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Научни трудове на Съюза на учените в България-Пловдив. Серия В. Техника и технологии, естествен ии хуманитарни науки, том XVI., Съюз на учените сесия "Международна конференция на младите учени" 13-15 юни 2013. Scientific research of the Union of Scientists in Bulgaria-Plovdiv, series C. Natural Sciences and Humanities, Vol. XVI, ISSN 1311-9192, Union of Scientists, International Conference of Young Scientists, 13 - 15 June 2013, Plovdiv.
SURFACE PLASMON EXCITATION ASSISTED BY THIN CHOLESTRIC LIQUID CRYSTAL FILM
Katerina Zhelyazkova and Georgi Dyankov Faculty of Physics and Engineering Technology, University of Plovdiv "Paissi Hilendarski", Bulgaria e-mail: katiajeliazkova@abv.bg e-mail: dyankov@uni-plovdiv.bg
Abstract
In this work, we propose a structure based on an anisotropic thin film that convert the polarization and can trigger the forbidden polarization to excite surface plasmon resonance. We have simulated light propagation in three-layered structure: BK7 prism/cholesteric liquid crystal/ air for conditions, corresponding to plasmon excitation. Simulations are based on 4x4 method for Maxwell equations in anisotropic media. The simulations have been provided for different thickness, pitch length, and type of the liquid crystal. We have shown that train of plasmons can be excited by p- polarized light. S-polarization also participates in this process. The efficiency of excitation depends on the configuration of the structure.
1. Introduction
Surface plasmon resonance (SPR) in thin metal films is highly sensitive to optical and structural properties of the metal interface. This feature is the base of SPR sensor. The main problem for SpR sensor is distinguishing between induced refractive index changes on the surface and refractive index changes in the background. The most successful solution of the problem is when two plasmons at different wavelengths are excited. The first one (with a shorter wavelength) is sensitive only to the changes on the boundary metal/bio-agent, while the second one is sensitive to the changes in the background. A specific treatment of the both signals gives the opportunity for distinguishing the effects.
In this work we demonstrate a new method for excitation of two or more plasmon at different wavelengths. We show that the plasmon can be excited even by s-polarized light.
The structure we propose is based on the configuration that was first investigated by Abele [1]. The main feature of our structure is that the buffer is a liquid crystal film. We consider the structure without a metal film, but for conditions (buffer thickness and incident angle) which guarantee a plasmon excitation. Our previous investigation [2] shows that an effective plasmon excitation occurs when the buffer thickness is less than 1^m. As is well known, the plasmon is excited at incident angels higher than the angle of total inner reflection. Keeping in mind these constrains we have simulated three layered structure BK7- liquid crystal film - air.
2. Calculation of reflection spectra
In our structure we consider cholesteric liquid crystal film or twisted smectic C phase. The optical-frequency-dielectric-tensor at any one point in the liquid crystal has three principal axes
£j. e2 and 8, e. hose directions with respect to x, y and z axes may be defined by the Euler angles 0, <1> and v|/ shown in Fig. 1. Angels 0. <J> arc considered as parameters, the azimuth <J> is proportional to z and goes through 2n radians in one pitch length.
Figurel. Euler angles of optical dielectric tensor with respect to the rectangular coordinates, at some arbitrary value of z.
To describe the light propagation in anisotropic multi-layered structure, such as liquid crystal, we use the 4x4 matrix formalisms. According to the formalism an inhomogeneous medium is divided into a sufficiently large number of plane-parallel layers, with each being considered homogeneous.
Maxwell's equations for plane waves in anisotropic media stratified in the z-direction written in matrix form are:
f Ex " fA Aj Aj
d Hy ia A, A A3
dz Ey c 0 0 0
l- Hx J lA3 Aj 4
0 Y E }
y
H
Ey
- H
x J
where, the terms of the A matrix give the relation between dielectric tensor and incident angle. The explicit form of A matrix elements can be found in [3].
The reflectance is simulated as a function of relation pitch/wavelength. The wavelength is measured in micrometers. In our consideration the pitch length is unity and buffer consists in integer number of pitch. Following the conditions for plasmon excitation we assume an angle of incidence higher that 41.3 deg, which is the total inner reflection angle for BK7/air.
We consider liquid crystal film with dielectric constants e1=e2=2.00 and e3=3.00. For precise simulation one pitch is divided to 500 layers and the 4x4 method is applied for all structure.
Fig.2 shows our main results concerning the computed reflectance as a function of pitch/ wavelength ratio. R and Rs present the reflectance of p-polarized light when the incident light is p- or s-polarized, respectively. The maximum of reflectance indicates the potential possibility of
plasmon excitation.
Fig. 2a shows the reflectance at incident angle 45 deg and tilt angle 0 = 80 deg. Obviously, the effectiveness of plasmon excitation for p-polarized incident light is higher for pitch/wavelength < 1.4. For values > 1.4 the effectiveness of plasmon excitation is better for s-polarized incident light.
Fig. 2b shows that the effectiveness of plasmon excitation can be almost equal for p- and s- polarized incident light. For example, this happens for the same tilt angle but for incident angle 60 deg. Fig. 2a and Fig. 2b show that train of plasmons can be excited by p- and s- polarized light.
Fig. 2c shows that at specific incident and tilt angle the effectiveness of plasmon excitation of s-polarized light can be higher than that one of p-polarized light. The ability of s-polarized light for plasmon excitation can be explained by the property of cholesteric or twisted smectic liquid crystal film for polarization conversion.
Fig 2d demonstrates the effect of increasing of number of pitch. Comparing with Fig. 2b we see that the oscillation of reflectivity is with a shorter period. So, more plasmons can be excited in this case.
The effectiveness of excitation of p- and s-polarized light is different for different relation pitch/wavelength (see Fig. 2a, 2b and 2d). However, both polarization participate in plasmon excitation. In the proposed structure the plasmon can be excited only with s-polarized light (see Fig. 2c) for specific conditions. The effectiveness of this case can be optimized by looking for a liquid crystal with optimal dielectric constants. We performed our consideration for a model liquid crystal molecule, not for a real one. A real structure can be considered for exactly defined buffer thickness and metal thickness which will determine the resonance wavelength. The wide range of ratio pitch/wavelength with multitude peaks with high reflectivity shows the possibility for matching the resonance wavelength.
11 m
Gjf
nil C T-
fl 4 '
J C * [ ] ■
A3 G 1
tA
-0.L
rv'
vvyi
Rin
c
i p.t r
■! :1i "il I-'-LT U
45*1,« tngto
T - ,- - r-..T - T- -— —,
(I 91 14 U n II IQ U
wjvq «jn^lh
Figure 2.Computed reflectance vs. pitch/wavelength for Rpp and Rsp spectra at different tilt and incident angle. The corresponding tilt and incident angle are marked at each graphic. See the explanation in the text.
3. Conclusion
In this work we demonstrate the possibility of plasmon excitation in Abele structure when the buffer is a liquid crystal film. At each peak with high reflectance a plasmon could be excited. Our simulations correspond to conditions (buffer thickness and incident angle) which guarantee plasmon excitation. However, in our structure a metal film is not included and the resonance wavelength is unknown. In spite of this one can expect that the plasmon excitation is possible because the positions of peaks with high reflectance are tunable by changing the parameters of liquid crystal film, keeping the buffer and metal film thickness constant.
Many peaks with high reflectance suggest the possibility for excitation of two or more plasmons. One can expect that a color plasmon or train of plasmons [4] can be excited. This option has to be carefully studied.
Our simulations show the opportunity for plasmon excitation with s-polarized incident light what is a consequence of the polarization conversion performed by the liquid crystal film.
Our study shows that a structure glass-liquid crystal film-metal is a perspective plasmon structure and will be studied in details in near future.
References
1. Abele F., Lorez-Rios T., Opt. Commun. 11, 89-92, 1974
2. Dyankov G., Zekriti M. and Bousmina M., Plasmonics 6, 643, 2011
3. D.Berreman, Mol. Cryst. Liquid Cryst. 22, 175-184, 1973
4. Dyankov G, Sekkat Z. and Bousmina M., Appl. Opt. 49, 4304, 2010
