2. Nonlinear models of molecule interaction with short-pulse radiation

UV-C radiation is effective for inactivating protozoa, bacteria, viruses, and many microorganisms. According to literature [17–21], the use of UV-C radiation is especially a good, environment-friendly, and chemical-free method to inactivate dangerous pathogens in diverse condition. UV-C cannot pass through our atmosphere, so it does not contribute to DNA damage. However, it is worth to mention that UV-C lamps give effective results in killing bacteria and microbes.

The process of decontamination by UV radiation, which can cause thymine dimers of bacteria and viruses, is not yet fully understood [17]. Bactericidal mechanism of UV-C has a maximal damage to RNA and DNA. This process is accompanied by generation of pyrimidine residues in the nucleic acid strands. The consequence of this modification is a production of cyclobutane pyrimidine dimers that induces deformation of the DNA molecule. This might cause local vibration energy of the modes that may be coupled by nonharmonic, nonlinear term. For example, two vibration defects in cell replication can lead to cell death eventually (Figure 1).

Ref. [22] demonstrated that when exposing E. coli DNA to UV-C irradiation, randomly placed, dose-dependent, single-strand breaks are generated. It was proposed that the negative supercoiling strain on the DNA backbone is generated by the conformational relaxation. It has been often proved that as a result of the inactivation of bacteria and DNA viruses under UV action, thymine dimers are produced. A dose of 4.5 J/m<sup>2</sup> is testified to cause 50,000 pyrimidine dimers per cell [23]. It has been reported that 100 J/m<sup>2</sup> induces approximately Efficient Microbial Decontamination of Translucent Liquids and Gases Using Optical Metamaterials http://dx.doi.org/10.5772/intechopen.80639 173

system, which allows reaching large penetration of the radiation inside contaminated liquids (or gases). Second, it is needed to use the method of selective short pulse decontamination [9, 12, 13] for the estimation of the potential penetration depth in translucent liquids. For example, in Refs. [12, 13], the authors proposed a photonic approach for selective neutralization of viruses. In Ref. [12], a near-infrared (IR) ultrashort pulsed (USP) subpicoseconds fiber laser source is used instead of UV lamps to avoid IR absorption. This UPS targets only the weak links on the protein shells of viral particles. By selecting the appropriate laser parameters, the authors reveal that it is possible to damage the protein shells, conducting to their inactivation, but without affecting mammalian cells. More exactly, they demonstrated that this method can discriminate and inactivate viral particles, from nonpathogenic viruses such as M13 bacteriophage and tobacco mosaic virus (TMV) to pathogenic ones like human papillomavirus (HPV) and human immunodeficiency virus (HIV). Concomitantly, the sensitive materials, for example, human Jurkat T cells, human red blood cells, and mouse dendritic cells, keep unaffected. In Ref. [13], a mechanical model is proposed. It has a normal mode where it oscillates around its equilibrium geometry. By selecting the visible or near-IR laser pulse duration to be shorter or near to the normal oscillation period, the authors of Ref. [12] have demonstrated that a single beam excitation laser pulse can bring a macroparticle, as for example, a virus, into oscillation by impulsive stimulated Raman [14]. It is worthy to mention that similar coherent Raman effect for larger frequencies of UV pulses is used for diagnostics of the various bio-

2. Nonlinear models of molecule interaction with short-pulse radiation

UV-C radiation is effective for inactivating protozoa, bacteria, viruses, and many microorganisms. According to literature [17–21], the use of UV-C radiation is especially a good, environment-friendly, and chemical-free method to inactivate dangerous pathogens in diverse condition. UV-C cannot pass through our atmosphere, so it does not contribute to DNA damage. However, it is worth to mention that UV-C lamps give effective results in killing bacteria and microbes.

The process of decontamination by UV radiation, which can cause thymine dimers of bacteria and viruses, is not yet fully understood [17]. Bactericidal mechanism of UV-C has a maximal damage to RNA and DNA. This process is accompanied by generation of pyrimidine residues in the nucleic acid strands. The consequence of this modification is a production of cyclobutane pyrimidine dimers that induces deformation of the DNA molecule. This might cause local vibration energy of the modes that may be coupled by nonharmonic, nonlinear term. For example, two vibration defects in cell replication can lead to cell death

Ref. [22] demonstrated that when exposing E. coli DNA to UV-C irradiation, randomly placed, dose-dependent, single-strand breaks are generated. It was proposed that the negative supercoiling strain on the DNA backbone is generated by the conformational relaxation. It has been often proved that as a result of the inactivation of bacteria and DNA viruses under UV action, thymine dimers are produced. A dose of 4.5 J/m<sup>2</sup> is testified to cause 50,000 pyrimidine dimers per cell [23]. It has been reported that 100 J/m<sup>2</sup> induces approximately

molecules (e.g., lipids) with optical equipment [15, 16].

eventually (Figure 1).

172 Advanced Surface Engineering Research

Figure 1. (A) Dimer bond generation under UV-C radiation of DNA according to Ref. [22] and (B) two-dimension potential with two minimums. First minimum corresponds to nondimer DNA and second minimum is similar to the dimer phototransformation of DNA under the UV-C radiation.

seven pyrimidine dimers per viral genome in SV40, which is sufficient to strongly inhibit viral DNA synthesis [24]. Thymine dimers formed within short pulse of UV excitation are properly oriented [19]. Only a few percent of the thymine doublets are expected to be favorably sited for reaction and dimerization at the moment of UV excitation.


converts into a viral protein covalently linked. Moreover, a slow destruction process of capsid occurred and photoproducts were produced. In the virus irradiated by UV appeared a covalent linkage of viral RNA to viral polypeptides, the most probably due to close vicinity of RNA and proteins in the capsid. The protein linked covalently to the RNA does not surpass 1.5% of the total protein capsid. The authors of Ref. [26] studied Venezuelan equine encephalitis (VEE) under UV irradiation and found evidence suggesting that the formation of uracil dimers led to extensive contacts of the RNA with protein in the nucleocapsid.

Taking into consideration the important advantages of vibrational spectroscopy based on nonlinear coherent anti-Stokes generation mechanism, the new technique coherent anti-Stokes Raman spectroscopy (CARS) was reported by authors of Ref. [27] as an attractive tool for rapid excitation of vibrational modes. The application of USP lasers in coherent Raman scattering (CRS) or CARS opens the new possibilities in the decontamination procedures of fluids by dangerous pathogens (viruses and bacteria). In many cases for the effective inactivation procedure of pathogens on the implant surface, it is necessary to take into consideration the relative dimensions of viruses and bacteria and their possible molecular vibration symmetry [28, 29]. Most natural viruses depend upon the existence of capsids with specific geometry, protective shells of various sizes composed of protein subunits (Figure 3). Up to now, the general shaping capsid design is still elusive. Therefore, the correct understanding of their properties may help to realistically block the virus life cycle and, consequently, design of efficient nanoassemblies.

In our opinion, intrinsic topology of DNA dimmers (see Figure 4) may help to properly consider the symmetry vibration modes of this virus structure, such as to estimate the probable nonharmonic excitation of virus constituents by selectively annihilating them for the duration of the coherent Raman excitation. In the following, the method for exciting local vibration

Figure 3. Relative dimension of viruses (bacteria) and their commensurability with the evanescent zone of a fiber optic. The spherical symmetry of the human papilloma, cowpea chlorotic mottle, and polo viruses. Some topological structures

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175

Most natural viruses depend upon the existence of spherical capsids: protective shells of various sizes composed of protein subunits (see Figure 4). Here, we must estimate the commensurability of virus dimensions with the depth of the evanescent zone of radiation around the metamaterials. So far, general evolutionary pressures shaping capsid design have remained elusive, even though an understanding of such properties may help in rationally

Figure 4. Two-dimensional potential with two minimums which correspond to destroy DNA schemes represented in Figures 1 and 2. First minimum corresponds to nondimmer DNA and second minimum to the dimerization of DNA under the UV-C radiation. In the right hand, the transfer of DNA from first minimum to the second minimum is plotted. The thick line represents the behavior of R tð Þ, the red line to nonlinear oscillatory frequency in the relative units <sup>Ω</sup><sup>2</sup>

=Ω<sup>0</sup>

modes of biomolecule nanoassemblies is presented.

and τ ¼ t=Ω0.

of polyhedral and helical viruses. Reproduced with permission from [6].

impeding the virus life cycle and designing efficient nanoassemblies.

The authors of Ref. [30] reveal an exceptional and species-independent evolutionary pressure on virus aphids. It is based on the concept that the simplest capsid designs are the best. This holds true for all existing virus capsids. As a consequence of theories, it results a substantially significant periodic table of virus capsids that reveals strong and predominant evolutionary pressures. It also offers geometric explanations for other capsid properties (rigidity, pleomorphic, auxiliary requirements, etc.), which earlier were considered to be unique for an individual virus.

Figure 2. (A) Damage bonds and generation of dimer bonds under UV-C radiation of DNA. UV-C may also induce crosslinks between nonadjacent thymine illustrated in (B). Cross-linking can occur with proteins, cytosine, and guanine (C).

Efficient Microbial Decontamination of Translucent Liquids and Gases Using Optical Metamaterials http://dx.doi.org/10.5772/intechopen.80639 175

converts into a viral protein covalently linked. Moreover, a slow destruction process of capsid occurred and photoproducts were produced. In the virus irradiated by UV appeared a covalent linkage of viral RNA to viral polypeptides, the most probably due to close vicinity of RNA and proteins in the capsid. The protein linked covalently to the RNA does not surpass 1.5% of the total protein capsid. The authors of Ref. [26] studied Venezuelan equine encephalitis (VEE) under UV irradiation and found evidence suggesting that the formation of uracil dimers led to extensive contacts of the RNA with protein in the

Taking into consideration the important advantages of vibrational spectroscopy based on nonlinear coherent anti-Stokes generation mechanism, the new technique coherent anti-Stokes Raman spectroscopy (CARS) was reported by authors of Ref. [27] as an attractive tool for rapid excitation of vibrational modes. The application of USP lasers in coherent Raman scattering (CRS) or CARS opens the new possibilities in the decontamination procedures of fluids by dangerous pathogens (viruses and bacteria). In many cases for the effective inactivation procedure of pathogens on the implant surface, it is necessary to take into consideration the relative dimensions of viruses and bacteria and their possible molecular vibration symmetry [28, 29]. Most natural viruses depend upon the existence of capsids with specific geometry, protective shells of various sizes composed of protein subunits (Figure 3). Up to now, the general shaping capsid design is still elusive. Therefore, the correct understanding of their properties may help to realistically block the virus life cycle and, consequently, design of efficient nanoassemblies. The authors of Ref. [30] reveal an exceptional and species-independent evolutionary pressure on virus aphids. It is based on the concept that the simplest capsid designs are the best. This holds true for all existing virus capsids. As a consequence of theories, it results a substantially significant periodic table of virus capsids that reveals strong and predominant evolutionary pressures. It also offers geometric explanations for other capsid properties (rigidity, pleomorphic, auxiliary

requirements, etc.), which earlier were considered to be unique for an individual virus.

Figure 2. (A) Damage bonds and generation of dimer bonds under UV-C radiation of DNA. UV-C may also induce crosslinks between nonadjacent thymine illustrated in (B). Cross-linking can occur with proteins, cytosine, and guanine (C).

nucleocapsid.

174 Advanced Surface Engineering Research

Figure 3. Relative dimension of viruses (bacteria) and their commensurability with the evanescent zone of a fiber optic. The spherical symmetry of the human papilloma, cowpea chlorotic mottle, and polo viruses. Some topological structures of polyhedral and helical viruses. Reproduced with permission from [6].

In our opinion, intrinsic topology of DNA dimmers (see Figure 4) may help to properly consider the symmetry vibration modes of this virus structure, such as to estimate the probable nonharmonic excitation of virus constituents by selectively annihilating them for the duration of the coherent Raman excitation. In the following, the method for exciting local vibration modes of biomolecule nanoassemblies is presented.

Most natural viruses depend upon the existence of spherical capsids: protective shells of various sizes composed of protein subunits (see Figure 4). Here, we must estimate the commensurability of virus dimensions with the depth of the evanescent zone of radiation around the metamaterials. So far, general evolutionary pressures shaping capsid design have remained elusive, even though an understanding of such properties may help in rationally impeding the virus life cycle and designing efficient nanoassemblies.

Figure 4. Two-dimensional potential with two minimums which correspond to destroy DNA schemes represented in Figures 1 and 2. First minimum corresponds to nondimmer DNA and second minimum to the dimerization of DNA under the UV-C radiation. In the right hand, the transfer of DNA from first minimum to the second minimum is plotted. The thick line represents the behavior of R tð Þ, the red line to nonlinear oscillatory frequency in the relative units <sup>Ω</sup><sup>2</sup> =Ω<sup>0</sup> and τ ¼ t=Ω0.

Local vibration energy of the modes may be coupled by nonharmonic nonlinear term. For example, two vibration modes Q and Θ can be represented as a symmetric function relative to the square value of these normal coordinates:

$$\begin{split} H\_{0} &= \frac{M\_{q}}{2} \left( \frac{d\boldsymbol{Q}}{dt} \right)^{2} + \frac{M\_{\theta}}{2} \left( \frac{d\boldsymbol{\Theta}}{dt} \right)^{2} + \frac{M\_{\theta}\Omega\_{q}^{2}\boldsymbol{Q}^{2}}{2} + \frac{M\_{\theta}\Omega\_{\theta}^{2}\boldsymbol{\Theta}^{2}}{2} - \kappa\_{\theta}\boldsymbol{Q}^{4} - \kappa\_{\theta}\boldsymbol{\Theta}^{4} \\ &- \kappa\_{\theta,q}\boldsymbol{\Theta}^{2}\boldsymbol{Q}^{2} + \chi\_{q}\boldsymbol{Q}^{6} + \chi\_{\theta}\boldsymbol{\Theta}^{6} + \chi\_{\theta,\theta}\boldsymbol{\Theta}^{2}\boldsymbol{Q}^{4} + \chi\_{\theta,q}\boldsymbol{\Theta}^{4}\boldsymbol{Q}^{2} \end{split} \tag{1}$$

Short laser pulses applied externally interact with the molecular dipole of virus components. Consequently, the Hamiltonian takes the traditional form HI ¼ �ð Þ Pð Þ E ; Eð Þ t; z . Following the common representation [34–36], the laser field induces the biomolecule polarization, in which components, in similar representation, have tensor character. They depend on the symmetry of excited molecules (virus' or bacteria's constituents) Pjð Þ¼ E αjlEl. Because of the tensor character of the two oscillation modes, we can decompose the recognizability αjlð Þ Q; Θ in Taylor

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∂αjl

By introducing this expression in the interaction Hamiltonian, we observe that the interaction

where Q<sup>1</sup> ¼ Q, Q<sup>2</sup> ¼ Θ, and the tensor αjlk<sup>0</sup> ¼ ∂αjl=∂Qk must be maximally symmetrical according to the symmetry of the virus or bacteria biomolecules. Considering that laser pulses have same polarization, we represent it through the time-dependent Gaussian function Ei ¼ E0exp

� �<sup>2</sup> h i cos ð Þ <sup>ω</sup>it . For this, we substitute the generalized driving forces Fj ¼ �∂UI=∂Qj in the system of Eq. (2). The numerical solution of symmetrized nonlinear Eq. (3) for the following

the system is represented in Figure 4. Here, we have used the relative attenuation constant

ω<sup>a</sup> � ω<sup>s</sup> ¼ Ω0, and Ω0τ<sup>L</sup> ¼ 1 were chosen as parameters. As follows from the numerical solution of Eq. (3), in the relative time moment τ � 25, the nonlinear oscillator achieves the local maximum potential between the wells represented in the left figure of Figure 4. After this relative time point (τ > 25), the nonlinear oscillator relaxes in the second minimum of double well potential according to the numerical representation in Figure 4. This localized state

Let us give the analytical representation of this excitation process described by the system of nonlinear Eq. (2). According to Refs. [13, 29], we observe a same exponential dependence on the <sup>Ω</sup>jτL, in the initial stage of excitation Qj <sup>¼</sup> <sup>Q</sup>0jexp �Γjt � � sin <sup>Ω</sup>jt � �, when nonlinear frequency is approximated with linear part Ωjð Þ Q; Θ ≈ Ωj, j ¼ 1, 2. Here we consider that Q ¼ Q<sup>1</sup> and Θ ¼ Q2. After the first pulse with duration, Ω0τ<sup>L</sup> ≪ 1, the amplitude has the following

4:7 � exp �ð Þ τ � 5n

. In case of short laser pulses with relative intensity,

<sup>0</sup> <sup>¼</sup> <sup>X</sup> 8

corresponds to the damage situations of DNA discussed in Figure 2.

1

0

<sup>2</sup> h i sin ð Þ<sup>τ</sup> h i,

� � <sup>¼</sup> <sup>R</sup><sup>2</sup> �4:<sup>1</sup> � <sup>10</sup>�<sup>5</sup>

<sup>0</sup>, pulse duration, τL, and local oscillation frequency of the

<sup>R</sup><sup>4</sup> <sup>þ</sup> <sup>4</sup>:<sup>5</sup> � <sup>10</sup>�<sup>10</sup>R<sup>6</sup> of

UI ¼ α<sup>0</sup>

<sup>∂</sup><sup>Θ</sup> <sup>Θ</sup> <sup>þ</sup> <sup>ε</sup> <sup>Q</sup><sup>2</sup>

jlkEjElQk,

; Θ<sup>2</sup> ; QΘ � �:

series relative to the normal components Q and Θ

� <sup>t</sup><sup>=</sup> ffiffiffi 2 <sup>p</sup> <sup>τ</sup><sup>L</sup>

<sup>2</sup>Γ=Ω<sup>0</sup> <sup>¼</sup> <sup>10</sup>�<sup>3</sup>

dependence on the intensity, E<sup>2</sup>

normal mode j, Ω<sup>j</sup>

αjl ≃α<sup>0</sup> jl þ ∂αjl <sup>∂</sup><sup>Q</sup> <sup>Q</sup> <sup>þ</sup>

with the local vibration modes can be described by the function

expression of the parameters of the potential 2U<sup>=</sup> <sup>j</sup>MΩ<sup>2</sup>

<sup>F</sup>ð Þ<sup>τ</sup> <sup>=</sup>Ω<sup>2</sup>

Here Mi, Ωi, and κ<sup>i</sup> are the effective mass, frequency, and nonharmonic parameter for the vibration mode i; κθ, <sup>q</sup> is the nonlinear coupling of the normal modes of molecule oscillations. The nonharmonic terms present in the Hamiltonian describe the possible inactivation of pathogens at higher excitation.

Two situations of the vibration of this molecular system represented by DNA or tubulins in protein packing in the bacteria microtubule are considered. Collective nonlinear coupled modes, for example, phonons in the condensed mater [31, 32], were introduced and described by the Hamiltonian (1). Therefore, two vibration modes, Q and Θ, become aperiodic according to the theory of catastrophe [33], for higher excitation of the system with short laser pulses [13, 30] with the pulse duration τ<sup>L</sup> < 1=Ωi:

$$\begin{aligned} \frac{d^2}{dt^2}Q &+ \left\{\Omega\_q^2 - 4\ddot{\chi}\_q\mathcal{Q}^2 + 6\ddot{\chi}\_q\mathcal{Q}^4 - 2\ddot{\chi}\_{q\theta}\Theta^2 + 2\ddot{\chi}\_{\theta,q}\Theta^4 + 4\ddot{\chi}\_{q,\theta}\Theta^2\mathcal{Q}^2\right\}Q + 2\Gamma\_q\frac{d}{dt}Q = F\_{\theta}(t);\\ \frac{d^2}{dt^2}\Theta &+ \left\{\Omega\_\theta^2 - 4\ddot{\chi}\_\theta\Theta^2 + 6\ddot{\chi}\_\theta\Theta^4 - 2\ddot{\chi}\_{q\theta}Q^2 + 2\ddot{\chi}\_{q,\theta}\Theta^4 + 4\ddot{\chi}\_{\theta,q}\Theta^2\mathcal{Q}^2\right\}\Theta + 2\Gamma\_\theta\frac{d}{dt}\Theta = F\_{\theta}(t). \end{aligned} \tag{2}$$

Here, we have introduced the attenuation constant, Γi, of each coupling mode through nonlinear interaction, χ~ij ¼ χij=Mi; κ~<sup>q</sup><sup>θ</sup> ¼ κθ, <sup>q</sup>=Mi. The nonharmonic term of each mode is described by the nonlinear constant <sup>~</sup>ki <sup>¼</sup> ki=Mi. The first and second equations of (2) use the corresponding component for anisotropy effective masses Mq and MΘ. The nonharmonic potential is described by the two-dimensional localization potential in Figures 1 and 4. If it is absent, the mass anisotropy and two dimensions become symmetrical and we may do the substitution <sup>Q</sup> <sup>¼</sup> <sup>R</sup>cos<sup>φ</sup> and <sup>Θ</sup> <sup>¼</sup> <sup>R</sup>sin<sup>φ</sup> so that the terms MqΩ<sup>2</sup> <sup>q</sup>Q<sup>2</sup> <sup>þ</sup> <sup>M</sup>θΩ<sup>2</sup> <sup>θ</sup>Θ<sup>2</sup> � �=2, <sup>κ</sup>Q<sup>4</sup> <sup>þ</sup> <sup>κ</sup>Θ<sup>4</sup> <sup>þ</sup>2κΘ<sup>2</sup> Q2 , and <sup>χ</sup>Q<sup>6</sup> <sup>þ</sup> <sup>χ</sup>Θ<sup>6</sup> <sup>þ</sup> <sup>3</sup>χΘ<sup>2</sup> <sup>Q</sup><sup>4</sup> <sup>þ</sup> <sup>3</sup>χΘ<sup>4</sup> Q<sup>2</sup> in Hamiltonian (1) can be substituted by MΩ<sup>2</sup> R2 =2, κR<sup>4</sup> , and χR<sup>6</sup> . Taking into consideration the symmetric form of the Hamiltonian,

$$H\_0 = \frac{M}{2} \left[ \left( \frac{d\mathbf{Q}}{dt} \right)^2 + \left( \frac{d\Theta}{dt} \right)^2 \right] + \frac{M\Omega\_0^2 R^2}{2} - \kappa R^4 + \chi R^6 \lambda$$

we reduce the system of Eq. (2) to a single equation for radial component of nonlinear oscillator

$$\frac{d^2}{dt^2}R + \left\{\Omega\_0^2 - 4\tilde{\kappa}R^2 + 6\tilde{\chi}R^4\right\}R + 2\Gamma\frac{d}{dt}R = F(t). \tag{3}$$

Short laser pulses applied externally interact with the molecular dipole of virus components. Consequently, the Hamiltonian takes the traditional form HI ¼ �ð Þ Pð Þ E ; Eð Þ t; z . Following the common representation [34–36], the laser field induces the biomolecule polarization, in which components, in similar representation, have tensor character. They depend on the symmetry of excited molecules (virus' or bacteria's constituents) Pjð Þ¼ E αjlEl. Because of the tensor character of the two oscillation modes, we can decompose the recognizability αjlð Þ Q; Θ in Taylor series relative to the normal components Q and Θ

Local vibration energy of the modes may be coupled by nonharmonic nonlinear term. For example, two vibration modes Q and Θ can be represented as a symmetric function relative to

> MqΩ<sup>2</sup> qQ<sup>2</sup> 2 þ

Here Mi, Ωi, and κ<sup>i</sup> are the effective mass, frequency, and nonharmonic parameter for the vibration mode i; κθ, <sup>q</sup> is the nonlinear coupling of the normal modes of molecule oscillations. The nonharmonic terms present in the Hamiltonian describe the possible inactivation of patho-

Two situations of the vibration of this molecular system represented by DNA or tubulins in protein packing in the bacteria microtubule are considered. Collective nonlinear coupled modes, for example, phonons in the condensed mater [31, 32], were introduced and described by the Hamiltonian (1). Therefore, two vibration modes, Q and Θ, become aperiodic according to the theory of catastrophe [33], for higher excitation of the system with short laser pulses

Here, we have introduced the attenuation constant, Γi, of each coupling mode through nonlinear interaction, χ~ij ¼ χij=Mi; κ~<sup>q</sup><sup>θ</sup> ¼ κθ, <sup>q</sup>=Mi. The nonharmonic term of each mode is described by the nonlinear constant <sup>~</sup>ki <sup>¼</sup> ki=Mi. The first and second equations of (2) use the corresponding component for anisotropy effective masses Mq and MΘ. The nonharmonic potential is described by the two-dimensional localization potential in Figures 1 and 4. If it is absent, the mass anisotropy and two dimensions become symmetrical and we may do the substitution

> <sup>q</sup>Q<sup>2</sup> <sup>þ</sup> <sup>M</sup>θΩ<sup>2</sup> θΘ<sup>2</sup> � �

Q<sup>2</sup> in Hamiltonian (1) can be substituted by MΩ<sup>2</sup>

<sup>2</sup> � <sup>κ</sup>R<sup>4</sup> <sup>þ</sup> <sup>χ</sup>R<sup>6</sup>

MθΩ<sup>2</sup> θΘ<sup>2</sup>

<sup>Q</sup><sup>4</sup> <sup>þ</sup> χθ, <sup>q</sup>Θ<sup>4</sup>

<sup>2</sup> � <sup>κ</sup>qQ<sup>4</sup> � κθΘ<sup>4</sup>

Q þ 2Γ<sup>q</sup>

Θ þ 2Γ<sup>θ</sup>

,

dt <sup>R</sup> <sup>¼</sup> F tð Þ: (3)

d

d

<sup>=</sup>2, <sup>κ</sup>Q<sup>4</sup> <sup>þ</sup> <sup>κ</sup>Θ<sup>4</sup> <sup>þ</sup>2κΘ<sup>2</sup>

R2 =2, κR<sup>4</sup> ,

dt <sup>Q</sup> <sup>¼</sup> Fqð Þ<sup>t</sup> ;

dt <sup>Θ</sup> <sup>¼</sup> <sup>F</sup>θð Þ<sup>t</sup> :

(1)

(2)

Q2 ,

Q2

þ

the square value of these normal coordinates:

dQ dt � �<sup>2</sup>

þ M<sup>θ</sup> 2

dΘ dt � �<sup>2</sup>

<sup>Q</sup><sup>2</sup> <sup>þ</sup> <sup>χ</sup>qQ<sup>6</sup> <sup>þ</sup> χθΘ<sup>6</sup> <sup>þ</sup> <sup>χ</sup>q,θΘ<sup>2</sup>

<sup>q</sup> � <sup>4</sup>κ~qQ<sup>2</sup> <sup>þ</sup> <sup>6</sup>χ~qQ<sup>4</sup> � <sup>2</sup>κ~<sup>q</sup>θΘ<sup>2</sup> <sup>þ</sup> <sup>2</sup>χ<sup>~</sup> <sup>θ</sup>, <sup>q</sup>Θ<sup>4</sup> <sup>þ</sup> <sup>4</sup>χ~q,θΘ<sup>2</sup> <sup>Q</sup><sup>2</sup> n o

<sup>θ</sup> � <sup>4</sup>κ~θΘ<sup>2</sup> <sup>þ</sup> <sup>6</sup>χ<sup>~</sup> <sup>θ</sup>Θ<sup>4</sup> � <sup>2</sup>κ~<sup>q</sup>θQ<sup>2</sup> <sup>þ</sup> <sup>2</sup>χ~q,θQ<sup>4</sup> <sup>þ</sup> <sup>4</sup>χ<sup>~</sup> <sup>θ</sup>, <sup>q</sup>Θ<sup>2</sup> <sup>Q</sup><sup>2</sup> n o

. Taking into consideration the symmetric form of the Hamiltonian,

dΘ dt

þ MΩ<sup>2</sup> 0R<sup>2</sup>

we reduce the system of Eq. (2) to a single equation for radial component of nonlinear oscillator

<sup>0</sup> � <sup>4</sup>κ~R<sup>2</sup> <sup>þ</sup> <sup>6</sup>χ~R<sup>4</sup> � �<sup>R</sup> <sup>þ</sup> <sup>2</sup><sup>Γ</sup> <sup>d</sup>

þ

� �<sup>2</sup> " #

<sup>H</sup><sup>0</sup> <sup>¼</sup> Mq 2

176 Advanced Surface Engineering Research

gens at higher excitation.

d2

d2

and χR<sup>6</sup>

dt<sup>2</sup> <sup>Q</sup> <sup>þ</sup> <sup>Ω</sup><sup>2</sup>

dt<sup>2</sup> <sup>Θ</sup> <sup>þ</sup> <sup>Ω</sup><sup>2</sup>

and <sup>χ</sup>Q<sup>6</sup> <sup>þ</sup> <sup>χ</sup>Θ<sup>6</sup> <sup>þ</sup> <sup>3</sup>χΘ<sup>2</sup>

� κθ, <sup>q</sup>Θ<sup>2</sup>

[13, 30] with the pulse duration τ<sup>L</sup> < 1=Ωi:

<sup>Q</sup> <sup>¼</sup> <sup>R</sup>cos<sup>φ</sup> and <sup>Θ</sup> <sup>¼</sup> <sup>R</sup>sin<sup>φ</sup> so that the terms MqΩ<sup>2</sup>

<sup>H</sup><sup>0</sup> <sup>¼</sup> <sup>M</sup> 2

d2

dt<sup>2</sup> <sup>R</sup> <sup>þ</sup> <sup>Ω</sup><sup>2</sup>

<sup>Q</sup><sup>4</sup> <sup>þ</sup> <sup>3</sup>χΘ<sup>4</sup>

dQ dt � �<sup>2</sup>

$$
\alpha\_{jl} \simeq \alpha\_{jl}^0 + \frac{\partial \alpha\_{jl}}{\partial Q} Q + \frac{\partial \alpha\_{jl}}{\partial \Theta} \Theta + \varepsilon \left( Q^2; \Theta^2; Q\Theta \right).
$$

By introducing this expression in the interaction Hamiltonian, we observe that the interaction with the local vibration modes can be described by the function

$$\mathcal{U}\_I = \alpha'\_{jlk} E\_f E\_l Q\_{k'} $$

where Q<sup>1</sup> ¼ Q, Q<sup>2</sup> ¼ Θ, and the tensor αjlk<sup>0</sup> ¼ ∂αjl=∂Qk must be maximally symmetrical according to the symmetry of the virus or bacteria biomolecules. Considering that laser pulses have same polarization, we represent it through the time-dependent Gaussian function Ei ¼ E0exp � <sup>t</sup><sup>=</sup> ffiffiffi 2 <sup>p</sup> <sup>τ</sup><sup>L</sup> � �<sup>2</sup> h i cos ð Þ <sup>ω</sup>it . For this, we substitute the generalized driving forces Fj ¼ �∂UI=∂Qj in the system of Eq. (2). The numerical solution of symmetrized nonlinear Eq. (3) for the following expression of the parameters of the potential 2U<sup>=</sup> <sup>j</sup>MΩ<sup>2</sup> 0 � � <sup>¼</sup> <sup>R</sup><sup>2</sup> �4:<sup>1</sup> � <sup>10</sup>�<sup>5</sup> <sup>R</sup><sup>4</sup> <sup>þ</sup> <sup>4</sup>:<sup>5</sup> � <sup>10</sup>�<sup>10</sup>R<sup>6</sup> of the system is represented in Figure 4. Here, we have used the relative attenuation constant <sup>2</sup>Γ=Ω<sup>0</sup> <sup>¼</sup> <sup>10</sup>�<sup>3</sup> . In case of short laser pulses with relative intensity,

$$F(\tau)/\Omega\_0^2 = \sum\_{1}^{8} \left[ 4.7 \cdot \exp\left[ - (\tau - 5n)^2 \right] \sin\left(\tau\right) \right],$$

ω<sup>a</sup> � ω<sup>s</sup> ¼ Ω0, and Ω0τ<sup>L</sup> ¼ 1 were chosen as parameters. As follows from the numerical solution of Eq. (3), in the relative time moment τ � 25, the nonlinear oscillator achieves the local maximum potential between the wells represented in the left figure of Figure 4. After this relative time point (τ > 25), the nonlinear oscillator relaxes in the second minimum of double well potential according to the numerical representation in Figure 4. This localized state corresponds to the damage situations of DNA discussed in Figure 2.

Let us give the analytical representation of this excitation process described by the system of nonlinear Eq. (2). According to Refs. [13, 29], we observe a same exponential dependence on the <sup>Ω</sup>jτL, in the initial stage of excitation Qj <sup>¼</sup> <sup>Q</sup>0jexp �Γjt � � sin <sup>Ω</sup>jt � �, when nonlinear frequency is approximated with linear part Ωjð Þ Q; Θ ≈ Ωj, j ¼ 1, 2. Here we consider that Q ¼ Q<sup>1</sup> and Θ ¼ Q2. After the first pulse with duration, Ω0τ<sup>L</sup> ≪ 1, the amplitude has the following dependence on the intensity, E<sup>2</sup> <sup>0</sup>, pulse duration, τL, and local oscillation frequency of the normal mode j, Ω<sup>j</sup>

$$Q\_{0j} = \frac{\sqrt{\pi}\tau\iota E\_0^2 \alpha\_j'}{2\Omega\_j} \exp\left[-\left(\Omega\_j\tau\_L\right)^2/4\right].$$

Ω2

Ω2

or

components is introduced:

<sup>p</sup> ð Þ z; t , E<sup>þ</sup>

† , ^s † , and ^a †

<sup>p</sup> ð Þ z; t E�

<sup>s</sup> ð Þ z; t , and E<sup>þ</sup>

¼ G kp; ka ^b^a†

<sup>a</sup> ð Þþ z; t E<sup>þ</sup>

<sup>s</sup> ð Þ z; t E�

exp iΩ0t � i ka � kp

<sup>p</sup> ð Þ z; t

<sup>z</sup> <sup>þ</sup> G ks; kp

strength components of Raman process, expressed by the generation of photon operators in

annihilation operators is introduced in expression (5). The frequency Ω<sup>0</sup> ¼ ω<sup>p</sup> � ω<sup>s</sup> ¼ ω<sup>a</sup> � ω<sup>p</sup> is approximately equal to local vibration mode of the biomolecule Ω. Accordingly, the interaction Hamiltonian with the local nonlinear mode of viruses or bacteria may be described by:

Figure 5. Comparison of 5-protofilament bacterial microtubule architectures. (A) α and β tubulins are represented in blue and red, respectively. (B) Representation of a 13-protofilament eukaryotic microtubule: α—tubulin in red; and β—tubulin in blue. Seams and start-helices are indicated in green and red, respectively. (C) The biomolecular structure of α and β

Π�ð Þ¼ t; z E<sup>þ</sup>

Here, E<sup>þ</sup>

each mode ^b

tubulins is indicated.

<sup>q</sup> � <sup>4</sup>χ<sup>q</sup> <sup>Q</sup><sup>2</sup>

<sup>θ</sup> � <sup>4</sup>χ<sup>q</sup> <sup>Θ</sup><sup>2</sup>

n � <sup>2</sup>χ<sup>q</sup><sup>θ</sup> <sup>Θ</sup><sup>2</sup>

n � <sup>2</sup>χθ<sup>q</sup> <sup>Q</sup><sup>2</sup>

In fact, this effect may be observed in a single pulse excitation of nonlinear system of Eq. (2). The above-described excitation method depends on the condition imputed for applied pulse duration relative to the vibration frequency of biomolecules Ωτ<sup>L</sup> < 1. The local molecular oscillator is described by nonlinear equations; therefore the local frequency depends on the excited energy of such biomolecule. To surpass this difficulty, it is better to consider a longer laser pulse ΩΓ�<sup>1</sup> > Ωτ<sup>L</sup> > 1, so that during the excitation to apply for selective excitations of virus and bacteria (see Figure 5). This excitation method is alike to the diagnostics of molecular systems suggested in Refs. [14–16]. The method attracted many specialists in CARS diagnostics and studies of molecular and cellular subsystem design. According to this theory, the strength product [5] of two possible fields through the Stokes and anti-Stokes generation

n <sup>¼</sup> <sup>0</sup>;

Efficient Microbial Decontamination of Translucent Liquids and Gases Using Optical Metamaterials

n <sup>¼</sup> <sup>0</sup>:

^s^b†

<sup>a</sup> ð Þ z; t are the positively defined pump, Stokes, and anti-Stokes

, respectively. The related negative field component expressed by the

exp iΩ0t � i kp � ks z ,

http://dx.doi.org/10.5772/intechopen.80639

(5)

179

For simplicity, let us add the next square terms in the system of Eq. (2). As in Refs. [13, 29], we address the problem so as to excite the system of coupling oscillators (2). Consequently, the "nonlinear frequency" ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ω2 <sup>q</sup> � <sup>4</sup>χ<sup>q</sup> <sup>Q</sup><sup>2</sup> � � � <sup>2</sup>χ<sup>q</sup><sup>θ</sup> <sup>Θ</sup><sup>2</sup> <sup>q</sup> � � reached zero value, which equals to the termination of the local vibration mode after a finite number of short laser pulses. Let us consider a set of "n" consequent pulses generated in the time interval T < Γ�<sup>1</sup> <sup>j</sup> . The cumulative energy of the local oscillator after the precursor pulse may be used for the next excitations. For example, after the first pulse, Q and Θ amplitudes of models are described by the expression above. Introducing this expression in the system of Eq. (2), we obtain the following mean values of Q<sup>2</sup> and Θ<sup>2</sup> ,

$$
\left\langle \mathbf{Q}\_{\circ}^{2} \right\rangle = \frac{\pi \tau\_{L}^{2} E\_{0}^{4} \alpha\_{\circ}'^{2}}{2 2^{2} \Omega\_{\circ}^{2}} \exp\left[ - \left( \Omega\_{\circ} \tau\_{L} \right)^{2} / 2 \right].
$$

In other words, we obtain the new frequencies of nonlinear oscillator modes of the system of Eq. (2) described by linearized differential equations with renormalized frequencies by the first pulse

$$\begin{aligned} \frac{d^2}{dt^2}O(t) + \left\{\Omega\_q^2 - 4\chi\_q \langle \mathcal{Q}^2 \rangle - 2\chi\_{q\theta} \langle \Theta^2 \rangle \right\} Q + 2\Gamma\_q \frac{d}{dt}O(t) &= F\_q(t);\\ \frac{d^2}{dt^2}\Theta(t) + \left\{\Omega\_\theta^2 - 4\chi\_? \langle \Theta^2 \rangle - 2\chi\_{\theta q} \langle \mathcal{Q}^2 \rangle \right\} \Theta + 2\Gamma\_\theta \frac{d}{dt}\Theta(t) &= F\_\theta(t). \end{aligned} \tag{4}$$

The solutions of these equations are similar to expression (2) in which, instead of Q0j, it is used by the new expression;

$$Q(t\_2) = Q\_{01} \exp\left[-\Gamma\_q t\_2\right] \sin\left(\tilde{\Omega}\_q t\_2\right) + Q\_{02} \exp\left[-\Gamma\_q t\_2\right] \sin\left(\tilde{\Omega}\_q t\_2\right)$$

Here, the second part contains the particular solution of the excitation of oscillator after the second pulse

$$Q\_{02} = \frac{\sqrt{\pi}\tau\_L E\_0^2 \alpha\_q'}{2\tilde{\Omega}\_q} \exp\left[-\left(\tilde{\Omega}\_q \tau\_L\right)^2 / 4\right].$$

where <sup>Ω</sup><sup>~</sup> <sup>q</sup> <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ω2 <sup>q</sup> � <sup>4</sup>χ<sup>q</sup> <sup>Q</sup><sup>2</sup> � � � <sup>2</sup>χ<sup>q</sup><sup>θ</sup> <sup>Θ</sup><sup>2</sup> <sup>q</sup> � �. This procedure to excite a nonlinear oscillator may continue till one of the amplitudes of oscillation attains the maximal separation line of nonlinear potential function U0ð Þ Q; Θ , as represented in Figure 5. It corresponds to the case when the frequency achieves the zero value after "n" short pulses

$$
\Delta\_q^2 - 4\chi\_q \langle Q\_n^2 \rangle - 2\chi\_{q\theta} \langle \Theta\_n^2 \rangle = 0;
$$

or

Q0<sup>j</sup> ¼

Q2 j D E

Ω2

"nonlinear frequency"

178 Advanced Surface Engineering Research

values of Q<sup>2</sup> and Θ<sup>2</sup>

pulse

,

d2

d2

Ω2

by the new expression;

second pulse

where <sup>Ω</sup><sup>~</sup> <sup>q</sup> <sup>¼</sup>

dt<sup>2</sup> O tðÞþ <sup>Ω</sup><sup>2</sup>

dt<sup>2</sup> <sup>Θ</sup>ð Þþ <sup>t</sup> <sup>Ω</sup><sup>2</sup>

Q tð Þ¼ <sup>2</sup> Q01exp �Γqt<sup>2</sup>

Q<sup>02</sup> ¼

when the frequency achieves the zero value after "n" short pulses

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffi <sup>π</sup> <sup>p</sup> <sup>τ</sup>LE<sup>2</sup> 0α0 q

<sup>2</sup>Ω<sup>~</sup> <sup>q</sup>

ffiffiffi <sup>π</sup> <sup>p</sup> <sup>τ</sup>LE<sup>2</sup> 0α0 j

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

consider a set of "n" consequent pulses generated in the time interval T < Γ�<sup>1</sup>

<sup>¼</sup> πτ<sup>2</sup> LE4 0α<sup>0</sup> <sup>2</sup> j

222 Ω2 j

2Ω<sup>j</sup>

exp � Ωjτ<sup>L</sup> � �<sup>2</sup>

For simplicity, let us add the next square terms in the system of Eq. (2). As in Refs. [13, 29], we address the problem so as to excite the system of coupling oscillators (2). Consequently, the

termination of the local vibration mode after a finite number of short laser pulses. Let us

energy of the local oscillator after the precursor pulse may be used for the next excitations. For example, after the first pulse, Q and Θ amplitudes of models are described by the expression above. Introducing this expression in the system of Eq. (2), we obtain the following mean

In other words, we obtain the new frequencies of nonlinear oscillator modes of the system of Eq. (2) described by linearized differential equations with renormalized frequencies by the first

<sup>q</sup> � <sup>4</sup>χ<sup>q</sup> <sup>Q</sup><sup>2</sup> � � � <sup>2</sup>χ<sup>q</sup><sup>θ</sup> <sup>Θ</sup><sup>2</sup> n o � � <sup>Q</sup> <sup>þ</sup> <sup>2</sup>Γ<sup>q</sup>

<sup>θ</sup> � <sup>4</sup>χ? <sup>Θ</sup><sup>2</sup> � � � <sup>2</sup>χθ<sup>q</sup> <sup>Q</sup><sup>2</sup> n o � � <sup>Θ</sup> <sup>þ</sup> <sup>2</sup>Γ<sup>θ</sup>

The solutions of these equations are similar to expression (2) in which, instead of Q0j, it is used

Here, the second part contains the particular solution of the excitation of oscillator after the

continue till one of the amplitudes of oscillation attains the maximal separation line of nonlinear potential function U0ð Þ Q; Θ , as represented in Figure 5. It corresponds to the case

� � sin <sup>Ω</sup><sup>~</sup> <sup>q</sup>t2Þ þ <sup>Q</sup>02exp �Γqt<sup>2</sup>

exp � <sup>Ω</sup><sup>~</sup> <sup>q</sup>τL<sup>Þ</sup>

<sup>q</sup> � <sup>4</sup>χ<sup>q</sup> <sup>Q</sup><sup>2</sup> � � � <sup>2</sup>χ<sup>q</sup><sup>θ</sup> <sup>Θ</sup><sup>2</sup> <sup>q</sup> � �. This procedure to excite a nonlinear oscillator may

h

� �

2 =4 � i

,

exp � Ωjτ<sup>L</sup> � �<sup>2</sup>

=4

:

<sup>j</sup> . The cumulative

(4)

h i

<sup>q</sup> � <sup>4</sup>χ<sup>q</sup> <sup>Q</sup><sup>2</sup> � � � <sup>2</sup>χ<sup>q</sup><sup>θ</sup> <sup>Θ</sup><sup>2</sup> <sup>q</sup> � � reached zero value, which equals to the

=2

:

d

d

dt O tðÞ¼ Fqð Þ<sup>t</sup> ;

dt <sup>Θ</sup>ðÞ¼ <sup>t</sup> <sup>F</sup>θð Þ<sup>t</sup> :

� � sin <sup>Ω</sup><sup>~</sup> <sup>q</sup>t2<sup>Þ</sup>

h i

$$
\Delta\_{\theta}^{2} - 4\chi\_{q} \langle \Theta\_{n}^{2} \rangle - 2\chi\_{\theta q} \langle Q\_{n}^{2} \rangle = 0.
$$

In fact, this effect may be observed in a single pulse excitation of nonlinear system of Eq. (2).

The above-described excitation method depends on the condition imputed for applied pulse duration relative to the vibration frequency of biomolecules Ωτ<sup>L</sup> < 1. The local molecular oscillator is described by nonlinear equations; therefore the local frequency depends on the excited energy of such biomolecule. To surpass this difficulty, it is better to consider a longer laser pulse ΩΓ�<sup>1</sup> > Ωτ<sup>L</sup> > 1, so that during the excitation to apply for selective excitations of virus and bacteria (see Figure 5). This excitation method is alike to the diagnostics of molecular systems suggested in Refs. [14–16]. The method attracted many specialists in CARS diagnostics and studies of molecular and cellular subsystem design. According to this theory, the strength product [5] of two possible fields through the Stokes and anti-Stokes generation components is introduced:

$$\begin{split} \Pi^-(t, \mathbf{z}) &= \mathbf{E}\_p^+(\mathbf{z}, t)\mathbf{E}\_a^-(\mathbf{z}, t) + \mathbf{E}\_s^+(\mathbf{z}, t)\mathbf{E}\_p^-(\mathbf{z}, t) \\ &= \mathbf{G}(k\_p, k\_t)\hat{b}\hat{a}^\dagger \exp\left[i\Omega\_0 t - i(k\_d - k\_p)\mathbf{z}\right] + \mathbf{G}(k\_s, k\_p)\hat{s}\hat{b}^\dagger \exp\left[i\Omega\_0 t - i(k\_p - k\_s)\mathbf{z}\right], \end{split} \tag{5}$$

Here, E<sup>þ</sup> <sup>p</sup> ð Þ z; t , E<sup>þ</sup> <sup>s</sup> ð Þ z; t , and E<sup>þ</sup> <sup>a</sup> ð Þ z; t are the positively defined pump, Stokes, and anti-Stokes strength components of Raman process, expressed by the generation of photon operators in each mode ^b † , ^s † , and ^a † , respectively. The related negative field component expressed by the annihilation operators is introduced in expression (5). The frequency Ω<sup>0</sup> ¼ ω<sup>p</sup> � ω<sup>s</sup> ¼ ω<sup>a</sup> � ω<sup>p</sup> is approximately equal to local vibration mode of the biomolecule Ω. Accordingly, the interaction Hamiltonian with the local nonlinear mode of viruses or bacteria may be described by:

Figure 5. Comparison of 5-protofilament bacterial microtubule architectures. (A) α and β tubulins are represented in blue and red, respectively. (B) Representation of a 13-protofilament eukaryotic microtubule: α—tubulin in red; and β—tubulin in blue. Seams and start-helices are indicated in green and red, respectively. (C) The biomolecular structure of α and β tubulins is indicated.

$$
\hat{H}\_I = -\hat{\Phi}^+(t, z)\hat{\Pi}^-(t, z) + H.c.\tag{6}
$$

∂ ∂t

Here Ω<sup>R</sup> ≃g ffiffiffiffiffiffiffiffiffiffiffiffi

resonance Δ:

v ¼ ΩR=γ.

and <sup>y</sup> <sup>¼</sup> ffiffiffiffiffiffiffiffiffi

permission from [6].

The normalized constant is

W t ^ ðÞ¼�<sup>i</sup> <sup>Δ</sup>D^ <sup>z</sup>; W t ^ ð Þ h i <sup>þ</sup> <sup>i</sup><sup>κ</sup> <sup>D</sup>^ <sup>þ</sup>

2nanp

<sup>n</sup> <sup>¼</sup> <sup>N</sup>

<sup>2</sup> �<sup>X</sup> N

<sup>A</sup> <sup>¼</sup> <sup>X</sup> N

n¼0

n¼0 n D^ �

; W t ^ ð Þ h i <sup>þ</sup> <sup>i</sup>Ω<sup>R</sup> <sup>D</sup>^ <sup>þ</sup>

Γð Þ N þ n Γð Þ 2n Γð Þ 2j � n

Γ 1 þ i <sup>~</sup><sup>δ</sup> <sup>þ</sup> <sup>n</sup><sup>Þ</sup> � �

� � � � �

(

<sup>~</sup>v2<sup>n</sup> <sup>Γ</sup> <sup>1</sup> <sup>þ</sup> <sup>i</sup>~<sup>δ</sup> � � � � �

the coherent scattering rate of the applied anti-Stokes field component, while na and np are the numbers of photons in the anti-Stokes and pump modes. When detuning Δ is positive, the excitation of nonlinear oscillator is compensated by the nonharmonic term in the master Eq. (9), which is proportional to the nonlinear parameter, κ. This excitation is complemented by the improving of resonance between the excited vibration levels of molecular oscillator. It may be defined as a jump of the number of excitations with increasing of the external field intensity. Using the solution of the equation, the number of excitations of the nonlinear oscillator can be given as a function of intensity of applied field ΩR, nonlinear parameter κ, and detuning from

W t ^ ð Þ h i <sup>þ</sup> <sup>D</sup>^ �

<sup>p</sup> and <sup>γ</sup> <sup>≈</sup> <sup>2</sup>g<sup>2</sup>naε<sup>=</sup> <sup>Δ</sup><sup>2</sup> <sup>þ</sup> <sup>ε</sup><sup>2</sup> � � are the two-photon Rabbi frequency and

Efficient Microbial Decontamination of Translucent Liquids and Gases Using Optical Metamaterials

Γ 1 þ i <sup>~</sup><sup>δ</sup> <sup>þ</sup> <sup>n</sup> � � � � �

� 2 )

� 2

Here, <sup>~</sup><sup>δ</sup> <sup>¼</sup> <sup>δ</sup>ð Þ <sup>1</sup> <sup>þ</sup> <sup>i</sup><sup>χ</sup> <sup>=</sup> <sup>1</sup> <sup>þ</sup> <sup>χ</sup><sup>2</sup> � �; <sup>~</sup><sup>v</sup> <sup>¼</sup> <sup>v</sup>=ð Þ <sup>1</sup> <sup>þ</sup> <sup>i</sup><sup>χ</sup> , where the new parameters represent the relative values of the detuning δ ¼ Δ=γ; nonlinear parameter χ ¼ κ=γ, and the intensity of the field

Figure 6. The dependence of the potential energy of the nonlinear oscillator on two normalized modes <sup>x</sup> <sup>¼</sup> ffiffiffiffiffiffiffiffiffi

M=2 p ΩΘ, energy scheme for such nonlinear potential with possible Raman excitation. Reproduced with

<sup>~</sup>v<sup>2</sup><sup>n</sup> <sup>Γ</sup> <sup>1</sup> <sup>þ</sup> <sup>i</sup>~<sup>δ</sup> � � � � �

( ) <sup>1</sup>

Γð Þ N þ n <sup>Γ</sup>ð Þ <sup>2</sup><sup>n</sup> <sup>Γ</sup>ð Þ <sup>2</sup><sup>j</sup> � <sup>n</sup> :

� 2

� 2

W t ^ ð Þ, <sup>D</sup>^ <sup>þ</sup> h i <sup>þ</sup> <sup>H</sup>:c:

http://dx.doi.org/10.5772/intechopen.80639

<sup>2</sup><sup>A</sup> : (10)

(11)

181

M=2 p ΩQ

n o, (9)

The operator Φ^ <sup>þ</sup> ð Þ t; z is proportional to the displacement of local oscillator mode from the equilibrium position, P t ^ð Þ� ; <sup>z</sup> Q t ^ ð Þ� ; <sup>z</sup> <sup>∣</sup><sup>e</sup> >< <sup>g</sup><sup>∣</sup> <sup>þ</sup> <sup>∣</sup><sup>g</sup> >< <sup>e</sup>∣. The two-mode Raman transitions from the first excited to the ground states of the local oscillator are given in Figure 6.

Bistable excitation process of nonlinear oscillator in external biharmonic field was in the center of attention in many papers (see, e.g. [34, 37]). Following the ideas of Ref. [37], we simplify the local vibration system (2) to single vibration mode Q described by the nonlinear Hamiltonian:

$$
\hat{H}\_0 = \hbar \Omega \hat{q}^\dagger \hat{q} - \hbar \kappa \left(\hat{q}^\dagger\right)^2 (\hat{q})^2 \tag{7}
$$

Introducing the new excitations, <sup>D</sup>^ <sup>þ</sup> <sup>¼</sup> <sup>q</sup> ^† ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ω0=κ � q ^† q q ^, and de-excitation, <sup>D</sup>^ � <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ω0=κ � q ^† q q ^q ^ operators in the vibration mode of the nonlinear Hamiltonian (6) [38], we observe that their commutation relation D^ <sup>þ</sup> ; <sup>D</sup>^ � h i <sup>¼</sup> <sup>2</sup>D^ <sup>z</sup>. For biomolecules with a positive nonharmonic parameter <sup>κ</sup> <sup>&</sup>gt; 0, we observe that the inversion <sup>D</sup>^ <sup>z</sup> ¼ �Ω0=ð Þþ <sup>2</sup><sup>κ</sup> <sup>q</sup> ^† q ^, together with two x and y polarization components, <sup>D</sup>^ <sup>x</sup> <sup>¼</sup> <sup>D</sup>^ <sup>þ</sup> <sup>þ</sup> <sup>D</sup>^ � � �=2 and <sup>D</sup>^ <sup>x</sup> <sup>¼</sup> <sup>D</sup>^ <sup>þ</sup> � <sup>D</sup>^ � � �=2i, forms the square pseudovector <sup>D</sup>^ <sup>2</sup> <sup>¼</sup> <sup>D</sup>^ <sup>z</sup> 2 <sup>þ</sup> <sup>D</sup>^ <sup>2</sup> <sup>x</sup> <sup>þ</sup> <sup>D</sup>^ <sup>2</sup> <sup>y</sup>, which is conserved during the excitations. These operators are similar to angular momentum generators in quantum mechanics and belong to SUð Þ2 algebra. Similar operators can be introduced for bimodal field in Raman scattering (7), <sup>L</sup>^<sup>z</sup> <sup>¼</sup> ^<sup>a</sup> † ^a � ^s † ^s; <sup>L</sup>^� <sup>¼</sup> ffiffiffi 2 <sup>p</sup> ^b^s† <sup>þ</sup> ^a^b† � �; <sup>L</sup>^<sup>þ</sup> <sup>¼</sup> ffiffiffi 2 <sup>p</sup> ^s^b† <sup>þ</sup> ^b^a† � �. Here, in rotating wave approximation, we obtain the following symmetrical form of the Hamiltonian:

$$
\hat{H} = \hbar \Delta \hat{D}\_z - \hbar \kappa \hat{\mathbf{D}}^+ \hat{\mathbf{D}}^- - \hbar \mathbf{g} \left\{ \hat{L}^- \hat{\mathbf{D}}^+ + \hat{\mathbf{D}}^- \hat{L}^+ \right\}, \tag{8}
$$

which describes the interaction of three discrete modes of microcavity (or nanofiber) with nonlinear vibration of biomolecule with conservation of total number of photons and two pseudovectors, <sup>D</sup><sup>2</sup> and <sup>L</sup><sup>2</sup> <sup>¼</sup> <sup>L</sup>^<sup>z</sup> 2 <sup>þ</sup> <sup>L</sup>^<sup>y</sup> 2 <sup>þ</sup> <sup>L</sup>^<sup>x</sup> 2 . In the Hamiltonian (8), we have Δ ¼ Ω � Ω0, which is the detuning from resonance to the frequency of bimodal vector of Raman field, Ω0, and the frequency of local oscillator, Ω. κ is the nonharmonic parameter, which drastically reduces the distance between the level of harmonic vibrations of the molecular system. The coupling constant ℏg describes the biharmonic coupling between the vibrational mode of biomolecules and Stokes, pump, and anti-Stokes modes of the electromagnetic field. Let us study the case when Ωτ<sup>L</sup> > 1 and the damping rate of excited oscillator is lesser than life time of Stokes, anti-Stokes, and pump photons in nanofibers. Here, the operators of electromagnetic field in the density matrix of the system might be adiabatically eliminated. If we consider that the photons are organized in the anti-Stokes mode, we obtain a master equation, which characterizes the dynamic behavior of biomolecule nonlinear oscillators:

Efficient Microbial Decontamination of Translucent Liquids and Gases Using Optical Metamaterials http://dx.doi.org/10.5772/intechopen.80639 181

$$i\frac{\partial}{\partial t}\hat{W}(t) = -i\left[\Delta\hat{D}\_z,\hat{W}(t)\right] + i\kappa \left[\hat{D}^+\hat{D}^-,\hat{W}(t)\right] + \left\{i\Omega\_\mathbb{R}\left[\hat{D}^+\hat{W}(t)\right] + \left[\hat{D}^-\hat{W}(t),\hat{D}^+\right] + H.c.\right\},\tag{9}$$

Here Ω<sup>R</sup> ≃g ffiffiffiffiffiffiffiffiffiffiffiffi 2nanp <sup>p</sup> and <sup>γ</sup> <sup>≈</sup> <sup>2</sup>g<sup>2</sup>naε<sup>=</sup> <sup>Δ</sup><sup>2</sup> <sup>þ</sup> <sup>ε</sup><sup>2</sup> � � are the two-photon Rabbi frequency and the coherent scattering rate of the applied anti-Stokes field component, while na and np are the numbers of photons in the anti-Stokes and pump modes. When detuning Δ is positive, the excitation of nonlinear oscillator is compensated by the nonharmonic term in the master Eq. (9), which is proportional to the nonlinear parameter, κ. This excitation is complemented by the improving of resonance between the excited vibration levels of molecular oscillator. It may be defined as a jump of the number of excitations with increasing of the external field intensity. Using the solution of the equation, the number of excitations of the nonlinear oscillator can be given as a function of intensity of applied field ΩR, nonlinear parameter κ, and detuning from resonance Δ:

$$n = \frac{N}{2} - \sum\_{n=0}^{N} n \frac{\Gamma(N+n)}{\Gamma(2n)\Gamma(2j-n)} \left\{ \frac{\left| \Gamma \{ 1 + i\tilde{\delta} + n \} \right|^2}{\tilde{v}^{2n} \left| \Gamma \{ 1 + i\tilde{\delta} \} \right|^2} \right\} \frac{1}{2A}. \tag{10}$$

The normalized constant is

<sup>H</sup>^ <sup>I</sup> ¼ �Φ^ <sup>þ</sup>

^ð Þ� ; <sup>z</sup> Q t

The operator Φ^ <sup>þ</sup>

equilibrium position, P t

180 Advanced Surface Engineering Research

commutation relation D^ <sup>þ</sup>

pseudovector <sup>D</sup>^ <sup>2</sup> <sup>¼</sup> <sup>D</sup>^ <sup>z</sup>

<sup>L</sup>^<sup>z</sup> <sup>¼</sup> ^<sup>a</sup> † ^a � ^s †

Introducing the new excitations, <sup>D</sup>^ <sup>þ</sup> <sup>¼</sup> <sup>q</sup>

polarization components, <sup>D</sup>^ <sup>x</sup> <sup>¼</sup> <sup>D</sup>^ <sup>þ</sup>

^s; <sup>L</sup>^� <sup>¼</sup> ffiffiffi

pseudovectors, <sup>D</sup><sup>2</sup> and <sup>L</sup><sup>2</sup> <sup>¼</sup> <sup>L</sup>^<sup>z</sup>

2 <sup>þ</sup> <sup>D</sup>^ <sup>2</sup>

2

; <sup>D</sup>^ � h i

ter <sup>κ</sup> <sup>&</sup>gt; 0, we observe that the inversion <sup>D</sup>^ <sup>z</sup> ¼ �Ω0=ð Þþ <sup>2</sup><sup>κ</sup> <sup>q</sup>

<sup>x</sup> <sup>þ</sup> <sup>D</sup>^ <sup>2</sup>

tion, we obtain the following symmetrical form of the Hamiltonian:

<sup>H</sup>^ <sup>¼</sup> <sup>ℏ</sup>ΔD^ <sup>z</sup> � <sup>ℏ</sup>κD^ <sup>þ</sup>

2 <sup>þ</sup> <sup>L</sup>^<sup>y</sup> 2 <sup>þ</sup> <sup>L</sup>^<sup>x</sup> 2

characterizes the dynamic behavior of biomolecule nonlinear oscillators:

<sup>p</sup> ^b^s† <sup>þ</sup> ^a^b† � �

ð Þ <sup>t</sup>; <sup>z</sup> <sup>Π</sup>^ �

Bistable excitation process of nonlinear oscillator in external biharmonic field was in the center of attention in many papers (see, e.g. [34, 37]). Following the ideas of Ref. [37], we simplify the local vibration system (2) to single vibration mode Q described by the nonlinear Hamiltonian:

> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ω0=κ � q ^†

operators in the vibration mode of the nonlinear Hamiltonian (6) [38], we observe that their

are similar to angular momentum generators in quantum mechanics and belong to SUð Þ2 algebra. Similar operators can be introduced for bimodal field in Raman scattering (7),

<sup>D</sup>^ � � <sup>ℏ</sup><sup>g</sup> <sup>L</sup>^�

which describes the interaction of three discrete modes of microcavity (or nanofiber) with nonlinear vibration of biomolecule with conservation of total number of photons and two

which is the detuning from resonance to the frequency of bimodal vector of Raman field, Ω0, and the frequency of local oscillator, Ω. κ is the nonharmonic parameter, which drastically reduces the distance between the level of harmonic vibrations of the molecular system. The coupling constant ℏg describes the biharmonic coupling between the vibrational mode of biomolecules and Stokes, pump, and anti-Stokes modes of the electromagnetic field. Let us study the case when Ωτ<sup>L</sup> > 1 and the damping rate of excited oscillator is lesser than life time of Stokes, anti-Stokes, and pump photons in nanofibers. Here, the operators of electromagnetic field in the density matrix of the system might be adiabatically eliminated. If we consider that the photons are organized in the anti-Stokes mode, we obtain a master equation, which

q

from the first excited to the ground states of the local oscillator are given in Figure 6.

^† q ^ � ℏκ q ^† � �<sup>2</sup> ð Þ q

<sup>H</sup>^ <sup>0</sup> <sup>¼</sup> <sup>ℏ</sup>Ω<sup>q</sup>

^†

<sup>þ</sup> <sup>D</sup>^ � � �

; <sup>L</sup>^<sup>þ</sup> <sup>¼</sup> ffiffiffi 2 <sup>p</sup> ^s^b† <sup>þ</sup> ^b^a† � �

q

ð Þ t; z is proportional to the displacement of local oscillator mode from the

^ ð Þ� ; <sup>z</sup> <sup>∣</sup><sup>e</sup> >< <sup>g</sup><sup>∣</sup> <sup>þ</sup> <sup>∣</sup><sup>g</sup> >< <sup>e</sup>∣. The two-mode Raman transitions

^, and de-excitation, <sup>D</sup>^ � <sup>¼</sup>

<sup>¼</sup> <sup>2</sup>D^ <sup>z</sup>. For biomolecules with a positive nonharmonic parame-

<sup>y</sup>, which is conserved during the excitations. These operators

^† q

<sup>=</sup>2 and <sup>D</sup>^ <sup>x</sup> <sup>¼</sup> <sup>D</sup>^ <sup>þ</sup> � <sup>D</sup>^ � � �

D^ <sup>þ</sup>

<sup>þ</sup> <sup>D</sup>^ � <sup>L</sup>^<sup>þ</sup> n o

. In the Hamiltonian (8), we have Δ ¼ Ω � Ω0,

ð Þþ t; z H:c:, (6)

^ <sup>2</sup> (7)

q

^, together with two x and y

. Here, in rotating wave approxima-

=2i, forms the square

, (8)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ω0=κ � q ^†

q ^q ^

$$A = \sum\_{n=0}^{N} \left\{ \left| \frac{\Gamma \{ 1 + i\tilde{\delta} + n \} }{\tilde{\nu} 2n \left| \Gamma \{ 1 + i\tilde{\delta} \} \right|^{2}} \right\} \frac{\Gamma(N + n)}{\Gamma(2n)\Gamma(2j - n)}. \tag{11}$$

Here, <sup>~</sup><sup>δ</sup> <sup>¼</sup> <sup>δ</sup>ð Þ <sup>1</sup> <sup>þ</sup> <sup>i</sup><sup>χ</sup> <sup>=</sup> <sup>1</sup> <sup>þ</sup> <sup>χ</sup><sup>2</sup> � �; <sup>~</sup><sup>v</sup> <sup>¼</sup> <sup>v</sup>=ð Þ <sup>1</sup> <sup>þ</sup> <sup>i</sup><sup>χ</sup> , where the new parameters represent the relative values of the detuning δ ¼ Δ=γ; nonlinear parameter χ ¼ κ=γ, and the intensity of the field v ¼ ΩR=γ.

Figure 6. The dependence of the potential energy of the nonlinear oscillator on two normalized modes <sup>x</sup> <sup>¼</sup> ffiffiffiffiffiffiffiffiffi M=2 p ΩQ and <sup>y</sup> <sup>¼</sup> ffiffiffiffiffiffiffiffiffi M=2 p ΩΘ, energy scheme for such nonlinear potential with possible Raman excitation. Reproduced with permission from [6].

circle multiplied by the attenuation depth of the radiation inside the contaminated liquid (see Figure 8). Conversely, if the light penetrates the liquid through the base of a quartz semisphere,

Efficient Microbial Decontamination of Translucent Liquids and Gases Using Optical Metamaterials

increases, becoming equal to the surface of semisphere multiplied by attenuation depth. If the light is introduced inside the cone through its base, a considerable increase of the contact surface metamaterial (liquid) occurs. Here, the multiple refractions of UV-C radiation inside the cone improve the contact surface between the quartz cone and the translucent liquid. It increases significantly when the cone generator is larger than the cone radius. The multiple optical contacts between metamaterial elements (spheres, granules, conic elements, fibers) lead to a drastically

Let us analyze the liquid decontamination by traditional method, which makes use of UV-C pulsed light (see Figure 9(a)). If the contaminated liquid flows inside a cylinder and it is irradiated from all directions with UV radiation, the total decontamination surface is S ¼ 2πR Lð Þ þ R . The first term designates the lateral surface, the last term the surface of the bases, R the radius of the base, while L is the length of the cylinder. Using classical decontamination, a

Vcl ¼ π2πR Lð Þ þ R dp;

where Vcl represents the efficient decontamination volume and dp � λ is the UV radiation penetration depth into liquid. Further down, we suggest a decontamination method making

Sensing properties are anticipated to be related to nanoscale system dimensions. In a first step, the contact surface of flowing gas or liquid is estimated. To increase the contact surface of the contaminated liquid, we examined the UV radiation propagation in two types of metamaterials: type A corresponds to the packing of photonic crystal fibers (PCFs) and type B to the photonic

Figure 8. The multiple reflection and refractions of the UV light passing through the bases of semispherical (a) and conical (b) elements of metamaterial. Figure A represents the decontamination core filled up with conical structures. The radiation of six UV lamps is guided inside the center of decontamination tube through the bases of such conical structures

crystals (PCs) (see Figure 9(b and c)). Both metamaterials are transparent in UV region.

L � Vcl ≫ Vcl,

dispersed light inside the contaminated fluid that flows between these elements.

Vcon <sup>¼</sup> <sup>π</sup>R<sup>2</sup>

use of metamaterials in order to increase the decontamination volume.

. The decontamination volume also

http://dx.doi.org/10.5772/intechopen.80639

183

the contact surface increases two times, becoming 2πR2

large volume, Vcon, of infected liquid remains contaminated:

where the nontransparent contaminated liquid has the maximal flow velocity.

Figure 7. The dependence of number of excitation n as function of (a) coherent excitation, ν, and nonlinearity, χ, for constant detuning, δ ¼ 2, and (b) coherent excitation, ν, and detuning, δ, for the constant nonlinearity, χ ¼ 2. Here, the total number of excitation is N = 10. Reproduced with permission from [6].

The number of excitations for a nonlinear oscillator is defined by the ratio N ¼ Ω=κ. Following the solutions (10) presented in literature in various publications (see, e.g. Ref. [37]), we displayed in Figure 7 the mean number of excitations as a function of the intensity and nonlinearity of applied field or as a function of excited field and detuning. This phase transition is typically described by a bistable behavior of the nonlinear oscillator. Taking into account other nonlinear terms (e.g., Q<sup>6</sup> ) in the Hamiltonian (1), we may terminate the nonharmonic oscillator moved to other metastable position.

#### 3. Decontamination volume estimated for different metamaterials

Latest investigations consider the geometry of metamaterial elements for different applications [38–43]. Conical metallic nanoparticles in an array configuration could be used for localization of SPR [38]. The geometry of nanoparticles and their arrangement improve the biochemical sensing and detection for drug delivery, heating therapy, etc. Ref. [40] describes a similar localized SPR. An electromagnetic sensor made of nonspherical gold nanoparticles deposited on a silica substrate having a matrix configuration with the interparticle distance much smaller than the incident wavelength is proposed. Other applications of the different geometry of elements of metamaterials are related with optical proprieties of each element. Explicitly, the cylindrical elements of metamaterials could be used as a performing resonator in the optical cloaking [41]. The authors of Ref. [42] mentioned that macroscopic characteristics depend not only on molecular structure but also on specific geometry. Advances and potential applications of optical electromagnetic metamaterials and metasurfaces for refractive index sensing and sensing light properties are presented in Ref. [43]. These metamaterials can be simply integrated with several electronic devices.

Here, we give a clear explanation for the increasing of the penetration depth of UV-C radiation inside the decontamination core. It is due to multiple refractions and reflections of radiation on the spherical and conical structures of metamaterials. If the light enters into the translucent liquid through a circular surface, the decontamination volume may be proportional to the surface of the circle multiplied by the attenuation depth of the radiation inside the contaminated liquid (see Figure 8). Conversely, if the light penetrates the liquid through the base of a quartz semisphere, the contact surface increases two times, becoming 2πR2 . The decontamination volume also increases, becoming equal to the surface of semisphere multiplied by attenuation depth. If the light is introduced inside the cone through its base, a considerable increase of the contact surface metamaterial (liquid) occurs. Here, the multiple refractions of UV-C radiation inside the cone improve the contact surface between the quartz cone and the translucent liquid. It increases significantly when the cone generator is larger than the cone radius. The multiple optical contacts between metamaterial elements (spheres, granules, conic elements, fibers) lead to a drastically dispersed light inside the contaminated fluid that flows between these elements.

Let us analyze the liquid decontamination by traditional method, which makes use of UV-C pulsed light (see Figure 9(a)). If the contaminated liquid flows inside a cylinder and it is irradiated from all directions with UV radiation, the total decontamination surface is S ¼ 2πR Lð Þ þ R . The first term designates the lateral surface, the last term the surface of the bases, R the radius of the base, while L is the length of the cylinder. Using classical decontamination, a large volume, Vcon, of infected liquid remains contaminated:

The number of excitations for a nonlinear oscillator is defined by the ratio N ¼ Ω=κ. Following the solutions (10) presented in literature in various publications (see, e.g. Ref. [37]), we displayed in Figure 7 the mean number of excitations as a function of the intensity and nonlinearity of applied field or as a function of excited field and detuning. This phase transition is typically described by a bistable behavior of the nonlinear oscillator. Taking into account

Figure 7. The dependence of number of excitation n as function of (a) coherent excitation, ν, and nonlinearity, χ, for constant detuning, δ ¼ 2, and (b) coherent excitation, ν, and detuning, δ, for the constant nonlinearity, χ ¼ 2. Here, the

3. Decontamination volume estimated for different metamaterials

Latest investigations consider the geometry of metamaterial elements for different applications [38–43]. Conical metallic nanoparticles in an array configuration could be used for localization of SPR [38]. The geometry of nanoparticles and their arrangement improve the biochemical sensing and detection for drug delivery, heating therapy, etc. Ref. [40] describes a similar localized SPR. An electromagnetic sensor made of nonspherical gold nanoparticles deposited on a silica substrate having a matrix configuration with the interparticle distance much smaller than the incident wavelength is proposed. Other applications of the different geometry of elements of metamaterials are related with optical proprieties of each element. Explicitly, the cylindrical elements of metamaterials could be used as a performing resonator in the optical cloaking [41]. The authors of Ref. [42] mentioned that macroscopic characteristics depend not only on molecular structure but also on specific geometry. Advances and potential applications of optical electromagnetic metamaterials and metasurfaces for refractive index sensing and sensing light properties are presented in Ref. [43]. These metamaterials can be simply inte-

Here, we give a clear explanation for the increasing of the penetration depth of UV-C radiation inside the decontamination core. It is due to multiple refractions and reflections of radiation on the spherical and conical structures of metamaterials. If the light enters into the translucent liquid through a circular surface, the decontamination volume may be proportional to the surface of the

) in the Hamiltonian (1), we may terminate the nonharmonic

other nonlinear terms (e.g., Q<sup>6</sup>

182 Advanced Surface Engineering Research

oscillator moved to other metastable position.

total number of excitation is N = 10. Reproduced with permission from [6].

grated with several electronic devices.

$$V\_{cl} = \pi 2\pi R(L+R)d\_{p\dot{\nu}}$$

$$V\_{\text{con}} = \pi R^2 L - V\_{cl} \gg V\_{cl\nu}$$

where Vcl represents the efficient decontamination volume and dp � λ is the UV radiation penetration depth into liquid. Further down, we suggest a decontamination method making use of metamaterials in order to increase the decontamination volume.

Sensing properties are anticipated to be related to nanoscale system dimensions. In a first step, the contact surface of flowing gas or liquid is estimated. To increase the contact surface of the contaminated liquid, we examined the UV radiation propagation in two types of metamaterials: type A corresponds to the packing of photonic crystal fibers (PCFs) and type B to the photonic crystals (PCs) (see Figure 9(b and c)). Both metamaterials are transparent in UV region.

Figure 8. The multiple reflection and refractions of the UV light passing through the bases of semispherical (a) and conical (b) elements of metamaterial. Figure A represents the decontamination core filled up with conical structures. The radiation of six UV lamps is guided inside the center of decontamination tube through the bases of such conical structures where the nontransparent contaminated liquid has the maximal flow velocity.

Figure 9. Methods of decontamination: (a) traditional decontamination; (b) decontamination using photonic crystal fibers in the hexagonal packed bundle; (c) metamaterial like photon crystal. Reproduced with permission from [6].

When the PCF system is positioned in a cylinder containing contaminated liquid (see Figure 9(b)), this liquid will fill completely the space between fibers. Therefore, the decontamination surface grows substantially

$$S\_d = \pi r (r + 2rLN)\_\prime \tag{12}$$

It is obvious also that the decontamination volume is proportional to ffiffiffiffi

for fluid decontamination. Consequently, the fiber radius is <sup>r</sup> � <sup>R</sup><sup>=</sup> ffiffiffiffi

estimated the decontamination surfaces of metamaterials like PC (see Figure 9(c)).

Sd ¼ 4πr

contamination zone if the thickness of the fiber is decreased.

the free volume between three fibers vf <sup>¼</sup> <sup>r</sup><sup>2</sup> ffiffiffi

decontamination volume can be expressed as

microspheres, described by a N<sup>1</sup>=<sup>3</sup> dependence.

spheres may be considered a decontamination zone.

ensures the best medical support against potential viruses or bacteria.

symmetrically, in comparison with PCF.

When L < πN<sup>1</sup>=<sup>3</sup>

Vf <sup>¼</sup> <sup>π</sup>R<sup>2</sup>

L ffiffiffi 3

is yet not clear what happens with the free volume of liquid flowing between fibers, which is placed at a bigger distance in comparison with λ=2. This volume may be implicated in the

Using a standard hexagonal packed bundle symbolized in Figure 9(b), it is possible to estimate

volume in the big bundle does not depend on the diameter of the fiber and is equal to

When this expression reaches zero value, the whole volume between the fibers can be used

expression can be obtained for other types of fiber packing. Using the same method, we have

where L is the edge length of the cube, r is the radius of one microsphere, and N is the number of microspheres of the metamaterial. The liquid fills the space between microspheres and the

2 <sup>N</sup> � <sup>π</sup>L<sup>2</sup>

Vd � dSd <sup>¼</sup> <sup>4</sup>πdR<sup>2</sup>

We mention here that the increase of decontamination volume depends on the number of

At a first glance, it appears that the decontamination volume is smaller than in PCF, but this is just an illusion. Because the number of microspheres in a PC-like metamaterial is much larger than the number of fibers in PCF, decontamination volume is much higher in the second case. Another priority of last metamaterial consists in the fact that this works in all directions

The free volume between spheres in a PC can be expressed as vfr <sup>¼</sup> ð Þ <sup>2</sup><sup>r</sup> <sup>3</sup> � <sup>4</sup> <sup>π</sup>r<sup>3</sup>=<sup>3</sup> � � <sup>¼</sup> <sup>8</sup>r<sup>3</sup> ð Þ� 1 � π=6 0:48vc. The free volume between large cubes with dimension L have the same proportion Vfr ¼ 0:48V. In this case, the difference Vfr � Vd is proportional to V½ � 0:1=3=ð Þ 2L .

classical aspect of evanescent zone is not acceptable. Consequently, the volume between the

Metamaterials, as optical fibers or periodic photonic structures, open new possibilities to manipulate and annihilate viruses and bacteria in contaminated areas of liquids or organic tissue. For example, a good contact area between the implant and cells can be obtained if such metamaterials will cover the surface. The UV radiation guided along the surface of the implant

The depth and the volume of the evanescent zone of periodical waveguide structures influence UV action against bacteria and viruses. In Figure 10, we represent a periodical structure

=0:98, a further increase of surface becomes impossible and therefore the

3

Efficient Microbial Decontamination of Translucent Liquids and Gases Using Optical Metamaterials

<sup>p</sup> � <sup>π</sup>=<sup>2</sup> � �. The unused volume may be expressed as Va <sup>¼</sup> <sup>π</sup>RL <sup>0</sup>:18<sup>R</sup> � ffiffiffiffi

N<sup>1</sup>=<sup>3</sup> , N

<sup>p</sup> � <sup>π</sup>=<sup>2</sup> � �<sup>L</sup> <sup>¼</sup> <sup>0</sup>:18r<sup>2</sup>L. In this case, the free

N

N<sup>1</sup>=<sup>3</sup> (16)

<sup>p</sup> � <sup>λ</sup>=0:18: A similar

<sup>p</sup> (Vd=Vcl � ffiffiffiffi

http://dx.doi.org/10.5772/intechopen.80639

N <sup>p</sup> ). But it 185

N <sup>p</sup> <sup>λ</sup> � �.

where N is the number of fibers from PCF and r is the radius of one fiber. Last term stands for the fibers' lateral surface. It is assumed that the UV radiation is introduced by fibers in the cylinder. The UV radiation penetration depth (evanescent field) is influenced by the relative refractive indexes of fibers and contaminated liquid. The evanescent field intensity is given by:

$$I = I\_0 \exp\left[-z/d\right] \tag{13}$$

where I is the intensity of evanescent zone at distance z from fiber and d is characteristic exponential decay depth expressed as:

$$d = \frac{\lambda}{4\pi n\_2} \sqrt{\frac{\sin^2(\theta\_c)}{\sin^2(\theta) - \sin^2(\theta\_c)}}.$$

Here, θ<sup>c</sup> represents the critical angle of incidence sin θ<sup>c</sup> ¼ n2=n1, θ is the angle of incidence, θ > θc; n<sup>1</sup> is refractive index of the fibers, n<sup>2</sup> is refractive index of the liquid medium, while λ is the wavelength of UV radiation. In order to connect this approach with the classical decontamination method, it is necessary to indicate the decontamination area through the number of fibers. The estimates show that the small radius of fiber <sup>r</sup> is proportional to <sup>r</sup> � <sup>R</sup><sup>=</sup> ffiffiffiffi N <sup>p</sup> . If <sup>r</sup> is introduced in relation (12), the decontamination area of N cylindrical fibers is obtained:

$$\mathcal{S}\_d \sim 2\pi R L \sqrt{N}.\tag{14}$$

According to (14), the decontamination surface is proportional to the square root of N, number of fibers. Here, we consider negligibly the small surfaces of cylinder base as compared with the lateral surface of the fibers. Eqs. (13) and (14) demonstrate that decontamination volume of liquid is, in this case, proportional to

$$V\_d \sim 2\pi R L d\sqrt{N} \tag{15}$$

It is obvious also that the decontamination volume is proportional to ffiffiffiffi N <sup>p</sup> (Vd=Vcl � ffiffiffiffi N <sup>p</sup> ). But it is yet not clear what happens with the free volume of liquid flowing between fibers, which is placed at a bigger distance in comparison with λ=2. This volume may be implicated in the contamination zone if the thickness of the fiber is decreased.

Using a standard hexagonal packed bundle symbolized in Figure 9(b), it is possible to estimate the free volume between three fibers vf <sup>¼</sup> <sup>r</sup><sup>2</sup> ffiffiffi 3 <sup>p</sup> � <sup>π</sup>=<sup>2</sup> � �<sup>L</sup> <sup>¼</sup> <sup>0</sup>:18r<sup>2</sup>L. In this case, the free volume in the big bundle does not depend on the diameter of the fiber and is equal to Vf <sup>¼</sup> <sup>π</sup>R<sup>2</sup> L ffiffiffi 3 <sup>p</sup> � <sup>π</sup>=<sup>2</sup> � �. The unused volume may be expressed as Va <sup>¼</sup> <sup>π</sup>RL <sup>0</sup>:18<sup>R</sup> � ffiffiffiffi N <sup>p</sup> <sup>λ</sup> � �. When this expression reaches zero value, the whole volume between the fibers can be used for fluid decontamination. Consequently, the fiber radius is <sup>r</sup> � <sup>R</sup><sup>=</sup> ffiffiffiffi N <sup>p</sup> � <sup>λ</sup>=0:18: A similar expression can be obtained for other types of fiber packing. Using the same method, we have estimated the decontamination surfaces of metamaterials like PC (see Figure 9(c)).

$$S\_d = 4\pi r^2 N \sim \pi L^2 N^{1/3} \text{ \AA$$

When the PCF system is positioned in a cylinder containing contaminated liquid (see Figure 9(b)), this liquid will fill completely the space between fibers. Therefore, the decontamination surface

Figure 9. Methods of decontamination: (a) traditional decontamination; (b) decontamination using photonic crystal fibers

in the hexagonal packed bundle; (c) metamaterial like photon crystal. Reproduced with permission from [6].

where N is the number of fibers from PCF and r is the radius of one fiber. Last term stands for the fibers' lateral surface. It is assumed that the UV radiation is introduced by fibers in the cylinder. The UV radiation penetration depth (evanescent field) is influenced by the relative refractive indexes of fibers and contaminated liquid. The evanescent field intensity is given by:

where I is the intensity of evanescent zone at distance z from fiber and d is characteristic

Here, θ<sup>c</sup> represents the critical angle of incidence sin θ<sup>c</sup> ¼ n2=n1, θ is the angle of incidence, θ > θc; n<sup>1</sup> is refractive index of the fibers, n<sup>2</sup> is refractive index of the liquid medium, while λ is the wavelength of UV radiation. In order to connect this approach with the classical decontamination method, it is necessary to indicate the decontamination area through the number of

fibers. The estimates show that the small radius of fiber <sup>r</sup> is proportional to <sup>r</sup> � <sup>R</sup><sup>=</sup> ffiffiffiffi

introduced in relation (12), the decontamination area of N cylindrical fibers is obtained:

Sd � <sup>2</sup>πRL ffiffiffiffi

According to (14), the decontamination surface is proportional to the square root of N, number of fibers. Here, we consider negligibly the small surfaces of cylinder base as compared with the lateral surface of the fibers. Eqs. (13) and (14) demonstrate that decontamination volume of

Vd � <sup>2</sup>πRLd ffiffiffiffi

N

N

s

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sin <sup>2</sup>ð Þ θ<sup>c</sup> sin <sup>2</sup>ð Þ� θ sin <sup>2</sup>ð Þ θ<sup>c</sup>

<sup>d</sup> <sup>¼</sup> <sup>λ</sup> 4πn<sup>2</sup>

Sd ¼ πr rð Þ þ 2rLN , (12)

I ¼ I0exp ½ � �z=d , (13)

<sup>p</sup> : (14)

<sup>p</sup> (15)

N <sup>p</sup> . If <sup>r</sup> is

:

grows substantially

184 Advanced Surface Engineering Research

exponential decay depth expressed as:

liquid is, in this case, proportional to

where L is the edge length of the cube, r is the radius of one microsphere, and N is the number of microspheres of the metamaterial. The liquid fills the space between microspheres and the decontamination volume can be expressed as

$$V\_d \sim dS\_d = 4\pi dR^2 N^{1/3} \tag{16}$$

We mention here that the increase of decontamination volume depends on the number of microspheres, described by a N<sup>1</sup>=<sup>3</sup> dependence.

At a first glance, it appears that the decontamination volume is smaller than in PCF, but this is just an illusion. Because the number of microspheres in a PC-like metamaterial is much larger than the number of fibers in PCF, decontamination volume is much higher in the second case. Another priority of last metamaterial consists in the fact that this works in all directions symmetrically, in comparison with PCF.

The free volume between spheres in a PC can be expressed as vfr <sup>¼</sup> ð Þ <sup>2</sup><sup>r</sup> <sup>3</sup> � <sup>4</sup> <sup>π</sup>r<sup>3</sup>=<sup>3</sup> � � <sup>¼</sup> <sup>8</sup>r<sup>3</sup> ð Þ� 1 � π=6 0:48vc. The free volume between large cubes with dimension L have the same proportion Vfr ¼ 0:48V. In this case, the difference Vfr � Vd is proportional to V½ � 0:1=3=ð Þ 2L . When L < πN<sup>1</sup>=<sup>3</sup> =0:98, a further increase of surface becomes impossible and therefore the classical aspect of evanescent zone is not acceptable. Consequently, the volume between the spheres may be considered a decontamination zone.

Metamaterials, as optical fibers or periodic photonic structures, open new possibilities to manipulate and annihilate viruses and bacteria in contaminated areas of liquids or organic tissue. For example, a good contact area between the implant and cells can be obtained if such metamaterials will cover the surface. The UV radiation guided along the surface of the implant ensures the best medical support against potential viruses or bacteria.

The depth and the volume of the evanescent zone of periodical waveguide structures influence UV action against bacteria and viruses. In Figure 10, we represent a periodical structure (containing fibers and spherical metamaterials), which is introduced in a cylinder inside the contaminated fluid flows. Using Eqs. (12), (15), and (16) (arrangements (b) and (c) in Figure 9), the relative decontamination coefficient is introduced:

which are studied in graphene, boron nitride, or planar superlattices [31]. During decontamination process, the trapping of pathogen particles (viruses and bacteria) near the surface of fibers (or spheres) can occur. This effect was also described in literature [44]. It involves the attractive force acting on the particles presenting higher refractive indexes relative to the refraction index of liquid. This force occurs as a consequence of the large gradient of electromagnetic field (EMF) in

Efficient Microbial Decontamination of Translucent Liquids and Gases Using Optical Metamaterials

http://dx.doi.org/10.5772/intechopen.80639

187

In the next section, the contact area between the radiation propagating through the metamaterial elements and contaminated translucent fluids is increased. The decontamination rate is proportional to periodical spherical structures (N stands for the number of metamaterial elements) [4–6]. The efficiency of UV-C action on microorganisms present in contaminated fluids depends

For the decontamination of translucent liquids by UV-C radiation, we proposed the equipment in Figure 11, formed from a UV-C transparent core tube, which can be filled with metamaterials. As was estimated in Section 3, the decontamination rate is influenced by the packing and optical properties of metamaterial elements. Two types of metamaterials were used: (a) quartz (SiO2) unordered granules with dimension around 1–5 mm and (b) transmission spectrum in UV region 240–260 nm (Figure 11(a and b)) spheres of glass material with diameter of 2 mm and transmission at 300 nm. The comparative analysis of the decontamination rate for these metamaterials is performed. Optical metamaterials can disperse UV-C light inside the fluid volume and improve the contact zone between radiation and contaminated fluids. In Figure 11(a), the UV-C core tube used for the decontamination of translucent fluids is shown, while Figure 11(b) presents the decontamination equipment for dynamic treatment regime. The decontamination equipment consists of six low-pressure Hg UV-C lamps (30 W) with 90 cm length and about 2.7 cm diameter. These lamps surrounding the decontamination core tube (Figure 10) are placed in the center of a reflecting aluminum cylinder (with a diameter of about 30 cm). The UV-C radiation (with Gaussian distribution) is focused along the axis, i.e., in the decontamination area. The core tube can be filled up with optical metamaterials, while polluted fluids can freely circulate between

The radiation penetration into the core tube offers a significant yield of the contact surface between the flowing fluid and UV radiation in a volume of <sup>0</sup>:<sup>9</sup> <sup>10</sup><sup>4</sup> m3. The fluid circulating through the decontamination zone changes arbitrarily the optical frontiers among metamaterial elements and fluid, in function of pathogen concentration and optical properties. Consequently, the decontamination efficiency depends on the contact surface between the contaminated fluid and periodical optical metamaterial, and it is proportional to the number of elements of metamaterial. The penetration of light radiation into translucent fluids flowing through elements of metamaterials increases due to the optical evanescent field around each element. For the dynamic treatment regime, the core tube is connected to an external reservoir through which the polluted biological fluid flows. The circulation of the fluid is conducted by an electrical pump device. The working principle of the installation can be described as follows. The UV-C irradiation

on the depth and volume of the evanescent zone of periodical waveguide structures.

4. Experimental decontamination equipment with metamaterials

the evanescent zone nearby the fiber (sphere).

elements, in interaction with evanescent waves.

$$
\rho = \frac{V\_d}{V\_c}.
$$

Since the cylinder has a lateral surface larger than that of the bases, the relative decontamination coefficient is <sup>r</sup> � <sup>d</sup> ffiffiffiffi N <sup>p</sup> <sup>=</sup>dp. A similar expression can be written for PC-like metamaterials if the cylinder is filled up with SiO2 periodical bubbles. For this, the relative decontamination coefficient is <sup>r</sup> � dN<sup>1</sup>=<sup>3</sup> =dp. The classical decontamination volume is considered to be the penetration of radiation into the spherical elementary volume 4πR<sup>2</sup> dp with the width ΔR � dp. Periodical fiber structures and periodical spherical materials were proposed for carrying out the preliminary measurements in decontamination procedures as a function of the intensity and pulse duration of UV pulses.

Taking this dependence into consideration, we used a funnel filled with 400 fibers. The relative coefficient, r, of contaminated liquid, which flows through the funnel filled up with fibers and a funnel without fibers for the same flowing volume, is calculated. This coefficient becomes 20 times larger for the same volume of liquid flowing inside the cylindrical part of the funnel filled with fibers (relative to funnel without fibers), when the penetration depth is comparable with the depth of the evanescent field d � dp, where d � 100 nm. A similar equipment for SiO2 cylinder filled with SiO2 spherical bubbles through which contaminated liquid flows under the intense UV irradiation delivered by six lamps (see Figure 10) is proposed and preliminary tested. The decontamination rate is proportional to N<sup>1</sup>=<sup>2</sup> for PCF and to N<sup>1</sup>=<sup>3</sup> for PC, respectively.

Our previous studies [4] were devoted to the research of chemical reactions, which are produced in the microorganisms under UV pulse action. Here, one should consider the quantified structure of a quasiparticle energy transmitted from one DNA segment to another, or connected to protein microtubule. These vibration structures are analogous with two-dimensional phonon flows,

Figure 10. Experimental schemes proposed for the improvement of UV radiation contacts with fluids in the periodic optical SiO2 structures in interacting with the contaminated liquids. Reproduced with permission from [6].

which are studied in graphene, boron nitride, or planar superlattices [31]. During decontamination process, the trapping of pathogen particles (viruses and bacteria) near the surface of fibers (or spheres) can occur. This effect was also described in literature [44]. It involves the attractive force acting on the particles presenting higher refractive indexes relative to the refraction index of liquid. This force occurs as a consequence of the large gradient of electromagnetic field (EMF) in the evanescent zone nearby the fiber (sphere).

(containing fibers and spherical metamaterials), which is introduced in a cylinder inside the contaminated fluid flows. Using Eqs. (12), (15), and (16) (arrangements (b) and (c) in Figure 9),

> <sup>r</sup> <sup>¼</sup> Vd Vc :

Since the cylinder has a lateral surface larger than that of the bases, the relative decontamina-

the cylinder is filled up with SiO2 periodical bubbles. For this, the relative decontamination

Periodical fiber structures and periodical spherical materials were proposed for carrying out the preliminary measurements in decontamination procedures as a function of the intensity

Taking this dependence into consideration, we used a funnel filled with 400 fibers. The relative coefficient, r, of contaminated liquid, which flows through the funnel filled up with fibers and a funnel without fibers for the same flowing volume, is calculated. This coefficient becomes 20 times larger for the same volume of liquid flowing inside the cylindrical part of the funnel filled with fibers (relative to funnel without fibers), when the penetration depth is comparable with the depth of the evanescent field d � dp, where d � 100 nm. A similar equipment for SiO2 cylinder filled with SiO2 spherical bubbles through which contaminated liquid flows under the intense UV irradiation delivered by six lamps (see Figure 10) is proposed and preliminary tested. The

Our previous studies [4] were devoted to the research of chemical reactions, which are produced in the microorganisms under UV pulse action. Here, one should consider the quantified structure of a quasiparticle energy transmitted from one DNA segment to another, or connected to protein microtubule. These vibration structures are analogous with two-dimensional phonon flows,

Figure 10. Experimental schemes proposed for the improvement of UV radiation contacts with fluids in the periodic

optical SiO2 structures in interacting with the contaminated liquids. Reproduced with permission from [6].

decontamination rate is proportional to N<sup>1</sup>=<sup>2</sup> for PCF and to N<sup>1</sup>=<sup>3</sup> for PC, respectively.

<sup>p</sup> <sup>=</sup>dp. A similar expression can be written for PC-like metamaterials if

=dp. The classical decontamination volume is considered to be the

dp with the width ΔR � dp.

the relative decontamination coefficient is introduced:

N

penetration of radiation into the spherical elementary volume 4πR<sup>2</sup>

tion coefficient is <sup>r</sup> � <sup>d</sup> ffiffiffiffi

186 Advanced Surface Engineering Research

and pulse duration of UV pulses.

coefficient is <sup>r</sup> � dN<sup>1</sup>=<sup>3</sup>

In the next section, the contact area between the radiation propagating through the metamaterial elements and contaminated translucent fluids is increased. The decontamination rate is proportional to periodical spherical structures (N stands for the number of metamaterial elements) [4–6]. The efficiency of UV-C action on microorganisms present in contaminated fluids depends on the depth and volume of the evanescent zone of periodical waveguide structures.
