*2.9. IHC Staining*

After depara ffinization, antigen retrieval, and blocking of peroxidase activity, the tissue sections were incubated with anti-Ki-67 antibody (1:200; Abcam, Cambridge, UK), anti-caspase-3 antibody (1:100; Cell Signaling), and anti-p62 antibody (1:100; Cell Signaling) at 4 ◦C overnight, separately. Slides were further incubated for 30 min with Super Enhance and polymer HRP. The bound antibody was elected by a species-specific secondary antibody and then developed with a 3-amino-9-ethylcarbazole (AEC) substrate. Images for IHC staining were captured with an EVOS ® microscope (Thermo Fisher Scientific, Waltham, MA, USA).


**Abstract**

Mycotoxins are chemically diverse and capable of inducing a wide diversity of acute and chronic symptoms, ranging from feed refusal to rapid death. Accurate detection and monitoring of mycotoxins is an essential component of the prevention, diagnosis, and remediation of mycotoxin-related issues in livestock and human food. Current trends in food analysis are focusing on the application of fast, simple procedure needed, and low-cost biosensor technologies that can detect with high sensitivity and selectivity different compounds associated with food safety. This chapter discussed the recent analytical methods-based biosensor technology for quantification of mycotoxins in food products. Mainly focus on the biosensor technology based on the immobilization of antibodies onto various nanomaterials such as nanoparticles, graphite, carbon nanotubes, and quantum dots. The nanomaterials are able to be functionalized with various biomolecules such as enzymes, antibodies, nucleic acids, DNA/RNA aptamers, bio- or artificial receptors that make them suitable for detection of various substances such as food toxins, bacteria, and other compounds important in food analysis. All the nanomaterials provide an effective platform for achieving high sensitivity that is similar and, in some cases, even better than conventional analytical methods. We believe that future trends will be emphasized on improving biosensor properties toward practical application in the food industry.

**Keywords:** mycotoxin, biosensor, nanomaterials, analytical methods, fungi

### **1. Introduction**

Fungi are an organism that exists either in single-celled or complex multicellular organisms. This number of the organism may cause diseases by producing toxic substances which known as mycotoxins. Mycotoxins are toxic secondary metabolites of various fungi that significantly impact global food safety and security, from toxin exposure, economic loss of crops, or the salability of said crops. They are a widespread mixture of contaminants in various agricultural and food products, with both acute and chronic toxicological effects on human health [1]. Mycotoxin produced mainly by mycelial structure of filamentous fungi or specifically molds that may cause a harmful effect to animals as well as humans such as carcinogenic, nephrotoxicity, mutagenic, immunosuppressive, estrogenic neurotoxicity, reproductive and developmental toxicity, hepatotoxicity and indigestion [2].

Mycotoxins including aflatoxins (AFs), ochratoxins (OT), trichothecenes, zearalenone (ZEN), fumonisins (F), tremorgenic toxins, and ergot alkaloids mostly affect the public health and agro-economic significance. Factors affecting the magnitude of toxicity to the living organism are by consuming mycotoxin-contaminated foods or feeds, including species, mechanisms/modes of action, metabolism, and defense mechanisms [3]. Most of the countries agreed to set the limits of mycotoxins present in food because of the effects of the mycotoxins to human health. The permitted level is slightly different, which depends on the type of food products. The minimum limits for mycotoxins in single ppb (part per billion) and even below (0.05 ppb for infant foods) are established in EU, with similar standards in China and Japan [4].

Guan et al. [5] reported about 98% of the agricultural commodities, including corn, compound animal feeds, silage, cornmeal, puffed corn, wheat, bran, soybean meal, rapeseed meal, cottonseed meal and whole cottonseed content various group of mycotoxins. Besides, Smith et al. [6] stated that several mycotoxins contaminate approximately 48% of 7049 feedstuffs. Thus, it is essential to detect mycotoxins in the food industry to address the mycotoxin-related health issues to humans and animals effectively.

Conventional techniques such as thin-layer chromatography (TLC), highperformance liquid chromatography (HPLC) and mass spectrometry have been suggested by international organizations as standard approaches to study the occurrence of mycotoxins in food products [7]. Besides, enzyme-linked immunosorbent assay (ELISA) had been widely used to identify different types of mycotoxins. However, it has slight defects of cross-reactivity and possible false-positive or falsenegative outcomes [8]. Also, those techniques usually costly and available in a specialized research laboratory needs highly personnel trained and laborious. Recently, advanced methods used to detect the presence of mycotoxins in food samples, which show high sensitivity, low cost, simple operation, and portable on-field use [9]. Besides, portable and easy-to-use biosensor devices suitable for express, in-field detection of mycotoxins. The development of biosensors for mycotoxins has risen sharply in the last decade with a large number of different bio-sensing technologies application. Zheng et al. (2006) reported biosensor as rapid methods which typically cost-effective, easy to be handled as well as a portable device to be used in an interchanging site compared to laboratory analysis.


**5. Applications**

### **5.1. Bulk electroporation**

From the last decade, the application of electroporation has been increasing rapidly. Nowa‐ days, the electroporation technique can be applied in many way to deliver drugs, antibodies, oligonucleotides, proteins, RNA, DNA and plasmid in vivo for clinical, biotechnological and biomedical applications [42, 99-101]. Table 4 described details about gene transfer by electro‐ poration technique with the variation of molecules/gene, targeted cells, different types of electric pulses [7, 102-117].

tissues scaffold. During irreversible electroporation, the membrane survives in two stages as (a) steady state current stage and (b) fluctuating current stage. The phenomena of irreversible electroporation can cause by charge pulse technique [80] in which membrane is charged at U=0.1 V (with pulse width 400 ns) and discharged was very slow. The large pulse of the same width, can charge the membrane towards 0.4 V, but after 300-400µs, charges can be decreased

From the last decade, the application of electroporation has been increasing rapidly. Nowa‐ days, the electroporation technique can be applied in many way to deliver drugs, antibodies, oligonucleotides, proteins, RNA, DNA and plasmid in vivo for clinical, biotechnological and biomedical applications [42, 99-101]. Table 4 described details about gene transfer by electro‐ poration technique with the variation of molecules/gene, targeted cells, different types of

> **Pulsing CD:E0;τ**

incub.

PBS

CD:3×8 KV/CM;5µs 200C, 10 min postincub., HBS (without Mg2+)

CD: 3× 14 KV/cm; 5 µsec40% PEG present, 200C, 10 min

CD: 3×8 KV/cm; 5µsec 200C, 10 min incub., DME medium + 20 mM MgCl2 (plastic cuvette)

Pulse: ISCO 494 power supply directly discharged through cuvette, no definite pulse parameters given, estimated: 320 V/cm; 17 msec, 00C, 5 min preincub.,10 min postincub.,

**Results**

Sharp optimum in field strength, incubation after pulse necessary, linear plasmid better than circular, 100col./106

Small objects, high electric field strength necessary, 10-fold increase in stable transformation.

Two to five copies of plasmid per genome integrated in transformed clones.

Up to 300 transf./106 cells, linear > supercoiled, low temperature favorable, few copy number (1-15) integrated, mitotic arrest by colcemid

favorable

cells/µg DNA

as a sigmoidal manner up to zero because of membrane rupture [78].

76 Advances in Micro/Nano Electromechanical Systems and Fabrication Technologies

**Plasmid /gene**

pAGO with tk gene herpes virus(HAT select.)

pUB110 from B. thuringiensis(kn resistance)

Plasmid with Ig κ

Mouse and human Ig κ gene

gene

**5. Applications**

**5.1. Bulk electroporation**

electric pulses [7, 102-117].

**Ref. Year Authors Recipient**

**7** 1982 Neumann et al.

**102** 1983 Shivarova et al.

**103** 1984 Falkner et al. Mouse lymphoid

**104** 1984 Potter et al. Mouse B and T

**cells**

Mouse L tk-Fibroblast cells

Bacillus cereus protoplasts

cell lines

lymphocytes and fibroblasts

**Table 4.** Modified table of gene delivery by electroporation technique. Permission to reprint obtained from Springer book series [94]

In vivo electroporation is a special kind of interest for all researchers because it is nonviral gene delivery with low cost, safety and ease of realization. Recently nucleic acid based gene transfer has been investigated successfully which could be helpful for more clinical trials in human body [118]. T This technique can be applied for food industry [119]. For cancer treatment, electrochemotherapy has emerged and this therapy successfully used for clinical trials [42,99, 120-123]. The different types of application of electroporation has mention below.


In a given node, the response matrices are determined based on the analytical solution (4.19). We need an efficient recipe for decomposing the entering currents into irreps and reconstructing the exiting currents on the faces. Since the only approximation in the procedure requires the continuity of the partial currents, we need to specify the representation of the partial currents and how to represent them. The simplest is a representation by discrete points along the boundary, the minimal number is four, the maximal number depends on the computer capacity. An alternative choice is to represent the partial currents by moments over the faces. Usually average, first and second moment suffice to get the accuracy needed by practice. The representation fixes the number of points we need on a side and the number

To project the irreps, we may use (Mackey, 1980) the cos((*k* − 1)2*π*/*n*), *k* = 1, . . . , *n*/2 and sin((*k*)2*π*/*n*), *k* = 1, . . . , *n*/2 vectors (after normalization). The following illustration shows

(Weiss, 1977), (Hegedus, 1991).

First we deal with the general features of the iteration.

Φ and *D∂n*Φ (the normal current) is prescribed .

• actual temperature of the node;

• the void content of the moderator;

• the power level;

**4.4 Exploiting symmetries**

of points (*n*) on the node boundary.

program because the material properties depend on:

• the initial composition of the fuel (e.g. enrichment);

the parametrization work in a production code.

• the actual composition of the fuel as it may change with burn-up;

5 Since *keff* depends on the entering currents, the problem is non-linear.

$$A = r + 2t\_1 + t\_2, \quad B = r - 2t\_1 + t\_2, \quad C = r - t\_2.$$

We summarize the following advantages of applying group theory:

6 After normalization of the row vectors, the **Ω** matrices become orthogonal: **Ω**+**Ω** is the unit matrix.

7 Here *Ent* is the integer division.

i/Order 0 1 2 3 4

 1 - (*x*2 + *y*2) - (*x*2*y*2), (*x*4 + *y*4) - - - - (*x*3*y* − *y*3*x*) - - (*x*2 − *y*2) - *x*4 − *y*4 - - *xy* - (*x*3*y* + *y*3*x*) - *x* - *x*3 - - - - *xy*2 - - - - *x*2*y* - - *y* - *y*3 -

Application of Finite Symmetry Groups to Reactor Calculations 309

Table 6. Irreducible components of at most fourth order polynomials under the symmetries

the same number of degrees of freedom (i.e. coefficients in the expansion) on the surface of the node as within the node. With the help of Table 6, for the case of a square node, we compare the required number of coefficients for different orders of polynomial expansion. A linear approximation along the four faces of the square has at least one component in each irreducible subspace. At the same time the first polynomial contributing to the second irrep is fourth order. Convergence requires the convergence in each subspace thus the approximation inside the square must be at least of fourth order. There is no linear polynomial approximation that would use the same number of coefficients on the surface as inside the volume. The appropriate choice of order of expansion is thus not straightforward but it is important to the accuracy of the solution, because a mismatch of degrees of freedom inside and on the surface of the node is likely to lead to a loss of information in the computational step that passes from one node to the next. A lack of convergence has been observed, see (Palmiotti, 1995), in the case of calculations with a square node when using first order polynomials on the surface. A convergent solution is obtained only with fourth or higher order polynomial interpolation inside the node. Similar relationships apply to nodes of other geometry. For a hexagonal node that there is no polynomial where the number of coefficients on the surface matches the

In a hexagonal node in (Palmiotti, 1995), the first convergent solution with a linear approximation on the surface requires at least a sixth order polynomial expansion within the node. Thus, in the case of a linear approximation on the surface, in the case of a square node a third order polynomial within the node does not lead to a convergent solution, although the number of coefficients is greater than those on the surface. In the case of the regular hexagonal node, a convergent solution is obtained only for the sixth order polynomial expansion in the node, while both a fourth and a fifth order polynomial have a greater number of coefficients inside the node than on the surface. It appears that some terms of the polynomial expansion contain less information than others, and are thus superfluous in the computational algorithm. If these terms can be "filtered out", a more efficient and convergent solution should result. The explanation becomes immediately clear from the decomposition of the trial functions inside the volume and on the boundary. In both the square and hexagon nodes, the first order approximation on the boundary is sufficient to furnish all irreducible subspaces whereas this is true for the interpolating polynomials inside *V* for surprisingly high order polynomials.

In analogy with the application of group theory in particle physics, where group theory leads to insights into the relationships between elementary particles, we present an application of

of a square *C*4*v*

number of coefficients inside the node.

**5. Reactor physics**

• It is more efficient to break up a problem into parts and solve each subproblem independently. Results have been reported for operational codes (Gadó et al., 1994).

The above considerations dealt with the local symmetries. However, if we decompose the partial currents into irreps, we get a decomposition of the global vector *x* in equation (4.28) as well. We exploit the linear independence of the irreducible components further on the global scale.

For most physical problems we have a priori knowledge about the solution to a given boundary value problem in the form of smoothness and boundedness. This is brought to bear through the choice of solution space. In the following, we introduce via group theoretical principles the additional information of the particular geometric symmetry of the node. This allows the decomposition of the solution space into irreducible subspaces, and leads, for a given geometry, not only to a rule for choosing the optimum combination of polynomial expansions on the surface and in the volume, but also elucidates the subtle effect that the geometry of the physical system can have on the algorithm for the solution of the associated mathematical boundary problem.

Consider the iteration (4.29) and decompose the iterated vector into irreducible component

$$
\underline{\underline{x}} = \sum\_{a} \underline{\underline{x}}^{a} \tag{4.34}
$$

where because of the orthogonality of the irreducible components

$$
\underline{x}^{\beta+} \underline{x}^{\alpha} = 0
$$

when *α* � *β*. The convergence of the iteration means that

$$\lim\_{N \to \infty} \underline{\mathfrak{x}}\_{N+k1} - \underline{\mathfrak{x}}\_{N+k2} = 0 \tag{4.35}$$

for any *k*1, *k*2. But that entails that as the iteration proceeds, the difference between two iterated vector must tend to zero. In other words, the iteration must converge in every irreducible subspace. This observation may be violated when the iteration process has not been carefully designed.

Let us assume a method, see (Palmiotti, 1995), in which *N* basis functions are used to expand the solution along the boundary of a node and *M* basis functions to expand the solution inside the node. It is reasonable to use the approximation of same order along each face, hence, in a square node *N* is a multiple of four. For an *M*th order approximation inside the node, the number of free coefficients is (*M* + 1)(*M* + 2)/2. It has been shown that an algorithm (Palmiotti, 1995) with a linear (*N* = 1) approximation along the four faces, with 8 free coefficients, of the boundary did not result in convergent algorithm unless *M* = 4 quartic polynomial, with 15 free coefficients, was used inside the node.

In such a code each node is considered to be homogeneous in composition. Central to the accuracy of the method are two approximations. In the first, we assume the solution on the boundary surface of the node to be expanded in a set of basis functions (*fi*(*ξ*); *i* = 1, . . . , *N*). In the second, the solution inside the volume is expanded in another set of basis functions (*Fj*(**r**); *j* = 1, . . . , *M*). Clearly the independent variable *ξ* is a limit of the independent variable **r**.

Any iteration procedure, in principle, connects neighboring nodes through continuity and smoothness conditions. For an efficient numerical algorithm it is therefore desirable to have 24 Will-be-set-by-IN-TECH

• It is more efficient to break up a problem into parts and solve each subproblem independently. Results have been reported for operational codes (Gadó et al., 1994). The above considerations dealt with the local symmetries. However, if we decompose the partial currents into irreps, we get a decomposition of the global vector *x* in equation (4.28) as well. We exploit the linear independence of the irreducible components further on the global

For most physical problems we have a priori knowledge about the solution to a given boundary value problem in the form of smoothness and boundedness. This is brought to bear through the choice of solution space. In the following, we introduce via group theoretical principles the additional information of the particular geometric symmetry of the node. This allows the decomposition of the solution space into irreducible subspaces, and leads, for a given geometry, not only to a rule for choosing the optimum combination of polynomial expansions on the surface and in the volume, but also elucidates the subtle effect that the geometry of the physical system can have on the algorithm for the solution of the associated

Consider the iteration (4.29) and decompose the iterated vector into irreducible component

*x* = ∑*α*

*xβ*+*xα* = 0

for any *k*1, *k*2. But that entails that as the iteration proceeds, the difference between two iterated vector must tend to zero. In other words, the iteration must converge in every irreducible subspace. This observation may be violated when the iteration process has not

Let us assume a method, see (Palmiotti, 1995), in which *N* basis functions are used to expand the solution along the boundary of a node and *M* basis functions to expand the solution inside the node. It is reasonable to use the approximation of same order along each face, hence, in a square node *N* is a multiple of four. For an *M*th order approximation inside the node, the number of free coefficients is (*M* + 1)(*M* + 2)/2. It has been shown that an algorithm (Palmiotti, 1995) with a linear (*N* = 1) approximation along the four faces, with 8 free coefficients, of the boundary did not result in convergent algorithm unless *M* = 4 quartic

In such a code each node is considered to be homogeneous in composition. Central to the accuracy of the method are two approximations. In the first, we assume the solution on the boundary surface of the node to be expanded in a set of basis functions (*fi*(*ξ*); *i* = 1, . . . , *N*). In the second, the solution inside the volume is expanded in another set of basis functions (*Fj*(**r**); *j* = 1, . . . , *M*). Clearly the independent variable *ξ* is a limit of the independent variable

Any iteration procedure, in principle, connects neighboring nodes through continuity and smoothness conditions. For an efficient numerical algorithm it is therefore desirable to have

where because of the orthogonality of the irreducible components

lim

when *α* � *β*. The convergence of the iteration means that

polynomial, with 15 free coefficients, was used inside the node.

*xα* (4.34)

*N*→∞ *xN*+*k*1 − *xN*+*k*2 = 0 (4.35)

scale.

mathematical boundary problem.

been carefully designed.

**r**.

Table 6. Irreducible components of at most fourth order polynomials under the symmetries of a square *C*4*v*

the same number of degrees of freedom (i.e. coefficients in the expansion) on the surface of the node as within the node. With the help of Table 6, for the case of a square node, we compare the required number of coefficients for different orders of polynomial expansion. A linear approximation along the four faces of the square has at least one component in each irreducible subspace. At the same time the first polynomial contributing to the second irrep is fourth order. Convergence requires the convergence in each subspace thus the approximation inside the square must be at least of fourth order. There is no linear polynomial approximation that would use the same number of coefficients on the surface as inside the volume. The appropriate choice of order of expansion is thus not straightforward but it is important to the accuracy of the solution, because a mismatch of degrees of freedom inside and on the surface of the node is likely to lead to a loss of information in the computational step that passes from one node to the next. A lack of convergence has been observed, see (Palmiotti, 1995), in the case of calculations with a square node when using first order polynomials on the surface. A convergent solution is obtained only with fourth or higher order polynomial interpolation inside the node. Similar relationships apply to nodes of other geometry. For a hexagonal node that there is no polynomial where the number of coefficients on the surface matches the number of coefficients inside the node.

In a hexagonal node in (Palmiotti, 1995), the first convergent solution with a linear approximation on the surface requires at least a sixth order polynomial expansion within the node. Thus, in the case of a linear approximation on the surface, in the case of a square node a third order polynomial within the node does not lead to a convergent solution, although the number of coefficients is greater than those on the surface. In the case of the regular hexagonal node, a convergent solution is obtained only for the sixth order polynomial expansion in the node, while both a fourth and a fifth order polynomial have a greater number of coefficients inside the node than on the surface. It appears that some terms of the polynomial expansion contain less information than others, and are thus superfluous in the computational algorithm. If these terms can be "filtered out", a more efficient and convergent solution should result. The explanation becomes immediately clear from the decomposition of the trial functions inside the volume and on the boundary. In both the square and hexagon nodes, the first order approximation on the boundary is sufficient to furnish all irreducible subspaces whereas this is true for the interpolating polynomials inside *V* for surprisingly high order polynomials.

#### **5. Reactor physics**

In analogy with the application of group theory in particle physics, where group theory leads to insights into the relationships between elementary particles, we present an application of

and the integration runs over volume *V* of the node. Note that only irrep *A*1 (i.e. complete symmetry) contributes to the average flux because of the orthogonality of the irreducible flux components. After eliminating *cA*1 from (5.1), we get the response matrix for determining the

Application of Finite Symmetry Groups to Reactor Calculations 311

This assures that *V* is completely described by matrix **W** and the diagonal matrices < *F*(*r*) > , < *f*(*r*) >, < *g*(*r*) > for each irrep. For example, we are able to reconstruct the cross-section matrix **Σ** from them. Note that **WT** = **T** < *F*/ *f* >, the eigenvectors of matrix **W** are the eigenvectors of **A**. Now we need only a numerical procedure to find the eigenvalues *λk* from

The question is, under what conditions are the above calculations feasible. We count the number of response matrices. The matrix elements we need to characterize *V* may be all different and the number of matrices depends on the shape of *V*, since the number of irreducible components of the involved matrices depends on the geometry. In a square shaped homogeneous *V*, we have four **R***i* matrices and one **W**. Altogether we have to determine 5 ∗ *G* ∗ *G* elements. In an inhomogeneous hexagonal volume, there are 6 ∗ *G* ∗ *G* matrix elements, whereas the homogeneous material is described by *G* ∗ (*G* + 1) parameters as in a homogeneous material there are altogether *G* ∗ *G* cross-sections and *G* diffusion constants8. Therefore the Selengut principle is not exact it may only be a good approximation under specific circumstances. Homogenization recipes preserve only specific reaction rates, but they

The basic elements of the theory of finite symmetry groups has been introduced. In particular, the use of the machinery associated with the decomposition into irreducible representations, in analogy with harmonic analysis of functions in function space, in the analysis of Nuclear Engineering problems. The physical settings of many Nuclear Engineering problems exhibit symmetry, as for example in the solution of the multi-group neutron diffusion equation. This symmetry can be systematically exploited via group theory, and elicit information that leads to more efficient numerical algorithms and also to useful insights. This is a result due to the added information inherent in symmetry, and the ability of group theory to define the "rules"

Allgower, E. L., et al. (1992). Exploiting symmetry in boundary element methods, *SIAM J.*

Falicov, L. M. (1996). *Group Theory and Its Physical Applications*, The University of Chicago

Atkins, P. W. et al. (1970). *Tables for group theory*, Oxford University Press, Oxford. Brooks, R. (1988). Constructing isospectral manifolds, *Amer. Math. Monthly*, 95, 823–839. Conway, J. H., et al. (2003). *The ATLAS of finite groups*, Oxford University Press, Oxford. Deniz, V. C. (1986). *The Theory of Neutron Leakage in Reactor Lattices*, in CRC Handbook of

Nuclear Reactor Calculations, vol. II, CRC Press, Boca Raton, (FL)

Φ¯ = **T** < *FA*1/ *fA*1 > **T**−1 < *F* >≡ **W** < *F* > . (5.6)

volume integrated flux Φ¯ from the face integrated flux *FA*1:

< *F*/ *f* >.

do not provide general equivalence.

of the symmetry and allows one to exploit them.

*Numer. Anal.*, 29, 534–552.

Press, Chicago, (IL)

8 Remember, here *G* is the number of energy groups.

**6. Conclusions**

**7. References**

group theory to the solution to a specific reactor physics problem. The question is whether it is possible to replace a part of a heterogeneous core by a homogeneous material so that the solution outside the homogeneous region remains the same? This old problem is known as homogenization (Selengut, 1960).

In particular, for non-uniform lattices, asymptotic theory has shown that a lattice composed of identical cells has a solution that is composed of a periodic microflux and a slowly varying macroflux. What happens if the cell geometry is the same but the material composition varies?

In reactor calculations, we solve an equation derived from neutron balance. In that equation, we encounter reaction rates, currents or partial currents. It is reasonable to derive all the quantities we need from one given basic quantity, say from the neutron flux at given points of the boundary. The archetype of such relation is the exiting current determined from the entering current by a response matrix. We show that by using irreducible components of the partial currents, the response matrix becomes diagonal.

The Selengut principle is formulated: if the response matrix of a given heterogeneous material in *V* can be substituted by the response matrix of a homogeneous material in *V*, there exist an equivalent homogeneous material with which one may replace *V*. This principle simplifies calculations considerably, and, therefore, has been widely used in reactor physics. We investigate the Selengut principle more closely(Makai, 2010),(Makai, 1992).

The analysis is based on the analytical solution of the diffusion equation derived in the previous Section. The problem is considered in a few energy groups, the boundary flux *F* is a vector, as well as the volume averaged flux Φ¯ . Using that solution, we are able to derive matrices mapping into each other the volume integrated fluxes, the surface integrated partial and net currents. The derivation of the corresponding matrices is as follows. Our basis is the boundary flux, that we derive for each irrep *i* from (4.13). The expression (4.13) has three components. The first one is vector *tk* which is independent of the position **r** and is multiplied by an exponential function with *λk***r** in the exponent. The third component is the weight *Wk* which is independent of **r** but varies with subscript *k*. The product is summed for subscript *k*, that labels the eigenvalues of the cross-section matrix in (4.14). That expression can be put into the following concise form:

$$\underline{F}\_{i} = \mathbf{T} < f\_{i} > \underline{c}\_{i'} \tag{5.1}$$

where *ci* comprises the third component. Here < *fi*(**r**) > is a diagonal matrix. Note that position dependent quantities like reaction rates, follow that structure. The normal component of the net current is *J net* obtained from the flux by taking the derivative and is given in irrep *i* as

$$J\_{\rm net,i} = -\mathbf{D}\mathbf{T} < \mathbf{g}\_i > \underline{\mathbf{c}}\_i. \tag{5.2}$$

We eliminate *ci* to get

$$\underline{J}\_{\text{net},i} = -\mathbf{D}\mathbf{T} < \mathcal{g}\_i/f\_i > \mathbf{T}^{-1}\underline{F}\_i \equiv \mathbf{R}\_i\underline{F}\_i. \tag{5.3}$$

Here **n** is the outward normal to face *Fi*,

$$\mathbf{g}\_{i} = -\nabla \mathbf{n} f\_{i}(\mathbf{r}).\tag{5.4}$$

The volume integrated flux Φ¯ is obtained after integration from (4.13) as

$$
\underline{\Phi} = \mathbf{T} < \overline{F}\_{A1} > c\_{A1\prime} \overline{F}\_{A1} = \int f\_{A1}(\mathbf{r}) d^3 \mathbf{r},\tag{5.5}
$$

and the integration runs over volume *V* of the node. Note that only irrep *A*1 (i.e. complete symmetry) contributes to the average flux because of the orthogonality of the irreducible flux components. After eliminating *cA*1 from (5.1), we get the response matrix for determining the volume integrated flux Φ¯ from the face integrated flux *FA*1:

$$
\underline{\Phi} = \mathbf{T} < \overline{F}\_{A1}/f\_{A1} > \mathbf{T}^{-1} < \overline{F} > \equiv \mathbf{W} < \overline{F} > . \tag{5.6}
$$

This assures that *V* is completely described by matrix **W** and the diagonal matrices < *F*(*r*) > , < *f*(*r*) >, < *g*(*r*) > for each irrep. For example, we are able to reconstruct the cross-section matrix **Σ** from them. Note that **WT** = **T** < *F*/ *f* >, the eigenvectors of matrix **W** are the eigenvectors of **A**. Now we need only a numerical procedure to find the eigenvalues *λk* from < *F*/ *f* >.

The question is, under what conditions are the above calculations feasible. We count the number of response matrices. The matrix elements we need to characterize *V* may be all different and the number of matrices depends on the shape of *V*, since the number of irreducible components of the involved matrices depends on the geometry. In a square shaped homogeneous *V*, we have four **R***i* matrices and one **W**. Altogether we have to determine 5 ∗ *G* ∗ *G* elements. In an inhomogeneous hexagonal volume, there are 6 ∗ *G* ∗ *G* matrix elements, whereas the homogeneous material is described by *G* ∗ (*G* + 1) parameters as in a homogeneous material there are altogether *G* ∗ *G* cross-sections and *G* diffusion constants8. Therefore the Selengut principle is not exact it may only be a good approximation under specific circumstances. Homogenization recipes preserve only specific reaction rates, but they do not provide general equivalence.

#### **6. Conclusions**

26 Will-be-set-by-IN-TECH

group theory to the solution to a specific reactor physics problem. The question is whether it is possible to replace a part of a heterogeneous core by a homogeneous material so that the solution outside the homogeneous region remains the same? This old problem is known as

In particular, for non-uniform lattices, asymptotic theory has shown that a lattice composed of identical cells has a solution that is composed of a periodic microflux and a slowly varying macroflux. What happens if the cell geometry is the same but the material composition varies? In reactor calculations, we solve an equation derived from neutron balance. In that equation, we encounter reaction rates, currents or partial currents. It is reasonable to derive all the quantities we need from one given basic quantity, say from the neutron flux at given points of the boundary. The archetype of such relation is the exiting current determined from the entering current by a response matrix. We show that by using irreducible components of the

The Selengut principle is formulated: if the response matrix of a given heterogeneous material in *V* can be substituted by the response matrix of a homogeneous material in *V*, there exist an equivalent homogeneous material with which one may replace *V*. This principle simplifies calculations considerably, and, therefore, has been widely used in reactor physics.

The analysis is based on the analytical solution of the diffusion equation derived in the previous Section. The problem is considered in a few energy groups, the boundary flux *F* is a vector, as well as the volume averaged flux Φ¯ . Using that solution, we are able to derive matrices mapping into each other the volume integrated fluxes, the surface integrated partial and net currents. The derivation of the corresponding matrices is as follows. Our basis is the boundary flux, that we derive for each irrep *i* from (4.13). The expression (4.13) has three components. The first one is vector *tk* which is independent of the position **r** and is multiplied by an exponential function with *λk***r** in the exponent. The third component is the weight *Wk* which is independent of **r** but varies with subscript *k*. The product is summed for subscript *k*, that labels the eigenvalues of the cross-section matrix in (4.14). That expression can be put

where *ci* comprises the third component. Here < *fi*(**r**) > is a diagonal matrix. Note that position dependent quantities like reaction rates, follow that structure. The normal

*J*

The volume integrated flux Φ¯ is obtained after integration from (4.13) as

Φ¯ = **T** < *FA*1 > *cA*1, *F*¯ *A*1 =

*J*

*Fi* = **T** < *fi* > *ci*, (5.1)

*net* obtained from the flux by taking the derivative and is

*net*,*i* = −**DT** < *gi* > *ci*. (5.2)

*gi* = −∇**n** *fi*(*r*). (5.4)

*fA*1(**r**)*d*3**r**, (5.5)

*net*,*i* = −**DT** < *gi*/ *fi* > **T**−1*Fi* ≡ **R***iFi*. (5.3)

We investigate the Selengut principle more closely(Makai, 2010),(Makai, 1992).

homogenization (Selengut, 1960).

into the following concise form:

component of the net current is *J*

Here **n** is the outward normal to face *Fi*,

given in irrep *i* as

We eliminate *ci* to get

partial currents, the response matrix becomes diagonal.

The basic elements of the theory of finite symmetry groups has been introduced. In particular, the use of the machinery associated with the decomposition into irreducible representations, in analogy with harmonic analysis of functions in function space, in the analysis of Nuclear Engineering problems. The physical settings of many Nuclear Engineering problems exhibit symmetry, as for example in the solution of the multi-group neutron diffusion equation. This symmetry can be systematically exploited via group theory, and elicit information that leads to more efficient numerical algorithms and also to useful insights. This is a result due to the added information inherent in symmetry, and the ability of group theory to define the "rules" of the symmetry and allows one to exploit them.

#### **7. References**

8 Remember, here *G* is the number of energy groups.

**14**

*University, Yozgat*

*Turkey*

**Neutron Shielding Properties of Some**

*1Faculty of Science and Art, Department of Physics, Ibrahim Cecen University, Ağr 2Department of Civil Engineering, Faculty of Engineering and Architecture, Bozok*

*3Department of Civil Engineering, Faculty of Engineering, Bartin University, Bartin*

Nuclear reactor technology is known as an emerging area of study from past to present. It is an implementation of the nuclear sciences including reactions about atomic nucleus and productions. During the construction of a nuclear reactor, the most important issue is nuclear safety. The term of security can be attributed radiation shielding processes. For nuclear reactors, there are several different materials used to radiation shielding. While determining the most appropriate material to shield, the type and energy of radiation is

There are two types of nuclear reactions reveals very large energies. These are the disintegration of atomic nuclei (fission) and merging small atomic nuclei (fusion) reactions. Therefore, nuclear reactors can be divided into two groups according to the type of reaction occurred during as fission reactors and fusion reactors. Currently a nuclear reactor working with fusion reactions is not available. Today, there are the hundreds of nuclear reactors based on the fission reactions. For the realization of nuclear fission, a large fissile atomic nucleus such as 235U can absorb a neutron particle. At the end of nuclear fission event, fission products (two or more light nucleus, kinetic energy, gamma radiation and free neutrons) arise. Fission reactions are controls by using neutron attenuators such as heavy water, cadmium, graphite, beryllium and several hydrocarbons. While designing a reactor

Vermiculite is a monoclinic-prismatic crystal mineral including Al2O3, H2O, MgO, FeO and SiO2. It is used in heat applications, as soil conditioner, as loose-fill insulation, as absorber package material and lightweight aggregate for plaster etc. Its chemical formula is known as (MgFe,Al)3(Al,Si)4O10(OH)2·4H2O and physical density of it about 2.5 g.cm-3. Melting point of vermiculite is above 13500C. This mineral can be used as additive building material in

Vermiculite is a component of the phyllosilicate or sheet silicate group of minerals. It has high-level exfoliation property. So if vermiculite is heated, it expands to many times its

shield materials against gamma and neutron radiations should be used.

**1. Introduction**

extremely important.

terms of mineral properties.

**Vermiculite-Loaded New Samples**

Turgay Korkut1, Fuat Köksal2 and Osman Gencel3

457-472.


**5. Discussion**

While there have been notable advancements in BCI and BBI technology and the body of literature of the ethical aspects of BCI technology has grown substantially since the original publication of Burwell and colleagues' research, our findings suggest that the original taxonomy developed by Burwell and colleagues remains a useful framework for understanding the body of literature specifically on the social factors of the ethics of BCI. We can use this taxonomy, with some slight modifications, which we outline below, to understand how the body of literature on the ethics of BCI is grappling with ethical issues arising from the applications of this rapidly advancing technology. Articles published since 2016 still mostly conform to the taxonomy and can be categorized using it in future iterations of the scoping review methodology.

There are, however, some areas within the growing body of literature on BCI ethics that have arisen since the original research was published that need to be incorporated into the taxonomy. We recommend the following modifications to the conceptual mapping outlined in Figure 1. First, expanding the discussion of the physical (e.g., harms to test animals) and psychological (e.g., radical psychological distress) effects of BCI technology. The publicly available information on commercial BCI endeavors (such as Neuralink) frequently mentions experiments with increasingly complex and even sentient animals, such as Neuralink's demonstration of their technology on live pigs [4]. The lack of ethical scrutiny of these studies is an essential cause for concern [18]. Thus, ethical discussions should be expanded to include public awareness of private industry research into BCI using animals. Secondly, while the risks of physical harm from BCI are fairly well-understood and covered in the literature, further research is needed to understand emerging psychological factors in BCI ethics, examining how human–AI intelligence symbiosis, brain-to-brain networking, and other novel applications of the technology [2] may affect psychological wellbeing in humans. For instance, in the interview study by Gilbert and colleagues, one patient mentioned that "she was unable to manage the information load returned by the device," which led to radical psychological distress [11] (p. 91).

Going forward, it is imperative to expand on the connection between ethics and policy in discussions of BCI technology and conduct more empirical studies that will help separate non-urgent policy concerns, which are based on not-yet attained e ffects of BCI, from the more urgent concerns based on the current state of science in regards to BCI technology. In this, we echo Voarino and colleagues [19] in stating that we must advance the discussion from merely mapping ethical issues, into an informed debate that explains which ethical concerns are high priority, which issues are moderately important, and what constitutes a low priority discussion of possible future developments.

That said, it is important to make sure that the ethics literature keeps pace with engineering advances and that policy does not lag behind. In that vein, following Dubljevi´c [20], we propose that the key ethical question for future work on BCI ethics is:

What would be the most legitimate public policies for regulating the development and use of various BCI neurotechnologies by healthy adults in a reasonably just, though not perfect, democratic society?

Additionally, we need to distinguish between ethical questions regarding BCI technology that ethicists and social scientists can answer for policy makers and those that cannot be resolved even with extensive research funding [21]. Therefore, following Dubljevi´c and colleagues [22], we posit that these four additional questions need to be answered to ensure that discussions of BCI technology are realistic:

By providing answers to such questions (and alternate or additional guiding questions proposed by others), ethicists can systematically analyze and rank issues in BCI technology based on an as-yet to be determined measure of importance to society. While we have not completed such analyses yet, we do provide a blueprint above, based on conceptual mapping and newly emerging evidence, of how this can be done.


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# **Photonic Crystals for Plasmonics: From Fundamentals to Superhydrophobic Devices**

Remo Proietti Zaccaria et al. \* *Nanobiotech Facility, Italian Institute of Technology, Genova Italy*

# **1. Introduction**

In the last couple of decades we have been witnessing an enormous technological advancement in the field of micro-technology to the extent that nowadays we talk about nanotechnology. Faster computers, LCD based mobiles, nanoparticles for UV absorption in suntan lotions are just few of many examples where nanotechnology plays a fundamental role. The merit of this is mainly in the advance of the fabrication methods. Present techniques such as Focused Ion Beam (FIB) lithography guarantee a resolution of less than 10 nanometers which is about five times more precise than ten years before. Also Photonic Crystals (PhCs), among the others, take advantage from this extremely high resolution level allowing a downscale that permits the realization of structures which in principle can work at vey high energy. Historically PhCs were known as Bragg mirrors and only in 1987 (Yablonovitch, 1987; Sajeev, 1987) with the works of Yablonovitch and Sajeev the term Photonic Crystals was introduced. Nowadays, besides their natural application as filters in particular under full band gap conditions, PhCs see a number of applications: optical fibers (Birks et al., 1997; Zhao et al., 2010), vertical cavity surface emitting lasers (Yokouchi et al., 2003), high reflection coatings, temperature sensors (Song et al., 2006), high efficiency solar cells (Bermel et al., 2007), electric field detectors (Song & Proietti Zaccaria, 2007), non-linear analysis (Malvezzi et al., 2002; Malvezzi et al., 2003), just to name a few. Many are the techniques for the fabrication of PhCs, for example by means of focused-ion beam (Cabrini et al., 2005), two-photon fabrication (Deubel et al., 2004), laser-interference (Proietti Zaccaria et al., 2008a) or waver-fusion techniques (Takahashi et al., 2006). Here we shall focus on the role that PhCs can play for another exciting discipline known as *Plasmonics*. It refers to the capability of some devices of sustaining an *optical surface* mode, namely an electromagnetic wave travelling at the interface between two different materials such as a dielectric and a metal. Such a wave originates from the coupling of incident photons on the interface with

\* Anisha Gopalakrishnan1 , Gobind Das 1 , Francesco Gentile 1**,**2 , Ali Haddadpour 3 , Andrea Toma1 , Francesco De Angelis 1 , Carlo Liberale 1 , Federico Mecarini 1 , Luca Razzari 1 , Andrea Giugni 1 , Roman Krahne 1 and Enzo Di Fabrizio1,2

*1Nanobiotech Facility, Italian Institute of Technology, Genova ,Italy*

*2BIONEM lab., Departement of Clinical and Experimental Medicine, Magna*

*Graecia University, viale Europa, Catanzaro, Italy*

*3Department of Electrical and Computer Engineering, University of Tabriz, Iran*

the existing free electrons. This kind of mode is known as Surface Plasmon Polariton (SPP). Photonic crystals, as a translational modulation of the refractive index, have already been playing a very crucial role in plasmonics. In fact, they can provide the missing wave vector for the coupling between photons and free electrons of a metal layer (Raether, 1988). Here we have chosen to face three situations relating PhCs and Plasmonics:

The first topic concerns the fundamentals of SPP and PhCs. No particular application will be suggested, but mostly we will focus on the theory behind the generation of SPP inside a metallic photonic crystal. The next two topics are, on the other hand, strictly related to applications. We will concentrate our attention on Raman spectroscopy, as a very important tool for the investigation of the optical properties of many kinds of samples, such as semiconductors or proteins. In particular, metallic ordered (periodic) structures will be used either as artificial SERS substrates or as combiners of SERS and super-hydrophobic effect for few molecules detection. This description will offer a general overview of the important functions that PhCs can hold in Plasmonics and how we could start thinking more intensively of PhCs realized with metallic materials.

# **2. Two dimensional metallic PhCs for maximum full band gap**

One of the main issues when dealing with two dimensional PhCs is the maximum full band gap that the crystal can provide. Specifically, in 2D the crystal manifests two non degenerative polarizations known as TE and TM. The former refers to solutions with the electric field *in* the plane of symmetry of the crystal, the latter with the magnetic field in the same plane. In order to produce a *full* band gap, both TE and TM must provide an optical gap in the *same* spectral region. This is not an easy task and different solutions have been proposed (Joannopoulos et al., 1995), however mostly referring to dielectric PhCs. Here we shall examine how metallic PhCs can improve the chance of a common band gap between TE and TM with respect to a dielectric structure.

## **2.1 Dielectric photonic crystals**

It has been demonstrated that the geometry of PhCs strongly affect whether TE or TM band gap will be generated. In particular, when the crystal is formed by isolated regions of high dielectric, the TM gap is favored; when the crystal is formed by connected regions of high dielectric, the TE gap is favored. Hence, the geometry plays a crucial role. In regards, when 2D photonic crystals are considered, only five possible geometrical arrangements exist. These are called Bravais lattices. Considering the complementary conditions for the realization of a TE/TM gaps, the best Bravais lattice to maximize the probability of obtaining a full band gap is the hexagonal one. This kind of Bravais lattice posses the highest possible rotational symmetry in two dimensions. In view of this information, we have instead chosen the square photonic crystal (Galli et al., 2002), namely a configuration not supporting a full band gap for isotropic dielectric materials (Wang et al., 2005; Proietti Zaccaria, 2008b). In this manner we expect to enhance the different results in terms of full band gap rising either from a dielectric crystal or a metallic one.

#### **2.1.1 Full band gap in dielectric 2D photonic crystals**

The chosen dielectric PhC is made of circular columns of high refractive index material, namely silicon (n=3.6) surrounded by air (n=1). The radius of the columns is r=300nm and lattice period P=1m. As expected, only TM polarization shows zero transmission regions, in particular three band gaps below 1m-1 are shown in Fig. 2.1. On the other hand, TE does not sustain any band gap. These results remain true even increasing the columns dielectric value or changing the columns radius. No full band gap is then found for this kind of structure.

Fig. 2.1. TM band structure for a 2D square silicon columns photonic crystal. Three band gaps are shown.

#### **2.2 Metallic photonic crystals**

The behavior of 2D metallic photonic crystals is fundamentally different from what expected by 2D dielectric photonic crystals (Zhao et al., 2009; Sakoda et al., 2001; Ito & Sakoda, 2001). In fact, the use of metallic dispersive materials strongly modifies the light behavior in periodic structures, both for TM and TE polarizations. In particular, TM polarization shows a cut-off frequency c and no modes are found below it. This implies the existence of a TM gap below c. From a physical point of view this is related to the existence of free electrons in metallic materials. Similarly, TE polarization shows a behavior which is absent in dielectric 2D photonic crystals. In fact, in specific range of frequencies, metallic photonic crystals show TE polaritonic band gap close to the plasma frequency. Physically it is associated to the creation of surface plasmon polaritons on the metallic columns of the crystal. These peculiarities of metallic PhCs have the merit of increasing the chance of a full band gap also for square crystals. Hence, maintaining the same geometrical configuration as in the previous section, namely a square structure of columns in air, we have numerically analyzed the band gap formation when metallic columns are considered instead of dielectric ones.

#### **2.2.1 Full band gap in metallic 2D photonic crystals: Drude vs. Lorentz model**

We start by considering the Drude model (Rakic´ et al., 1998) to describe the metallic parts of the crystal:

$$\varepsilon(\alpha) = 1 - \frac{f\_0 \alpha\_p^2}{\alpha^2 - i\alpha \,\Gamma\_0} \tag{2.1}$$

where p is the plasma frequency, 0 is the damping constant and *f0* is the oscillator strength. We recall that this model is a simplified version of the realistic Drude-Lorentz model, in fact it does not describe the material resonances (absorption) of the metal. Nevertheless, the Drude model is commonly used ought to the reduced calculation complexity. Furthermore, it is often assumed that for noble metals such as Ag or Au, no difference is expected between the Drude and the Drude-Lorentz description in the visible range. We will show that this assumption is not always justified.

By choosing p=2c/P, 0=0.01p and *f0*=1 in Eq. (1), a square PhC with columns of radius r=0.472P and TM polarization, the transmission spectrum of Fig. 2.2 was obtained. The figure shows different curves each associated to a different incident angle. In fact, in order to determine a band gap, two possible ways can be chosen: i) band structure calculation; b) transmission spectrum calculation. Considering the dispersive properties of the metal, the band structure calculation presents some difficulties which make the transmission spectra method the simplest way for the calculation of band gaps. However, when this method is considered, the light must impinge on the PhC under a number of angles, namely the angles covering the irreducible Brillouin zone (Zhao et al., 2009). In our case it means to look at the range [0-45] degrees. Zero transmission regions which are common to all the simulations can be identified as band gaps. For clarity we have chosen only 0 and 45 degrees (however, for the present case, this choice will not affect the identification of optical gaps).

Fig. 2.2. TM transmission spectra for a Drude square PhC. Different lines (colors) correspond to different incident angles (blue: 0o; green: 45o). Two band gaps are found.

Fig. 2.2 clearly shows two band gaps. In particular the lowest frequency one (above 1.35m) is associated to the cut-off frequency c as confirmed by the band structure calculation in (Sakoda et al., 2001).

Interesting, when TE polarization is considered, a wide band gap is obtained as shown in Fig. 2.3. This result stresses the difference with similar geometries having only dielectric parts where TE does not provide any gap. In fact, if the TE and TM transmission spectra are overlapped, a full band gap is found.

Fig. 2.3. TE transmission spectra for a Drude square PhC. Different lines (colors) correspond to different incident angles (blue: 0o; green: 45o).

These results confirm that the use of metallic PhCs increases the chance of a full band gap even for square-like Bravais lattices. However we have to keep in mind that the modeling leading to the previous results is based on a simplified Drude description. Hence, it is now important to asset the role that possible Lorentz contributes could play in the overall gap calculation. By moving to the Drude-Lorentz description from the Drude equation (1):

$$\varepsilon(oo) = 1 - \frac{f\_0 o o\_p^2}{o^2 - i o \Gamma\_0} + \sum\_{j=1}^k \frac{f\_j o\_p^2}{\left(o o\_j^2 - o^2\right) + i o \Gamma\_j} \tag{2.2}$$

and assuming k=1, *f1*=1, 1=800nm and 1=0.1p a different transmission spectrum is obtained as shown in Fig. 2.4.

We can see that considering also the Lorentz term strongly modifies the transmission spectrum to the extent that for the present case the gap around 1.1m is suppressed. It is then of fundamental importance to compare the Drude and the Drude-Lorentz models when real materials, such as Ag, Au or Al, are considered. In fact, their description implies taking into account a number of Lorentz peaks which, as we have seen, might strongly modify the transmission spectrum compared to a simple Drude description.

#### **2.2.2 Photonic crystal with realistic metallic materials**

We will consider two materials: Ag and Al. The former is usually considered for plasmonic applications in the visible range whereas the latter can play a very interesting role in the UV range. We shall calculate their transmission spectra both for TM and TE in order to identify possible full band gaps.

First we will assume a Drude description. In case of Al, the experimental parameters to build up the model are p= 14.98eV, 0=0.047eV and *f0*=0.523 (Rakic´ et al., 1998). Under these conditions the transmission/absorption spectra, both for TM and TE polarization, are shown in Fig. 2.5. We have considered two incident angles, 0o and 45o which, in the present case, will be enough to determine the existence of a full band gap.

Fig. 2.4. TM transmission spectra of a square metallic PhC with radius r=0.472·P and material properties defined by (continue line – Drude model) p= 2c/P and damping constant =0.01·p (0o incident angle of Fig. 2.2); (dashed line – Drude-Lorentz model) p= 2c/P and damping constant 1=10· for the resonance at 800nm. Incident angle of 0o was assumed.

The first important result to be noticed is the existence of a full band gap in the range 700- 750nm. This achievement is consistent with the full band gaps obtained with the arbitrary Drude model introduced in Figs. 2.2 and 2.3. Furthermore, it is interesting to observe the behavior of the absorption both for TM and TE. In fact, the former shows no peaks in any band gap region whereas the latter has a smooth behavior, inside the gap regions, only for high wavelengths. It is explained recalling that only TE polarization shows a peculiar band gap which originates from the creation of surface plasmon polaritons on the metallic cylinders of the crystal, namely absorption peaks have to be observed in the gaps. The frequency region supporting the surface plasmon polariton modes starts roughly just below the plasma frequency of the metal, which in case of Al is 14.98eV=83nm, and its width depends on the geometry of the crystal.

When the Drude-Lorentz model is considered the transmission for both TM and TE is shown in Fig. 2.6. By comparison with Fig. 2.5 not substantial differences in terms of band gaps can be noticed, neither for TM nor for TE. In fact, the 700-750nm full band gap is found also in the Drude-Lorentz description. The only noticeable change is the increase of the absorption with respect to the transmission mainly below 1.0m ought to the differences in the refractive index profile between the Drude and the Drude-Lorentz model of Al. In fig. 2.7 the two models are plotted. A strong absorptive peak around 800nm is shown in the Drude-Lorentz model.

Fig. 2.5. TM/TE absorption/transmission spectra for a Drude square PhC. Aluminium is considered. Lattice constant P=1m, cylinder radius=300nm. The source incident angle was 0o and 45o .

Moving now to PhCs based on Ag, the results for the Drude and Drude-Lorentz models are shown in Figs. 2.8 and 2.9, respectively. The optical parameters are p=9.01eV, 0=0.048eV, *f0*=0.845, 1=0.816eV, 1=3.866eV and *f1*=0.065 (Rakic´ et al., 1998). In this case the spectrum range was chosen from 50nm to 2m in order to exploit the band gap behavior from the UV to the IR region.

The Drude model for Ag shows a full band gap between 710nm and 750nm in a way similar to the Al structure (we recall that for both the materials we have used the same geometry). Once again, differently from square dielectric periodic structures, metallic square PhCs can provide full band gaps. Similarly to the Al case, the Drude-Lorentz model registers an increase in the absorption in the frequency region below 1.0m. In particular, the three lowest wavelengths absorption peaks shown in the Drude-Lorentz model of Fig. 2.9 correspond to three well defined resonant peaks of silver, as confirmed by Fig. 2.10.

Furthermore, by observing the TE spectra for the silver PhC of Fig. 2.9, it can be noticed that absorptive peaks inside zero transmission regions are shown below 400nm, namely close to the silver plasma frequency of 137nm. This is the fingerprint of polaritonic gaps created by surface plasmon polaritons on the surface of the silver columns. On the other hand, TM spectra show a zero transmission region above 1.4m which can be associated to the cut-off frequency c.

Fig. 2.6. TM/TE absorption/transmission spectra for a Drude-Lorentz square PhC. Aluminium is considered. Lattice constant P=1m, cylinder radius=300nm, incident angles 0o and 45o .

Fig. 2.7. Real (continuous/blue line) and imaginary (dashed/green line) parts of Al refractive index for the Drude and the Drude-Lorentz models.

Finally a consideration about the Drude and the Drude-Lorentz models for the Ag PhC. The simulations have shown that when moving to the Drude-Lorentz model the transmission spectrum remains similar to the Drude counterpart for energy far away from p. When this

value is approached, differences between the two models become appreciable. This is related to the typical absorption peaks of Ag located before 400nm.

Fig. 2.8. TM/TE absorption/transmission spectra for the Drude square PhC. Silver is considered. Lattice constant P=1m, cylinder radius=300nm, incident angles 0o and 45o .

In conclusion, we have shown that metallic PhCs can provide a full band gap not possible for analogues dielectric PhCs. This characteristic is related to the dispersive properties of the metallic parts of the crystal. Furthermore, we have shown that the Drude and Drude-Lorentz model provide the same results as long as the frequency range is far away from the metal plasma frequency. In fact, when approaching p, discrepancies between the two models start rising that implies the failure of the Drude model at low frequencies.

### **3. Metallic PhCs for surface enhanced Raman spectroscopy**

In recent years, plasmonics based sensor device such as surface enhanced Raman spectroscopy (SERS) has attracted lots of attention to the scientific community worldwide. SERS is a technique using which an increase in optical signal of the molecule situated in the vicinity of nano-metallic surface can be observed when electromagnetic light is being impinged on it (Haynes et al., 2005). There are many techniques such as electron beam lithography (EBL) (Das et al., 2009; Kahl et al., 1998), colloidal technique (Kneipp et al., 1997; Nie & Emory, 1997; Coluccio et al., 2009), metal island film (Constantino et al., 2001), etc. by which SERS substrate can be fabricated. There is always a competition regarding the quality of the nanostructure, fabrication area, time and cost. EBL is the most efficient technique to

Fig. 2.9. TM/TE absorption/transmission spectra for the Drude-Lorentz square PhC. Silver is considered. Lattice constant P=1m, cylinder radius=300nm, incident angles 0o and 45o .

Fig. 2.10. Real (continuous/blue line) and imaginary (dashed/green line) parts of Ag refractive index for the Drude-Lorentz model. Three resonant peaks are shown in the UV region. Silver plasma frequency p=9.04eV~137nm.

reproduce the nano-patterned SERS substrates but faces a critical limitations when it is about large area fabrication whereas colloidal technique is well known for large area metal deposition but showing minimum reproducibility. In the past, Zhang et al. (2006) reported a new technique called nanosphere lithography in which shadow evaporation through selfassembled arrays of polystyrene nanosphere was used to fabricate a large area SERS substrate. Herein, we propose a new way to fabricate a SERS substrate based on anodic porous alumina (APA) which could be a trade-off between the two above limits such as large fabrication area and SERS enhancement factor.

In the present work, APA substrate, having hexagonal periodicity, has been fabricated. The fabricated APA substrates were used as templates for the preparation of nanopatterned gold surfaces, obtained by gold film deposition of ~25 nm thickness covering the APA features. Using this technique, we are able to achieve reproducible SERS substrates with the wall thickness and pore diameter down to 40 and 60 nm, respectively. It is noticeable that the substrate shows very efficient SERS signal even in presence of intrinsically fluorescent molecules. The substrate surface morphology was characterized by both atomic force microscopy (AFM) and scanning electron microscopy (SEM), and the performance as a SERS substrate was tested with cresyl violet (CV). These substances fluoresce at distinct wavelengths in the visible spectrum from red to violet region. Even if it is known that nanometallic surface acts as a fluorescence quenching substrate (Dulkeith et al., 2002), it is the first time, in our knowledge, that the large area SERS substrate on APA template was employed for SERS analysis in such detail.

In order to provide the surfaces with plasmon functionality, gold was thermally evaporated from a tungsten boat onto the APA substrates (APA), starting the deposition at a base chamber pressure of 2.0x10-6 mbar and proceeding at a 0.5 Å/s until a final total thickness of ~25 nm was reached. During deposition the sample holder was rotated at 1 RPM in order to improve the uniformity and the morphological quality of the gold layer. The substance of interest was deposited over resulting gold-coated APA substrate (termed 'AuAPA') using chemisorption technique. In this process, the substrate was dipped in a solution containing the molecule of interest. After incubation, the substrate was removed from the solution, gently rinsed to remove excess molecules those are not attached directly to the metal surface. Thereafter, the samples were dried in N2 flow, and finally stored in a desiccator before SERS measurements. Cresyl violet (CV) dyes was tested for SERS probes with the concentration in the order of 10-6 M.

Fig. 3.1 shows the schematic picture of honey-comb structures, the SEM and AFM image of AuAPA SERS substrate. AFM and SEM images show the clear formation of SERS honeycomb structures. The gold-coating over APA template is fixed to the 25 nm.

CV (Fig. 3.2a for optical absorption spectrum and molecular structure) is an organic dye molecule intensively used in biology and medicine for histological stain. It is an effective stain applied for highlighting acidic components of tissues and is commonly used for nerve tissue sections. SERS measurements were carried out for CV deposited on AuAPA SERS substrate at different positions in the range of 300-1400 cm-1. Raman measurements were also performed after deposition of a 2 l drop of CV on a flat non-patterned silicon wafer substrate (see Fig. 3.2a) which can be considered as a positive control sample. The Raman spectrum of CV on Si surface is relatively featureless, with an exponentially increasing fluorescence background and a single characteristic peak of CV at ~591 cm-1 with low intensity. In the inset of Fig. 3.2a, the zoomed Raman spectrum of CV in the range of 400-650 cm-1 is also shown.

In Fig. 3.2a, SERS substrate background measurement (no dye on AuAPA pattern) was carried out and shown in the inset of Fig. 3.2a, which shows a flat background response

without any Raman band at all. Various measurements were carried out on this SERS AuAPA substrate at different points, giving identical Raman vibrational frequency of CV.

Fig. 3.1. a) Illustration of Honey-comb structure; SEM and AFM images after gold-coating of 25 nm are shown in Fig. b) and c).

Fig. 3.2. a) Cresyl violet deposited on Si substrate, showing high fluorescence background. Molecular structure, optical absorption spectrum and zoomed Raman spectrum of CV in the range of 400-650 cm-1 are shown in the inset of the same Fig.; b) SERS spectrum of CV is also illustrated, showing the CV spectrum due to an efficient fluorescence quenching by honey-comb structure.

SERS spectra of the CV molecule, performed on the AuAPA substrates with pore diameter (~60 nm) and wall thickness (~40 nm) (Fig. 3.2b), the characteristic vibrational bands of CV are observed (Vogel et al., 2000). Intense Raman bands centred at around 348, 591, 675 and 1186 cm-1 can be attributed to the out of plane sceleton deformation, combination of in-plane N-H2 and ring bending, ring deformation and combination of N-H2 rocking and C-Hx rocking, respectively (Vogel et al., 2000; Kudelski, 2005). From the vibrational bands

observed in the Fig. 3.2b it is most probable that the CV is oriented in such a way that the – N-H2 group is closer to the gold film, leading to the strong Raman scattering and, consequently, higher Raman signal. Additionally, in Fig. 3.2b, the high exponential background appeared in Fig. 3.2a for the CV on silicon substrate has disappeared. Hence, significant fluorescence quenching is also illustrated, as already observed in the past for gold nanoparticles (Dulkeith et al., 2002). SERS substrate background measurement (no dye on AuAPA pattern) was carried out and found a flat background response without any Raman band at all.

Fig. 3.3. a) The overall honey-comb structure. b) The overall electric field distribution in x-y plane, in this case, the polarization of incident light is along x-direction; c) absolute value of the electric field profile along the highlighted horizontal line. The excitation light is = 633 nm on gold surface with dielectric function real= 9.83 and imaginary= 1.97.

In order to demonstrate the enhanced electric field due to honey-comb nanostructure, we have also performed a series of simulations with the intent of calculating the near field electromagnetic distribution on AuAPA substrates. This kind of analysis can, in fact, provide information on the level of excitation of any sample deposited on a SERS substrate. In Fig. 3.3, simulations of the electric field due to the LSP generation on SERS substrates at z=0 nm (i.e. on the front surface of substrate) using CST software are presented. In particular, a 25 nm thick golden slab showing honeycomb pattern with periodicity of 100 nm, and sub-wavelength air holes (Lezec et al., 2004) with diameter of 60 nm, respectively, was simulated. The source light was fixed to 633 nm with linear polarization along the xaxis. The overall simulated structure is shown in Fig. 3.3a. For all the periodicity patterns, the results show an electric field strongly affected by the material discontinuity. In fact, the absolute value of the total electric field shows some nodes at the gold-air interface. The xpolarization creates anti-phase hot spots along the x-axis which determines the abrupt change of the electric field as in Fig. 3.3b. The profile, shown in Fig. 3.3c, gives even a better image of this behavior. The sharp doubled horns existing inside the holes are due to the

hexagonal geometry of the holes. Important features emerging from the simulations are both the mean (Emean) and the effective (Eeff) value of the electric field outside the holes (shaded regions in Fig. 3.3c). The former is simply defined as the average field whereas the latter is given by the difference between the maximum and minimum values in the hole.

In conclusion, home-built AuAPA substrates with pore size of 60 nm and wall thickness of 40 nm was utilized for large area SERS substrates. CV was deposited using chemisorption technique, using which a monolayer of molecules can be achieved. CST simulations of the electric field distribution on these ordered and reproducible SERS substrates were also performed, keeping the structural parameters as close as possible to the experimental honey-comb nanostructures. Theoretical results follow the same trend of experimental findings. The major advantage of using nanoporous alumina substrates, as compared to the traditional colloidal coating or lithographic processing, is a good trade-off between the high enhancement factor '*G*' obtained and the large surface area produced. The respective SERS enhancement factor '*G*' is estimated to be ~4106 .

Further research should be made in order to optimize '*G*' on the basis of the substrate parameters of pore size, wall thickness, and thickness of the gold coating. The next step towards reproducible micro-fabricated SERS devices would be the transfer of APA to technological substrates such as optical glass or silicon wafer, and combining APA patterning with optical lithography. In this way, large-area SERS bio- and chemical sensors assays for e.g. parallel biomedical screening of different body liquids or even tissues could be carried out, conveniently. The easy and inexpensive processing required for APA SERS fabrication would also make these substrates disposable, opening the way to their large scale applications. Such a high SERS enhancement as demonstrated here can provide single molecule sensitivity in a sensor based on labeling using fluorescence dyes.

# **4. Integration of biophotonics and superhydrophobic devices for the detection of few bio-molecules**

In biomedical disciplines including medicine, biology or biotechnology, there is a huge interest in understanding the pathogenesis of diseases, and to develop new biomarkers for their diagnosis. In particular, early detection can lead to significant benefits in terms of efficient and timely treatment. In these regards, the blood contains a multitude of unstudied and unknown biomarkers that could reflect the ongoing physiologic state of tissues and organs. The lowmolecular weight region of the blood proteome is an important source of diagnostic markers (Posadas et al., 2001). Nevertheless, this 'mine' of data for diagnosis is often practically inaccessible by conventional approaches, in that the solutions at study are extremely diluted, and contain a multitude of substances that would blur the signal of interest. To exploit this 'mine' of data for diagnosis, new devices are required with very low detection limits. *Nanotechnology*, as a whole, offers unprecedented opportunities to realize such devices, thus increasing the efficacy of diagnosis (Liotta et al., 2003). In the paragraphs above, the theory of plasmons and the use of plasmonic devices have been largely described. Here, the integration of this technology with superhydrophobic surfaces (SHSs) is introduced.

The aim of this paragraph is to expound on the contributions that this combination can possibly offer to clinical medicine, specifically in the discipline of early diagnostics. In particular, it revolves around the study and the micro/nano fabrication of SHSs which

incorporate biophotonic devices. Well assessed mechanisms such as (i) superhydrophobicity and (ii) SERS (Surface Enhanced Raman Scattering) are recapitulated and integrated into a single micro- nano- system. The combination of these two would represent a boost towards the detection and the analysis of few (or single) molecules. In the following, SHSs and nano optics based photonic devices are treated separately. After an introduction of the most important features of these, their combination and the effects thereof are discussed. Notice that, differently from plasmonic devices, SHSs are exposed to a good detail in that they are introduced here for the first time in the text.

In short, the major novelty, here, is the simultaneous use of wetting mechanisms (that arise due to the superhydrophobic surfaces, SHSs) and sensitive materials (that include, randomly distributed silver nanograin aggregates, regular arrays of metallic nano dots, adiabatic nanofocusing cones) to increase the response of nano optics based spectroscopy devices (see the cartoon representation of Fig. 4.1). By doing so, otherwise inaccessible information about the biological moieties at study is disclosed.

# **4.1 Superhydrophobic surfaces**

It is well known that a drop post upon a solid surface develops a contact with the solid described by the sole parameter e (Fig. 4.2A) that is the equilibrium contact angle at the interface between the liquid and the solid. e obeys the celebrated Young equation (Young, 1805):

$$\cos \theta\_{\varepsilon} = \frac{\mathcal{Y}\_{SV} - \mathcal{Y}\_{SL}}{\mathcal{Y}\_{LV}} \tag{4.1}$$

where ij is the surface tension between the phase i and j, and the letters S, L, V stand for the solid, liquid and vapour, and thus equation (1) may be regarded as a simple balance of forces. For sufficiently small droplets the dominant force becomes the liquid-vapor surface tension and gravitation may be neglected. The dimensionless Bond number can be consequently introduced as Bo=×g×R2/LV, where is the density of the liquid, R is the radius of the spherical drop prior the deposition upon the surface, and g is the acceleration due to gravity. When Bo<<1 gravitational effects vanish and the shape of the droplet may be assumed spherical everywhere. For a drop of water with LV=72.9 mJ/m2 , =1000 kg/m3 , and diameter d=2×R=1 mm, it follows that Bo~0.035, and thus the physics of micrometric or submillimetric drops is correctly governed by surface tension solely.

*Superhydrophobicity* (Fig. 4.2B) is a phenomenon whereby a drop post upon a surface would preserve its original spherical shape rather than spreading or wetting indefinitely the plane of contact (Lafuma & Quéré, 2003; Blossey, 2003). The theoretical conundrum explaining this mechanism dates back to the mid forties of the last century and is very well assessed. In the celebrated model of Cassie, a surface would be superhydrophobic on account of the pockets of air that remain trapped between the liquid and the substrate (Fig. 4.2C), and the smaller the fraction of solid in contact with the drop () the larger the apparent contact angle. In particular, the increased contact angle e c>e the drop experiences may be theoretically written as (Cassie & Baxter, 1944)

$$\cos \theta\_{\varepsilon}^{\varepsilon} = -1 + \phi\_{s} \left( \cos \theta\_{\varepsilon} + 1 \right) \tag{4.2}$$

where s is the fraction of solid in contact with the drop. The less s the larger the apparent contact angle. At the limit of s0, the drop would paradoxically float in air. The Cassie model is intuitive in that predicts that a drop upon a patterned surface 'sees' a contact angle that is proportional to the fraction of air in contact with the drop. A flat surface would have s=1 and accordingly e c=e. Another mechanism (Wenzel model) explains the increased contact angle on account of the roughness, and thus relies upon geometric effects solely (Fig. 4.2D). The modified angle e w is related to the unmodified contact angle e as (Lafuma & Quéré, 2003):

$$r\cos\theta\_{\varepsilon}^{w} = r\cos\theta\_{\varepsilon} \tag{4.3}$$

Where *r* is the solid roughness defined as the ratio between the real the projected surface, and thus the effect of surface roughness is to amplify the wetting. Noticeably, when e</2, *r* increases the hydrophilicity of the surface, whereas for e>/2 roughness promotes hydrophobicity. In spite of the fact that they do both induce hydrophobicity, these situations are very different when considering their adhesive properties. In Wenzel state drops are found to be highly pinned. On the contrary, in the Cassie state the drop sits mainly upon air, and this increases the contact angle.

Fig. 4.2. Superhydrophobicity and contact angle.

In the Cassie state the drop would roll upon the surface and it would progressively reduce its contact area during a process of evaporation. The drop would then maintain the Cassie state over time, thus avoiding collapse and any irreversible transition to Wenzel until a critical radius of impalement is achieved. The mechanisms inducing collapse in a slowly evaporating droplet are two and, namely, (i) the drop could either touch the surface below the posts, or (ii) the surface free energy gained as the drop collapses wins over the surface free energy lost by increased contact with the hydrophobic posts. While the first mechanism regards surfaces decorated with short posts or pillars, the second relies upon an energetic argument and is independent on the pillars' height. In many practical situations one should consider the latter criterion solely (De Angelis et al., 2011). In particular, both analytical calculations and numerical simulations show that the critical radius of impalement depends upon the distance between the pillars and e as

$$r\_{\min} = \frac{\delta}{\cos \theta\_{\varepsilon}}\tag{4.4}$$

and thus the closer the pillars the smaller the final area of contact. From the analysis above it stems out that surfaces with large (that is, with sufficiently dense pillars), would guarantee a stable Cassie configuration. Notice though that large would induce small contact angles, and thus the choice for the best design parameters is not trivial, and it is indeed a matter of optimization.

SHSs retain unique properties in terms of wettability that can be reviewed as follows: (i) SHSs have superior adhesive properties, in the sense that they exhibit vanishing friction coefficients; (ii) a droplet, post upon these surfaces, would accordingly preserve a quasispherical shape while evaporates, and the contact area at the interface would thus progressively reduce; (iii) SHSs can be artificially reproduced using micro and nano fabrication techniques. Using the properties above, micro textured surfaces may be successfully exploited to concentrate tiny amounts of moities over micrometric areas, and consequently measure these moieties with unprecedented accuracy (De Angelis et al., 2011; Accardo et al., 2011; Gentile et al., 2011a; Gentile et al., 2011b; Di Fabrizio et al., 2008).

#### **4.1.1 Fabrication of SHSs**

SHSs typically comprise a *periodic* hexagonal lattice of cylindrical Si micro pillars with a certain diameter and pitch (Fig. 4.3A). Due to the surface patterning the drop experiences an increased contact angle that can be theoretically predicted (Fig. 4.3B). The diameter *d* of the pillars and the distance between the pillars (gap) may be arbitrarily imposed, and can be chosen in accordance to a criterion of optimal design. This criterion would guarantee the best trade-off between sufficiently dense forests of pillars, that prevent the early collapse of the drop, and diluted structures, that instead assure large contact angles (De Angelis et al., 2011). The height of the pillars h is chosen to be as large as, at least, two times d, and this would avoid the spontaneous impalement of the drop. For the present configuration, d=10m,=20 m, and h=20 m. The pillars are arranged to recover a honeycomb lattice; notice that when these are combined with adiabatic nanofocusing cones the symmetry of the pattern is broken and, on account of this, the biomolecules are enforced to deposit upon the cones. The micro pillars are typically realized combining optical lithography, electroless

growth and Bosch Reactive Ion Etching (RIE) techniques. Non conventional biophotonic nanostructures as those described below, conveniently positioned upon the pillars, would complete a hierarchical structure thus permitting the identification of proteins in the single molecule regime (Fig. 4.3C). These 'two-stages' micro nano structures function as SHSs with an increased contact angle ranging from 155° to about 175°.

Fig. 4.3. SEM image of a photonic crystal for superhydrophobicity applications.

### **4.1.2 Current applications of SHSs**

Many applications exist revolving around the use of superhydrophobic surfaces and mainly founding upon two key features of these, that are the limited contact area and the ability of a drop to slide or slip upon such surfaces (Li et al., 2007). Water repellent coatings for radar domes, satellite dishes and glass are widely reported and currently in use. These coatings provide self-cleaning under the action of rain in that they mimic the self-cleaning action of the Lotus leaf. Other utilizations include antibiofouling paints for boats, antisticking of snow for antennas and windows, self-cleaning windshields for automobiles, the separation of water and oil, and the manufacture of water-proof fireretardant clothes. The latter would represent examples of a target market that is the huge household-commodity sector, nevertheless new analytical potentials also do exist which carry the promise of unparalleled opportunities in life sciences and in the high tech field of biotechnology. In Biotechnology many efforts are devoted to manipulate, control and analyse relevant molecules as DNA and proteins, and artificially (nanotech) fabricated superhydrophobic surfaces could be an effective advance towards this objective. Let's consider, for instance, the case of microarrays. These are libraries of biological or chemical entities (probes) immobolised in a grid on a solid surface, the probes would be then interacting with targets (i.e., geneses, proteins, cDNA...) to provide deep insight into DNA sequences. It is desirable that the drop containing the targets would evaporate avoiding pinning and the formation of noxious ring like structures (it is in fact well known that pinning during evaporations causes final solute formations disposed in doughnut shape, and this is commonly known as the coffee-ring effect, and here suitable superhydrophobic substrates come into play.

The transport, separation and mixing of moieties dispersed in droplets has an enormous interest likewise. Superhydrophobic surfaces are slippy, and thus a droplet would move upon the application of an infinitesimal external force field: tilting the surface (and thus gravitation) or electrostatic or surface waves induced force fields would move the droplet in a controllable way (see also below in materials and methods). On the other hand, variations in the patterning or texture of the surface would generate regions where the adhesive

properties are also different, thus creating well defined and distinguished tracks or patterns, and the drop could be exteriorly positioned into a precise area or point of the substrate. This argument is the ground for novel droplet-based microfluidic systems as reported in a number or publications and patents, and these surface would be in fact lab-on-chip systems which deliver the ability of performing bio-chemical detections and reactions with incomparable accuracy and efficiency. Recently, the use of superhydrophobic surfaces to concentrate and localize a solute has been proposed.

# **4.2 BioPhotonic devices**

Biophotonic nanostructures can be integrated to SHSs to obtain devices with advanced sensing capabilities. Here we shall recapitulate in short specific types of nano-geometry based plasmonic device, and namely (i) electroless grown random assemblies of silver nanograins; (ii) regular arrays of metallic nano dots; (iii) adiabatic nanofocusing cones. Nevertheless, the method can be extended to a number of different plasmonic nanostructures, as those broadly described in the paragraphs above (De Angelis et al., 2011; Accardo et al., 2011; Gentile et al., 2011a; Gentile et al., 2011b; Di Fabrizio et al., 2008; Gentile et al., 2010).

## **4.2.1 Electroless grown silver nanograins**

The electroless growth is a process whereby ionic silver is reduced and deposited as metallic silver upon silicon, via a redox reaction, and according to a mechanism that may be adequately described by a diffusion limited aggregation model. A satisfactory comprehension of the method may be found in (Coluccio et al., 2009). Here it is briefly recalled that, conveniently employing this process, and depending upon the growth parameters, silver nanograins may be obtained with an average size as small as few tens of nanometers, which compose efficient SERS substrates (Fig. 4.4A).

Fig. 4.4. SEM images of a metallic photonic crystal and plasmonic device.

# **4.2.2 Regular arrays of metallic nano dots**

These are gold or silver hemisphere positioned upon the substrate as to reproduce a regular square lattice. Optical lithography, electron beam lithography, Reactive Ion Etching, evaporation techniques are routinely used for the fabrication of these devices. Differently from the case above, the shape, dimension, position of the dots is deterministic in the limit of the fabrication process. Thereby SERS effects arise from the rational design of the nano

structure, founding upon the theory of surface plasmon polariton scattering (Fig. 4.4B) (De Angelis et al., 2011).

#### **4.2.3 Adiabatic nanoficusing cones**

These are extremely small conical geometries whereby crystal together with a plasmonic waveguide focuses the excitation laser to the apex of the waveguide, enabling a photon confinement equivalent to the radius of curvature of the nanofabricated tip (De Angelis et al., 2008; De Angelis et al., 2010). The fabrication process is accomplished on the basis of three steps. The grating is milled on the surface of the silicon micropillar by focused ion beam milling. The nanocones are growth on the top of the silicon tapered pillar by employing electron beam induced deposition (EBID) from a Platinum-based gas precursor. A thin layer of silver (40 nm) is finally deposited upon the device by means of thermal evaporation. These devices exploit the surface plasmon polariton adiabatic compression whereby the electro-magnetic field is locally enhanced (Fig. 4.4C) (De Angelis et al., 2011).

#### **4.3 The device as a whole**

The above analysis of SHSs and of the related properties thereof may be summarized as follows: (i) SHSs retain unique properties in terms of wettability, in particular a certain mass of water, in shape of a drop, would be repelled by such surfaces; (ii) SHSs have superior adhesive properties, in the sense that they exhibit vanishing friction coefficients; (iii) a droplet, post upon these surfaces, would accordingly preserve a quasi-spherical shape while evaporates, and the contact area at the interface would thus progressively reduce. Node (iii), above, is the key feature for such surfaces, in that it would enable to concentrate tiny amounts of agents (biomolecules) over micrometric areas. Imagine to deposit a drop of an extremely diluted solution upon a textured, superhydrophobic substrate. The drop would evaporate over time and thus the solution would get more and more concentrated. At the late stage of evaporation, the residual solute would be confined within an incredibly small region of the plane. With an appropriate design, few molecules may be conveniently enforced to confine into the smallest area conceivable, at the limit upon a sole pillar. Nano geometry based biophotonic devices, conveniently tiling these surfaces, would probe/detect the moieties with heretofore unattainable resolution limits (the process, as a whole, is recapitulated in Fig. 4.1).

The devices introduced would perform SERS measurements as well as (and definitely not better than) conventional SERS substrates. Nevertheless, here, the beneficial effects of super hydrophobicity and nanogeometry based spectroscopy are combined and conveyed into a unique platform, and from the combination of the two novel properties arise permitting the identification of proteins or analytes in the single molecule regime.

#### **4.4 Measurements**

Here, we report briefly on some experiments that would demonstrate the potentials of the method. Small drops of D.I. water containing Rhodamine molecules were gently positioned upon the substrates as in Fig. 4.4A. The evaporation process was followed over time until an irreversible transition to a pinning (Wenzel) state occurred. Few molecules were conveniently enforced to confine into a small area. Solutions were investigated with concentration as small as 10-18 M, that is, in the atto molar range. Figs. from 4.5A to C are SEM images of the residual solute of Rhodamine at the end of the process of evaporation. The magnification of the images is different: Fig. 4.5A was captured at the low magnification factor of 150, whereby the initial footprint of the drop is clearly visible; Fig. 4.5B and C were acquired setting higher magnification factors as 800 and 1500, respectively. Notice, from these, the solute extremely concentrated to the extent that the Rhodamine is accumulated into a small area clearly bridging the pillars. In any event, the residual solute is smaller than few tens of microns. Considering that the initial diameter of deposition is about 1200 m, while the final deposit is as large as 40 m, the concentration capability of the substrate is, at the very least, in the order of, roughly, (1200/40) 2~1000, that is, the problem is scaled down by three orders of magnitude. Notice that this analysis relies upon geometric effects solely.

Fig. 4.5. SEM images of a metallic photonic crystal for SERS measurement of Rhodamine.

Fig. 4.5D is a microscope image reporting the deposit of a Rhodamine evaporation process as above. To prove that the identification of the residue as Rhodamine is correct and it is not instead constituted by debris or other refuses, SERS spectroscopy measurements were carried out on the sample. While conventional Raman intensity is directly proportional to the number of molecules probed, in the case of SERS, solely the molecules that are in close proximity of the nano-metallic substrate assure the enhancement of the electric field. In the contour and 3D plot as in Fig. 4.5E and F the SERS intensity signal is consistent with the matter distribution as in Fig. 4.5D, and this would prove the hypothesis above. The mapping analysis was performed by referring the band centred at 1650 cm-1 .

# **5. Acknowledgment**

Authors would like to thanks Dr. Marco Salerno for providing APA template.

The authors also gratefully acknowledge support from European Projects SMD FP7-NMP-2008-SMALL-2 proposal No. CP-FP 229375-2 and Nanoantenna FP7-HEALTH-2009, Grant

No. 241818. FOCUS project proposal #270483- ICT-2009 8.7 - FET proactive 7: Molecular Scale Devices and Systems.

# **6. References**

Second-harmonic generation in reflection and diffraction by a GaAs photoniccrystal waveguide. *J. Opt. Soc. Am. B*, Vol. 19, No. 9, pp. 2122-2128

**Photonic Crystals - Innovative Systems, Lasers and Waveguides** Edited by Dr. Alessandro Massaro

ISBN 978-953-51-0416-2 Hard cover, 348 pages **Publisher** InTech **Published online** 30, March, 2012 **Published in print edition** March, 2012

The second volume of the book concerns the characterization approach of photonic crystals, photonic crystal lasers, photonic crystal waveguides and plasmonics including the introduction of innovative systems and materials. Photonic crystal materials promises to enable all-optical computer circuits and could also be used to make ultra low-power light sources. Researchers have studied lasers from microscopic cavities in photonic crystals that act as reflectors to intensify the collisions between photons and atoms that lead to lazing, but these lasers have been optically-pumped, meaning they are driven by other lasers. Moreover, the physical principles behind the phenomenon of slow light in photonic crystal waveguides, as well as their practical limitations, are discussed. This includes the nature of slow light propagation, its bandwidth limitation, coupling of modes and particular kind terminating photonic crystals with metal surfaces allowing to propagate in surface plasmon-polariton waves. The goal of the second volume is to provide an overview about the listed issues.

# **How to reference**

In order to correctly reference this scholarly work, feel free to copy and paste the following:

Remo Proietti Zaccaria, Anisha Gopalakrishnan, Gobind Das, Francesco Gentile, Ali Haddadpour, Andrea Toma, Francesco De Angelis, Carlo Liberale, Federico Mecarini, Luca Razzari, Andrea Giugni, Roman Krahne and Enzo Di Fabrizio (2012). Photonic Crystals for Plasmonics: From Fundamentals to Superhydrophobic Devices, Photonic Crystals - Innovative Systems, Lasers and Waveguides, Dr. Alessandro Massaro (Ed.), ISBN: 978-953-51-0416-2, InTech, Available from: http://www.intechopen.com/books/photonic-crystalsinnovative-systems-lasers-and-waveguides/photonic-crystals-for-plasmonics

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