Accurate measurement of the radius of curvature of a concave mirror and the power dependence in a high-finesse Fabry-Perot interferometer

Three-spherical-mirror test for radius of curvature measurement using a Fabry-Pérot cavity

A three-spherical-mirror test method that uses a Fabry-Pérot (FP) cavity is proposed for a radius of curvature measurement system, especially for radii larger than 10 m. By using the three-spherical-mirror test with mode spacing measurement in an FP cavity, the local value of the radius of curvature of a mirror can be determined in situ and this mirror can then be used as the reference spherical mirror in a radius of curvature measurement system. We demonstrated determinations of radii of curvature of around 10 m using the three-spherical-mirror test with uncertainties of around 1.5 × 10^-4 and then measured the radius of curvature of around 20 m with uncertainties of around 3.1 × 10^-4 by using the spherical mirror, of which the radius of curvature was determined by the three-spherical-mirror test, as the reference sphere. The proposed system has high practical applicability because measurements can be conducted under usual air conditions and the measurement results are directly traceable to the time standard because beat frequency measurement is used.

A deep optical cavity trap for atoms and molecules with rapid frequency and intensity modulation

We describe a deep far-off resonance trap for metastable argon atoms utilizing a medium finesse cavity and a high input power (30 W) to produce trap depths of up to 11 mK. The depth can be rapidly modulated allowing efficient loading of the trap, characterization of trapped atom temperature, and reduction of intensity noise. We measure the change in radius of curvature of the mirrors due to heating by the high circulating intensity and show that trapping is not adversely effected by this for all input powers.

Technique for in situ measurement of free spectral range and transverse mode spacing of optical cavities

Length and g-factor are fundamental parameters that characterize optical cavities. We developed a technique to measure these parameters in situ by determining the frequency spacing between the resonances of fundamental and spatial modes of an optical cavity. Two laser beams are injected into the cavity, and their relative frequency is scanned by a phase-lock loop, while the cavity is locked to either laser. The measurement of the amplitude of their beat note in transmission reveals the resonances of the longitudinal and the transverse modes of the cavity and their spacing. This method proves particularly useful to characterize complex optical systems, including very long and/or coupled optical cavities, as in gravitational-wave interferometers. This technique and the results of its application to the coupled cavities of a 40 m-long gravitational-wave interferometer prototype are presented here.

Modal frequency degeneracy in thermally loaded optical resonators

We observe power coupling from the fundamental mode to frequency-degenerate higher-order spatial modes in optical resonators illuminated with a 30 W laser. Thermally-induced modal frequency degeneracy facilitates power transfer from the fundamental mode to higher-order modes, reduces power coupling into the cavity, and triggers power fluctuations. Modeling thermoelastic deformation of a mirror's surface shows predicted modal frequency degeneracy to be in reasonable agreement with experimental observations. Predictions for the Laser Interferometer Gravitational-wave Observatory (LIGO) show that the circulating fundamental-mode power necessary for gravitational-wave detection is compromised at coating absorptions of 3.8 and 0.44 ppm for Enhanced and Advanced LIGO Fabry-Pérot cavities, respectively.

Characterization of scattering in an optical Fabry-Perot resonator

Roughness-induced scattering affects the performance of a resonator. We study the scattering of a single mirror first and compare the result with the losses of a two-mirror Fabry-Perot resonator. Besides some standard tools to characterize the losses, a new method based on the spectrally averaged transmission is introduced.

High-extinction-ratio resonant cavity polarizer for quantum-optics measurements

The use of a high-finesse Fabry-Perot ring cavity with an odd number of reflections as a high-extinction-ratio resonant polarizer is shown. Experimental results from quantum-noise measurements using resonant cavities as spatial and spectral filters and precision polarizers are presented.

Gouy phase of nonparaxial eigenmodes in a folded resonator

We study the effect of nonparaxiality in a folded resonator by accurate measurements of the Gouy phase as a function of the mode number for mode numbers up to 1500. Our experimental method is based on tuning the resonator close to a frequency-degenerate point. The Gouy phase shows a nonparaxial behavior that is much stronger in the folding plane than in the perpendicular plane. Agreement with ray-tracing simulations is established, and a link with aberration theory is made.