Grating design for interlayer optical interconnection of in-plane waveguides

Abstract

Interlayer grating-to-grating optical interconnect coupling efficiency is simulated and optimized using rigorous coupled-wave analysis (RCWA) for the case of binary rectangular-groove gratings. The "equivalent index slab (EIS)" concept is proposed to alleviate the numerical sensitivity problem inherent in the RCWA-leaky-wave approach, making the method applicable to any multilayer structure that has an arbitrary grating profile, large refractive-index differences, and a limited grating length. The method is easy to implement and computationally efficient and can provide optimal designs based on the system designer's need. To determine the viability of the RCWA-EIS approach, results are compared to those obtained using the finite-difference time-domain method, and an excellent agreement is found.

RCWA-EIS method for interlayer grating coupling

“…For each sublayer, the matrix of permittivity coefficientε h as defined in Eq. (17) in our previous paper [41] is no longer symmetric. Figure 6 shows two possible parallelogramic gratings, one with slant angle φ < 90°(designated as "forward-slanted" in this paper) and the other with φ > 90°(designated as "backward-slanted").…”

“…TE (y) polarized planar incidence is considered in all the models. The formulations of the grating models follow the previous RCWA work [33,34,41,42]. The permittivity formulations of each type of grating are introduced in Appendix A.…”

“…In the RCWA-EIS method, the grating layer is replaced by multiple homogenous slabs with specified refractive indices. A total of four equations related to the E fields and H fields of each of the 0 order and 1 order are involved (Equations (28)- (31) in our previous work [41]). The MATLAB function fsolve with the Levenberg-Marquardt (LM) algorithm was used to find the equivalent indices such that the function values of the four equations are close to zero.…”

“…This step involves the two equations relating the reflected amplitude and the transmitted amplitude for each diffracted order (the equations below Eq. (33) in [41]) that are solved for the one unknown α. The resulting least-squares problem was solved using fsolve with the LM algorithm.…”

“…In the present work, a general model based on the RCWA equivalent-index-slab (RCWA-EIS) method is introduced to analyze the diffraction behavior of arbitrary gratings in the chip-to-chip coupling configuration. This work is an extension of our previous work [41], in which a flexible and comprehensive tool for the interlayer optical coupling optimization of binary surface-relief gratings was introduced. Both works are based on the RCWA methods.…”