Interferometer Utilizing Free Masses as a Device for Measuring Gravitational Gradients

A Fabry–Perot–Michelson optical interferometer utilizing suspended mirrors is considered as a device for measuring low-frequency variations of the Earth's gravitational field. The operating principles of the instrument, the system for maintaining the angular alignment of the mirrors at the operating point, and a simplified model of the gravitational field are all described. The variations of the field at the location of the interferometer are modeled numerically and estimates are given of the magnitudes of the measurable effects. The results are used as a basis for modeling the operation of the instrument as a whole.     

Fourier transform interferometer alignment method

A rapid and convenient method has been developed to facilitate the alignment of the image-plane components of point-diffraction interferometers, including the phase-shifting point-diffraction interferometer. In real time, the Fourier transform of the detected image is used to calculate a pseudoimage of the electric field in the image plane of the test optic where thecritical alignment o f variousoptical components is performed. Reconstruction of the pseudoimage is similar to off-axis, Fourier transform holography. Intermediate steps in the alignment procedure are described. Fine alignment is aided by the introduction and optimization of a global-contrast parameter that is easily calculated from the Fourier transform. Additional applications include the alignment of image-plane apertures in general optical systems, the rapid identification of patterned image-plane alignment marks, and the probing of important image-plane field properties.     

Alignment of an interferometric gravitational wave detector

Interferometric gravitational wave detectors are designed to detect small perturbations in the relative lengths of their kilometer-scale arms that are induced by passing gravitational radiation. An analysis of the effects of imperfect optical alignment on the strain sensitivity of such an interferometer shows that to achieve maximum strain sensitivity at the Laser Interferometer Gravitational Wave Observatory requires that the angular orientations of the optics be within 10(-8) rad rms of the optical axis, and the beam must be kept centered on the mirrors within 1 mm. In addition, fluctuations in the input laser beam direction must be less than 1.5 x 10(-14) rad/ radicalHz in angle and less than 2.8 x 10(-10) m/ radicalHz in transverse displacement for frequencies f > 150 Hz in order that they not produce spurious noise in the gravitational wave readout channel. We show that seismic disturbances limit the use of local reference frames for angular alignment at a level approximately an order of magnitude worse than required. A wave-front sensing scheme that uses the input laser beam as the reference axis is presented that successfully discriminates among all angular degrees of freedom and permits the implementation of a closed-loop servo control to suppress the environmentally driven angular fluctuations sufficiently.     

Single actuator alignment control for improved frequency stability of a cavity-based optical frequency reference

We demonstrate a method of controlling the alignment of a laser beam to a Fabry-Perot resonator through synchronous detection of the misalignment arising from modulating the orientation of a single beam-steering mirror. The horizontal and vertical tilt of the mirror are modulated in quadrature to drive a circular motion of the beam orientation. A corresponding modulation of the intensity of the optical field circulating in the cavity is measured at either the reflected or transmitted port and demodulated synchronously to derive two error signals to indicate the vertical and horizontal misalignment. These signals are fed back to the beam-steering mirror to suppress fluctuations below 30 Hz. This method avoids the complexity of monitoring off-axis cavity modes and is particularly effective in the case where unwanted pointing fluctuations are introduced by one or two elements in the optical setup. We have applied the technique to two Fabry-Perot resonators in use as precision frequency references, delivering a result of 10 dB suppression of alignment fluctuations at 1 Hz and an improvement in frequency stability by up to a factor of 4.     

Systematic errors in nulling interferometers

Nulling interferometers combine on-axis suppression with high angular resolution, making them ideal instruments for the direct detection of faint planets close to their parent star. Analysis is developed to show that it is systematic errors, resulting from fluctuations in the null depth, that drive the instrument performance. A second-order combination of amplitude and phase errors is the dominant contributor. In the calculated example, the detection of an Earthlike planet around a Sunlike star at 15 pc requires that the arms of the interferometer must be phased to within approximately 1.5 nm and have their amplitudes matched to approximately 0.1%.     

Quantum-statistical analysis of multimode far-infrared and submillimeter-wave astronomical interferometers

We present a detailed quantum-statistical model of multimode far-infrared and submillimeter-wave astronomical interferometers. The scheme identifies explicitly the optical modes associated with each telescope and uses these to trace the quantum-statistical properties of the field from a source through the telescopes, through the beam combiners, and onto the detectors. The scheme can be used with any optical configuration, and elegant expressions result for the average rate at which photons are detected by the pixels of an imaging array, the mean-square fluctuations in the rates, and the correlations between the fluctuations in the rates of different pixels. Numerous extensions to the basic technique are possible.     

Effect of multiple equidistant imaging: analyzing the techniques of its monochromatic reproduction and the forms of manifestation

Monochromatic imaging systems with spatial-frequency filters in the form of Fabry-Perot interferometers, concentric ring masks, and diffractive multifocal lenses are shown to realize the same effect of multiple equidistant imaging. However, the forms of manifestation of this effect are not identical due to the difference in spectral content of generated wave fields. Self-imaging fields with a discrete angular spectrum inherent in the systems with masks and interferometers are found to comprise a subclass of periodically focused fields with a continuous angular spectrum peculiar to the systems with diffractive multifocal lenses. The advantages of the latter systems are the extremely high total light efficiency and the sharply defined longitudinal localization of generated wave fields, which enhance the brightness of the reproduced images and decreases their parasitic diffraction dispersion, background noise, and blurring.     

Quasi-Hermitian Hamiltonians,minimum-uncertainty (MU) angular momentum states and interferometers

Minimum-uncertainty (MU) angular momentum states which are eigenstates of a nonunitary angular momentum displacement operator are found also to be eigenstates of a quasi-Hermitian Hamiltonian which has a certain metric with real eigenvalues. Various properties of these states are discussed. The relations between electromagnetic (EM) MU angular momentum states which have been proposed for improving the resolution in interferometers and the present theory are discussed.     

In situ Interferometric alignment systems for the assembly of microchannel relay systems

An interferometric alignment technique developed for the assembly of microchannel relay systems is described. The method uses pairs of diffractive lenslets that are arranged to form compact in situ interferometers. The relative transverse, longitudinal, and rotational alignment of the two lenslet arrays can be quantitatively determined from the resulting interference patterns. The theoretical analysis is compared with the experimental performance.     

Phase-shifting technique for improving the imaging capacity of sparse-aperture optical interferometers

We describe the principle of a multiaperture interferometer that uses a phase-shifting technique and is suitable for quick snapshot imaging of astrophysical objects at extreme angular resolution through Fourier inversion. A few advantages of the proposed design are highlighted, among which are radiometric efficiency, field of view equivalent to those of Fizeau interferometers, and a preliminary calibration procedure allowing characterization of instrumental errors. For large telescope numbers, the proposed design also results in considerable simplification of the optical and mechanical design. Numerical simulations suggest that it should be possible to couple hundreds of telescopes on a single 4K × 4K detector array, using only conventional optical components or emerging technologies.     

A Spaceborne Gravity Gradiometer Concept Based on Cold Atom Interferometers for Measuring Earth’s Gravity Field

We propose a concept for future space gravity missions using cold atom interferometers for measuring the diagonal elements of the gravity gradient tensor and the spacecraft angular velocity. The aim is to achieve better performance than previous space gravity missions due to a very low white noise spectral behavior and a very high common mode rejection, with the ultimate goals of determining the fine structures of the gravity field with higher accuracy than GOCE and detecting time-variable signals in the gravity field better than GRACE.     

Optical polarimetry for noninvasive glucose sensing enabled by Sagnac interferometry

Optical polarimetry is used in pharmaceutical drug testing and quality control for saccharide-containing products (juice, honey). More recently, it has been proposed as a method for noninvasive glucose sensing for diabetic patients. Sagnac interferometry is commonly used in optical gyroscopes, measuring minute Doppler shifts resulting from mechanical rotation. In this work, we demonstrate that Sagnac interferometers are also sensitive to optical rotation, or the rotation of linearly polarized light, and are therefore useful in optical polarimetry. Results from simulation and experiment show that Sagnac interferometers are advantageous in optical polarimetry as they are insensitive to net linear birefringence and alignment of polarization components.     

Optimization of displacement-measuring quadrature interferometers considering the real properties of optical components

We present the influence of alignment and the real properties of optical components on the performance of a two-detector homodyne displacement-measuring quadrature laser interferometer. An experimental method, based on the optimization of visibility and sensitivity, was established and theoretically described to assess the performance and stability of the interferometer. We show that the optimal performance of such interferometers is achieved with the iterative alignment procedure described.     

Imaging properties of rotating nulling interferometers

Nulling interferometers combine on-axis suppression with high angular resolution, making them ideal instruments for the direct detection of faint planets close to their parent star. The synthesized point-spread function for a rotating nulling interferometer utilizing phase chopping is shown to consist of a main peak, satellite peaks, and their associated sidelobes, and simple analytic expressions are derived for the modulation efficiency and angular resolution. Sufficient angular resolution is vital for the detection and characterization of multiple-planet systems and requires that some configurations be substantially larger than previously thought. The corresponding increase in stellar leakage has a major effect on performance and can be a deciding factor in the choice of array configuration.     

Diode-laser-to-waveguide butt coupling

A diode-laser-to-waveguide butt-coupling model is described. The model takes into consideration the Fabry-Perot reflection and transmission of the étalon formed by the laser front facet and the waveguide entrance facet. The model predicts coupling efficiency and the coupled-power fluctuations that occur versus the separation between the laser and the waveguide. Calculations performed for Fabry-Perot-laser-to-KTP waveguide coupling show that the transverse and the angular alignment tolerances of the waveguide can be increased when the waveguide entrance facet is antireflection coated. The longitudinal alignment tolerance of the waveguide can be increased by use of an index-matching gel between the laser and the waveguide.     

Multiconjugate adaptive optics for large telescopes: analytical control of the mirror shapes

We present an analytical algorithm for deriving the shapes of the deformable mirrors to be used for multiconjugate adaptive correction on a large telescope. The algorithm is optimal in the limit where the overlap of the wave-front contributions from relevant atmospheric layers probed by the guide stars is close to the size of the pupil. The fundamental principle for correction is based on a minimization of the sum of the residual power spectra of the phase fluctuations seen by the guide stars after correction. On the basis of the expressions for the mirror shapes, so-called layer transfer functions describing the distribution of the correction of a single atmospheric layer among the deformable mirrors and the resulting correction of that layer have been derived. It is shown that for five guide stars distributed in a regular cross, two- and three-mirror correction will be possible only up to a maximum frequency defined by the largest separation of the conjugate altitudes of the mirrors and by the angular separation of the guide stars. The performance of the algorithm is investigated in the K band by using a standard seven-layer atmosphere. We present results obtained for two guide-star configurations: a continuous distribution within a given angular radius and a five-star cross pattern with a given angular arm length. The wave-front fluctuations are subjected to correction using one, two, and three deformable mirrors. The needed mirror dynamic range is derived as required root-mean-square stroke and actuator pitch. Finally the performance is estimated in terms of the Strehl ratio obtained by the correction as a function of field angle. No noise has been included in the present analysis, and the guide stars are assumed to be at infinity.     

Switching waves in thick bistable interferometers at an oblique radiation incidence

Special features of the switching wave propagation in thick (L/λ～100) Fabry-Perot interferometers were studied by numerical modeling. It is shown that the effects related to a change in the phase adjustment of the interferometer are comparable with an angular correction to the switching wave velocity.     

Optical path length fluctuations in the atmosphere

The effect of atmospheric fluctuations on measurements of distance has become increasingly important as laser interferometers become more widely used. The present study evaluates the precision with which dimensions can be monitored by interferometry involving optical path lengths in the open air under good atmospheric conditions. The size and time scale of optical path length fluctuations over distances of one meter, and correlations between fluctuations in nearby optical paths, are measured and analyzed.     

Frequency domain control of quantum state singlet/triplet character and prospects for an all-optical spin switch

In recent years, quantum optics has been expanded from atomic to molecular systems despite much weaker oscillator strengths and complex relaxation pathways that have presented serious challenges in the past. The richness of molecular excitation pathways and the variety of molecular interactions has made it possible to develop novel applications in this field. We have demonstrated how the Autler–Townes effect can be used to control molecular angular momentum alignment and how the Autler–Townes split line shape, combined with accurate control-laser electric field amplitude measurement, can be used to map the absolute magnitude of the molecular internuclear distance dependent electronic transition dipole moment function. In addition, the electric field amplitude in the control laser Rabi frequency can be used as a ‘tuning’ mechanism for the mixing coefficients of energy levels that are weakly perturbed by the spin–orbit interaction, i.e. to control the valence electron spin polarization and the spin multiplicity of molecular quantum. We propose an extension of this control mechanism to an all-optical spin switch.     

Reflective diffractive beam splitter for laser interferometers

The first realization of a reflective 50/50 beam splitter based on a dielectric diffraction grating suitable for high-power laser interferometers is reported. The beam splitter is designed to operate at a wavelength of 1064 nm and in s polarization. To minimize the performance degradation of the device that is due to fabrication fluctuations, during the design process special attention was paid to achieve high fabrication tolerances especially of groove width and depth. Applying this beam splitter to high-power laser interferometers, such as future gravitational wave detectors, will avoid critical thermal lensing effects and allow for the free choice of substrate materials.