Sagnac effect in ring lasers and ring resonators. How does the refraction index of the optical medium influence the sensitivity to rotation?
Federal Research Center Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation
The Sagnac effect in a ring laser (RL) results in that the generation differences of counterpropagating waves differ by an amount proportional to the RL’s angular rotation rate. This paper addresses the question of how an optical medium filling the whole or part of the RL influences the frequency difference of the counterpropagating waves. While the formulas for this difference in a rotating RL abound in the literature, there is no agreement between them as to whether the medium increases, decreases or leaves unchanged this difference. Nor do the available (and often contradictory) experimental data fully clarify the situation. Because the Sagnac effect is a special relativity effect, the relativistic velocity addition law is here used to calculate the frequency difference of counterpropagating waves in an RL. When a homogeneous optical medium fills the entire perimeter of the resonator of the rotating RL, it is shown that the frequency difference of the counterpropagating waves is inversely proportional to the refraction index of the medium. Also, the results obtained can be used to calculate the difference of the resonant frequencies of counterpropagating waves in rotating ring resonators in the presence of an optical medium.