Laser Gyroscope with Anomalous Dispersion

(research in collaboration with Prof. Jean-Claude Diels, University of New Mexico, Albuquerque, NM)

Lately, in the field of optical gyroscopes, we often hear about slow and fast light gyros. This started with a theoretical paper in 2000 [1]; a recent paper offers an overview and extensive references of theoretical research that has been done in this field [2]. The conclusion of the latter paper is that dispersion manipulation of passive gyros (e.g. Fiber Optics Gyros, FOG) does not lead to any improvement in performance, as it was originally suggested. In contrast, for the active laser gyro (Ring Laser Gyro, RLG), a steep anomalous dispersion results in an increase in sensitivity. This enhancement in sensitivity will indeed be at the expense of noise and dead band, if one considers only cw laser gyros, as it was done in [2]. However, it was demonstrated that in mode-locked operation, a ring laser gyro has no dead band if the pulse crossing points are placed in a region that is free of backscattering (air or ideally vacuum) [3]. More of that below.

Principle: The above figure shows three ways to visualize, what is happening in a rotating RLG. For simplification, a circular ring is assumed. A clockwise (CW) and a counterclockwise (CCW) wave are generated. (c - speed of light, R - radius, P - perimeter, A - area, λ=c/ν - wavelength at rest, Ω - angular velocity of the RLG, Δν - observed beat frequency)

Mode-locked RLG: Using a mode-locked ring laser gyro has the following advantages:

Dispersion: Adding a large amount of dispersion to the RLG amplifies (negative dispersion, dn/dν < 0) or counteracts (positive dispersion, dn/dν > 0) the rotation-induced frequency shift of the two waves (see image below). The larger the (anomalous) dispersion, the larger the theoretical enhancement of the sensitivity (d(Δν)/dΩ) of the RLG. Such large dispersion can be realized e.g. by electromagnetically induced transparency (EIT) or by specifically designed dielectric layers (Gires-Tournois-Interferometer). However, a huge dispersion like this can only be realized over a very narrow wavelength range, which is much smaller than the usual bandwidth of mode-locked lasers.

Remark: To use the terms slow and fast light seems to be out of place here, since only continuous wave (cw) laser gyros were considered so far. There is no significant change of the phase velocity of the light for the two counter-circulating waves. Only the group velocity changes and becomes very small for a large dispersion, which cannot be noticed for cw gyros.



[1] U. Leonhardt and P. Piwnicki "Ultrahigh sensitivity of slow–light gyroscope" Phys. Rev. A 62 (2000) 055801, also available at

[2] S. Schwartz, F. Goldfarb, and F. Bretenaker "Some considerations on slow and fast-light gyros" Opt. Eng. 53 (2014) 102706-1. (access via SPIE)

[3] M. Lai, J.-C. Diels, and M. Dennis "Nonreciprocal measurements in fs ring lasers" Opt. Lett. 17 (1992) 1535. (access via Optica)

[4] James Hendrie, Matthias Lenzner, Hanieh Afkhamiardakani, Jean Claude Diels, and Ladan Arissian "Impact of resonant dispersion on the sensitivity of intracavity phase interferometry and laser gyros" Opt. Express 24 (2016) 30402. (open access)

[5] X. Zhu, M. Lenzner, and J.-C. Diels "Phase Nanoscopy with Correlated Frequency Combs" sensors 23 (2023) 301. (open access)