## Abstract

We present a novel concept which enables the realization of unidirectional and irreversible grating assisted couplers by using gain-loss modulated medium to eliminate the reversibility. Employing a matched periodic modulation of both refractive index and loss (gain) we achieve a unidirectional energy transfer between the modes of the coupler which translates to light transmission from one waveguide to another while disabling the inverse transmission. The importance of self coupling coefficients is explored as well and a feasible implementation, where the real and imaginary perturbations are implemented in different waveguides is presented.

© 2004 Optical Society of America

Full Article |

PDF Article
### Equations (10)

Equations on this page are rendered with MathJax. Learn more.

(1)
$${P}_{m,n}\left(z\right)\propto {\int}_{0}^{z}f\left(z\right)\mathrm{exp}\{-i\left({\beta}_{m}-{\beta}_{n}\right)z\}\mathit{dz}$$
(2)
$${\dot{c}}_{1}=-i\phantom{\rule{.2em}{0ex}}\mathrm{exp}\left\{i\Delta \beta z\right\}{K}_{11}{c}_{1}-i\phantom{\rule{.2em}{0ex}}\mathrm{exp}\left\{i\Delta \beta z\right\}{K}_{12}{c}_{2}\mathrm{exp}\left\{i\Delta \beta z\right\}$$
(3)
$${\dot{c}}_{2}=-i\phantom{\rule{.2em}{0ex}}\mathrm{exp}\left\{i\Delta \beta z\right\}{K}_{21}{c}_{1}\phantom{\rule{.2em}{0ex}}\mathrm{exp}\{-i\Delta \beta z\}-i\phantom{\rule{.2em}{0ex}}\mathrm{exp}\left\{i\Delta \beta z\right\}{K}_{22}{c}_{2}$$
(4)
$${K}_{\mathit{mn}}=\frac{\omega {\epsilon}_{0}}{4P}\underset{-\infty}{\overset{+\infty}{\int}}\underset{-\infty}{\overset{+\infty}{\int}}\Delta (x,y){E}_{\mathit{mt}}^{*}{E}_{\mathit{nt}}\mathit{dxdy}$$
(6)
$${\dot{c}}_{2}=-i{K}_{21}{c}_{1}$$
(7)
$${c}_{1}\left(z\right)={C}_{01}$$
(8)
$${c}_{2}\left(z\right)=-i{K}_{21}{C}_{01}z+{C}_{02}$$
(9)
$${\dot{c}}_{1}=-i\left[{K}_{11}^{r}\mathrm{cos}\left(\Delta \beta z\right)+i{K}_{11}^{i}\mathrm{sin}\left(\Delta \beta z\right)\right]{c}_{1}-i\left[{K}_{12}^{r}\mathrm{cos}\left(\Delta \beta z\right)+i{K}_{12}^{i}\mathrm{sin}\left(\Delta \beta z\right)\right]{c}_{2}\mathrm{exp}\left\{i\Delta \beta z\right\}$$
(10)
$${\dot{c}}_{2}=-i\left[{K}_{21}^{r}\mathrm{cos}\left(\Delta \beta z\right)+i{K}_{21}^{i}\mathrm{sin}\left(\Delta \beta z\right)\right]{c}_{1}\mathrm{exp}\{-i\Delta \beta z\}-i\left[{K}_{22}^{r}\mathrm{cos}\left(\Delta \beta z\right)+i{K}_{22}^{i}\mathrm{sin}\left(\Delta \beta z\right)\right]{c}_{2}$$