Intracavity phase interferometry: frequency combs sensor inside a laser cavity

Abstract

In traditional interferometric measurements, a physical quantity that changes the phase of a resonator is monitored through a change of its transmission. Interferometry inside a laser exploits the ultimate Q‐factor of that resonator, and converts the phase to be measured into a frequency. A mode‐locked laser with two intracavity pulses emits two frequency combs of the same repetition rate. The quantity to be measured (a sub‐nano displacement, a nonlinear index, an acceleration or rotation, a magnetic or electric field) produces a minute phase change (≥10−10 rad) in one of the two intracavity pulses, which is converted into a frequency, measured by beating the two pulse trains emitted by the laser. This paper presents methods of operating mode‐locked lasers in which two independent pulses circulate, producing two frequency combs of the same repetition rate. Various examples of physical quantities that can be measured through this technique are presented.

Impact of resonant dispersion on the sensitivity of intracavity phase interferometry and laser gyros

“…In the general case of "Intracavity Phase Interferometry" (IPI), which involves linear as well as ring modelocked lasers, a physical quantity to be measured (nonlinear index, magnetic field, rotation, acceleration, electro-optic coefficient, fluid velocity, linear index) creates a differential phase shift ∆φ between the two pulses, which, because of the resonance condition of the laser, is translated into a difference in optical frequency [6]. This difference is measured as a beat note produced when interfering the two frequency combs generated by the laser.…”

“…1. In a mode-locked laser gyro, as with any implementation of intracavity phase interferometry, the two circulating pulses have to meet at the same point at every round-trip [6]. As the pulses circulating in opposite direction see an optical length differential, decreased or augmented by the giant dispersion, one would expect that the crossing point cannot be maintained, if the pulse velocity were simply equal to 1/(dk/dΩ).…”

“…The expression "gyro response" is usually understood as the beat note frequency measured between the two outputs corresponding to oppositely circulating beams in a ring laser, as a function of the rotation of the laser about an axis orthogonal to its plane. This is only a particular case of "Intracavity Phase Interferometry" (IPI) where a mode-locked laser is used as an interferometer in which two pulses circulate independently [6]. The frequency of the beat note obtained by interfering the two output frequency combs (corresponding to each of these intracavity pulses) is a measure of a differential phase shift at each round trip between the circulating pulses.…”

Controlling group and phase velocities in bidirectional mode-locked fiber lasers

“…The bandwidth of the beat note can be as small as 0.2 Hz [10], even though each comb has a bandwidth larger than 1 MHz, again indicating the correlation between combs. The beat note produced by the interference of the two combs can be expressed as [9]:…”

Self-induced transparency and coherent population trapping of ^87Rb vapor in a mode-locked laser

“…If the modes are locked, the laser produces a frequency comb, of which the characteristics-repetition rate and carrier frequency to envelope offset (CEO)-are extremely sensitive to the dispersive properties of intracavity elements. This property was exploited to measure intracavity phase shifts of less than 10 −8 [2]. Intracavity phase interferometry has been applied to magnetometry by inserting a transparent sample with nonzero Verdet constant in a ring laser with two-pulses per cavity roundtrip [3].…”