Abstract

We present the evolution of the eigenmode frequency spectrum in a nonplanar ring resonator based on the Jones matrix and the Fresnel–Kirchhoff diffraction integral. Taking the modes ${\mathrm{TEM}}_{(q+1)01}$ and ${\mathrm{TEM}}_{q10}$ with different polarization states as examples, we numerically derive the frequency difference between them versus the folding angles of the resonator by considering the polarization and the light field distribution of the eigenmodes synchronously. It can be found that the extreme values of frequency difference between ${\mathrm{TEM}}_{(q+1)01}$ and ${\mathrm{TEM}}_{q10}$ are particularly affected by the polarization states of the eigenmode, and the locations of these consecutive extreme values correspond to the total image rotation angle with values of the integer multiple of 90°. Moreover, the influence of the resonator structure on the frequency difference of eigenmodes with the identical polarization state is also analyzed. The results prove that the frequency difference between the fundamental mode and higher order modes declines with the increase of the spherical mirrors’ radius of curvature but increases with the augmentation of the resonator’s total length. These interesting findings are important for the mode selection in high-accuracy ring laser gyroscopes with nonplanar structure by modulating the polarization states and the light field distribution of the eigenmodes to control the frequency difference between them.

© 2016 Optical Society of America

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