Numerical Optimization Technique for Optimal Design of the n Grooves Surface Plasmon Grating Coupler

A gradient based numerical optimization technique to obtain an optimal design of the geometry of a metal grating and parameters of an incident Gaussian beam (GB) to excite surface plasmons is introduced. The numerical gradient is obtained by exploiting the available Finite Element Method discretization data, and by direct differentiation of the GB parameters, such as its angle of incidence and the position of the center.There are two approaches considered. One uses a fixed mesh via discrete geometry update steps for 4 grooves with a 14 dimensional gradient. Another approach uses a general n grooves grating with independent user defined dimensions of the rectangular grooves. With just doubling the number of grooves, the 8 grooves grating with a 26 dimensional gradient shows a much improved energy conversion rate (up to 77%) demonstrating considerable practical value of the methodology