Speckle reduction in laser projection systems by diffractive optical elements

In laser projection systems the observer in the far field of the image points on the screen will recognize serious speckle noise. There are many methods to reduce or eliminate speckles in the near field by reducing or eliminating temporal or spatial coherence of the laser. But for the far field it is hardly possible to change the coherence properties of laser sources so that speckles will disappear. We propose a new method for eliminating speckles in the far field by using a diffractive optical element. The intensity modulation depth in the far-field speckle pattern can be reduced to a few percent while good beam quality is preserved.     

Robustness of spatial-coherence multiplexing under receiver misalignment

It has been shown previously that the spatial coherence of a source can be modulated and demodulated; hence it can be used as the basis for a new dimension of multiplexing in high-speed optical communication links. We address the sensitivity of such a system to misalignments of the receiver with respect to the beam and examine how changing transverse modes affect the spatial coherence in the lateral direction. Specifically, we show that such a system is surprisingly robust for both lateral offsets, in which the receiver is not properly aligned on the beam center, and rotational offsets, in which the receiver is tilted with respect to the plane of the spatial coherence modulation. The presence of higher-order transverse modes or changes in the transverse-mode structure are also shown to have little effect on the system operation.     

Multifractality of laser beam spatial intensity in a turbulent medium

We present the results of a laser beam passing through a turbulent medium. First we measure the geometric parameters and the spatial coherence of the beam as a function of wind velocities. A multifractal detrended fluctuation analysis algorithm is applied to determine the multifractal scaling behavior of the intensity patterns. The measurements are fitted with models used in the analysis of river runoff records. We show the surprising result that the multifractality decreases when the spatial coherence of the laser is decreased. Universal scaling properties could be applied to the spatial characterization of a laser propagating in a turbulent medium or random medium.     

Laser beam intensity profile transformation with a fabricated mirror

A nonaxisymmetric mirror is designed by the same method as a computer-generated hologram for laser beam intensity profile transformation and is fabricated by plasma chemical vaporization machining. We successfully transformed a circular Gaussian beam of a He-Ne laser into a rectangular uniform beam maintaining spatial coherence and using a nonaxisymmetric surface profile mirror. There are ripples in the intensity profile of the transformed rectangular beam. These ripples in the intensity profile result from small ripples on the mirror surface. These results show that we can perform coordinate transformation using these fabricated mirrors, which has so far been possible only by using computer-generated holograms.     

Optimization of a beam delivery system for a short-pulse KrF laser used for material ablation

We present an optical arrangement for spatial homogenization of an UV beam carrying a short pulse (500 fs) to be used for material ablation. Conventional cylindrical fly's eye lens homogenizers (CFELH's) introduce unwanted interference effects into a beam caused by the high spatial coherence of short pulses. To prevent the disturbing effect of these intensity modulations, one can couple a low-loss distributed delay device to the CFELH. With the new design an intensity nonuniformity of <+/-5% rms can be obtained. High-resolution images of the beam profile show complete removal of the interference modulation. The pulse duration after homogenization is 12.5 ps. We performed preliminary ablation experiments in polyimide samples both by direct irradiation and by mask imaging. Uniformity and edge quality of the results are more than satisfactory, and the undesirable structure caused by interference is completely removed.     

A Comparison of Q-Switched and Intensity Modulated Laser Pulses for Ultrasonic NDT

The purpose of this work was to investigate the potential of intensity modulated laser pulses for ultrasonic signal enhancement in NDT using a numerical model. Q-switched lasers produce broadband ultrasound which is susceptible to measurement noise. Intensity modulation can alleviate this problem by focussing the ultrasonic energy into a band centered around the modulation frequency. Ultrasonic waveforms and their DFTs are considered here in both aluminum and steel for a wide range of observation angles, for Q-switched laser pulses and for a 1 MHz intensity modulated laser pulse. These waveforms are useful to NDT researchers becauses they indicate what kinds of signals can be expected from unflawed materials. It is found that P waves are not as easily enhanced by modulation as are SV or Rayleigh surface waves. The time window which should be used to measure ultrasonic signals produced by intensity modulated laser pulses is determined.     

A Multiple-beam Interferometer Coherence Analyser

A laser coherence analyser is described which yields simultaneous temporal and spatial coherence analysis of laser beams. It is of particular application to high power pulsed laser systems, for high speed holography and non-linear optics, where the short duration of the pulse (often less than 50 nsec) excludes the use of photoelectric spectrometers, employing time variation scanning of the optical path length. The instrument consists of two high quality spherical mirrors, having dielectric multilayer coatings of reflectivity typically 0.95 to 0.97, separated by a cylindrical invar spacer of adjustable length. In use, the spacer is normally set so that the pole separation of the plates is a few hundred micrometres less than their common radius of curvature (typically 10 cm). The resulting defocusing term combines with spherical aberration to yield a multiple beam interferogram having an annular region of nearly linear dispersion. Spectral resolving powers in the range 10⁷ to 10⁸ are readily obtainable. When the input beam possesses a high degree of spatial coherence, the fringes of the concentric rings interference pattern are alternately of high and low intensity, the visibility of the alternation being a direct measure of the spatial coherence. This alternation effect may be eliminated by obstructing one-half of the input aperture. Any spatial, spectral or intensity variations across the laser beam are superposed on the fringe pattern, since the spherical interferometer is not translationally invariant in a parallel beam. This is in contrast to the behaviour of a plane Fabry-Pérot etalon. The experimental characteristics of the instrument, and its properties, as predicted by numerical computation, are examined both for C.W. and pulsed lasers. The effect of the finite response time is described. This is particularly important when the coherence analyser is employed in conjunction with an image tube streak camera to obtain time-resolved spectra of pulsed systems. Both time-integrated and time-resolved fringe profiles are considered for various types of laser pulse. The effect of plate defects on fringe profiles is also considered in outline. In addition to providing quasi-linear dispersion and information on coherence and other spatial properties of the input, the instrument described has the advantages of providing high illumination, and of being easy to use in practice, the plates remaining permanently in alignment.     

Proposal for a magnetic-film memory accessed by combined photon and electron beams

A magnetic-film memory accessed by combined photon and electron beams is proposed. The electron beam is used to heat a selected bit, which results in lowering the switching threshold so that information can be written selectively into that bit by means of an external magnetic field. Reading is accomplished by simultaneously illuminating a bit with an electron and a photon beam. Then a thermally modulated magnetic-optical signal is generated by intensity modulation of the electron beam. This arrangement is advantageous since a high-resolution photon beam and photon deflector are not required. The frequency response for thermally modulating a 1-μm bit is calculated to be ∼500 MHz; the necessary temperature dependence of the magneto-optical coefficient and the coercive force can be obtained by using composite films made from layers having different Curie points. Various magneto-optical configurations are readily devised which yield the value of a bit (one or zero) in terms of the phase (0 or π) between the magneto-optical signal and the electron-beam intensity modulation. The shot noise limited signal-to-noise ratio (SNR) is determined by heating of a bit from the photon beam. It is calculated that for a low-loss magnetooptical material such as EuO a 1-μm bit can be read in 1 μs when illuminated with a 1000-μm photon beam. The base-line temperature rise due to heating from the photon beam can be kept small by using narrow pulses of light (widthsim10^{-11}second), as, for example, from a mode-locked laser.     

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.     

Atmospheric optical communication with a Gaussian Schell beam

We consider a wireless optical communication link in which the laser source is a Gaussian Schell beam. The effects of atmospheric turbulence strength and degree of source spatial coherence on aperture averaging and average bit error rate are examined. To accomplish this, we have derived analytic expressions for the spatial covariance of irradiance fluctuations and log-intensity variance for a Gaussian beam of any degree of coherence in the weak fluctuation regime. When spatial coherence of the transmitted source beam is reduced, intensity fluctuations (scintillations) decrease, leading to a significant reduction in the bit error rate of the optical communication link. We have also identified an enhanced aperture-averaging effect that occurs in tightly focused coherent Gaussian beams and in collimated and slightly divergent partially coherent beams. The expressions derived provide a useful design tool for selecting the optimal transmitter beam size, receiver aperture size, beam spatial coherence, transmitter focusing, etc., for the anticipated atmospheric channel conditions.     

Interferometric analysis of reorientational nonlinear phenomena at 10.6 microm in a nematic liquid crystal

We describe an infrared interferometric technique based on a two-dimensional spatial fringe analysis Fourier method for investigating the characteristic ring diffraction pattern generated by the self-phase-modulation effect induced in nematic liquid crystals (NLCs) by an infrared laser beam and for measuring the nonlinear refractive index of the NLCs. The experimental setup employs a Mach-Zehnder interferometer with a cw CO2 laser emitting at 10.6 microm and a pyroelectric optoelectronic sensor matrix to detect the modulated ring-pattern intensity distribution formed in the far field by a nematic E7 sample. A Fourier-transform-based analysis of the interference fringe pattern allows comparison of the measurements with the theoretical ring-pattern intensity distribution. We show that accurate determination of the nonlinear refractive index can be obtained by analyzing the two-dimensional phase distribution of the modulated ring pattern.     

Single-mode operation of a broad-area semiconductor laser with an anamorphic external cavity: experimental and numerical results

The emission of high-power broad-area semiconductor lasers inherently contains many lateral modes that increase the beam divergence and reduce the spatial coherence. Elimination of higher-order lateral modes from the output beams of commercially available broad-area lasers will be beneficial in many applications of these lasers. Experimental results obtained with a broad-area laser coupled to an anamorphic external cavity are presented and are compared with the predictions from our numerical model. We have predicted and observed with the anamorphic external cavity a greatly improved discrimination against high-order lateral modes. The measurement of the spectrally resolved near-field intensity patterns provides much more comprehensive information on their longitudinal- and lateral-mode content than do observations of near-field and far-field beam intensity profiles. With a broad-area laser of 100-mW nominal power, it has been possible to extract 40% of the maximal power in a stable single-lateral and single-longitudinal mode regime.     

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.     

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).     

Imaging of trace species distributions by degenerate four-wave mixing: diffraction effects, spatial resolution, and image referencing

We describe the theory of imaging by degenerate four-wave mixing (DFWM) using a standard diffraction theory of imaging by coherent light. We demonstrate that, even with the phase-conjugating geometry, no aberration correction can be achieved by DFWM imaging. We demonstrate the coherent nature of DFWM image formation using spatially modulated signals generated in flame OH in the phase-conjugating geometry. The intensity distribution in the Fourier plane of a telecentric lens system is shown to be the spatial Fourier transform of the object distribution characteristic of coherent imaging. The brightness of the DFWM signals exceeds that of similar laser-induced fluorescence signals that can be discriminated by restricting the aperture of the imaging system while still allowing a spatial resolution of approximately 70 ?m. DFWM imaging with the forward-folded boxcars geometry is demonstrated and used in a simple referencing scheme to compensate for structure on the images imposed by nonuniformity of the laser beams employed. Images formed in NO are used to illustrate that structure on a scale of less than 100 ?m arising from beam inhomogeneity can be removed by this referencing technique.     

Diffractive shaping of excimer laser beams

Abstract

We address the problem of shaping the intensity distribution of a highly directional partially coherent field, such as an excimer laser beam, by means of diffractive optics. Our theoretical analysis is based on modelling the multi-transverse-mode laser beam as a Gaussian Schell-model beam. It is shown numerically that a periodic element, which is unsuitable for the shaping of a coherent laser beam, works well with an excimer laser beam because of its partial spatial coherence. The conversion of an approximately Gaussian excimer laser beam into a flat-top beam in the Fourier plane of a lens is demonstrated with a diffractive beam shaper fabricated as a multilevel profile in SiOl by electron-beam lithography and proportional reactive-ion etching.     

Statistical distribution of the optical intensity obtained using a Gaussian Schell model for space-to-ground link laser communications

Abstract

Based on the characteristics of the laser device and the inevitable error of the processing technique, a laser beam emitted from a communication terminal can be represented by the Gaussian Schell model (GSM). In space-to-ground link laser communications, the optical intensity is affected by the source coherence parameter and the zenith angle. With full consideration of these two parameters, the statistical distribution model of the optical intensity with a GSM laser in both downlink and uplink is derived. The simulation results indicate that increasing the source coherence parameter has an effect on the statistical distribution of the optical intensity; this effect is highly similar to the effect of a larger zenith angle. The optical intensity invariably degrades with increasing source coherence parameter or zenith angle. The results of this work can promote the improvement of the redundancy design of a laser communication receiver system.     

X-ray imaging: a generalized approach using phase-space tomography

We discuss the role of coherence in x-ray imaging and consider how phase-space tomography can be used to extract information about partial coherence. We describe the application of phase-space tomography to x-ray imaging and recover the spatial coherence properties of a one-dimensional soft (1.5 keV) x-ray beam from a synchrotron undulator source. We present phase-space information from a Young's experiment and observe negative regions in the quasi-probability distribution. We show that, given knowledge of the coherence of the beam, we can use partially coherent diffraction data to recover fully coherent information, and we present some simple experimental demonstrations of this capability.     

Three-dimensional calculation of high-power, annularly distributed, laser-beam-induced thermal effects on reflectors and windows

Based on the three-dimensional transient heat conduction equation and the elastic stress-strain equation, the temperature rise, distortion, and equivalent stress distributions of a high-reflectivity silicon reflector and a white bijou window irradiated by a high-power sloped annularly distributed laser beam are simulated using a three-dimensional finite element model (FEM). The effects of laser intensity, output duration, beam obscure ratio, and laser intensity spatial gradient on the results are especially investigated. The effects of mirror and window thermal distortion on laser beam phase aberrations are also evaluated. This noncylindrosymmetric three-dimensional FEM can be used to evaluate high-power, high-energy, laser beam-induced thermal effects on optical components.     

Transverse coherence measurement using a folded Michelson interferometer

The transverse coherence of a 1 ps pulsed laser beam was measured using a technique involving a modified Michelson interferometer and separate reference images. Using this technique, the transverse coherence of a selected plane in the laser beam was determined, in this case at the exit of a channel in a metal foil self-drilled by the laser. Images of each arm were used as references. Through this technique, it is possible to use the interference patterns produced with uneven intensity distributions and for pulsed lasers on a single-shot basis. The results of these measurements were then shown to be in agreement with those obtained using a Young's double-slit setup.