Angular sensitivities of volume gratings for substrate-mode optical interconnects

The angular sensitivities of slanted volume gratings (VGs) illuminated by three-dimensional (3-D) converging-diverging spherical Gaussian beams for substratemode optical interconnects in microelectronics are analyzed by application of 3-D finite-beam rigorous coupled-wave analysis. Angular misalignments about the z, y, and x axes that correspond to yaw, pitch, and roll misalignments resulting from manufacturing tolerances of chips are investigated. Two cases of linear polarization of the central beam of the Gaussian are considered: E _|_ K and H _|_ K, where K is the grating vector. From worst-case manufacturing tolerances, the ranges of yaw, pitch, and roll misalignment angles are alpha=±1.17°, beta=±3.04°, and gamma=±3.04°, respectively. Based on these ranges of misalignment angles, the decreases of diffraction efficiencies for slanted VGs that are due to both the yaw and the roll misalignments are relatively small. However, the efficiency of substrate-mode optical interconnects achieved by slanted VGs could be reduced by 61.04% for E _|_ K polarization and by 58.63% for H _|_ K polarization because of the pitch misalignment. Thus the performance of a VG optical interconnect is most sensitive to pitch misalignment.