Open-loop operation experiments in a resonator fiber-optic gyro using the phase modulation spectroscopy technique

A detection system in the resonator fiber-optic gyro is set up by the phase modulation (PM) spectroscopy technique. The slope of the demodulated curve near the resonant point is found to affect the ultimate sensitivity of the gyro. To maximize the demodulated signal slope, the modulation frequency and index are optimized by the expansion of the Bessel function and optical field overlapping method. Using different PM frequencies for the light waves, the open-loop gyro output signal is observed. The modulation frequency in this PM technique is limited only by the cutoff frequency of the LiNbO3 phase modulators, which can reach several gigahertz. This detection technique and system can be applied to the resonator micro-optic gyro with a less than 10 cm long integrated optical ring.     

Expansion of linear range of Pound-Drever-Hall signal

We propose new solutions for expanding the linear signal range between the laser frequency deviation (or mirror position) and the voltage signal derived by the Pound-Drever-Hall (PDH) method for optical Fabry-Perot cavity resonance control. One solution is to perform not in-phase demodulation but near-Q-phase demodulation. Another solution is to take a suitable combination of signals demodulated by odd-harmonic modulation frequencies in the in phase. Although the PDH signal sensitivity will be diminished, the PDH signal linear range can be extended. From a practical standpoint, it is desirable that a sideband frequency for the PDH method is near the FP cavity resonance.     

Real-time interferometric characterization of a polyvinyl alcohol based photopolymer at the zero spatial frequency limit

We characterize the optical modulation properties of a polyvinyl alcohol/acrylamide (PVA/AA) photopolymer at the lowest end of recorded spatial frequencies. To achieve this goal we have constructed a double beam interferometer in combination with the setup to expose the recording material. This is a novel approach since usually holographic recording materials are only characterized at high spatial frequencies. Some benefits are provided by the approach we propose: a direct calculation of the properties of the material is possible, and on the other hand additional information can be obtained since the results are not influenced by diffusion processes. Furthermore, this characterization is needed to optimize the PVA/AA photopolymers for another range of applications, such as recording of diffractive optical elements, where very low spatial frequencies are recorded. Different PVA/AA compositions and layer thicknesses have been analyzed. We have found that, depending on the layer characteristics, we can achieve high values of the phase-shift modulation depth and enhance the sensitivity of the material.     

Terahertz optical-Hall effect for multiple valley band materials: n-type silicon

The optical-Hall effect comprises generalized ellipsometry at long wavelengths on samples with free-charge carriers placed within external magnetic fields. Measurement of the anisotropic magneto-optic response allows for the determination of the free-charge carrier properties including spatial anisotropy. In this work we employ the optical-Hall effect at terahertz frequencies for analysis of free-charge carrier properties in multiple valley band materials, for which the optical free-charge carrier contributions originate from multiple Brillouin-zone conduction or valence band minima or maxima, respectively. We investigate exemplarily the room temperature optical-Hall effect in low phosphorous-doped n-type silicon where free electrons are located in six equivalent conduction-band minima near the X-point. We simultaneously determine their free-charge carrier concentration, mobility, and longitudinal and transverse effective mass parameters.     

Compensating for Thermal Size Change in Platforms for Gyroscopes and Laser Angle Sensors

Devices are described for compensating the thermal size change in platforms for gyroscopes and laser rotation angle sensors that employ various optical systems. Ways are considered of reducing the measurement errors and improving the resolving power.     

Digital error-signal extraction technique for real-time automatic control of optical interferometers

We describe an efficient and robust method for the extraction of the longitudinal error signal for the automatic control of optical interferometers, which can also be applied when the uncontrolled optical system spans hundreds of fringes. The method is based on classic modulation techniques (phase modulation, mechanical modulation, etc.), but extends their performances by the use of the information available only at the output photodiode. We digitally implemented such a method by following modular hardware and software architectures. We then tested the whole procedure in the automatic control of a suspended Michelson interferometer, showing its feasibility and the good performances.     

Measurement of radio-frequency temporal phase modulation using spectral interferometry

We present an optical method to measure radio-frequency electro-optic phase modulation profiles by employing spectrum-to-time mapping realized by highly chirped optical pulses. We directly characterize temporal phase modulation profiles of up to 12.5 GHz bandwidth, with temporal resolution comparable to high-end electronic oscilloscopes. The presented optical set-up is a valuable tool for direct characterization of complex temporal electro-optic phase modulation profiles, which is indispensable for practical realization of deterministic spectral-temporal reshaping of quantum light pulses     

Numerical studies on time-domain responses of on-off-keyed modulated optical signals through a dense fog

We present a numerical technique to simulate the propagation characteristics of an on-off-keyed modulated optical signal through fog. The on-off-keyed modulated light (a square wave) is decomposed into a finite number of harmonic components, and a numerical solution for the vector radiative transfer equation is obtained for each harmonic that corresponds to the modulation frequency. With this method we study the distortion and the pulse spread in the received signal due to attenuation and scattering. We investigate the propagation characteristic of the modulated signal with different communication system parameters. This information can be used to study communication channel reliability.     

Multi-spatial-frequency and phase-shifting profilometry using a liquid crystal phase modulator

Optical profilometry is widely applied for measuring the morphology of objects by projecting predetermined patterns on them. In this technique, the compact size is one of the interesting issues for practical applications. The generation of pattern by the interference of coherent light sources has a potential to reduce the dimension of the illumination part. Moreover, this method can make fine patterns without projection optics, and the illumination part is free of restriction from the numerical aperture of the projection optics. In this paper, a phase-shifting profilometry is implemented by using a single liquid crystal (LC) cell. The LC phase modulator is designed to generate the interference patterns with several different spatial frequencies by changing selection of the spacing between the micro-pinholes. We manufactured the LC phase modulator and calibrated it by measuring the phase modulation amount depending on an applied voltage. Our optical profilometry using the single LC cell can generate multi-spatial frequency patterns as well as four steps of the phase-shifted patterns. This method can be implemented compactly, and the reconstructed depth profile is obtained without a phase-unwrapping algorithm.     

Optical characterization of ophthalmic lenses by means of modulation transfer function determination from a laser speckle pattern

A method is presented for measuring the modulation transfer function of ophthalmic lenses by use of the generation of laser speckle with an integrating sphere. The measurements are performed with a rectangular double-slit aperture positioned at the output port of the integrating sphere. The distance between the lens and the detector determines the spatial frequency being tested; therefore high frequencies are tested close to the lens and low frequencies are tested far away from the lens. We can conclude that the double-slit method can be a versatile technique for comparing the optical quality of ophthalmic lenses from different makers.     

Scanning transmission microscopy using a position-sensitive detector

Optical data manipulation technologies increasingly employ densely aperiodic optical 3D phase elements. Refinement of such technologies will require the capability to quantitatively characterize the volumetric dielectric modulation of an optical sample to a high level of precision and spatial resolution. We present a scanning transmission microscopy system that uses a position-sensitive detector to impart sensitivity to both the phase and absorption components. We describe the layout of the instrument and then derive its phase and absorption transfer functions. Simulations and experiments are presented to validate the analysis. For phase detection, the instrument possesses depth-sectioning properties similar to those of a confocal microscope without the use of a pinhole, enabling full 3D object reconstruction.     

Optical frequency-domain reflectometry for microbend sensor demodulation

The operation of an incoherent optical frequency-domain reflectometer for monitoring the continuous Rayleigh backscatter in a multimode optical fiber is presented. A simple but effective model to predict the value of beat frequencies arising in the system when excited by a linearly frequency-swept amplitude modulation has been developed. We have verified the model's predictions by experimental measurement of beat frequencies and modulation depth indices of different lengths of standard graded-index multimode optical fiber. Demonstration of the system sensitivity to the detection of microbending loss is then discussed. In particular the detection of loss in a hydrogel-based water-sensing cable allows an alternative interrogation to conventional optical time-domain reflectometry techniques to be implemented. We demonstrate that the incoherent optical frequency-domain reflectometer is capable of detecting and locating sections of increased loss in a multimode optical fiber, and we discuss the fundamental limits on spatial resolution and dynamic range.     

High-power efficient multiple optical vortices in a single beam generated by a kinoform-type spiral phase plate

We propose using a solitary kinoform-type spiral phase plate structure to generate an array of vortices located in a single beam. Kinoform-type spiral surfaces allow each wavelength component of the phase modulation value to be wrapped back to its 2 pi equivalent for optical vortices of high charge. This allows the surface-relief profiles of high-charge vortices to be microfabricated with the same physical height as spiral phase plates of unity-charged optical vortices. The m-charged optical vortex obtained interacts with the inherent coherent background, which changes the propagation dynamics of the optical vortex and splits the initial m charge into /m/ unity-charged optical vortices within the same beam. Compared to a hologram, a multistart spiral phase plate is more efficient in the use of available spatial frequencies and beam energy and also is computationally less demanding. Furthermore, using microfabrication techniques will allow for greater achievable tolerances in terms of smaller feature sizes.     

Resolution of multicomponent fluorescence emission using frequency-dependent phase angle and modulation spectra

We describe a new fluorescence method that allows the resolution of both the decay times and emission spectra of mixtures of fluorophores. This method is completely general and does not require any assumptions or knowledge of the decay times or emission spectra of the individual fluorophores. We use the phase angle spectra and modulation spectra of the mixture, measured over a range of suitable light modulation frequencies and emission wavelengths. These data are analyzed by nonlinear least-squares analysis to recover the emission spectra and the associated decay times. The principle of the method and the nature of the data are illustrated by using two-component mixtures with increasing spectral overlap. We then demonstrate the recovery of minor components, of structure emission spectra, and of a three-component mixture with completed overlapping emission spectra. And finally, we describe the resolution of a two-component mixture with decay times of 0.8 and 1.4 ns using modulation frequencies up to 774 MHz.     

Quantum-limited optical phase detection at the 10(-10)-rad level.

Interferometric detection of gravitational waves at a level of astrophysical interest is expected to require measurement of optical phase differences of < or = 10(-10) rad. A fundamental limit to the phase sensing is the statistics of photon detection--Poisson statistics for light in a coherent state. We have built a laboratory-scale interferometer to achieve and investigate the phase detection sensitivity required for the Laser Interferometer Gravitational-Wave Observatory. With 70 W of circulating power, we have obtained a phase sensitivity of 1.28 x 10(-10) rad/square root(Hz) at frequencies above 600 Hz, limited by quantum noise. Below 600 Hz, excess noise above the quantum limit is seen, and we present our investigations into the sources of this excess. Compared with the results of previous such experiments, the phase sensitivity over the full 100-Hz-10-kHz band of interest has been improved by factors of up to 100, with a factor-of-2.5 improvement in the quantum-limited level.     

Ultrasonic backscatter imaging by shear-wave-induced echo phase encoding of target locations

We present a novel method for ultrasound backscatter image formation wherein lateral resolution of the target is obtained by using traveling shear waves to encode the lateral position of targets in the phase of the received echo. We demonstrate that the phase modulation as a function of shear wavenumber can be expressed in terms of a Fourier transform of the lateral component of the target echogenicity. The inverse transform, obtained by measurements of the phase modulation over a range of shear wave spatial frequencies, yields the lateral scatterer distribution. Range data are recovered from time of flight as in conventional ultrasound, yielding a B-mode-like image. In contrast to conventional ultrasound imaging, where mechanical or electronic focusing is used and lateral resolution is determined by aperture size and wavelength, we demonstrate that lateral resolution using the proposed method is independent of the properties of the aperture. Lateral resolution of the target is achieved using a stationary, unfocused, single-element transducer. We present simulated images of targets of uniform and non-uniform shear modulus. Compounding for speckle reduction is demonstrated. Finally, we demonstrate image formation with an unfocused transducer in gelatin phantoms of uniform shear modulus.     

Vibration characteristics of composite piezoceramic plates at resonant frequencies: experiments and numerical calculations

The experimental measurement of the resonant frequencies for the piezoceramic material is generally performed by impedance analysis. In this paper, we employ an optical interferometry method called the amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) to investigate the vibration characteristics of piezoceramic/aluminum laminated plates. The AF-ESPI is a powerful tool for the full-field, noncontact, and real-time measurement method of surface displacement for vibrating bodies. As compared with the conventional film recording and optical reconstruction procedures used for holographic interferometry, the interferometric fringes of AF-ESPI are produced instantly by a video recording system. Because the clear fringe patterns measured by the AF-ESPI method will be shown only at resonant frequencies, both the resonant frequencies and corresponding vibration mode shapes are obtained experimentally at the same time. Excellent quality of the interferometric fringe patterns for both the in-plane and out-of-plane vibration mode shapes are demonstrated. Two different configurations of piezoceramic/aluminum laminated plates, which exhibit different vibration characteristics because of the polarization direction, are investigated in detail. From experimental results, we find that some of the out-of-plane vibration modes (Type A) with lower resonant frequencies cannot be measured by the impedance analysis; however, all of the vibration modes of piezoceramic/aluminum laminated plates can be obtained by the AF-ESPI method. Finally, the numerical finite element calculations are also performed, and the results are compared with the experimental measurements. Excellent agreements of the resonant frequencies and mode shapes are obtained for both results.     

Hilbert transform analysis of a time series of speckle interferograms with a temporal carrier

We present an optical phase measurement method based on the Hilbert transform for the analysis of a time series of speckle interferograms modulated by a temporal carrier. We discuss the influence of nonmodulating pixels, modulation loss, and noise that affect the bias and modulation intensities of the interferometric signal and propose the application of the empirical mode decomposition method for its minimization. We also show the equivalence between the phase recovery approaches that are based on the Hilbert and the Fourier transforms. Finally, we present a numerical comparison between these methods using computer-simulated speckle interferograms modulated with a temporal carrier.     

Two-dimensional binary halftoned optical intensity channels [optical wireless communications]

The capacity of two-dimensional (2D) optical intensity channels in which transmit images are constrained to be binary-level has been considered. Examples of such links exist in holographic storage, page-oriented memories, optical interconnects, 2D barcodes as well as multiple-input/multiple-output wireless optical links. Data are transmitted by sending a series of time-varying binary-level optical intensity images from transmitter to receiver. Neither strict spatial alignment between transmitter and receiver nor independence among the spatial channels is required. The approach combines spatial discrete multitone modulation developed for spatially frequency selective channels with halftoning to produce a binary-level output image. Data are modulated in spatial frequency domain as dictated by a water pouring spectrum over the optical transfer function as well as channel and quantisation noise. A binary-level output image is produced by exploiting the excess spatial bandwidth available at the transmitter to shape quantisation noise out of band. A general mathematical framework has been presented, in which such systems can be analysed and designed. In a pixelated wireless optical channel application, halftoning achieves 99.8% of the capacity of an equivalent unconstrained continuous amplitude channel using lmegapixel arrays.     

Enhanced third-order nonlinear optical response of photonic bandgap materials

Abstract

We calculate the nonlinear phase shift acquired by a laser beam in propagating through a one-dimensional photonic bandgap material, that is a material in which the linear refractive index is periodically modulated along the direction of propagation. We find that the nonlinear phase shift shows resonances for laser frequencies close to the edge of the stop band of the photonic bandgap structure. Enhancements of the nonlinear phase shift compared with that of a homogeneous nonlinear optical material by a factor of approximately five are predicted under realistic laboratory conditions. We find that similar enhancements of the two-photon absorption rate can occur for a material with an imaginary nonlinear susceptibility. We also treat the case of a photonic bandgap material containing a ′defect,' that is a central region somewhat too thick to conform to the periodicity of the system, and find that the nonlinear phase shift can be enhanced by a factor of approximately thirty.