High-Q whispering gallery traveling wave resonators for oscillator frequency stabilization

Usually a frequency-stabilized standing wave resonator-oscillator incorporating a resonator as a frequency discriminator requires a circulator to separate the injected and reflected wave, A ferrite circulator is a noisy device and can limit the phase noise or frequency stability. Moreover, we show that the noise in a circulator varies, and detailed low noise measurements are necessary to choose an appropriate quiet circulator. Thus, by realizing a configuration that does not require a circulator, an improvement in performance and reliability can be obtained. A solution to this problem is to design a high-Q whispering gallery traveling wave (WGTW) resonator. This device naturally separates the injected and reflected wave in the same way as a ring cavity at optical frequencies, without degrading the frequency discrimination. Q-factor measurements of a WGTW sapphire resonator are presented, along with a derivation of critical parameters to maximize the frequency discrimination. New measurements of noise in ferrite circulators and isolators have also been made, which is followed with a discussion on oscillator design.     

Analysis of light noise sources in a recycled Michelson interferometer with Fabry-Perot arms

We present a method by which the effect of laser field variations on the signal output of an interferometric gravitational wave detector is rigorously determined. Using the Laser Interferometer Gravitational Wave Observatory (LIGO) optical configuration of a power recycled Michelson interferometer with Fabry-Perot arm cavities as an example, we calculate the excess noise after the input filter cavity (mode cleaner) and the dependence of the detector strain sensitivity on laser frequency and amplitude noise, radio frequency oscillator noise, and scattered-light phase noise. We find that noise on the radio frequency sidebands generally limits the detector's sensitivity.     

Experimental demonstration of resonant sideband extraction in a sagnac interferometer

Sagnac interferometers have recently been proposed as a potential alternative to Michelson interferometers for the purpose of large-scale laser interferometric gravitational-wave detectors. We report on an experimental investigation of the Sagnac interferometer in two configurations: with arm cavities, and with resonant sideband extraction. Resonant sideband extraction was shown to increase the signal bandwidth by a factor of 6.5 compared with the arm cavity device, corresponding to an increase in sensitivity of as much as 6 dB for signals outside the arm cavity bandwidth. Moreover, we compare the performance of a Sagnac interferometer with resonant sideband extraction to a Michelson interferometer with resonant sideband extraction.     

Interferometric antenna response for gravitational-wave detection

The interferometric antenna response to gravitational-wave excitation is studied with the Fermi Normal Coordinate (FNC) reference system, with the limit that the gravitational wavelength must be much larger than the interferometric arm length. An optical configuration of the antenna, quite similar to the one generally considered in the long-baseline antenna projects, has been studied, i.e., Fabry-Perot optical cavities in the interferometer arms and reflectors at the input and the output of the interferometer for the purpose of recycling both the laser power and the output signals. An exact computation of the antenna response is given in a form that is also suitable to provide directly the responses for simplier optical configurations without the power or the signal recycling. Furthermore the response of the antenna for the narrow-band detection mode is also calculated. The results obtained in the FNC gauge at rest with the antenna are consistent with the ones given in the literature that were computed in the transverse traceless gauge at rest with the gravitational radiation.     

Dispersion-insensitive measurement of thickness and group refractive index by low-coherence interferometry

We describe a low-coherence interferometric technique for simultaneous measurement of geometric thickness and group refractive index of highly dispersive samples. The technique is immune to the dispersion-induced asymmetry of the interferograms, thus overcoming limitations associated with some other low-coherence approaches to this simultaneous measurement. We use the experimental configuration of a tandem interferometer, with the samples to be characterized placed in an air gap in one arm of the measurement interferometer. Unambiguous, dispersion-insensitive measurements of critical group-delay imbalances in the measurement interferometer are determined from the optical frequency dependence of interferogram phases, by means of dispersive Fourier transform spectrometry. Sample thickness and group refractive index are calculated from these group delays. A thickness measurement precision of 0.2 mum and group index measurement accuracy of 5 parts in 10(5) across a wavelength range of 150 nm have been achieved for BK7 and fused-silica glass samples in the thickness range 2000 to 6000 mum.     

Fabry-Perot resonator with interferometric read-out for low noise applications

New readout configurations for a Fabry-Perot (FP) resonator (or frequency discriminator) that combine the reflected and transmitted waves are analyzed in detail. The waves may be combined in a Sagnac (S) or Mach-Zehnder (MZ) configuration and tuned to a dark port (DP) to suppress the carrier frequency. To achieve this in a standard FP resonator, the mirror reflectance must be extremely well matched, which is a difficult and expensive task. Suppressing the carrier minimizes the Shot noise floor of a Pound-Drever-Hall (PDH) frequency-stabilized laser. Moreover, depending on the amount of carrier suppression, a high amount of power may be injected into the resonator without saturating or destroying the photodetector at the discriminator output. Because the sensitivity of the frequency discriminator is also proportional to the injected power, a large improvement in frequency noise can be achieved for high power PDH-stabilized lasers utilizing only a small phase modulation index.     

移相干涉仪环境微扰的外差检测及信号处理

对环境微振动干扰进行补偿可减小移相干涉测量的误差,其中振动量的检测是实现振动补偿的前提。以声光调制器作为光学移频器,在移相式平面干涉仪中组合成外差干涉测振系统,可以实现光程差微小变化(范围为0到1/2波长)的实时检测。在外差信号处理中采用单片RF/IF相位测量芯片直接对两路40MHz模拟信号进行比相,简化了通常使用的数字测相方法,其精确测相的典型非线性值小于1度。用该系统实际测量了周期性振动和地面冲击振动对干涉仪的影响,获得了干涉仪所受微振动的幅度和相位。     

Power-recycled resonant sideband extraction interferometer with polarization detection

Second-generation interferometric gravitational-wave detectors will use a technique called resonant sideband extraction (RSE) to improve the sensitivity in a narrow, tunable, frequency band. We present a configuration in which we use polarization detection to allow a continuously tunable power-recycled RSE interferometer for a control scheme similar to those of the first-generation detectors. A mathematical model describing this configuration and the results from a tabletop prototype are presented that demonstrate this configuration.     

Reflective grating interferometer: a folded reversal wave-front interferometer

We present a new, folded reversal interferometer. It is based on the reflective grating interferometer and can be applied for optical isolation and testing of coma aberration. The interferometer has several advantages in respect to other existing optical reversal configurations. A carrier can be easily added for phase retrieval in interferometric fringe patterns for mapping coma aberration. Furthermore, in an asymmetric optical configuration a lateral shear can also be added, transforming it in a reversal shearing interferometer. The principle of operation of the interferometer is described, and the application for measuring the coma aberration of a parabolic mirror used off axis is demonstrated.     

Comparison of linear and rotationally shearing interferometric layouts for extrasolar planet detection from space

We use the point spread function and the modulation transfer function (MTF) as two figures-of-merit to evaluate the performance of the multiaperture interferometric configurations for the detection of a faint planet in the vicinity of its bright star. We design nonredundant interferometric layouts that provide satisfactory coverage of the spatial frequencies of interest. We propose a design incorporating a rotating, rotationally shearing interferometer in a gravity-free environment and compare its performance with the Earth-based, fixed, linear configurations. The side peak of its MTF may be centered on the coordinate associated with a likely planet spatial frequency, resulting in planet signal enhancement and isolation.     

Working-point control method for readout of dynamic phase changes in interferometric fiber-optic sensors by tuning the laser frequency

A simple but reliable method, namely the working-point control by tuning the laser frequency, for the dynamic phase shift measurement in a passive homodyne interferometric fiber-optic sensor is proposed. A dc voltage calculated from the photodetector output is applied to the light source to control the interferometer at the condition of maximum sensitivity. Then the signal's phase shift can be obtained from the components of zero and fundamental frequencies. To test the method, an all polarization-maintaining Mach-Zehnder interferometer with a piezoelectric ceramic (PbZrTiO(3), or PZT) cylinder in one arm is constructed. The experimental results show that the simulation signal's phase shift generated by the PZT cylinder can be read out correctly with the method. It has the advantages of simplicities of operation, no-active element in the sensing head, and large operating bandwidth. It can be used for readout of dynamic phase shifts in various interferometric fiber-optic sensors.     

Interferometric measurement of laser heating in praseodymium-doped YAG crystal

Temperature measurement is required for many applications but can be difficult in some cases. Laser heating or cooling studies demand accurate measurements of temperature changes. A Michelson interferometer configuration has been used to investigate laser heating in solids. An analytical formula was derived to estimate the temperature change from the fringe count by taking into account the temperature dependence of the sample length and refractive index. When 115?mW of a focused Ar+ laser beam (488?nm) passes through a Pr(3+)-doped YAG sample, its temperature increased by 11.7±1.0?K along the beam path due to nonradiative relaxation. The power dependence of the fringe count/movement was recorded. The temperature change was estimated by the interferometric method and is in agreement with that measured by a thermocouple.     

Optical frequency-domain ranging using a frequency-shifted feedback distributed-feedback laser

A distributed-feedback (DFB) laser is used in a frequency-shifted external cavity configuration to generate a frequency comb. The frequency comb generates a beat frequency in a Michelson interferometer, which is proportional to the path difference of a target and reference arm. The calculated and actual readings for the beat frequency are in good agreement. A proof of principle demonstration of using a DFB laser for optical frequency-domain ranging is shown for the first time.     

Modeling the interferometric radius measurement using Gaussian beam propagation

We model the interferometric radius measurement using Gaussian beam propagation to identify biases in the measurement due to using a simple geometric ray-trace model instead of the more complex Gaussian model. The radius measurement is based on using an interferometer to identify the test part's position when it is at two null locations, and the distance between the positions is an estimate of the part's radius. The null condition is observed when there is no difference in curvature between the reflected reference and the test wavefronts, and a Gaussian model will provide a first-order estimate of curvature changes due to wave propagation and therefore changes to the radius measurement. We show that the geometric ray assumption leads to radius biases (errors) that are a strong function of the test part radius and increase as the radius of the part decreases. We tested for a bias for both microscaled (<1 mm) and macroscaled parts. The bias is of the order of parts in 10(5) for micro-optics with radii a small fraction of a millimeter and much smaller for macroscaled optics. The amount of bias depends on the interferometer configuration (numerical aperture, etc.), the nominal radius of the test part, and the distances in the interferometer.     

Direct Static Strain Measurement Utilizing Signal Fading and Spectrum Analysis in a Fibre Optic Interferometric Sensor

Abstract

An accurate linear method of static phase shift measurement in a fibre optic interferometric strain sensor, based on the concurrent utilization of signal fading, photovoltage spectrum analysis and the arctangent function, is presented. The static phase shift is superimposed on a controlled dynamic phase modulation derived from an optical phase modulator in one arm of the interferometer. Good agreement is demonstrated between the phase shift obtained through experiment and that from the theoretical expression. This detection scheme has wide applications to static and dynamic phase shift measurements in fibre optic interferometric sensors, and to optical interferometry in general.     

Generalized formula for continuous-wave end-pumped Yb-doped material amplifier gain and laser output power in various pumping configurations

We present a general formula fitted for computing the amplification and laser output power in a Yb-doped material under various quasi-end-pumping configurations. These configurations include single pass pumping, backreflection pumping in which the pump is reflected by a mirror set on the rear face of the amplifier medium, contrapropagation pumping where two pump beams are launched on both sides of the amplifier and, for every configuration, regenerative pumping in which the transmitted or reflected pump beam is recycled using the proper apparatus. We show that, with regenerative pumping, the efficiency is drastically improved and the optimum amplifier length leading to the maximum laser output power is shorter compared with the one obtained with conventional pumping. In this model, we do not take temperature effect into account.     

Self-referenced rectangular path cyclic interferometer with polarization phase shifting

A polarization phase shifting interferometer using a cyclic path configuration for measurement of phase nonuniformities in transparent samples is presented. A cube beam splitter masked by two linear polarizers is used to split the source wavefront into two counter propagating linearly polarized beams that pass through the sample. At the output of the interferometer, the two orthogonally polarized beams are rendered circularly polarized in the opposite sense through the use of a quarter wave plate. Finally, phase shifting is achieved by rotating a linear polarizer before the recording plane. In a rectangular path interferometer, although the two counter propagating wavefronts are laterally folded with respect to each other in the interferometer arms, the beams finally emerge mutually unfolded at the output of the interferometer. This phenomenon is utilized to create a reference if the sample is introduced in one lateral half of the beam in any one of the interferometer arms. The polarization phase shifting technique is used to generate four phase-shifted interferograms, which are utilized to evaluate the phase profile of the phase sample. Experimental results presented validate the proposed technique.     

Resonance ring interferometry with incoherent light

A new method of measuring the phase nonreciprocity in a passive ring resonator using a light source of low coherence is described. The method provides effective suppression of noise from the backscattering of light in the ring resonator and insensitivity of the interferometer to excursions of the resonance frequencies of the resonator due to reciprocal effects (e.g., thermal expansion) and also permits modulation and compensation of the phase nonreciprocity by using a device outside the resonator to shift the frequency of the light. One version of a low-coherent resonance ring interferometer is examined, viz., a two-transit asymmetric interferometer with a rotating mirror. Pis’ma Zh. Tekh. Fiz. 24, 24–29 (September 12, 1998)     

Signal extraction in a power-recycled michelson interferometer with fabry-perot arm cavities by use of a multiple-carrier frontal modulation scheme

We present a signal extraction scheme for longitudinal sensing and control of an interferometric gravitational-wave detector based on a multiple-frequency heterodyne detection technique. Gravitational-wave detectors use multiple-mirror resonant optical systems where resonance conditions must be satisfied for multiple degrees of freedom that are optically coupled. The multiple-carrier longitudinal-sensing technique provides sensitive signals for all interferometric lengths to be controlled and successfully decouples them. The feasibility of the technique is demonstrated on a tabletop-scale power-recycled Michelson interferometer with Fabry-Perot arm cavities, and the experimentally measured values of the length-sensing signals are in good agreement with theoretical calculations.     

Polarization characterization of a Mach-Zehnder interferometer

Polarization characterization of a Mach-Zehnder interferometer, based on the state of polarization (SOP) and power measurement at the interferometer output, is presented. We study the SOP and degree of polarization (DOP) of the output light, first as a function of the light power in each arm of the interferometer for a fixed input SOP and DOP, and second as a function of the SOP's in each arm of the interferometer for a fixed input power. Stokes formalism and the Poincaré sphere are used for simultaneous representation of the SOP and DOP, as well as their evolution. It is shown that the SOP and DOP stability and also the output light power are highly dependent on the light source coherence. Knowledge of these different parameters leads to configurations that allow simultaneous control of the SOP and DOP. We can hence realize a quasi-monochromatic nonpolarized light source, which is useful for the polarization-independent characterization of optical components.