Spectral manifestation of optical Tamm states in a metal-cholesteric liquid crystals stack

The reflection spectrum of linearly polarized light by a system consisting of a metal film and two adjacent sequentially located cholesteric liquid crystals (CLCs) with opposite helical twists is theoretically studied. The system contains a dielectric index-matching layer (DIML) between the metal film and the CLC layers. It is shown that in such a system the excitation of optical Tamm states (OTSs) by linearly polarized light is possible. The influence of the CLC pitch, refractive indices, and thicknesses of the DIML and metal film on the OTS manifestation in the reflection spectrum of the system is studied. The strong influence of the DIML thickness on the OTS wavelength and the appearance of multiple OTSs with an increase in the DIML thickness is noted.

Figure 1

Schematic of the structure “metal film-DIML-CLC layers” together with directions of the light beams propagating in the system. Letters $A$ and $B$ denote complex amplitudes of waves with right-handed circular polarization, while letters $\tilde{A}$ and $\tilde{B}$ (with tilde) denote complex amplitudes of waves with left-handed circular polarization; $r-CLC$ and $l-CLC$ denote CLC with right-handed and left-handed helical twists, respectively. Slanted lines indicate waves reflected from the CLC with the same helical twist as a circular polarization of incident wave; they are directed away from the corresponding incident wave arrow and are therefore inclined in the figure. $n_a$, $n_m$, and $\overline{n}$ are the refractive indices defined in the text of the paper.

Figure 2

(a) Reflection dip (solid line) in the spectral region of the CLC band gap (dashed line). CLC pitch $p=400\mathrm{nm}$, thickness of the DIML $d=0.3p$, thickness of the Ag film $l=36\mathrm{nm}$. (b) Spatial profile of the amplitude of the electric component of the electromagnetic field at the OTS wavelength.

Figure 3

Influence of the DIML thickness on the OTS spectral distribution in the CLC band gap: (a) $p=300\mathrm{nm}$; (b) $p=500\mathrm{nm}$; $d/p=0.2$: 1; $0.3$: 2; $0.4$: 3; $l=36\mathrm{nm}$. Dashed lines show the band gap.

Figure 4

Influence of the CLC pitch value on the OTS spectral position: $p\left(nm\right)=390$: 1; 400: 2; 410: 3; $d=120\mathrm{nm}$, $l=36\mathrm{nm}$, $L=4100\mathrm{nm}$.

Figure 5

Magnitude of the OTS spectral dip in the CLC reflection band at different values of the Ag film thickness: $l\left(\mathrm{nm}\right)=20$: 1; 40: 2; 60: 3; (a) $p=300\mathrm{nm}$; (b) $p=400\mathrm{nm}$, $d/p=0.3$.

Figure 6

Influence of the CLC refractive indices $n_e$ and $n_o$ on the spectral position of the OTS dip in the CLC band gap; ($n_o=1.4,n_e=1.6$): 1; ($n_o=1.5,n_e=1.6$): 2; ($n_o=1.5,n_e=1.7$): 3; $p=400\mathrm{nm}$; $d/\mathrm{p}=0.3$, $l=36\mathrm{nm}$. Dashed lines of the corresponding color show the band gaps for CLC using the same values of $n_o$ and $n_e$.

Figure 7

Reflection dips in the spectral region of the CLC band gap for different thicknesses of the DIML: (a) $d=4.6p$; (b) $d=8.3p$. CLC pitch $p=400\mathrm{nm}$, thickness of the Ag film $l=36\mathrm{nm}$.