Geometric phase in plane-wave transmission by a dielectric structurally chiral slab with a central phase defect

A slab made of a dielectric structurally chiral medium (DSCM) strongly reflects the cohanded circularly polarized plane wave, but not the crosshanded circularly polarized plane wave, in a spectral regime called the circular Bragg regime. The effect of inserting a central phase defect in a DSCM slab with a modest number of structural periods is a spectral reflection hole in the circular Bragg regime, for cohanded incidence only. However, if the incident plane wave is left-circularly polarized, the geometric phase of the transmitted plane wave contains evidence of both the circular Bragg regime and the spectral reflection hole, regardless of the structural handedness of the DSCM. This evidence is indicative of the type of phase defect. The effect of inserting a central phase defect in a DSCM slab with a large number of structural periods is a spectral transmission hole in the circular Bragg regime, for crosshanded incidence only. The spectral transmission hole may be difficult to observe experimentally because of absorption inside the DSCM slab, but it will still be evident in the geometric phase of the transmitted plane wave, if the incident plane wave is left-circularly polarized.

Figure 1

$T_{\mathrm{R}}$, $T_{\mathrm{L}}$, and ${\mathrm{\Phi }}_{\mathrm{L}}$ as functions of ${\lambda }_0$ and ${\theta }_{\mathrm{inc}}$ of a DSCM slab without a central phase defect ($L_{\mathrm{CTF}}=0$ and ${\phi }_{\mathrm{t}}=0^{\circ }$), calculated for $\psi =0^{\circ }$, $\mathrm{\Omega }=150$ nm, and $N=5$. Other parameters are as follows: $p_{\mathrm{a}}=2.3$, $p_{\mathrm{b}}=3.0$, $p_{\mathrm{c}}=2.2$, ${\lambda }_{\mathrm{a}}={\lambda }_{\mathrm{c}}=260$ nm, ${\lambda }_{\mathrm{b}}=270$ nm, and $N_{\mathrm{a}}=N_{\mathrm{b}}=N_{\mathrm{c}}=130$. Top row: $h=1$. Bottom row: $h=-1$.

Figure 2

$T_{\mathrm{R}}$, $T_{\mathrm{L}}$, and ${\mathrm{\Phi }}_{\mathrm{L}}$ as functions of ${\lambda }_0$ and ${\theta }_{\mathrm{inc}}$ of a DSCM slab with a central twist defect ($L_{\mathrm{CTF}}=0$ and ${\phi }_{\mathrm{t}}={90}^{\circ }$), calculated for $\psi =0^{\circ }$, $\mathrm{\Omega }=150$ nm, and $N=5$. Other parameters are as follows: $p_{\mathrm{a}}=2.3$, $p_{\mathrm{b}}=3.0$, $p_{\mathrm{c}}=2.2$, ${\lambda }_{\mathrm{a}}={\lambda }_{\mathrm{c}}=260$ nm, ${\lambda }_{\mathrm{b}}=270$ nm, and $N_{\mathrm{a}}=N_{\mathrm{b}}=N_{\mathrm{c}}=130$. Top row: $h=1$. Bottom row: $h=-1$.

Figure 3

$T_{\mathrm{R}}$, $T_{\mathrm{L}}$, and ${\mathrm{\Phi }}_{\mathrm{L}}$ as functions of ${\lambda }_0$ and ${\theta }_{\mathrm{inc}}$ of a DSCM slab with a central layer defect ($L_{\mathrm{CTF}}=\mathrm{\Omega }/2$ and ${\phi }_{\mathrm{t}}=0^{\circ }$), calculated for $\psi =0^{\circ }$, $\mathrm{\Omega }=150$ nm, and $N=5$. Other parameters are as follows: $p_{\mathrm{a}}=2.3$, $p_{\mathrm{b}}=3.0$, $p_{\mathrm{c}}=2.2$, ${\lambda }_{\mathrm{a}}={\lambda }_{\mathrm{c}}=260$ nm, ${\lambda }_{\mathrm{b}}=270$ nm, and $N_{\mathrm{a}}=N_{\mathrm{b}}=N_{\mathrm{c}}=130$. Top row: $h=1$. Bottom row: $h=-1$.

Figure 4

$T_{\mathrm{R}}$, $T_{\mathrm{L}}$, and ${\mathrm{\Phi }}_{\mathrm{L}}$ as functions of ${\lambda }_0$ and ${\theta }_{\mathrm{inc}}$ of a DSCM slab with central layer and twist defects ($L_{\mathrm{CTF}}=\mathrm{\Omega }/4$ and ${\phi }_{\mathrm{t}}={135}^{\circ }$), calculated for $\psi =0^{\circ }$, $\mathrm{\Omega }=150$ nm, and $N=5$. Other parameters are as follows: $p_{\mathrm{a}}=2.3$, $p_{\mathrm{b}}=3.0$, $p_{\mathrm{c}}=2.2$, ${\lambda }_{\mathrm{a}}={\lambda }_{\mathrm{c}}=260$ nm, ${\lambda }_{\mathrm{b}}=270$ nm, and $N_{\mathrm{a}}=N_{\mathrm{b}}=N_{\mathrm{c}}=130$. Top row: $h=1$. Bottom row: $h=-1$.

Figure 5

$T_{\mathrm{R}}$, $T_{\mathrm{L}}$, and ${\mathrm{\Phi }}_{\mathrm{L}}$ as functions of ${\lambda }_0$ and $\psi$ of a DSCM slab with central layer and twist defects ($L_{\mathrm{CTF}}=\mathrm{\Omega }/4$ and ${\phi }_{\mathrm{t}}={135}^{\circ }$), calculated for ${\theta }_{\mathrm{inc}}=0^{\circ }$, $\mathrm{\Omega }=150$ nm, and $N=5$. Other parameters are as follows: $p_{\mathrm{a}}=2.3$, $p_{\mathrm{b}}=3.0$, $p_{\mathrm{c}}=2.2$, ${\lambda }_{\mathrm{a}}={\lambda }_{\mathrm{c}}=260$ nm, ${\lambda }_{\mathrm{b}}=270$ nm, and $N_{\mathrm{a}}=N_{\mathrm{b}}=N_{\mathrm{c}}=130$. Left column: $h=1$. Right column: $h=-1$.

Figure 6

$T_{\mathrm{R}}$, $T_{\mathrm{L}}$, and ${\mathrm{\Phi }}_{\mathrm{L}}$ as functions of ${\lambda }_0$ and ${\theta }_{\mathrm{inc}}$ of a DSCM slab with central layer and twist defects ($L_{\mathrm{CTF}}=\mathrm{\Omega }/4$ and ${\phi }_{\mathrm{t}}={135}^{\circ }$), calculated for $\psi =0^{\circ }$, $\mathrm{\Omega }=150$ nm, and $N=25$. Other parameters are as follows: $p_{\mathrm{a}}=2.3$, $p_{\mathrm{b}}=3.0$, $p_{\mathrm{c}}=2.2$, ${\lambda }_{\mathrm{a}}={\lambda }_{\mathrm{c}}=260$ nm, ${\lambda }_{\mathrm{b}}=270$ nm, and $N_{\mathrm{a}}=N_{\mathrm{b}}=N_{\mathrm{c}}=130$. Left column: $h=1$. Right column: $h=-1$.

Figure 7

$T_{\mathrm{R}}$, $T_{\mathrm{L}}$, and ${\mathrm{\Phi }}_{\mathrm{L}}$ as functions of ${\lambda }_0$ and ${\theta }_{\mathrm{inc}}$ of a DSCM slab with central layer and twist defects ($L_{\mathrm{CTF}}=\mathrm{\Omega }/4$ and ${\phi }_{\mathrm{t}}={135}^{\circ }$), calculated for $\psi =0^{\circ }$, $\mathrm{\Omega }=162$ nm, and $N=25$. Other parameters are as follows: $p_{\mathrm{a}}=2.3$, $p_{\mathrm{b}}=3.0$, $p_{\mathrm{c}}=2.2$, ${\lambda }_{\mathrm{a}}={\lambda }_{\mathrm{b}}={\lambda }_{\mathrm{c}}=10$ nm, and $N_{\mathrm{a}}=N_{\mathrm{b}}=N_{\mathrm{c}}=130$. Left column: $h=1$. Right column: $h=-1$.