**6. Concluding Remarks**

Dysregulation of the ubiquitin–proteasome system including the positive or negative regulation of E3 ligases, DUBs, or proteasomes seriously a ffects cellular homeostasis and causes the development of serious pathologic conditions, such as tumor suppression or promotion in cancer, protein accumulation in neurodegenerative diseases, and forming an ine ffective immune response in the body (Figure 3). Thus, recently a great deal of work has been devoted to the development of novel drugs, targeting proteins that either interfere or inhibit ubiquitination and proteasome activity in disease-dependent manner. Ongoing research studies of a wide range of molecules targeting di fferent ligases show promising data in several pathogenic conditions; nevertheless, the translation of these data into clinical application is still a major challenge. For instance, some compounds are shown to inhibit E3 ligases generally in in vitro conditions, but the e ffects of such compounds remain unclear in in vivo models [193]. Proteasome-associated DUBs have been suggested as remarkable drug targets due to their lower side e ffects compared to proteasome-targeted drugs. Currently, DUBs-targeted inhibitors are mainly small molecules, and their development is still in the preclinical stage for inflammatory disease and cancer treatment [194]. The major restriction of DUBs inhibitors is their selectivity, as they may have complex intracellular interactions with several signaling pathways. Proteasome activity is another target in UPS-dependent therapy that became a popular idea to recover prominently in neurodegenerative diseases. Proteasome inhibitors, including bortezomib, carfilzomib, and ixazomib are well-tolerated by patients and therefore approved by the FDA for clinical applications. On the other hand, marizomib and oprozomib are currently under clinical trials [195]. In upcoming years, novel molecules targeting E3 ligases, DUBs, or proteasomes are expected to be validated for therapeutic approaches; thus, a better understanding of the molecular signaling pathways involved in ubiquitination and proteasomal degradation will allow the discovery of novel targeting molecules in cancer, neurodegenerative disease, and immune-related pathological conditions.

**Figure 3.** Summary of DUBs and E3 enzymes that play important roles in cancer progression, immune regulation, and neurodegenerative diseases. According to diseases, the enzymes positively or negatively regulate the mechanisms in mitophagy, cell differentiation, cell development, signaling, protein accumulation, neural malfunction, synaptogenesis, inhibition of apoptosis, cell cycle stimulation, mitochondrial regulation, autophagic flux, ER homeostasis, and protein degradation. E3 ligases and DUBs in the upside or downside of the semicircle indicate negative (red area) or positive regulators (green area) of these diseases.

**Author Contributions:** G.C., H.K., E.O.; original draft preparation, O.K., review, and editing. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.


**About the Editors**

**Giovanni Ruggieri** holds a Ph.D. in Mineralogy and Petrology and was awarded the Johndino Nogara prize of the Italian Society of Mineralogy and Petrology. He is a researcher at IGG-CNR and a member of the Commission on Ore Mineralogy of the IMA. He coordinates the participation of CNR in the EU H2020 project GEMex. Specialized in fluid inclusions, stable isotopes, hydrothermal alteration and minero-petrographic studies, his fields of interests include geothermal exploration, fluid-rock interactions and fluid flow in hydrothermal systems, ore genesis, travertine formation, CO2 sequestration by serpentine carbonation, and experimental mineralogy.

**Fabrizio Gherardi** received his PhD from the University of Pisa, Italy, defending a dissertation on gas-water-rock interactions and fluid geochemistry of high-enthalpy geothermal systems. A geochemist with a background in isotope hydrology, fluid geochemistry and gas-water-rock interactions, he uses numerical models to investigate geochemical reactivity in natural and anthropogenically disturbed systems. His recent research focuses on noble gas geochemistry, geochemical and reactive transport modelling of gas-water-rock interactions in hydrothermal/geothermal systems, and sites for geological confinement of greenhouse gases.


**3. FAERS database annotation of COVID-19 drug trials**

FDA Adverse Event Reporting System (FAERS) Public Dashboard is the Bioinformatics approach in curating side effects of drug trials from clinical data [29, 30]. It has special public dashboard for COVID-19 emergency use authorization (EUA) products, as seen in the **Figure 1**.

The FAERS database has annotated COVID-19 drug trials side effects, such as the trials with hydroxychloroquine/chloroquine, bamlanivimab, Ribavirin-Interferon and ivermectin [31–37]. Moreover, cancer patients who were old (65 year-old and above), males, and taking immunosuppressive treatment, as well as those with hematological malignancies, were at a higher risk of death due to COVID-19 infection, according to FAERS data [34]. Hence, pertaining the existing COVID-19 standard drugs, the finding in FAERS database did not affect current FDA's endorsement as it is considered still a relatively novel development. More trials will be necessary. Thus, extensive computational and wet lab studies of the leads' pharmacological and toxicological properties should be carefully examined [38].

#### **Figure 1.**

*COVID-19 emergency use authorization (EUA) FAERS public dashboard (source: https://www.fda.gov/drugs/ questions-and-answers-fdas-adverse-event-reporting-system-faers/fda-adverse-event-reporting-system-faerspublic-dashboard).*


**4. Ceramic-metal brazing problems**

Brazing is a process for joining similar or dissimilar materials using filler metal [35, 36]. The filler metal is heated slightly above its melting point so it flows, but the temperature remains lower than the melting point of the ceramic metal joints (**Figure 11**). Flux or an inert atmosphere is utilized to keep two surfaces that have joined and brazing material from oxidation during the heating process. The filler material flows over the base metal and ceramic, and the entire assembly is then cooled to join the pieces together. Brazing forms very strong, permanent joints. Brazing is considered to be well-established commercial processes for ceramic metal joints also [37], where it is widely used in industry, in different parts, because almost every metallic and ceramic material can be joined by this process. Generally, brazing can easily be performed by manual techniques, but, in many cases, it can just as easily be automated if necessary.

**Figure 11.** Brazing schematic [38].

where *b* is the thickness and *a* is the width of the specimen.

to four-point to tensile testing and as specimen size increases.

**4. Ceramic-metal brazing problems**

necessary.

point and *M* = (*F*/2)⋅*d* for four-point test.

Therefore, for three-point bending:

174 Joining Technologies

And for four-point bending test:

From **Figure 10**, it is possible to illustrate the derivation of the three-point and four-point flexure formulas for rectangular bars. We can observe that: *M* = (*L*/2)⋅(*F*/2) in the case of three-

> 3P 2 3. . 2. . = = s

> > 4Pt 2 3. .

For most ceramic materials, the apparent strength will decrease when going from three-point

Whatever joining processes are used, the successful formation of the joint depends on ach‐ ievement of intimate contact between the base materials, conversion of the intimate contact into an atomic bonding/reaction, accommodation of residual stresses induced by different thermal and mechanical properties between the base materials undergoing temperature change. Each joining process is characterized by the methods and conditions employed to

Brazing is a process for joining similar or dissimilar materials using filler metal [35, 36]. The filler metal is heated slightly above its melting point so it flows, but the temperature remains lower than the melting point of the ceramic metal joints (**Figure 11**). Flux or an inert atmosphere is utilized to keep two surfaces that have joined and brazing material from oxidation during the heating process. The filler material flows over the base metal and ceramic, and the entire assembly is then cooled to join the pieces together. Brazing forms very strong, permanent joints. Brazing is considered to be well-established commercial processes for ceramic metal joints also [37], where it is widely used in industry, in different parts, because almost every metallic and ceramic material can be joined by this process. Generally, brazing can easily be performed by manual techniques, but, in many cases, it can just as easily be automated if

. = = s

achieve intimate contact and to promote bond formation between the work pieces.

*F d S*

*a b* (10)

*a b* (11)

*F L S*

Brazing has numerous focal points over other metal-joining methods, for example, welding [39]. Since brazing does not fuse the base metal of the joint, it permits much more tightly control over resilience and produces a perfect join without the requirement for optional wrapping up. Furthermore, dissimilar metals and ceramic can be brazed. When all is said in done, brazing likewise creates less thermal deformation than welding because of the uniform heating of a brazed piece [39]. Complex and multi-part assemblies can be brazed cost-effective. Another feature is that the brazing can be covered or clad for defensive purposes. Finally, brazing is effectively adjusted for large scale manufacturing and it is anything but difficult to mechanize on the grounds that the individual procedure parameters are less delicate to variety [40].

One of the major disadvantages is the absence of joint strength when contrasted with a welded joint because of the softer filler metals utilized. The strength of the brazed joint is liable to be not as much as base metals but more than the filler metal [41]. Another disadvantage is that brazed joints can be damaged under high temperatures. The brazed material joints require a high purity when done in an industrial environment. Also some applications for brazing require the utilization of satisfactory fluxing agents to control cleanliness. The colour of joint is frequently not quite the same as that of the base metal, making a stylish disadvantage.

The two major problems when the joining these materials by brazing process are firstly the differences in physical properties between ceramics and metals, and secondly the poor wettability of ceramics by most metals and alloys [42, 43]. The first problem in joining ceramics to metals for high-temperature results from the huge contrasts in thermal expansion behav‐ iour. At the point when the thermal expansion of these materials get together is modified, these differences in the thermal expansion behaviour can prompt high stresses [42]. This condition is regularly subsequently heightened by thermal inclinations that rise as a result of thermal diffusivity contrasts between the metal and ceramic. Ceramic for the most part have high elastic moduli and low-relaxation characteristics which prevent relief or redistribution of the stresses. The low tensile strengths of most ceramics may then make them unable to resist fracture under such stresses [44, 45]. Another problem of wettability is overcome with the use of an activated braze alloy, where an active element, e.g. Al, Zr and Ti, alters the surface chemistry of the ceramic by the formation of intermediate reaction layer and lowers the wetting angle of the molten braze on the ceramic [46, 47]. The compounds that form are commonly spinels for the oxide ceramics and complex nitrides for the ceramic nitrides [39]. For the purpose of address‐ ing this problem should be used high vacuum or high-purity reducing or inert-gas atmos‐ pheres are necessary for the successful brazing process.

Cazajus et al. [48] have studied the thermal stresses in the ceramic-metal joining after brazing process. The framework of this study is the thermomechanical analysis and the simulation of the brazing process of ceramic and metal joining. **Figure 12** gives the physical phenomena involved during brazing and their coupling relations. The brazing is a joining process which produces the coalescence of materials by heating them to a suitable temperature or by using a filler metal, having liquids under the solids of the base materials. The difference between ceramic and metal thermal expansion coefficient (CTE) leads to the development of residual thermal stresses during cooling from brazing process to room temperature which reduce the join strength. The design of joints in material engineering and the optimization of the industrial brazing process require to control and to examine such a phenomenon. The conclusions from that paper can be drawn for different parameter effects on residual stresses during the brazing process simulation. The mechanical behaviour and geometrical parameters have a significant influence on the residual stress distribution and their maximum values. The difference between ceramic and metallic material's CTE and the metallic materials elastoplastic proper‐ ties are the most important parameters of the assembly mechanical behaviour. The ratio between the alumina height and stainless steel (*H*A/*H*SS) represents the most important geometrical factor (**Figure 13**). The cooling conditions and the filler metal yield stress evolution depending on temperature have only a significant impact on the residual stresses evolution during the brazing process and not on the final value [49, 50].

**Figure 13.** Geometrical parameters of the ceramic metal assembly [50].

[51].

Shirzadi et al. [51] developed the general method for brazing ceramics to metals using compliant metallic foam as a buffer layer. Using stainless steel foams, bonds between alumina and 316 Stainless Steel with shear strengths up to 33 MPa have been achieved. From this study, it is found that the utilization of metallic foam as a buffer layer between ceramic and metal could be an efficient method to avoid the mismatch that occurs in thermal expansion between the two materials when bonded together by brazing. They have been exhibited that the joints were tolerant to serious thermal cycling tests. The number of thermal cycles (200–800 °C in normal condition) to disappointment of 67 ± 3 through the thermal cycling test. According to shear test results, the fracture mode was ductile because of the flexibility in the region based on the layer of foam. The fracture surfaces of the samples brazed without and with foam after

Current Issues and Problems in the Joining of Ceramic to Metal

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177

**Figure 14.** Fracture surfaces of joints without and with metallic foam following thermal cycling between 200 and 800 °C in air. Number of cycles to failure were <1 and 60 ± 4 for samples without and with a foam interlayer, respectively

**Figure 12.** Physical phenomena during brazing process and their couplings [48].

**Figure 13.** Geometrical parameters of the ceramic metal assembly [50].

diffusivity contrasts between the metal and ceramic. Ceramic for the most part have high elastic moduli and low-relaxation characteristics which prevent relief or redistribution of the stresses. The low tensile strengths of most ceramics may then make them unable to resist fracture under such stresses [44, 45]. Another problem of wettability is overcome with the use of an activated braze alloy, where an active element, e.g. Al, Zr and Ti, alters the surface chemistry of the ceramic by the formation of intermediate reaction layer and lowers the wetting angle of the molten braze on the ceramic [46, 47]. The compounds that form are commonly spinels for the oxide ceramics and complex nitrides for the ceramic nitrides [39]. For the purpose of address‐ ing this problem should be used high vacuum or high-purity reducing or inert-gas atmos‐

Cazajus et al. [48] have studied the thermal stresses in the ceramic-metal joining after brazing process. The framework of this study is the thermomechanical analysis and the simulation of the brazing process of ceramic and metal joining. **Figure 12** gives the physical phenomena involved during brazing and their coupling relations. The brazing is a joining process which produces the coalescence of materials by heating them to a suitable temperature or by using a filler metal, having liquids under the solids of the base materials. The difference between ceramic and metal thermal expansion coefficient (CTE) leads to the development of residual thermal stresses during cooling from brazing process to room temperature which reduce the join strength. The design of joints in material engineering and the optimization of the industrial brazing process require to control and to examine such a phenomenon. The conclusions from that paper can be drawn for different parameter effects on residual stresses during the brazing process simulation. The mechanical behaviour and geometrical parameters have a significant influence on the residual stress distribution and their maximum values. The difference between ceramic and metallic material's CTE and the metallic materials elastoplastic proper‐ ties are the most important parameters of the assembly mechanical behaviour. The ratio between the alumina height and stainless steel (*H*A/*H*SS) represents the most important geometrical factor (**Figure 13**). The cooling conditions and the filler metal yield stress evolution depending on temperature have only a significant impact on the residual stresses evolution

pheres are necessary for the successful brazing process.

176 Joining Technologies

during the brazing process and not on the final value [49, 50].

**Figure 12.** Physical phenomena during brazing process and their couplings [48].

Shirzadi et al. [51] developed the general method for brazing ceramics to metals using compliant metallic foam as a buffer layer. Using stainless steel foams, bonds between alumina and 316 Stainless Steel with shear strengths up to 33 MPa have been achieved. From this study, it is found that the utilization of metallic foam as a buffer layer between ceramic and metal could be an efficient method to avoid the mismatch that occurs in thermal expansion between the two materials when bonded together by brazing. They have been exhibited that the joints were tolerant to serious thermal cycling tests. The number of thermal cycles (200–800 °C in normal condition) to disappointment of 67 ± 3 through the thermal cycling test. According to shear test results, the fracture mode was ductile because of the flexibility in the region based on the layer of foam. The fracture surfaces of the samples brazed without and with foam after

**Figure 14.** Fracture surfaces of joints without and with metallic foam following thermal cycling between 200 and 800 °C in air. Number of cycles to failure were <1 and 60 ± 4 for samples without and with a foam interlayer, respectively [51].

thermal cycling (200–800 °C in air) as shown in **Figure 14**. It showed the former 'cup and cone' break inside the ceramic after the first cycle, while the latter failed from the interface of the ceramic foam after more than 60 cycles.

**5. Ceramic–metal solid-state joining**

each will be qualified.

**5.1. Ceramic-metal friction welding**

Solid state joining is a gathering of joining procedures which produces cohesion at tempera‐ tures basically underneath the melting point of the base materials being joined, without the expansion of brazing filler metal. Pressure might possibly be utilized. These procedures are infrequently mistakenly called solid state bonding forms: this gathering of joining procedures incorporates friction welding, diffusion and laser welding. In all of these welding processes, the parameters such as temperature, time and pressure separately or together to produce ceramic metal joint without melting of the base metal. Solid-state bonding process contains some of very oldest processes and some of them new. The bonding processes provide certain advantages as the base metal do not melt and compose an interface. The materials that joined keep their original properties without the heat-affected zone problems included when there is no melting for base materials [53]. At the point when dissimilar metals are joined their thermal expansion and conductivity is of substantially less significance with solid state welding than with the arc welding processes. Time, temperature and pressure are included; nonetheless, in some processes the time component is to a great degree short, in the microsec‐ ond run or up to a few moments. In different cases, the time is reached out to a few hours. As temperature expands time is generally decreased. Since each of these processes is different

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Friction welding is a solid state joining that produces a bond under the compressive force of one rotating workpiece to another stationary workpiece [54]. Heat is generated at the weld interface during the friction between two materials because of the non-stop rubbing for different contact surfaces, which is produced later in the softening of metal (**Figure 16**). Finally, the metal side at the weld interface begins to flow elastically and forms an axial shortening [55]. When a certain amount of forging had occurred, the rotation stops and the compressive force are maintained or slightly increased to consolidate the weld. Some of the important operational parameters in friction welding are friction time, friction pressure and rotation speed [56].

Friction welding, like any welding process, has its specific advantages and disadvantages. The following are some advantages of friction welding such as no filler metal is needed. Flux and shielding gas are not required. The process is environmentally clean, no arcs, sparks, smoke or fumes are generated by clean parts [58]. Surface cleanliness is not as significant, compared with other welding processes, since friction welding tends to disrupt and displace surface films. There are narrow heat affected zones. The process is suitable for welding most engi‐ neering materials and is well suited for joining many dissimilar material combinations. In some cases of weld, the strength of the joint is equal to or greater than the strength of the weaker of the two materials joined. The bond that is created by the mechanical intermixing and solidifi‐ cation of the two materials is strong and free from voids and porosity. It can be cost effective

and offers design engineers many more options than other methods.

The article of Walker and Hodges [52] is intended to familiarize the designer with brazing methods commonly used to join metals to ceramics, discussed the advantages and disadvan‐ tages of two methods, and show the relative tensile strengths obtained from samples fabricated using these methods. In most article cases discussed, 94% alumina ceramic (6% glassy phase) ASTM-F19 tensile button samples were joined to Fe-29Ni-17Co alloy using a gold-or silverbased braze filler metal (**Figure 15**). The article is limited to the two metallization methods most commonly used for joining metals to ceramics: the molybdenum-manganese/nickel plating method and physical-vapour deposition or thin-film method.

**Figure 15.** Commonly used ceramic metallization methods: (A) moly-manganese metallization process; (B) thin-film metallization process [52].

At the point when ceramics production are to be brazed, especially in those conditions where the coupling part is a metal, the individual differential thermal coefficient of thermal expansion between the coupling parts is of foremost significance. When in doubt engineers have a tendency to expect that the coefficient of thermal extension of a metal will be a few times that of a ceramic. This is not generally genuine, be that as it may. For instance ceramic, for example, silicon nitride and silicon carbide do, in fact, have low coefficient of thermal extension, and issues emerging from stresses produced amid the cooling stage can be normal in conditions where such materials are brazed to stainless steels or copper both of which being metals that have a high coefficient of thermal expansion. However, titanium, titanium alloys and some exceptional materials, for example, invar and kovar each have a coefficient of thermal expan‐ sion which is near that of alumina, while expansion coefficients of molybdenum and tungsten are near those of both silicon carbide and silicon nitride. This implies while picking the 'active' filler material that will be utilized for a specific employment it is fundamental to decide the differential coefficient of expansion that exists between the materials that are to be joined.


Meet the editors

Dr. S. Sundaresan has been working in the field of cancer chemoprevention, cancer immunotherapy, and tumor marker detection. Translational research (TR) has been described as translating research into medical practice and translating science into better healthcare. Translational research on tumor biomarkers has successfully promoted the development of tumor treatment and has brought new hope for cancer patients. It is

important to direct cancer research on diagnosis and treatment toward applying fundamental research findings to the clinic as soon as possible, and applying novel tumor molecular markers to early diagnosis, targeted therapy, and individualized treatment. Focused medical treatment should be given through the analysis of new tumor biomarkers and appropriate treatments. Dr. S. Sundaresan has been working with oral cancer and cancer biomarkers. There are newer molecular markers that are of clinical significance and they need to be studied in various populations. The administration of indoles and triterpenes for preventive and curative effects was studied in laboratory animals. Dr. S. Sundaresan's research study also demonstrates interferon beta synergistically works with chemotherapeutic drug cisplatin for liver, breast, and cervix cancer cells.

Dr. Yeun-Hwa Gu is working as a Professor for the Department of Radiation Oncology, Graduate School of Health Science, Junshin Gakuen University, Japan. He has worked as a Professor for the Department of Health and Medicine, Suzuka Medical Science University for 15 years. He graduated from the University of Tokyo with his Master's and Ph.D. degrees. He is currently working as an academic advisory committee member of the Korea Society

of Health Sciences and academic director of the Korean Ultrasound Cancer Therapy (HIFU) Society and co-researcher of the Russia Space Radiation Chemistry Protection Study Group. He is a board member and editor of the International Journal of Food Science, Editor-in-Chief of Clinical Microbiology and Infectious Diseases and Current Traditional Medicine. He has published more than 250 papers in various peer-reviewed journals.

Contents

in Cancer

*and Tao Lu*

IL10 as Cancer Biomarker

*Carmen Maldonado-Bernal*

for Diagnostics with Antibodies

Chalcones: Potential Anticancer Agents *by Adam McCluskey and Cecilia Russell*

*by Yeun-Hwa Gu*

with Hypoxia

Stem Cells

**Preface XI**

**Chapter 1 1**

**Chapter 2 25**

**Chapter 3 43**

**Chapter 4 65**

**Chapter 5 75**

**Chapter 6 101**

**Chapter 7 115**

**Chapter 8 127**

New Screening for the Development of Radioprotectors: Radioprotection

Evaluation by Monte Carlo Simulation of Doses Distribution in Tumors

Bozepinib: A Promising Selective Derivative Targeting Breast Cancer

Discovery of Small Molecule Inhibitors for Histone Methyltransferases

*by Aishat A. Motolani, Mengyao Sun, Matthew Martin, Steven Sun*

Ion Channels and Transporters as Cancer Biomarkers and Targets

*by Maria Teresa Gonzalez-Garza, Delia Elva Cruz-Vega and*

*by Jessica Iorio, Claudia Duranti and Elena Lastraioli*

Translational Perspective in Hepatocellular Carcinoma *by Sivapatham Sundaresan and Palanirasu Rajapriya*

and Anti-Cancer Effect of β-Glucan (*Enterococcus faecalis*)

*by Mirko Salomón Alva-Sánchez and Thatiane Alves Pianoschi*

*by Joaquín M. Campos, Ana Conejo-García and Olga Cruz-López*


**3.1 Method of moments**

The linear MoM presented here is based in the linear current approximation with an equivalent surface impedance model of the cylindrical conductors, with sinusoidal test and base functions [18]. The method will be explained for the particular example of a single dipole radiating in a free space, composed by plasmonic cylindrical elements made of gold.

**Figure 3** shows the geometry of the original problem, the equivalent MoM and circuit models of the nanodipole. In this figure, *L* is the length of the arms, *d* is the nanodipole gap and *a* is the dipole radius. The total length of this antenna is *Lt* = 2 *L* + *d*. In present analysis, we do not take into account the capacitance generated by the air gap (*Cgap*) of the nanodipole. In this case, our input impedance is equivalent to that *Za* presented in [20] without *Cgap*.

In the radiation problem of **Figure 3**, the gold material of the antenna is represented by the Lorentz-Drude model for complex permittivity *ε*Au = *ε*0*εr*Au:

$$
\varepsilon\_{r\text{Au}} = \varepsilon\_{\infty} - \frac{\alpha\_{p1}^2}{\alpha^2 - j\Gamma\alpha} + \frac{\alpha\_{p2}^2}{\alpha\_0^2 - \alpha^2 + j\gamma\alpha},\tag{1}
$$

*Zs* ¼ *TJ*0ð Þ *Ta*

*Complex permittivity of gold obtained by Lorentz-Drude model of (1) and experimental data of Johnson-*

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas*

*μ*0*ε*0

tangential to the surface of the metal, *Es* is the scattered electric field due to the induced linear current *I* on the conductor, *Ei* the incident electric field from the voltage source (**Figure 3**), and *I* is the longitudinal current in a given point of the

The integral equation for the scattered field along the length *l* of the nanodipole

*Ig R*ð Þ*dl*0 þ

ð

*dI*

*dl*0 ∇*g R*ð Þ*dl*0

3

*ZmnIn, m* ¼ 1*,* 2*,* 3*,* …*, N*–1*,* (4)

5*,* (3)

∣ is the

*l*

being *T* ¼ *k*0

nanodipole.

**Figure 4.**

*Christy [21].*

is given by

**5**

ffiffiffiffiffiffiffiffi

*DOI: http://dx.doi.org/10.5772/intechopen.88482*

field at the conductor surface is *Es* þ *Ei*

*Es*ð Þ¼ *r*

1 *jωε*0

*Vm* ¼ *ZsIm*Δ*m* �X

*k*2 0 ð

2 4

*l*

where *g R*ð Þ¼ *e*�*jk*0*R=*4*πR* is the free space Green's function, and *R* ¼ ∣*r* � *r*0

of segments in *L* � 0.5*d* with the size Δ*L* = (*L* � 0.5*d*)/*Na* (white segments in **Figure 3**), and two segments in the middle with the size Δ*L* = *d* (gray segments in **Figure 3**). Later, the current in each segment is approximated by sinusoidal basis functions. The expansion constants *In* are shown in **Figure 3** where each constant defines one triangular sinusoidal current. To calculate these constants, we use *N* � 1 rectangular pulse test functions with unitary amplitude and perform the conventional testing procedure. As a result, the following linear system of equations is obtained:

*N*�1

*n*¼1

distance between source and observation points. The numerical solution of the problem formulated by (1)–(3) is performed by linear MoM as follows. Firstly, we divide the total length *Lt* = 2 *L* + *d* in *N* = 2*Na* + 2 straight segments, where *Na* is the number

*εrAu* p and *k*0 ¼ *ω* ffiffiffiffiffiffiffiffiffi

2*πajωεAuJ*1ð Þ *Ta ,* (2)

p . The boundary condition for the electric

� � � *al* ¼ *ZsI*, where *al* is a unitary vector

where the parameters in this equation are as follows [1]: *ε*∞ = 8, *ωp*1 = 13.8 � 1015s �1 , Γ = 1.075 � 1014s �1 , *ω*0 = 2π*c*/*λ*0, *c* = 3 � 108 m/s, *λ*0 = 450 nm, *ωp*2 = 45 � 1014s �1 , *γ* = 9 � 1014s �1 , and *ω* is the angular frequency in rad/s. **Figure 4** presents the real and imaginary part of (1) versus wavelength (*λ*). This figure also shows the experimental data of [21]. We observe a good agreement between the results of the Lorentz-Drude model of (1) and the experimental data for *λ* > 500 nm.

The losses in metal are described by the surface impedance *Zs*. This impedance can be obtained approximately by considering cylindrical waveguide with the mode TM01. In this case, the surface impedance is given by [22].

**Figure 3.** *Geometry of nanodipole: original problem (left), MoM model (middle), and equivalent circuit model (right).*

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas DOI: http://dx.doi.org/10.5772/intechopen.88482*

#### **Figure 4.**

**3. Numerical model**

*Nanoplasmonics*

MoM [18] and FEM [19].

**3.1 Method of moments**

*ωp*1 = 13.8 � 1015s

*ωp*2 = 45 � 1014s

*λ* > 500 nm.

**Figure 3.**

**4**

�1

�1

plasmonic cylindrical elements made of gold.

is equivalent to that *Za* presented in [20] without *Cgap*.

*εr*Au ¼ *ε*∞ � *ω*2

, Γ = 1.075 � 1014s

TM01. In this case, the surface impedance is given by [22].

, *γ* = 9 � 1014s

In this section, we present the numerical methods used in the analysis of the wireless optical nanolinks described in the last section. The methods used here are

The linear MoM presented here is based in the linear current approximation with an equivalent surface impedance model of the cylindrical conductors, with sinusoidal test and base functions [18]. The method will be explained for the particular example of a single dipole radiating in a free space, composed by

**Figure 3** shows the geometry of the original problem, the equivalent MoM and circuit models of the nanodipole. In this figure, *L* is the length of the arms, *d* is the nanodipole gap and *a* is the dipole radius. The total length of this antenna is *Lt* = 2 *L* + *d*. In present analysis, we do not take into account the capacitance generated by the air gap (*Cgap*) of the nanodipole. In this case, our input impedance

In the radiation problem of **Figure 3**, the gold material of the antenna is represented by the Lorentz-Drude model for complex permittivity *ε*Au = *ε*0*εr*Au:

*p*1

�1

presents the real and imaginary part of (1) versus wavelength (*λ*). This figure also shows the experimental data of [21]. We observe a good agreement between the

The losses in metal are described by the surface impedance *Zs*. This impedance can be obtained approximately by considering cylindrical waveguide with the mode

*Geometry of nanodipole: original problem (left), MoM model (middle), and equivalent circuit model (right).*

where the parameters in this equation are as follows [1]: *ε*∞ = 8,

results of the Lorentz-Drude model of (1) and the experimental data for

�1

*ω*2 � *j*Γ*ω* þ *ω*2

*ω*2

*p*2

0 � *ω*2 þ *jγω,* (1)

, *ω*0 = 2π*c*/*λ*0, *c* = 3 � 108 m/s, *λ*0 = 450 nm,

, and *ω* is the angular frequency in rad/s. **Figure 4**

*Complex permittivity of gold obtained by Lorentz-Drude model of (1) and experimental data of Johnson-Christy [21].*

$$Z\_s = \frac{T\mathcal{J}\_0(Ta)}{2\pi a j a e\_{Au} J\_1(Ta)},\tag{2}$$

being *T* ¼ *k*0 ffiffiffiffiffiffiffiffi *εrAu* p and *k*0 ¼ *ω* ffiffiffiffiffiffiffiffiffi *μ*0*ε*0 p . The boundary condition for the electric field at the conductor surface is *Es* þ *Ei* � � � *al* ¼ *ZsI*, where *al* is a unitary vector tangential to the surface of the metal, *Es* is the scattered electric field due to the induced linear current *I* on the conductor, *Ei* the incident electric field from the voltage source (**Figure 3**), and *I* is the longitudinal current in a given point of the nanodipole.

The integral equation for the scattered field along the length *l* of the nanodipole is given by

$$\overline{E}\_{\mathbf{r}}(\overline{r}) = \frac{1}{j\alpha\varepsilon\_{0}} \left[ k\_{0}^{2} \int\_{l} \overline{\mathbf{J}} \mathbf{g}(\mathbf{R}) dl' + \int\_{l} \frac{dI}{dl'} \nabla \mathbf{g}(\mathbf{R}) dl' \right],\tag{3}$$

where *g R*ð Þ¼ *e*�*jk*0*R=*4*πR* is the free space Green's function, and *R* ¼ ∣*r* � *r*0 ∣ is the distance between source and observation points. The numerical solution of the problem formulated by (1)–(3) is performed by linear MoM as follows. Firstly, we divide the total length *Lt* = 2 *L* + *d* in *N* = 2*Na* + 2 straight segments, where *Na* is the number of segments in *L* � 0.5*d* with the size Δ*L* = (*L* � 0.5*d*)/*Na* (white segments in **Figure 3**), and two segments in the middle with the size Δ*L* = *d* (gray segments in **Figure 3**). Later, the current in each segment is approximated by sinusoidal basis functions. The expansion constants *In* are shown in **Figure 3** where each constant defines one triangular sinusoidal current. To calculate these constants, we use *N* � 1 rectangular pulse test functions with unitary amplitude and perform the conventional testing procedure. As a result, the following linear system of equations is obtained:

$$V\_m = Z\_s I\_m \Delta\_m - \sum\_{n=1}^{N-1} Z\_{mn} I\_n, m = 1, 2, 3, \dots, N-1,\tag{4}$$

#### **Figure 5.**

*Mesh of the problem of Figure 2 generated in COMSOL. (a) Nanolink mesh and its surroundings. (b) Enlarged Yagi-Uda antenna mesh.*

where *Zmn* is the mutual impedance between sinusoidal current elements *m* and *n*, Δ*m* = 1/2[Δ*Lm* + Δ*Lm* + 1], and *Vm* is non-zero only in the middle of the antenna (*m* = *N*/2), where *VN*/2 = *Vs*. The solution of (4) gives the current along the dipole and the input current *Is*. For *Vs* = 1 V, the input impedance is *Zin* = 1/ *Is* = (*Rr* + *RL*) + *jXin* = *Rin* + *jXin*, where *Rr*, *RL*, *Rin*, and *Xin* are the radiation resistance, loss resistance, input resistance, and input reactance, respectively. The total input power is calculated by *Pin* = 0.5Re(*VsIs*\*) = 0.5(*RL* + *Rr*)|*Is*| 2 = 0.5*Rin*| *Is*| 2 = *Pr* + *PL*, *Pr* is the radiated power, and *PL* the loss power dissipated at the antenna's surface which is calculated by

$$P\_L = 0.5 \text{Re}(Z\_s) \sum\_{n=1}^{N-1} |I\_n|^2 \Delta\_{n\nu} \tag{5}$$

resonances are in the frequency range of 100–400 THz considered. The parameters of the isolated dipole are based on [23] and those of the elements of the Yagi-Uda antenna were chosen so that the reflecting element was larger than the dipole and the smaller dipole directors. In **Table 1**, *a* = *ar* = *adT* = *ad* = *adR* and *d* = *dhr* = *dhd*. **Figure 6** shows the input impedance (*Zin*) for the Yagi-Uda antennas (**Figure 6a**) and dipole (**Figure 6b**). These input impedances were calculated by FEM with the COMSOL software, and by a linear MoM applied to cylindrical plasmonic nanoantennas [18], by coding the mathematical model in Matlab soft-

*Input impedance (Zin) of the transmitting antennas Yagi-Uda and dipole. (a) Yagi-Uda without substrate, compared to MoM, and with SiO2 substrate. (b) Dipole without substrate, compared to MoM, and with SiO2*

**Variable** *hdT ddT a hr hd hdR ddr d dTR* Values 220 20 15 700 250 220 20 100 5000

*Nanolink parameters used in simulations. All parameters are in nanometer (nm).*

*DOI: http://dx.doi.org/10.5772/intechopen.88482*

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas*

**Table 1.**

**Figure 6.**

*substrate.*

**7**

ware [24]. We observe a good agreement between these two methods.

The radiated power can be obtained by *Pr* = *Pin* � *PL*, and the resistances by *Rr* = 2*Pr*/|*Is*| 2 and *RL* = 2*PL*/|*Is*| 2 . The radiation efficiency is defined by *er* = *Pr*/ *Pin* = *Pr*/(*Pr* + *PL*) = *Rr*/(*Rr* + *RL*) = *Rr*/*Rin*.

#### **3.2 Finite element method**

The nanolinks of **Figure 3** were also analyzed numerically by FEM. **Figure 5a** shows the mesh of the nanolink of **Figure 2** modeled in the COMSOL, where the antennas are in a spherical domain of air, with scattering absorbing condition (PLM) applied at their ends. **Figure 5b** shows an enlarged image of the Yagi-Uda nanoantenna mesh and its surroundings.

### **4. Numerical results**

#### **4.1 Isolated antennas in transmitting mode**

In this section, the transmitting antennas Yagi-Uda and dipole (**Figure 2** without reflector and directors) are analyzed separately. For this analysis, the values of the antennas parameters are those shown in **Table 1**, where with these values the main

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas DOI: http://dx.doi.org/10.5772/intechopen.88482*

**Table 1.**

where *Zmn* is the mutual impedance between sinusoidal current elements *m* and *n*, Δ*m* = 1/2[Δ*Lm* + Δ*Lm* + 1], and *Vm* is non-zero only in the middle of the antenna (*m* = *N*/2), where *VN*/2 = *Vs*. The solution of (4) gives the current along the dipole and the input current *Is*. For *Vs* = 1 V, the input impedance is *Zin* = 1/ *Is* = (*Rr* + *RL*) + *jXin* = *Rin* + *jXin*, where *Rr*, *RL*, *Rin*, and *Xin* are the radiation resistance, loss resistance, input resistance, and input reactance, respectively. The

*Mesh of the problem of Figure 2 generated in COMSOL. (a) Nanolink mesh and its surroundings.*

2 = *Pr* + *PL*, *Pr* is the radiated power, and *PL* the loss power dissipated at the

The radiated power can be obtained by *Pr* = *Pin* � *PL*, and the resistances

The nanolinks of **Figure 3** were also analyzed numerically by FEM. **Figure 5a** shows the mesh of the nanolink of **Figure 2** modeled in the COMSOL, where the antennas are in a spherical domain of air, with scattering absorbing condition (PLM) applied at their ends. **Figure 5b** shows an enlarged image of the Yagi-Uda

In this section, the transmitting antennas Yagi-Uda and dipole (**Figure 2** without reflector and directors) are analyzed separately. For this analysis, the values of the antennas parameters are those shown in **Table 1**, where with these values the main

*N* X�1 *n*¼1

j j *In* 2

. The radiation efficiency is defined by *er* = *Pr*/

2 = 0.5*Rin*|

Δ*n,* (5)

total input power is calculated by *Pin* = 0.5Re(*VsIs*\*) = 0.5(*RL* + *Rr*)|*Is*|

*PL* ¼ 0*:*5Reð Þ *Zs*

2

antenna's surface which is calculated by

*(b) Enlarged Yagi-Uda antenna mesh.*

2 and *RL* = 2*PL*/|*Is*|

*Pin* = *Pr*/(*Pr* + *PL*) = *Rr*/(*Rr* + *RL*) = *Rr*/*Rin*.

nanoantenna mesh and its surroundings.

**4.1 Isolated antennas in transmitting mode**

**3.2 Finite element method**

**4. Numerical results**

*Is*|

**6**

**Figure 5.**

*Nanoplasmonics*

by *Rr* = 2*Pr*/|*Is*|

*Nanolink parameters used in simulations. All parameters are in nanometer (nm).*

#### **Figure 6.**

*Input impedance (Zin) of the transmitting antennas Yagi-Uda and dipole. (a) Yagi-Uda without substrate, compared to MoM, and with SiO2 substrate. (b) Dipole without substrate, compared to MoM, and with SiO2 substrate.*

resonances are in the frequency range of 100–400 THz considered. The parameters of the isolated dipole are based on [23] and those of the elements of the Yagi-Uda antenna were chosen so that the reflecting element was larger than the dipole and the smaller dipole directors. In **Table 1**, *a* = *ar* = *adT* = *ad* = *adR* and *d* = *dhr* = *dhd*.

**Figure 6** shows the input impedance (*Zin*) for the Yagi-Uda antennas (**Figure 6a**) and dipole (**Figure 6b**). These input impedances were calculated by FEM with the COMSOL software, and by a linear MoM applied to cylindrical plasmonic nanoantennas [18], by coding the mathematical model in Matlab software [24]. We observe a good agreement between these two methods.

#### *Nanoplasmonics*

Also, the input impedances of the antennas are calculated for two situations, the first with the antennas in the free space (without substrate) and the second on a SiO2 substrate with a permittivity of 2.15.

antennas in the free space. This effect of the substrate is similar to that observed in

**Figure 7** shows the results of directivity (*D*) and gain (*G*), radiation efficiency (*er*) and reflection coefficient (Γ), all in dB, versus frequency for the Yagi-Uda antennas (**Figure 7a**) and dipole (**Figure 7b**). The directivity and gain are calculated in the + *y* direction (**Figure 2**). In **Figure 7b** it is observed the conventional characteristic of the isolated dipole, where in a wide range of 150–300 THz one has

approximately *D* ≈ 1.6, *er* ≈ 0.6 e *G* ≈ 1 (*G* = *erD*). In the case of Yagi-Uda

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas*

(**Figure 7a**), there is a peak of *D* = 12, near *F* = 264 THz, but at this frequency the radiation efficiency is minimal *er* ≈ 0.1, and the gain is (*G* = 0.86). However, if greater gain and efficiency are desired rather than high directivity, the frequency near *F* ≈ 240 THz is more adequate, where the maximum gain is approximately *Gmax* ≈ 1.6. The reflection coefficient of both antennas was calculated considering a transmission line with characteristic impedance of 50 Ω connected to antennas. With this result, it is observed that the best impedance matching for both antennas occurs around the first resonant frequency, however the maximum radiation effi-

**Figure 8** shows the 3D far field gain radiation diagrams of the Yagi-Uda and dipole antennas, calculated at the frequency of 240 THz. It is observed that the maximum gain of the Yagi-Uda (*Gmax* ≈ 1.6) is approximately 60% greater than the maximum gain (*Gmax* ≈ 1) of the dipole. For the case of the Yagi-Uda antenna, the maximum gain occurs in the +*y* direction with a small lobe in

In this section, we present the results obtained in the analysis of the dipole/ dipole nanolinks (**Figure 2**, without reflector and transmitter directors), Yagi-Uda/ dipole (**Figure 2**) and Yagi-Uda/Yagi-Uda (**Figure 2**, with the receiving antenna equal to the transmitting antenna) for the frequency range of 100–400 THz. The parameters used for the receiving antennas are same as those of the transmitting

**Figure 9** shows the power transmission in dB (or power transfer function) for the three nanolinks, calculated by the ratio between the power delivered to the *ZC* load and the power delivered by the source *Vs* at the transmitting antenna terminals.

*3D far-field gain radiation diagram of (a) dipole antenna, and (b) Yagi-Uda (b), both in F = 240 THz.*

antennas, with *ZC* = 50 and 1250 Ω for each nanolink model.

The results show that the Yagi-Uda/Yagi-Uda nanolink presents a small

antennas in the microwave regime [25].

*DOI: http://dx.doi.org/10.5772/intechopen.88482*

ciency occurs at higher frequencies.

the *y* direction.

**Figure 8.**

**9**

**4.2 Nanolinks analysis**

Comparing the input impedance result between the Yagi-Uda and free-space dipole antennas, it is noted that the first two resonant frequencies are close, which shows that the directors and reflectors do not significantly affect the original resonant frequencies of the isolated dipole. The main differences between these two transmitting antennas are observed near the frequencies of 175 and 260 THz, which correspond physically to the dipole resonances of the reflector and directors, respectively. These resonances can be observed in the distributions of currents in these frequencies, which are not shown here.

**Figure 6** also shows the effect of the substrate in the input impedance and resonant properties of the antennas. It is observed that by placing the antennas on the substrate, their resonances are shifted to smaller frequencies in relation to the

**Figure 7.** *Directivity (D), gain (G), radiation efficiency (er) and reflection coefficient (Γ) of antennas (a) Yagi-Uda and (b) dipole.*

**8**

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas DOI: http://dx.doi.org/10.5772/intechopen.88482*

antennas in the free space. This effect of the substrate is similar to that observed in antennas in the microwave regime [25].

**Figure 7** shows the results of directivity (*D*) and gain (*G*), radiation efficiency (*er*) and reflection coefficient (Γ), all in dB, versus frequency for the Yagi-Uda antennas (**Figure 7a**) and dipole (**Figure 7b**). The directivity and gain are calculated in the + *y* direction (**Figure 2**). In **Figure 7b** it is observed the conventional characteristic of the isolated dipole, where in a wide range of 150–300 THz one has approximately *D* ≈ 1.6, *er* ≈ 0.6 e *G* ≈ 1 (*G* = *erD*). In the case of Yagi-Uda (**Figure 7a**), there is a peak of *D* = 12, near *F* = 264 THz, but at this frequency the radiation efficiency is minimal *er* ≈ 0.1, and the gain is (*G* = 0.86). However, if greater gain and efficiency are desired rather than high directivity, the frequency near *F* ≈ 240 THz is more adequate, where the maximum gain is approximately *Gmax* ≈ 1.6. The reflection coefficient of both antennas was calculated considering a transmission line with characteristic impedance of 50 Ω connected to antennas. With this result, it is observed that the best impedance matching for both antennas occurs around the first resonant frequency, however the maximum radiation efficiency occurs at higher frequencies.

**Figure 8** shows the 3D far field gain radiation diagrams of the Yagi-Uda and dipole antennas, calculated at the frequency of 240 THz. It is observed that the maximum gain of the Yagi-Uda (*Gmax* ≈ 1.6) is approximately 60% greater than the maximum gain (*Gmax* ≈ 1) of the dipole. For the case of the Yagi-Uda antenna, the maximum gain occurs in the +*y* direction with a small lobe in the *y* direction.

#### **4.2 Nanolinks analysis**

Also, the input impedances of the antennas are calculated for two situations, the first with the antennas in the free space (without substrate) and the second on a

Comparing the input impedance result between the Yagi-Uda and free-space dipole antennas, it is noted that the first two resonant frequencies are close, which shows that the directors and reflectors do not significantly affect the original resonant frequencies of the isolated dipole. The main differences between these two transmitting antennas are observed near the frequencies of 175 and 260 THz, which correspond physically to the dipole resonances of the reflector and directors, respectively. These resonances can be observed in the distributions of currents in

**Figure 6** also shows the effect of the substrate in the input impedance and resonant properties of the antennas. It is observed that by placing the antennas on the substrate, their resonances are shifted to smaller frequencies in relation to the

*Directivity (D), gain (G), radiation efficiency (er) and reflection coefficient (Γ) of antennas (a) Yagi-Uda and*

SiO2 substrate with a permittivity of 2.15.

*Nanoplasmonics*

these frequencies, which are not shown here.

**Figure 7.**

*(b) dipole.*

**8**

In this section, we present the results obtained in the analysis of the dipole/ dipole nanolinks (**Figure 2**, without reflector and transmitter directors), Yagi-Uda/ dipole (**Figure 2**) and Yagi-Uda/Yagi-Uda (**Figure 2**, with the receiving antenna equal to the transmitting antenna) for the frequency range of 100–400 THz. The parameters used for the receiving antennas are same as those of the transmitting antennas, with *ZC* = 50 and 1250 Ω for each nanolink model.

**Figure 9** shows the power transmission in dB (or power transfer function) for the three nanolinks, calculated by the ratio between the power delivered to the *ZC* load and the power delivered by the source *Vs* at the transmitting antenna terminals. The results show that the Yagi-Uda/Yagi-Uda nanolink presents a small

**Figure 8.** *3D far-field gain radiation diagram of (a) dipole antenna, and (b) Yagi-Uda (b), both in F = 240 THz.*

#### **Figure 9.**

*Power transmission versus frequency for the dipole/dipole nanolinks, Yagi-Uda/dipole and Yagi-Uda/Yagi-Uda, for ZC = 50 (a), e 1250 Ω (b).*

improvement in power transmission, at some frequency points, in relation to the dipole/dipole and Yagi-Uda/dipole nanolinks. In addition, it can be observed that the links can operate with good transmission power at the frequency points 170 and 240 THz, for *ZC* equal to 50 and 1250 Ω, respectively, where the power transmission are maximum.

**Figure 10** shows the magnitude and phase of the electric near field, which is defined by *E* = 20 log10(|Re (*Ex*)|), in the plane *z* = 25 nm, of the dipole/dipole nanolinks (a, b), Yagi-Uda/dipole (c, d) and Yagi-Uda/Yagi-Uda (e, f). The receiver antennas are positioned at a distance *dTR* = 5 μm from the transmitting antennas, with *F* = 170 THz and *ZC* = 50 Ω for the fields of figures (a), (c) and (e), and with *F* = 240 THz and *ZC* = 1250 Ω for the cases of figures (b), (d) and (f). In all types of nanolinks shown in this figure, the radiated wave can be visualized by propagating from the transmitting antennas to the receiving antennas, with the appropriated wavelength. It is observed the amplitude decay of the electric field with the distance and the decrease of the wavelength with the increase of the frequency.

**5. Conclusions**

**Figure 10.**

**11**

It was presented in this work, a comparative analysis of nanolinks formed by Yagi-Uda and dipole plasmonic nanoantennas, where was investigated the power transmission for Yagi-Uda/Yagi-Uda, Yagi-Uda/dipole and dipole/dipole nanolinks

*Electric near field distribution of the magnitude and phase (E = 20 log10(|Re (Ex)|)), in the plane z = 25 nm, of the dipole/dipole nanolinks (a, b), Yagi-Uda/dipole (c, d) and Yagi-Uda/Yagi-Uda (e, f). The receiver antennas are positioned at 5 μm from the transmitting antennas, with F = 170 THz and ZC = 50 Ω for figures*

*(a), (c) and (e), and with F = 240 THz and ZC = 1250 Ω for figures (b), (d) and (f).*

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas*

*DOI: http://dx.doi.org/10.5772/intechopen.88482*

*Wireless Optical Nanolinks with Yagi-Uda and Dipoles Plasmonic Nanoantennas DOI: http://dx.doi.org/10.5772/intechopen.88482*

**Figure 10.**

improvement in power transmission, at some frequency points, in relation to the dipole/dipole and Yagi-Uda/dipole nanolinks. In addition, it can be observed that the links can operate with good transmission power at the frequency points 170 and 240 THz, for *ZC* equal to 50 and 1250 Ω, respectively, where the power transmission

*Power transmission versus frequency for the dipole/dipole nanolinks, Yagi-Uda/dipole and Yagi-Uda/Yagi-*

**Figure 10** shows the magnitude and phase of the electric near field, which is defined by *E* = 20 log10(|Re (*Ex*)|), in the plane *z* = 25 nm, of the dipole/dipole nanolinks (a, b), Yagi-Uda/dipole (c, d) and Yagi-Uda/Yagi-Uda (e, f). The receiver antennas are positioned at a distance *dTR* = 5 μm from the transmitting antennas, with *F* = 170 THz and *ZC* = 50 Ω for the fields of figures (a), (c) and (e), and with *F* = 240 THz and *ZC* = 1250 Ω for the cases of figures (b), (d) and (f). In all types of nanolinks shown in this figure, the radiated wave can be visualized by propagating from the transmitting antennas to the receiving antennas, with the appropriated wavelength. It is observed the amplitude decay of the electric field with the distance

and the decrease of the wavelength with the increase of the frequency.

are maximum.

**10**

*Uda, for ZC = 50 (a), e 1250 Ω (b).*

**Figure 9.**

*Nanoplasmonics*

*Electric near field distribution of the magnitude and phase (E = 20 log10(|Re (Ex)|)), in the plane z = 25 nm, of the dipole/dipole nanolinks (a, b), Yagi-Uda/dipole (c, d) and Yagi-Uda/Yagi-Uda (e, f). The receiver antennas are positioned at 5 μm from the transmitting antennas, with F = 170 THz and ZC = 50 Ω for figures (a), (c) and (e), and with F = 240 THz and ZC = 1250 Ω for figures (b), (d) and (f).*