- Published 2006

The Sagnac effect is the phase difference between two counter-propagating laser beams in the same ring resonator due to rotation, originally introduced by Sagnac in 1913[1]. It has become the basis for the operation of the optical gyroscopes such as ring laser gyroscopes and fiber optic gyroscopes after the invention of lasers and optical fibers in 1970’s [2, 3, 4, 5] because the phase and frequency difference between clockwise (CW) and counterclockwise (CCW) propagating beams are proportional to the applied angular velocity. These optical gyroscopes are normally used in airplanes, rockets, and ships etc. since they are the most precise rotation velocity sensors among any other types of gyroscopes. The Sagnac effect had been theoretically derived for the slender waveguides like optical fibers or the ring cavities composed of more than three mirrors by assuming that the light propagates one-dimensionally and the wavelength of the light is much shorter than the sizes of the waveguides or the ring cavities[1, 2, 6]. However, the sizes of the resonant cavities can be reduced to the order of the wavelength by modern semiconductor technologies [7, 8, 9]. The conventional description of the Sagnac effect is not applicable to such small resonant microcavities. Especially, the resonance wave functions are standing waves which can never be represented by the superposition of counter-propagating waves. The assumption of the existence of CW and CCW waves plays the most important role for the conventional theory of the Sagnac effect. In this Letter, by perturbation theory typically used in quantum mechanics, we show that the Sagnac effect can also be observed even in resonant microcavities if the angular velocity of the cavity is larger than a certain threshold where the standing wave resonance function changes into the rotating wave. It is also shown that numerical results of the quadrupole cavity correspond very well to the theoretical prediction. Theoretical and numerical approaches shown in this Letter do not assume that the CW and CCW waves exist in the cavity, but the pair of the counter-propagating waves is automatically produced by mixing the nearly degenerate resonance wave functions due to rotation of the cavity. According to the general theory of relativity, the electromagnetic fields in a rotating resonant microcavity are subject to the Maxwell equations generalized to a noninertial frame of reference in uniform rotation with angular velocity vector Ω[1, 2, 6, 10]. By neglecting O(h), we obtain the following wave equation for the electric field E,

@inproceedings{Sunada2006SagnacEI,
title={Sagnac Effect in Resonant Microcavities},
author={Satoshi Sunada and Takahisa Harayama},
year={2006}
}