## Abstract

A pump–probe optical switching mechanism that uses a nonlinear chiral photonic bandgap structure is proposed. The switching is achieved by shifting the bandgap of the structure; the chirality permits the use of the same frequency for the pump and the probe beam. The pump beam is never transmitted, so there is no discrimination problem. A new extension of the finite-difference time-domain technique is developed to simulate the propagation of an electromagnetic wave in a Kerr nonlinear chiral medium.

© 1999 Optical Society of America

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### Equations (11)

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(1)
$$\mathbf{D}=\overline{\u220a}\xb7\mathbf{E}+\chi |\mathbf{E}{|}^{2}\mathbf{E}$$
(2)
$$\overline{\u220a}=\left[\begin{array}{ccc}{\u220a}_{x}& 0& 0\\ 0& \u220a& i\beta \\ 0& -i\beta & \u220a\end{array}\right].$$
(3)
$$\frac{1}{c}\frac{\partial \mathbf{B}}{\partial t}=-\nabla \times \mathbf{E},$$
(4)
$$\frac{1}{c}\frac{\partial \mathbf{D}}{\partial t}=\nabla \times \mathbf{B},$$
(5)
$${D}_{y}=\u220a{E}_{y}+i\beta {E}_{z}+\chi (|{E}_{y}{|}^{2}+|{E}_{z}{|}^{2}){E}_{y},$$
(6)
$${D}_{z}=\u220a{E}_{z}-i\beta {E}_{y}+\chi (|{E}_{y}{|}^{2}+|{E}_{z}{|}^{2}){E}_{z}.$$
(7)
$${E}_{1}=\frac{1}{\sqrt{2}}({E}_{y}+{\mathit{iE}}_{z}),$$
(8)
$${E}_{2}=\frac{1}{\sqrt{2}}({E}_{y}-{\mathit{iE}}_{z}).$$
(9)
$$q[(\u220a+q{)}^{2}-{\beta}^{2}{]}^{2}-\chi (|{D}_{y}{|}^{2}+|{D}_{z}{|}^{2})[(\u220a+q{)}^{2}+{\beta}^{2}]$$
(10)
$$+4\chi \beta \mathrm{Im}({D}_{y}{D}_{z}^{*})(\u220a+q)=0.$$
(11)
$$\mathbf{E}(x,t)=(\stackrel{\u02c6}{y}+\stackrel{\u02c6}{\mathit{iz}}){E}_{0}exp\{-i{\omega}_{0}/c[\mathit{ct}-\sqrt{{\u220a}_{0}}(x-{x}_{0})]-[\mathit{ct}-\sqrt{{\u220a}_{0}}(x-{x}_{0}){]}^{2}(\mathrm{\Delta}\omega /c{)}^{2}/2\},$$