Optimization of Photonic Crystal Polarization Handling Devices Using Trust Region Algorithms

In this paper, the trust region optimization techniques are used for the design of photonic crystal polarization handling devices. The trust region algorithms are based on quadratic surrogate models with no derivative requirements to replace the objective function in the optimization process. A new box constrained trust region algorithm is employed for the first time to the best of our knowledge along with full vectorial finite difference methods to optimize a passive polarization rotator (PR) based on silica photonic crystal fiber (PCF). The reported PCF PR has a device length of 204 μm with nearly 100% polarization conversion ratio at operating wavelength λ of 1.55 μm. Further, an unconstrained trust region (UTR) algorithm is used for optimizing the coupling characteristics of a soft glass nematic liquid crystal (NLC) PCF coupler. The optimized coupler can separate the two polarized beams with compact length of 380 μm and low crosstalk at λ = 1.55 μm. Furthermore, a polarization independent NLC-PCF multiplexer-demultiplexer is proposed for wavelengths of 1.3 and 1.55 μm using the UTR technique with a compact device length of 475 μm and low crosstalk for the two polarization states.