Analytical analysis of and quasi- symmetry in thick diffraction gratings using coupled-wave theory.

The concept of parity-time () symmetry in optics could potentially provide emerging solutions to exploit the benefits of optical gain in optical processing. With this regard, and quasi- symmetry were studied in thick optical diffraction gratings by derivation of explicit analytical expressions using the coupled-wave theory and verified by numerical calculations. The conditions to observe and quasi- symmetry were discussed in terms of the gain-loss ratio and the refractive index modulation amplitudes for both reflective and transmissive gratings. The results show that the criterion to attain quasi- symmetry for the reflective and transmissive gratings is in reverse in terms of the ratio of the modulation amplitude of the imaginary to that of the real part of the refractive index (). According to the model, a grating with fringes parallel to the surface experiences broken symmetry for a wide range of gain-loss ratios. Furthermore, by varying the gain-loss ratio or , some extrema could be observed in the normalized transmission power of the diffraction orders, while operating in the quasi- symmetry regime. The analytical solutions could predict and justify the positions of those extrema which could be advantageous to the design purposes. [ABSTRACT FROM AUTHOR]