Sub-nanoradian phase sensing in Optical Parametric Oscillator cavities

In a typical sensor, the quantity to be measured modifies the phase of a probe optical beam, which is detected by interference with a reference beam. If these two interfering beams are produced in an active laser cavity, the resonance condition of the laser converts the phase shift into a frequency (phase per round-trip time). The sensor measures a beat frequency, with a larger dynamic range and less noise than the amplitude measurement of two interfering beams. So far, this property is only exploited in laser gyroscopes, where the probe and reference are two counter circulating beams. This intracavity interferometry can be extended to linear cavities by using, instead of cw beams, ultrashort pulses. Detection of an electro-optic phase with a sensitivity better than 0.4 nanoradian is demonstrated with an Optical Parametric Oscillator (OPO) synchronously pumped by a mode-locked Ti:sapphire laser of half cavity length. The phase-photon number uncertainty was lower to 0.66, close to the quantum limit of 0.5. A phase difference of 0.4 nanoradians corresponds to an elongation of 0.1 fm. This type of precision is beyond mechanical stability of bulk optics but can be exploited in an integrated circuit implementation (OPO on a chip) that is described. A theory is presented showing that, for a given phase detection, the frequency of the beat note can be amplified, without a proportional increase in noise. The enhancement, obtained through resonant negative dispersion at selected modes, does not come at the expense of noise (Petermann factor remains = 1).