Theoretical study on the spectral shifts of partially coherent array beams passing through ABCD optical systems

According to the extended Huygens–Fresnel integral, the expressions for the on-axis spectrum of partially coherent Gaussian Schell-model (GSM) rectangular array beams passing through ABCD optical systems have been derived. The generalized Fresnel number of the system, the spatial coherent parameter of array beamlets and the array beam parameters including the number of beamlets and the separation distance between beamlets have been taken as the characteristic parameters to compare the spectral shifts of GSM array beams for the two types of the superposition, i.e. the correlated superposition and the uncorrelated superposition. In particular, the effect of characteristic parameters on the on-axis relative spectral shifts has been discussed in detail. The results show that the spectral intensity of GSM array beams for the two types of the superposition passing through ABCD systems depends on the source spectral density S ⁰(ω), the spatial coherent parameter of array beamlets β, the generalized Fresnel number of the system F and the array beam parameters. Furthermore, for the uncorrelated superposition, the spectrum of GSM array beams only exhibit the blue-shift, whereas for the correlated superposition, GSM array beams exhibit the spectral switch and the number of spectral switches increases with the increase of array beam parameters in the near field due to the interference between beamlets. In particular, the effect of the array beam parameters on the on-axis relative spectral shift is more obvious.     

Randomly phased geometrical laser array

A novel geometrical laser array is presented in which high far-field intensities can be generated without phase control of the laser elements. The array was analyzed by randomly varying the phasing of the elements and calculating the maximum far-field intensity. In the worst possible phasing conditions, the maximum far-field intensity remained high and was nearly constant with regard to the number of array elements. By increasing the geometrical spacing factor, the maximum intensity will approach that of a perfectly phased array.     

Laser beam projection with adaptive array of fiber collimators. I. Basic considerations for analysis

We present a mathematical model and provide an analysis of optical beam director systems composed of adaptive arrays of fiber collimators (subapertures), referred to here as conformal optical systems. Performances of the following two system architectures are compared: A conformal-beam director with mutually incoherent output laser beams transmitted through fiber collimators (beamlets), and a corresponding coherent system whose beamlets can be coherently combined (phase locked) at a remote target plane. The effect of the major characteristics of the conformal systems on the efficiency of laser beam projection is evaluated both analytically and through numerical simulations. The characteristics considered here are the number of fiber collimators and the subaperture and conformal aperture fill factors, as well as the accuracy of beamlet pointing.     

Beam propagation properties of radial laser arrays

A detailed study of phase-locked and non-phase-locked radial laser arrays is presented. The closed-form propagation expressions for the beamlets and the resulting beam are given, which enable us to study beam propagation properties of radial laser arrays for both phase-locked and non-phase-locked cases. Numerical calculation examples are given to illustrate the application of our analytical results and the differences between phase-locked and non-phase-locked radial arrays.     

Arrays of anamorphic phase-matched Fresnel elements for diode-to-fiber coupling

A method for designing microlens arrays that inherently takes into account application requirements and fabrication constraints is presented. Elements with numerical apertures of up to 0.5 have been designed and fabricated by laser beam writing in photoresist and replication in plastic material. In a laser-diode-to-fiber array coupling experiment, an overall optical throughput of 60% was achieved. By means of anamorphic microlens arrays, correction of the laser-diode longitudinal astigmatism and circularization of the image-plane irradiance distribution are demonstrated.     

High frequency optoacoustic arrays using etalon detection

Two-dimensional phased arrays for high frequency (>30 MHz) ultrasonic imaging are difficult to construct using conventional piezoelectric technology. A promising alternative involves optical detection of ultrasound, where the array element size is defined by the focal spot of a laser beam. Element size and spacing on the order of a few microns are easily achieved, suitable for imaging at frequencies exceeding 100 MHz. We have previously shown images made from a receive-only, two-dimensional optoacoustic array operating at 10 to 50 MHz. The main drawback of optical detection has been poor sensitivity when compared with piezoelectric detection. In this paper, we explore a different form of optical detection demonstrating improved sensitivity and offering a potentially simple method for constructing two-dimensional arrays. Results from a simple experiment using an etalon sensor confirm that the sensitivity of etalon detection is comparable with piezoelectric detection. This paper concludes with a proposal for a high frequency optoacoustic array system using an etalon.     

Controlling gradient phase distributions in a model of active antenna array with locally coupled elements

The regime of synchronization with a certain gradient phase distribution and the possibility of controlling such distribution in a linear array of oscillators coupled by phase-locked loops (PLLs) have been theoretically studied. It is shown that a constant phase progression can be controlled by manipulating collective dynamics, with oscillator eigenfrequencies and coupling coefficients being the control parameters. The proposed principle of control, based on the nonlinear dynamics of PLL-coupled oscillators, can be used in solving the problems of phasing and controlled beam scanning in antenna arrays operating in different frequency bands.     

Influence of laser array performance on spectrally combined beam

Abstract

Incoherent spectral beam combining (SBC) of multiple laser beams is accomplished along the emitters’ arraying direction. Considering that the output beams from a laser array (LA) usually have deflection angles, positional displacements and divergence angles even after being collimated, a propagation model of SBC systems based on multilayer dielectric gratings has been built up. On the basis, properties of the spectrally combined beam affected by parameters of the LA have been discussed in detail. Simulation results show that with the increase in the deflection angle, both the power and the beam quality of the combined beam degrade dramatically. The positional displacement has little impact on the intensity distribution and the beam quality of combined beam but change the wavelength composition of the combined beam. The divergence angle strongly affects the intensity distribution and the beam quality of the combined beam. Additionally, the effect of the deflection angle on the output beam quality is more obvious and may shift the beam spot when comparing with that of the divergence angle.     

Accommodation of speckle in object-based phasing

This work addresses the physical basis of the measurement process for object-based phasing of an array of telescopes. In this regard an enhanced least-squares estimator that is capable of differentiating among three families of array aberrations in an object-based phasing system is developed. In a system of this nature the system to be phased illuminates the object of interest and the return radiation is detected. Telescope aberrations, atmospheric aberrations, and speckle-induced aberrations are all reported by the estimator to facilitate correction of telescope and atmospheric aberrations. This is accomplished by proper handling of the unobservable modes and recognizing that the five global aberrations-telescope array piston, atmospheric array piston and tilt, and speckle array piston and tilt-cannot be measured accurately so they need to be projected out of the estimated piston commands. Except for these relatively benign array aberrations, the disturbances for all three families of array aberrations are estimated exactly. An interesting feature of the speckle array aberrations is that a synthetic aperture is developed that is almost twice as large as the array of telescopes under consideration.     

Target-based coherent beam combining of an optical phased array fed by a broadband laser source

The target-based phasing of an optical phased array (OPA) fed by a broadband master oscillator laser source is investigated. The specific scenario examined here considers an OPA phasing through atmospheric turbulence on a rough curved object. An analytical expression for the detected or received intensity is derived. Gleaned from this expression are the conditions under which target-based phasing is possible. A detailed OPA wave optics simulation is performed to validate the theoretical findings. Key aspects of the simulation set-up as well as the results are thoroughly discussed.     

Study of an ultrafast analog-to-digital conversion scheme based on diffractive optics

A potentially ultrafast optical analog-to-digital (A/D) converter scheme is proposed and was partly studied experimentally. In the A/D converter scheme the input signal controls the wavelength of a diode laser, whose output beam is incident on a grating. The beam from the grating hits a diffractive optical element in an array. The wavelength determines which element is illuminated. Each element fans out a unique spot-pattern bit code to be read out in parallel by individual detectors. In the experiment all patterns but one from 64 array elements were read out correctly.     

Focusing of Rayleigh waves: simulation and experiments

A linear array of surface wave transducers has been developed to generate focused surface wave motion. A novel theoretical approach, whereby time-harmonic surface wave motion is represented by a carrier wave that satisfies a reduced wave equation on the surface of the body and supports the subsurface motion, is used to model the beam generated by a single element of the array. Comparison of theoretical and experimental results show that, for a single element, the opening angle of the beam is about 20 degrees and its cross-section can be represented by a Gaussian distribution of the normal displacements. For an eight-element array, the focused beam is subsequently obtained by superposition considerations. For the focused beam comparisons of theoretical and experimental results, in which the latter have been obtained by the use of a laser interferometer, show excellent agreement both for the normal displacements along a radial line and across the width of the beam. The array can be used for self-focusing of surface waves on a surface defect.     

In-phase supermode selection in a multicore fiber laser array by means of a self-Fourier external cavity

A procedure is developed to determine the transverse-mode structure of a cavity consisting of a dense, evanescently coupled, waveguide laser array, which, in addition, is externally coupled by feedback from an external cavity. The formalism is used to determine the loss and phasing properties of a multicore fiber array coupled to an external self-Fourier cavity. Best performance is predicted for linear arrays of up to five cores, or two-dimensional arrays of up to 25 cores. A low-loss, in-phase, fundamental array mode is predicted, which achieves better than 30 dB discrimination against higher-order modes at periodically spaced values of the array length. However, we show that a shift in operating wavelength of typically a few nanometers can bring about near-perfect phasing and loss operation over a continuum of fiber lengths. With increased fill factor, significantly more of the output power can be concentrated in the central lobe of the far field but at the penalty of increased loss in the fundamental eigenmode.     

Multipass Michelson interferometer with the use of a wavelength-modulated laser diode

An improved multipass Michelson interferometer is implemented. This technique uses the fact that the wavelength of a laser diode varies in proportion to the diode's injection current. With this method the sensitivity augmentation is accomplished by inserting a beam splitter into one arm of the interferometer, resulting in multiple reflections between the end mirror and the beam splitter. In addition, the interference of laser beams reflected from two arms can be accomplished with unequal arms in the condition of a short coherence length. The sensitivity increase of interference fringes and the compensation of the short coherence length have been demonstrated in experiments.     

Ground-to-Satellite Narrow-Laser-Beam Pointing by Use of a Backscattered Image

A technique for transmitting a narrow laser beam from a ground station to a satellite has been developed. The principle of pointing a laser beam to a distant target in a scattering medium by use of a backscattered laser beam image is described. We calculated the intensity distribution of the image by using a typical model of atmospheric coefficients. The method was applied to transmit a laser beam from a ground station to Engineering Test Satellite-VI. The accuracy of pointing the laser beam to the satellite was approximately 10 murad in this experiment.     

Shack-Hartmann sensor for fast infrared wave-front testing

Abstract

A Shack-Hartmann sensor has been designed for testing the wave front of CO₂ lasers. Fabrication of a lens array and a detector array with tight tolerances on position accuracy are essential steps. Parallel electronics allow for high-speed wave-front measurements with 1 kHz sampling frequency. The device has been used to investigate the behaviour of a high-power CO₂ laser. Besides the expected thermal drifts of beam direction at the beginning of laser action, periodic changes of beam direction, have been detected. The Shack-Hartmann sensor seems the appropriate device for controlling adaptive optics in high-power laser applications.     

Effects of Broadband Laser Generated Ultrasound on Array Gain

Array gain is a common parameter used in laser phased array research. This paper will present a new parameter called the frequency modulation of laser phased array (FMLPA). The array gain model for laser phased arrays was derived using an assumption that ultrasound from each array member interferes with each other. This would be always true if laser generated ultrasound is narrow band. However, laser generation of ultrasound is broad band. Broad band ultrasound signals have short duration in the time domain. If the time delay between generated wave fronts from each array member is longer than the duration of the broad band ultrasound signal from each array member, the ultrasound signals from each array member will not interfere with each other. The time delay between generated wave fronts from each array member is 0 s at a laser phased array’s beam steering angle and increases away from the beam steering angle. Therefore, ultrasound from each array member always interfere at angles close to the beam steering angle. However, ultrasound from each array member may not interfere at angles away from the beam steering angle depending on the time delay between generated wave fronts and duration of the broad band ultrasound signal. A theoretical model of the FMLPA was developed and experimentally verified for use when ultrasound from each array member does not interfere with each other. It was experimentally verified that current array gain equations still apply when ultrasound from array members interfere with each other. The FMLPA can be used to create new techniques for measuring weld penetration depth, crack location, and dimensions of objects.     

A Large-Area PVDF Pyroelectric Sensor for CO 2 Laser Beam Alignment

We present the design of a large-area (50 mm times 50 mm) polyvynilidene fluoride (PVDF) pyroelectric sensor array for industrial CO₂ (lambda = 10.6 mum) laser beam positioning. The array dimensions were chosen to match the area typically monitored in the alignment procedure of external optics (beam steering moving arm system, for example) used to redirect the laser beam from the laser output window to a remote working station. The instrument is provided with a tilted, high reflection, ZnSe plate which partially transmits the laser beam onto the sensor array. From positioning simulations with a Gaussian laser intensity profile with a sigma = 3.2 mm standard deviation (equivalent spot size 3sigma cong 20 mm), the positional accuracy along the two orthogonal array dimensions was found to be better than 0.02 mm for an 8 times 8 array and one order of magnitude higher for a 16 times 16 array. The centroid position of a CO₂ industrial laser beam was evaluated by integrating the pyroelectric current for a time comparable to the time duration (100-200 ms) of the laser pulses used in the alignment procedure.     

Acousto-optical deflection-based laser beam scanning for fluorescence detection on multichannel electrophoretic microchips

Laser beam scanning driven by an acousto-optical deflector (AOD) is presented for multimicrochannel laser-induced fluorescence (LIF) detection during microchip-based electrophoresis. While fast laser beam scanning for LIF detection on capillary or microchannel arrays can been achieved with galvanometric scanning or a translating stage, it can also be accomplished by using acoustic waves to deflect the laser beam in a manner that is dependent on the acoustic frequency. AOD scanning differs from other approaches in that no moving parts are required, and the scan frequency is faster than conventional approaches. Using a digital/analog (D/A) converter to provide addressing voltages to a voltage/frequency converter, rapidly changing the frequency input to the AOD allows the laser beam to be addressed accurately on a microchip. With the ability to change the frequency on the nanosecond time scale, scanning rates as high as 30 Hz for Windows-based LabView programming are possible, with much faster scan rates achievable if a microprocessor-embedded system is utilized. In addition to spatial control, temporal control is easily attainable via raster scanning or random addressing, allowing for the scanning process to be self-aligning. Since the D/A output voltages drive the scanning of the laser beam over all channels, the software can define addressing voltages corresponding to the microchannel centers and, subsequently, fluorescence data can be collected from only those locations. This method allows for flexible, high-speed, self-align scanning for fluorescence detection in capillary or microchip electrophoresis and has the potential to be applied to a number of applications.     

半导体激光器列阵二元光学准直器的设计和制作

阐述了二元光学元件用于半导体激光器列阵准直的新方法 ,并设计制作了二元光学准直器。针对半导体激光器列阵的特点 ,采用综合平衡方法进行设计和制作 ,使其理论衍射效率超过 5 1 %。