We review photonic applications of dielectric whispering-gallery mode (WGM) resonators-tracing the growth of the technology from experiments with levitating droplets of aerosols to ultrahigh-Q solid state crystalline and integrated on-chip microresonators.

Optical resonators with whispering-gallery modes-part II: applications

The preparation, or generation of coherent states, squeezed states, and photon number states is discussed. The quantum noise is evaluated for various simultaneous measurements of two quadrature components: heterodyning, the beam splitter followed by two single quadrature measurements, the parametric amplifier, the (degenerate and/or nondegenerate) four-wave mixer, the Brillouin and Raman amplifiers, and the laser amplifier. A quantum nondemolition measurement followed by a measurement of the conjugate variable is also categorized as a simultaneous measurement. It is shown that, for all of these schemes, the minimum uncertainty product of the measured variables is exactly equal to that required for a simultaneous measurement of two noncommuting variables. On the other hand, measurements of a single quadrature component are noise-free. Such measurements are degenerate heterodyning, degenerate parametric amplification, and cavity degenerate four-wave mixing and photon counting by a photomultiplier or avalanche photodiode. The Heisenberg uncertainty principle and the quantum-mechanical channel capacity of Shannon are discussed to address the question "How much information can be transmitted by a single photon?" The quantum-mechanical channel capacity provides an upper bound on the achievable information capacity and is ideally realized by photon number states and photon counting detection. Its value is $\frac{\ensuremath{\hbar}\ensuremath{\omega}}{(\mathrm{ln}2)kT}$ bit per photon. The use of coherent or squeezed states and a simultaneous measurement of two quadrature field components or the measurement of one single quadrature field component does not achieve the ultimate limit.

Preparation, measurement and information capacity of optical quantum states

A stimulated Brillouin fiber ring laser with a spectral width of 2 kHz and an intrinsic linewidth of less than 30 Hz has been demonstrated. Applications of such a laser include laser linewidth narrowing, microwave frequency generation, high-rate amplitude modulation, and optical inertial rotation sensing.

Narrow-linewidth stimulated Brillouin fiber laser and applications

A passive fiber-optic resonator technique for rotation sensing has been investigated. Preliminary data show a noise-equivalent rotation-rate sensitivity of 0.5°/h (τ= 1 sec), which is an order of magnitude above the photonshot-noise limit. The major sources of error and ways of reducing such errors are discussed.

Passive fiber-optic ring resonator for rotation sensing.

Over the last two decades a series of large ring laser gyroscopes have been built having an unparalleled scale factor. These upscaled devices have improved the sensitivity and stability for rotation rate measurements by six orders of magnitude when compared to previous commercial developments. This progress has made possible entirely new applications of ring laser gyroscopes in the fields of geophysics, geodesy, and seismology. Ring lasers are currently the only viable measurement technology, which is directly referenced to the instantaneous rotation axis of the Earth. The sensor technology is rapidly developing. This is evidenced by the first experimentally viable proposals to make terrestrial tests of general relativistic effects such as the frame dragging of the rotating Earth.

Invited Review Article: Large ring lasers for rotation sensing

As part of a program to develop sensitive laser inertial rotation sensors, we have studied the performance of a passive-resonator technique using a 0.7-m × 0.7-m optical cavity. For an averaging time τ of 10 sec, the random drift was 1.1 × 10−2 deg/h, which was consistent with the shot-noise limit for the present setup. For a longer averaging time the random drift was 5.6 × 10−3 deg/h (τ = 90 sec), showing a slight departure from the shot-noise limit. The problems encountered in the present apparatus, as well as those that are critical in the development of much larger resonators for geophysics and relativity applications, are discussed.

Passive ring resonator method for sensitive inertial rotation measurements in geophysics and relativity

Measurements of the Fresnel drag in moving glass media were performed using a passive ring-resonator method. The effective drag coefficient was measured for various glass samples of different indices of refraction and dispersions. When we averaged 15 separate measurements, we obtained overall agreement with theory that was well within our ±2.8 × 10−4 measurement uncertainty, thus providing, to our knowledge, the most accurate verification of Fresnel drag thus far.

Measurement of Fresnel drag in moving media using a ring-resonator technique

The observation of a dependence of the measured resonance frequency of an optical cavity on the size and position of the detector is reported and attributed to the presence of higher-order transverse modes in the cavity. This effect, which is due to the nonorthogonality of these modes when averaged over a limited aperture or an inhomogeneous detector surface, has been carefully studied. The results of our calculations are in good agreement with experimental observations. Methods of minimizing such frequency-pulling effects are suggested.

Observation of spatial variations in the resonance frequency of an optical resonator

The resonators investigated include a mirror resonator and also an all -fiber resonator.Preliminary performance data and important sources of error are presented.The interest in passive ring resonator gyros' rather than active resonator2 ones(commonly referred to as ring laser gyros or RLG) is based on the fact that the passiveresonator approach offers very simple solutions to the major problems encountered in RLG's,such as lock -in and other gain medium related effects. In addition, the passive resonatorapproach lends itself to the development of an all solid state optical gyro.The operation of a passive ring resonator gyro is based on the measurement of thedifference in resonance frequency, Af, for counter -propagating fields induced by an inertialrotation rate,

Passive Resonator Gyro

The drift performance of an optical rotation sensor employing a passive ring cavity is presented. With a square cavity of about 17 cm on a side, and a 1 mW external laser, the rms fluctuation in the measurement of rotation was 0.45°/hour for an integration time of 1 second. This is consistent with the shot-noise-limited performance expected for the present setup.

Passive Cavity Optical Rotation Sensor

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