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<sup>0.39</sup>, 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.
This study presents numerical simulations of the maximum sensitivity to absolute rotation of a number of coupled resonator optical waveguide (CROW) gyroscopes consisting of a linear array of coupled ring resonators. It examines in particular the impact on the maximum sensitivity of the number of rings, of the relative spatial orientation of the rings (folded and unfolded), of various sequences of coupling ratios between the rings and various sequences of ring dimensions, and of the number of input/output waveguides (one or two) used to inject and collect the light. In all configurations the sensitivity is maximized by proper selection of the coupling ratio(s) and phase bias, and compared to the maximum sensitivity of a resonant waveguide optical gyroscope (RWOG) utilizing a single ring-resonator waveguide with the same radius and loss as each ring in the CROW. Simulations show that although some configurations are more sensitive than others, in spite of numerous claims to the contrary made in the literature, in all configurations the maximum sensitivity is independent of the number of rings, and does not exceed the maximum sensitivity of an RWOG. There are no sensitivity benefits to utilizing any of these linear CROWs for absolute rotation sensing. For equal total footprint, an RWOG is √N times more sensitive, and it is easier to fabricate and stabilize.
We use coupled-mode theory with strong perturbation to model the loss and backscattering coefficients of a commercial
hollow-core fiber (NKT Photonics’ HC-1550-02 fiber) induced by the frozen-in longitudinal perturbations of the fiber
cross section. Strong perturbation is used, for the first time to the best of our knowledge, because the large difference
between the refractive indices of the two fiber materials (silica and air) makes conventional weak-perturbation less
accurate. We first study the loss and backscattering using the mathematical description of conventional surface-capillary
waves (SCWs). This model implicitly assumes that the mechanical waves on the core wall of a PBF have the same
power spectral density (PSD) as the waves that develop on an infinitely thick cylindrical tube with the same diameter as
the PBF core. The loss and backscattering coefficients predicted with this thick-wall SCW roughness are 0.5 dB/km and
1.1×10<sup>-10</sup> mm<sup>-1</sup>, respectively. These values are more than one order of magnitude smaller than the measured values
(20−30 dB/km and ~1.5×10<sup>-9</sup> mm<sup>-1</sup>, respectively). This result suggests that the thick-wall SCW PSD is not representative
of the roughness of our fiber. We found that this discrepancy occurs at least in part because the effect of the finite
thickness of the silica membranes (only ~120 nm) is neglected. We present a new expression for the PSD that takes into
account this finite thickness and demonstrates that the finite thickness substantially increases the roughness. The
predicted loss and backscattering coefficients predicted with this thin-film SCW PSD are 30 dB/km and 1.3×10<sup>-9</sup> mm<sup>-1</sup>,
which are both close to the measured values. We also show that the thin-film SCW PSD accurately predicts the
roughness PSD measured by others in a solid-core photonic-crystal fiber.