Comparison of two approaches to the design of interference optical elements on photonic crystal structures

Using examples of photonic crystal interference optical elements such as bends of waveguide structures, an intersection of three waveguides, a radiation input node, a Y-shaped logical gate NOT, and a logical gate NOT on a crystal with self-collimation, we discuss two approaches to the synthesis of integrated optics elements: non-stochastic methods of gradient-free optimization (zero-order optimization methods) and a genetic algorithm. Both approaches involve solving the direct diffraction problem using the FDTD method. We conclude that these approaches are suited for designing photonic crystal optical elements: a comparison of the calculated results in terms of the efficiency criterion demonstrates an advantage of the author's modified genetic algorithm over the coordinate descent and Hooke-Jeeves methods for elements in which radiation does not propagate along a straight path. Meanwhile for elements that conduct radiation along a straight waveguide, zero-order optimization methods provide the same efficiency as genetic optimization (more than 99%), while the computational complexity of these methods is lower. Particular attention is paid to the analysis of the “partial enumeration” method. Using the example of a photonic crystal waveguide with a 120°-bending, it is shown that the element designed using this method is characterized by virtually lossless radiation transmission, while its computational complexity is 2 times lower than that of the genetic algorithm.