The frequency response of the ring gyrometer in the linear approximation

We consider an optical ring resonator on a rotating basis taking into account the back reflection of the traveling waves propagated in it, and offer a model of the resonator including all of the above factors. Within the study we solve the spectral problem generated by the equations of this model, and obtain the expressions for the natural frequencies and modes (natural vibrations). The findings of the research illustrate that the difference of the natural frequencies functionally depends on the angular rotation velocity of the resonator, i.e. it is the frequency response of the ring gyrometer. This feature preserves the main features of the frequency characteristics of the real laser gyrometer: has a dead band and a characteristic dependence outside of it. It enables us to consider the frequency response calculated within the research to be an acceptable linear approximation of the frequency response of the real (nonlinear) gyrometer. Consequently, we conclude that that the modes of the ring resonator with backscattering are not the traveling waves, and on each of the natural frequencies there is a mixed wave. As a result, we make the calculation ofsuch waves and build the computer graph of the frequency response.

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