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Rotation sensitivity analysis of a two-dimensional array of coupled resonators

机译：耦合谐振器二维阵列的旋转灵敏度分析

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In this paper, we study the rotation sensitivity of a gyroscope made of a two-dimensional array of coupled resonators consisting of N columns of one-dimensional coupled resonant optical waveguides (CROWs) connected by two bus waveguides, each CROW consisting of M identical ring resonators. We show that the maximum rotation sensitivity of this structure is a strong function of the parity of the number of rows M. For an odd number of rows, and when the number of columns is small, the maximum sensitivity is high, and it is slightly lower than the maximum sensitivity of a single-ring resonator with two input/output waveguides (the case M=N= 1), which is a resonant waveguide optical gyroscope (RWOG). For an even M and small N, the maximum sensitivity is much lower than that of the RWOG. Increasing the number columns N increases the sensitivity of an even-row 2D CROW sublinearly, as N~(0.39), up to 30 columns. In comparison, the maximum sensitivity of an RWOG of equal area increases faster, as √N. The sensitivity of the 2D CROW therefore always lags behind that of the RWOG. For a 2×2 CROW, if the spacing between the columns L is increased sufficiently the maximum sensitivity increases linearly with L due to the presence of a composite Mach-Zehnder interferometer in the structure. However, for equal footprints this sensitivity is also not larger than that of a single-ring resonator. Regardless of the number of rows and columns and the spacing, for the same footprint and propagation loss, a 2D CROW gyroscope is not more sensitive than an RWOG.
机译：在本文中，我们研究陀螺仪的旋转灵敏度，该陀螺仪由耦合谐振器的二维阵列组成，该阵列由N列一维耦合谐振光波导（CROW）组成，两个波导由两个总线波导连接，每个CROW由M个相同的环组成谐振器。我们表明，此结构的最大旋转灵敏度是行数M的奇偶性的强大函数。对于奇数行，并且当列数小时，最大灵敏度高，而在低于具有两个输入/输出波导的单环谐振器的最大灵敏度（情况M = N = 1），后者是谐振波导光学陀螺仪（RWOG）。对于偶数M和较小的N，最大灵敏度远低于RWOG。增加列数N可将偶数行2D CROW的灵敏度线性地提高为N〜（0.39），最多可增加30列。相比之下，等面积的RWOG的最大灵敏度提高为√N。因此2D CROW的灵敏度始终落后于RWOG的灵敏度。对于2×2 CROW，如果列L之间的间距足够大，则由于结构中存在复合Mach-Zehnder干涉仪，因此最大灵敏度随L线性增加。但是，对于相同的占位面积，该灵敏度也不大于单环谐振器的灵敏度。无论行和列的数量以及间距如何，对于相同的覆盖区和传播损耗，二维CROW陀螺仪都不会比RWOG灵敏。

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