a metal coated probe. c) Gold nanoparticle at the tip apex acts like a plasmonic nanoantenna.

31

[1] M. Born and E. Wolf. Principles of Optics. Oxford: Pergamon, 6th edn. (1970). [2] E. Abbe. "Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung" In: Archiv f. Miroskop. Anat. 9, 1 (1873), pp. 413–468.

[3] F. Lord Rayleigh. "Investigations in optics, with special reference to the spectro-

[4] F. Lord Rayleigh. "On the theory of optical images with special reference to the

[7] Q. Wu, G. Feke, R. Grober, and L. Ghislain. "Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens" In: Appl. Phys. Lett. 75, 26

[8] E. Stelzer and S. Grill. "The uncertainty principle applied to estimate focal spot

[9] G. Toraldo di Francia. "Alcuni fenomeni di diffrazione trattati mediante il

[10] G. Toraldo di Francia. "Le onde evanescenti nella diffrazione" In: Ottica 7

[11] M. Schaffner and G. Toraldo di Francia. "Micoonde evanescenti generate per

[13] J. Jackson. Classical Electrodynamics. New York, John Wiley and Sons, 3th

[15] R.Webb. "Confocal optical microscopy" In: Rep. Prog. Phys. 59 (1996), pp.

[17] W. Denk andW.W. Strickler J.H. "Two-Photon Laser Scanning Fluorescence

[18] W. Zipfel, R.Williams, andW.Webb. "Nonlinear magic: multiphoton micros-

[19] W. Moerner and L. Kador. "Optical detection and spectroscopy of single mole-

[20] W. Moerner and M. Orrit. "Illuminating Single Molecules in Condensed Mat-

[16] T. Wilson. Confocal Microscopy. London: Academic Press, (1990).

copy in the biosciences" In: Nat. Biotechnol. 21 (2003), pp. 1369–1377.

cules in a solid" In: Phys. Rev. Lett. 62, 21 (1989), pp. 2535–2538.

[14] M. Minsky. "Memoir on inventing the confocal scanning microscope" In: Scan-

[12] B. H. L. Novotny. Principles of Nano-Optics. Cambridge University Pr.,

[5] E. Hecht. Optics. Adelphi university international edition, 4th edn., (2001). [6] G. Airy. "On the diffraction of an object glass with circular aperture" In: Trans.

scope" In: Philos. Mag. (fifth series) 8, 49 (1879), pp. 261–274.

microscope" In: Philos. Mag. 5 (1896), pp. 167–195.

dimensions" In: Opt. Commun. 173 (2000), pp. 51–56.

principio dell'interferenza inversa" In: Ottica 7 (1942), p. 117.

diffrazione" In: Il Nuovo Cimento 6, 2 (1949), pp. 126–130.

Microscopy" In: Scanning. 248, 4951 (1990), pp. 73–76.

ter" In: Science 283, 5408 (1999), pp. 1670–1676.

Camb. Phil. Soc. 5 (1834), pp. 283–291.

(1999), pp. 4064–4066.

(1942), p. 197.

(2006).

edn., (1998).

427– 471.

ning. 10, 4 (1988), pp. 128–138.

**References**

### **References**

30

Figure 1.9: Schematics of functionalized near-field probes. a) Single molecule light source grafted at the end of the tip. b) Bow-tie aperture at the apex of a metal coated probe. c) Gold nanoparticle at the tip apex acts like a plasmonic nanoantenna.

[1] M. Born and E. Wolf. Principles of Optics. Oxford: Pergamon, 6th edn. (1970).

[2] E. Abbe. "Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung" In: Archiv f. Miroskop. Anat. 9, 1 (1873), pp. 413–468.

[3] F. Lord Rayleigh. "Investigations in optics, with special reference to the spectroscope" In: Philos. Mag. (fifth series) 8, 49 (1879), pp. 261–274.

[4] F. Lord Rayleigh. "On the theory of optical images with special reference to the microscope" In: Philos. Mag. 5 (1896), pp. 167–195.

[5] E. Hecht. Optics. Adelphi university international edition, 4th edn., (2001).

[6] G. Airy. "On the diffraction of an object glass with circular aperture" In: Trans. Camb. Phil. Soc. 5 (1834), pp. 283–291.

[7] Q. Wu, G. Feke, R. Grober, and L. Ghislain. "Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens" In: Appl. Phys. Lett. 75, 26 (1999), pp. 4064–4066.

[8] E. Stelzer and S. Grill. "The uncertainty principle applied to estimate focal spot dimensions" In: Opt. Commun. 173 (2000), pp. 51–56.

[9] G. Toraldo di Francia. "Alcuni fenomeni di diffrazione trattati mediante il principio dell'interferenza inversa" In: Ottica 7 (1942), p. 117.

[10] G. Toraldo di Francia. "Le onde evanescenti nella diffrazione" In: Ottica 7 (1942), p. 197.

[11] M. Schaffner and G. Toraldo di Francia. "Micoonde evanescenti generate per diffrazione" In: Il Nuovo Cimento 6, 2 (1949), pp. 126–130.

[12] B. H. L. Novotny. Principles of Nano-Optics. Cambridge University Pr., (2006).

[13] J. Jackson. Classical Electrodynamics. New York, John Wiley and Sons, 3th edn., (1998).

[14] M. Minsky. "Memoir on inventing the confocal scanning microscope" In: Scanning. 10, 4 (1988), pp. 128–138.

[15] R.Webb. "Confocal optical microscopy" In: Rep. Prog. Phys. 59 (1996), pp. 427– 471.

[16] T. Wilson. Confocal Microscopy. London: Academic Press, (1990).

[17] W. Denk andW.W. Strickler J.H. "Two-Photon Laser Scanning Fluorescence Microscopy" In: Scanning. 248, 4951 (1990), pp. 73–76.

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