Generation of partially coherent laser beam directly from spatial-temporal phase modulated optical resonators

Abstract

The generation of a partially coherent laser beam directly from a spatial-temporal phase modulated optical resonator is investigated both experimentally and theoretically. The laser material used in the experiment is Nd:YAG rod pumped by Krypton lamps working in continuous wave mode. The phase modulation is fulfilled by an intra-cavity LiNbO₃ electro-optic crystal driven by high voltage. The experimental results show that intracavity phase modulation is an effective way to generate partially coherent laser beams. The theoretical analysis and numerical simulation shows that the output beam can be characterized by Gaussian Schell-model (GSM) beams. The two-slit interference experiment confirms that the output beam is partially coherent.     

Spatial-coherence modulation for optical interconnections

The spatial coherence of a laser beam depends on the number and the relative weights of the spatial modes supported by the laser waveguide. By electro-optic modulation of the cavity geometry, the spatial-coherence function can be modulated between zero and one at predictable locations across the beam and thus carry information. A simple integrated-optic interferometer is used to decode the signal. Spatial coherence can be modulated independently of the beam intensity and can be used as another level of multiplexing in addition to amplitude modulation, wavelength-division modulation, etc. One can implement a free-space optical interconnection scheme by carrying data on the intensity and address information on the spatial coherence.     

Rapid optical coherence tomography and recording functional scattering changes from activated frog retina

Optical coherence tomography (OCT) has important potential advantages for fast functional neuroimaging. However, dynamic neuroimaging poses demanding requirements for fast and stable acquisition of optical scans. Optical phase modulators based on the electro-optic effect allow rapid phase modulation; however, applications to low-coherence tomography are limited by the optical dispersion of a broadband light source by the electro-optic crystal. We show that the optical dispersion can be theoretically estimated and experimentally compensated. With an electro-optic phase modulator-based, no-moving-parts OCT system, near-infrared scattering changes associated with neural activation were recorded from isolated frog retinas activated by visible light.     

Self-mixing interferometry based on a double-modulation technique for absolute distance measurement

A new, to the best of our knowledge, method for the measurement of the absolute distance of a remote target based on the laser diode self-mixing interferometry is presented. A double-modulation technique is introduced to improve the measurement resolution. Wavelength modulation of the laser beam is obtained by modulating the injection current of the laser diode. Phase modulation of the laser beam is obtained by an electro-optic crystal in the external cavity. Absolute distance of the external target is determined by the Fourier analysis method. Theoretical analysis and numerical simulations are given. Experimental results show that a resolution of +/-0.3 mm can be achieved for absolute distance ranging from 277 to 477 mm.     

Propagation of coherently combined truncated laser beam arrays with beam distortions in non-Kolmogorov turbulence

The propagation properties of coherently combined truncated laser beam arrays with beam distortions through non-Kolmogorov turbulence are studied in detail both analytically and numerically. The analytical expressions for the average intensity and the beam width of coherently combined truncated laser beam arrays with beam distortions propagating through turbulence are derived based on the combination of statistical optics methods and the extended Huygens-Fresnel principle. The effect of beam distortions, such as amplitude modulation and phase fluctuation, is studied by numerical examples. The numerical results reveal that phase fluctuations have significant influence on the spreading of coherently combined truncated laser beam arrays in non-Kolmogorov turbulence, and the effects of the phase fluctuations can be negligible as long as the phase fluctuations are controlled under a certain level, i.e., a>0.05 for the situation considered in the paper. Furthermore, large phase fluctuations can convert the beam distribution rapidly to a Gaussian form, vary the spreading, weaken the optimum truncation effects, and suppress the dependence of spreading on the parameters of the non-Kolmogorov turbulence.     

Diffractive optical elements designed for highly precise far-field generation in the presence of artifacts typical for pixelated spatial light modulators

Diffractive optical elements (DOEs) realized by spatial light modulators (SLMs) often have features that distinguish them from most conventional, static DOEs: strong coupling between phase and amplitude modulation, a modulation versus steering parameter characteristic that may not be precisely known (and may vary with, e.g., temperature), and deadspace effects and interpixel cross talk. For an optimal function of the DOE, e.g. as a multiple-beam splitter, the DOE design must account for these artifacts. We present an iterative design method in which the optimal setting of each SLM pixel is carefully chosen by considering the SLM artifacts and the design targets. For instance, the deadspace-interpixel effects are modeled by dividing the pixel to be optimized, and its nearest neighbors, into a number of subareas, each with its unique response and far-field contribution. Besides the customary intensity control, the design targets can also include phase control of the optical field in one or more of the beams in the beam splitter. We show how this can be used to cancel a strong unwanted zeroth-order beam, which results from using a slightly incorrect modulation characteristic for the SLM, by purposely sending a beam in the same direction but with the opposite phase. All the designs have been implemented on the 256 x 256 central pixels of a reflective liquid crystal on silicon SLM with a selected input polarization state and a direction of transmission axis of the output polarizer such that for the available different pixel settings a phase modulation of ~2pi rad could be obtained, accompanied by an intensity modulation depth as high as >95%.     

Electro-optic modulation in an anisotropic artificial Kerr medium

We describe the performance of intensity and phase modulators that use an aqueous suspension of polytetrafluoroethylene (PTFE) microparticles. In this medium, the electro-optic effect is caused by the reorientation of anisotropic microparticles in an applied electric field. The intensity modulator was constructed in the Kerr geometry by the use of a sample path length of 20 μm. The response time of the modulator is less than 25 ms, and the depth of modulation was measured to be 28 dB for a switching voltage of 134 V(rms). The switching voltage necessary to achieve a π-phase shift with the phase modulator is less than 30 (Vrms).     

Heterodyne wavelength meter for continuous-wave lasers

A wavelength meter based on a heterodyne interferometer is presented. A single-wavelength test laser beam is modulated to two orthogonal linearly polarized components with different frequencies by a pair of acousto-optic modulators. Then the modulated laser beam and a two-wavelength laser beam are sent to a heterodyne interferometer in a common path. The ratio of two laser interference phase shifts in the heterodyne interferometer is equal to the ratio of their wavelengths. The heterodyne technique measures the heterodyne interference phase but not the interference intensity, which means that it could measure a light source whose intensity is not stable. The heterodyne interference signal is an alternating signal that can easily magnify and process the circuit that makes up the heterodyne wavelength meter and could be used to measure the low-intensity light source even when there are environmental disturbances. A tunable diode laser wavelength range of 630-637 nm has been measured to an accuracy of 5 parts in 10(7).     

Dynamic optical manipulation of colloidal systems using a spatial light modulator

Abstract

A method and mathematical foundation are presented for generating multiple-beam optical tweezers capable of introducing complex trapping beam configurations that enable optical manipulation for a variety of colloidal structures. The method is based on the generalized phase contrast technique for generating high intensity beam patterns from an input phase modulation encoded on a spatial light modulator. The mathematical foundation describes issues concerning how the method provides high photon efficiency adequate for generating large array traps while maintaining dynamic features. Experimental results show multiple trapping of up to 25 particles using a 200 mW laser diode operating at 830 nm. Arbitrary array beam configurations are also shown where the shape, position and size can easily be reconfigured and applied for dynamic manipulation of colloidal particles.     

On the real-time reconstruction of digital holograms displayed on photosensitive liquid crystal systems

Dynamic optical reconstruction of digital binary holograms projected on optically addressed liquid crystal spatial light modulators with the use of a computer driven multimedia projector is described. A high spatial resolution, sensitivity and full reversibility of the manufactured spatial light modulators are achieved by the use of a photoconducting PVK:TNF polymer layer serving as a transducer of incoming light intensity pattern into modulation of refractive index inside the adjacent LC layer. Linearly polarized laser light reconstructs the phase holograms at the video rate. The advantages and drawbacks of the presented system are discussed.     

Acousto-optic interaction of a Gaussian laser beam with an ultrasonic wave of cylindrical symmetry

We present experimental studies of the interaction between a narrow Gaussian laser beam and a standing cylindrical ultrasonic wave. As a theoretical approach, a Fourier-optics-based successive diffraction model is used. Depending on the ratio of the Gaussian laser beam diameter to the first nodal diameter of the cylindrical ultrasound, light refraction or diffraction is observed. We experimentally investigate the time-averaged light intensity as well as the modulation of light in the far field of light refraction-diffraction by a cylindrical ultrasound. It is revealed that significant focusing appears if the phase front of the incident light is curved. The focusing effects of the acousto-optic system depend on the width of the laser beam and curvature of the phase front. Finally, possible applications are discussed.     

Effect of polarization state on electro-optic coupling and its application to polarization rotation

The effect of the polarization state on electro-optic coupling is studied by using the wave coupling theory of the linear electro-optic effect. The numerical results show that the polarization state obviously influences the electro-optic coupling. The conditions for realizing perfect coupling are emphasized. As an application of perfect coupling, a novel polarization rotator, which can rotate the polarization of a light beam with an arbitrary angle but keep the output intensity unchanged, is presented.     

Spatial amplitude and phase modulation using commercial twisted nematic LCDs

We present a method for full spatial phase and amplitude control of a laser beam using a twisted nematic LCD combined with a spatial filter. By spatial filtering we combine four neighboring pixels into one superpixel. At each superpixel we are able to independently modulate the phase and the amplitude of light. We experimentally demonstrate the independent phase and amplitude modulation using this novel technique. Our technique does not impose special requirements on the spatial light modulator and allows precise control of fields even with imperfect modulators.     

Fringing fields in a liquid crystal spatial light modulator for beam steering

Abstract

Phase modulating spatial light modulators (SLMs) can be used to alter the shape of a laser wavefront to achieve a deflection or change in the shape of a laser beam. This paper reports the results of characterization, simulation and optimization of a one-dimensional liquid crystal (LC) SLM. The device has a large ratio between LC layer thickness and pixel pitch that results in a fringing field between pixels. In effect, the applied phase patterns will be lowpass filtered and the loss of high frequency components limits, for instance, the usable steering range. A method is presented where intensity measurements in the far field are used to determine how the phase modulation at the SLM is distorted. The inhomogeneous optical anisotropy of the device was determined by modelling the liquid crystal director distribution within the electrode-pixel structure. Finite-difference time-domain (FDTD) simulations were used to calculate the light propagation through the LC. The simulated phase distortion was compared with the experimental results. A voltage compensation scheme to improve the diffraction efficiency was developed utilizing the measured and simulated results. It is demonstrated that a modification of the voltage patterns can give a better realization of high frequency components in the phase distribution and an increase in maximum steering angle by a factor two.     

Experimental studies of electro-optic polymer modulators and waveguides

The results of an experimental study of electro-optic modulators and waveguides based on polymeric materials are presented. Included are the design, fabrication, and testing of integrated Mach-Zehnder modulators, which are based on polymer films that contain a novel, nonlinear electro-optic chromophore. Studies also show the efficacy of photolithography or photobleaching by the use of this chromophore to form passive, branching waveguides, which are operated at the 1300-nm wavelength.     

On the Theory of a Non-linear Optical Resonator

The properties are considered of an optical resonator excited by an external light beam and filled with a non-linear (Raman or Mandel'stam-Brillouin active) medium for single-mode (exciting and the first Stokes) radiation components in the resonator. The form of the hysteresis of light intensity inside the resonator and of the intensity of the beam transmitted through the resonator for both the radiation components on the variation of the external beam intensity are investigated. Also, periodic pulsations of the radiation component intensities are discussed and the phase modulation of the components at the regimes in question is predicted, the conditions for these pulsations being derived. Conditions are also found under which the resonator amplifies the amplitude (phase) modulation of the external light beam and the properties of the regimes of the amplification are also discussed. The use of the resonator in question as the element of optical memory, a switching device, the generator of optical pulses and optical ‘transistor’ is proposed.     

Broadband radio-frequency spectrum analysis in spectral-hole-burning media

We demonstrate a 20 GHz spectrum analyzer with 1 MHz resolution and >40 dB dynamic range using spectral-hole-burning (SHB) crystals, which are cryogenically cooled crystal hosts lightly doped with rare-earth ions. We modulate a rf signal onto an optical carrier using an electro-optic intensity modulator to produce a signal beam modulated with upper and lower rf sidebands. Illuminating SHB crystals with modulated beams excites only those ions resonant with corresponding modulation frequencies, leaving holes in the crystal's absorption profile that mimic the modulation power spectrum and persist for up to 10 ms. We determine the spectral hole locations by probing the crystal with a chirped laser and detecting the transmitted intensity. The transmitted intensity is a blurred-out copy of the power spectrum of the original illumination as mapped into a time-varying signal. Scaling the time series associated with the transmitted intensity by the instantaneous chirp rate yields the modulated beam's rf power spectrum. The homogeneous linewidth of the rare-earth ions, which can be <100 kHz at cryogenic temperatures, limits the fundamental spectral resolution, while the medium's inhomogeneous linewidth, which can be >20 GHz, determines the spectral bandwidth.     

Generalized beam-propagation factor of partially coherent beams propagating through hard-edged apertures

The second-order intensity moments and beam-propagation factor (M2 factor) of partially coherent beams have been generalized to include the case of hard-edged diffraction. A laser beam with amplitude modulation and phase fluctuation and a Gaussian Schell-model beam are taken as two typical examples of partially coherent beams. Analytical expressions for the generalized M2 factor are derived.     

Complex modulation using tandem polarization modulators

A novel photonic technique for implementing frequency up-conversion or complex modulation is proposed. The proposed circuit consists of a sandwich of a quarter-wave plate between two polarization modulators, driven, respectively, by an in-phase and quadrature-phase signals. The operation of the circuit is modelled using a transmission matrix method. The theoretical prediction is then validated by simulation using an industry-standard software tool. The intrinsic conversion efficiency of the architecture is improved by 6 dB over a functionally equivalent design based on dual parallel Mach–Zehnder modulators. Non-ideal scenarios such as imperfect alignment of the optical components and power imbalances and phase errors in the electric drive signals are also analysed. As light travels, along one physical path, the proposed design can be implemented using discrete components with greater control of relative optical path length differences. The circuit can further be integrated in any material platform that offers electro-optic polarization modulators.     

Advanced modulation formats for fiber optic communication systems

Choice of modulation format plays a critical role in the design and performance of fiber optic communication systems. We discuss the basic physics of electro-optic phase and amplitude modulation and derive model transfer functions for ideal and non-ideal Mach-Zehnder modulators. We describe the generation and characteristics of the standard nonreturn-to-zero (NRZ) modulation format, as well as advanced formats such as return-to-zero (RZ), carrier-suppressed RZ (CSRZ), duobinary, modified duobinary, differential phase-shift keyed (DPSK), and return-to-zero DPSK (RZ-DPSK). Finally, we discuss the relative merits of these formats with respect to a variety of system impairments.