Fiber-coupling of high-brightness laser diode bars requires shaping and superposition of the images of the individual emitters on the fiber facet. Employment of micro-optical elements together with bulk-optical components enables the design and manufacturing of efficient coupling schemes with small form-factor. In this presentation we describe optical system design, manufacturing of micro-optical elements, system integration and characterization of two coupling schemes: The beam twister approach uses tilted cylindrical mirolens telescopes to rotate the images of the individual emitters by 90° with subsequent beam compression and focusing optics, while a skew ray coupling scheme applies an array of blazed diffractive elements in the pupil plane of a relay optics to superpose the images of the individual emitters. The optics design is based on raytracing procedures, taking into account diffractive effects, which could lower coupling efficiency. Micro-optical components are realized by polymer-on-glass replication of reflow lenses or grating structures manufactured by laser-lithography. System assembly is based on precise glueing with active alignment in the submicrometer range. We realized several optics schemes for coupling of high-power, high-brightness laser diode bars into fibers with 100µm core diameter. The systems are compared with each other with respect to achievable coupling efficiency, adjustment tolerances and pointing stability.

Several issues on the optimal diffractive beam shaping with a dynamic phase spatial light modulator are addressed. As for design theories, the optimal design method of the phase holograms considering the functional relationship between phase and amplitude modulations of the phase spatial light modulator is described. To achieve the optimal trade-off between diffraction efficiency and smoothness of the obtained diffraction images, the iterative Fourier transform algorithm with adaptive regularization parameter distribution is devised. Regarding experimental issues, we propose a beam shaping system configuration with the genetic feedback tuning loop in which the simplified genetic algorithm is employed to finely compensate the internal aberration of the optics in the beam shaping system. It is shown that the real-time tuning of the phase holograms for accurate beam shaping is possible using the dynamic behavior of the spatial light modulator.

Evaluating the success of beam shaping techniques requires the measurement of the resulting beam profile. Laser beam profilers have been used extensively throughout the laser industry to enable users to evaluate the "quality" of their laser beam. Profilers have made many strides in recent technology, including new cameras, new beam sampling optics, new calculation algorithms, and new profile displays. New cameras include high resolution, megapixel arrays, digital CCDs, FireWire cameras, and phosphor coated CCDs for extending near IR response. Improved beam sampling optics includes components for eliminating polarization effects and optics for sampling high power multi-kilowatt YAG and CO₂ lasers. In recent years ISO has refined calculation definitions for measurement of beam width, divergence, flattop beams, and many others, thus standardizing laser profile characterization. Beam profile displays in both 2D and 3D have been improved to provide more intuitive insight.

In this paper we implement a new technique of intracavity bimorph flexible mirror control, that allows to manipulate laser beam parameters (increase power, decrease divergence) and to form a given intensity profile at any distance including a far-field. Intracavity mirror surface profile is controlled by number of voltages calculated by means of genetic algorithm combined with hill-climbing one. Then the traditional Fox-Li approach is applied. We have numerically shown the possibility of successful formation of super Gaussian beam in near field, ring-like beam in far-field, and the possibility of significant power increase of TEM₀₀ mode and far-field peak intensity enlargement.

The method of Kreuzer for irradiance redistribution with aspheric lenses can be used to derive a differential equation for the sag curve of a single aspheric surface which transforms the irradiance profile of a beam without regard to the phase of the wavefront of the shaped beam. It is shown that in the paraxial approximation the sag curve naturally splits into a quadratic term and an integral expression that depends on the shapes of the input and output profiles. For the special case where the input beam is Gaussian and the output profile is uniform, the integral term that appears in the sag curve is identical to the phase function derived by Dickey, Romero, and Holswade using the formalism of Fourier optics. The identity derived here demonstrates the equivalence, in the paraxial limit, of two apparently different methods of solving the beam shaping problem.

In several previous publications we have outlined how a freeform optical surface can be tailored to achieve a desired irradiance on a reference surface. The shape of the surface is determined by numerically solving a differential equation. This approach has the advantage of being able to accommodate a huge amount of detail, equivalent to several thousand to millions of parameters for which classical optimisation techniques are not feasible. Laser beam shaping requires controlling the phase of the wave front as well. One surface is not sufficient, but two surfaces can be calculated by simultaneously solving a system of coupled differential equations. Justin L. Kreuzer patented this idea in 1965 (US Patent No. 3476463). Wassermann and Wolf outlined already in 1949 a procedure by which two aspheric surfaces are determined by solving differential equations such as to render an imaging optical system aplanatic. The work of Kreuzer as well as that of Wassermann and Wolf refers to rotational systems, where the cross section curve suffices to determine the surface and the equations are less demanding. We show how to extend the method of three-dimensional tailoring to simultaneously tailor two surfaces which are not necessarily rotationally symmetric, such as to achieve non-rotational irradiance distributions or off-axis devices. The desired irradiance translates into an equation which combines the first and the second derivatives of the surfaces.

Many laser material processing applications depend only on the intensity profile at a given working plane. A single diffractive optic has been shown to produce useful results in the material processing environment where the intensity is the only concern. However, for laser application that depend on the intensity profile and the phase profile together, it seems self-evident that a minimum of two diffractive phase elements is required. Although, this two element approach can be effective, it requires more complex alignment and a higher energy loss for the diffractive system, relative to a single element solution. For demanding laser applications like holography, both phase and intensity are critical to the process. This paper will discuss the theory and experimental data to support the use of a single diffractive optic for use in holography, and other phase critical applications for round uniform shaped beams.

A class of annular light beams with flat-topped Gaussian profile (i.e., Gaussian doughnut mode) is introduced. Field distribution of this kind of beams can be obtained by subtracting from a flat-topped Gaussian function [Proc. of SPIE, 5525, 128-137 (2004)] with another flat-topped Gaussian function of different width. The proposed expression can be easily expanded into a series containing the lowest order Gaussian modes of different waist parameters. This situation significantly improves the numerical calculation efficiency in the investigation of propagation properties of annular beams and also provides the possibility to investigate the aperture effect that a beam may be experienced when the beam passes progressively from smooth Gaussian aperture toward the hardedge limit. Results are illustrated by examples and compared with the prediction of Lommel theory of diffraction of plane waves at an annular aperture.

The term Helmholtz-Gauss beam refers to a field whose disturbance at the plane z =0 reduces to the product of the transverse field of an arbitrary nondiffracting beam (i.e. a solution of the two-dimensional Helmholtz equation) and a two-dimensional Gaussian function. In this work, the transverse shape and the propagation of Helmholtz-Gauss beams is experimentally studied for the four fundamental orthogonal families of Helmholtz-Gauss beams: cosine-Gauss beams, Bessel-Gauss beams, stationary and helical Mathieu-Gauss beams, and stationary and traveling parabolic-Gauss beams. The power spectrum of the Helmholtz-Gauss beams is also recorded and its intensity distribution is assessed. Potential applications are discussed.

The development of technology of small dimensions requires a different treatment of electromagnetic beams with transverse dimensions of the order of the wavelength. These are the nonparaxial beams either in two or three spatial dimensions. Based on the Helmholtz equation, a theory of nonparaxial beam propagation in two and three dimensions is developed by the use of the Mathieu and oblate spheroidal wave functions, respectively. Mathieu wave functions are the solutions of the Helmholtz equation in planar elliptic coordinates that is a special case of the prolate spheroidal geometry. So we may simply refer to the solutions, either in two or three dimensions, as spheroidal wave functions. Besides the order mode, the spheroidal wave functions are characterized by a parameter that will be referred to as the spheroidal parameter. Divergence of the beam is characterized by choosing the numeric value of this spheroidal parameter, having a perfect control on the nonparaxial properties of the beam under study. When the spheroidal parameter is above a given threshold, the well known paraxial Laguerre-Gauss and Hermite-Gauss beams are recovered, in their respective dimensions. In other words, the spheroidal wave functions represent a unified theory that can describe electromagnetic beams in the nonparaxial regime as well as in the paraxial one.

A number of flattened irradiance distributions have been proposed and analyzed in the literature, including the super-Gaussian, flattened-Gaussian, Fermi-Dirac, and super-Lorentzian as well as generalizations of these functions to include multiple shape parameters. Previous work has made comparisons between these different families of functions and examined the effects of propagation (diffraction) on the shape of the beam profile. In this paper, we examine the normalization of different functions, comparisons of profile shapes using different parameters within each family, the slope of the profiles at the half-height point of the irradiance, and two conditions that permit matching shapes of profiles from different families. Then, we summarize the results of diffraction for variation of the profile shape parameters, beam propagation, and diameter of the exit aperture on the shape of a beam as it leaves the optics. Results are also presented which identify the regions and amounts of aspheric surface sag that is required to produce a flattened beam profile as compared to a top-hat profile profile.

The one-particle type temporal soliton exists by maintaining a balance between dispersive linear contributions on the one hand and non-linear effects on the other. The linear contributions occur from processes such as group velocity and polarization mode dispersion. The nonlinear features occur from Kerr, or power law non-Kerr behavior. In addition, a variety of perturbations, such as damping, Brillouin scattering, and Raman effects exist to alter the simple soliton solution. In this paper, we review the propagation of temporal solitons in power law non-Kerr media. This is developed through the higher nonlinear Schroedinger's equation (HNLSE). Also, the fundamentals of multiple-scales are presented that will be used to yield quasi-stationary solitons when perturbations are present. In waveguides, the one-particle type spatial soliton exists by maintaining a balance between the linear propagational diffraction and non-linear self-focusing, while possibly being subjected to a variety of perturbations. Here, we use a spatial optical soliton solution to the nonlinear Schroedinger equation in an inhomogeneous triangular refractive index profile as a small index perturbation to illustrate the oscillation property within a two dimensional waveguide. We determine, from the motion of spatial soliton, its effective acceleration, period of oscillation, and compare results with the Gaussian refractive index profile. Such spatial solitons behave as point masses existing in a Newtonian gravitational potential hole.

In this paper a new algorithm of bimorph deformable mirror the best-suited electrodes shape and position determination is suggested. This algorithm is based on solving an inverse problem of defining the best electrodes position from the required phase distribution formation. The first part of the algorithm is an approximate determination of mirror electrodes position, which is based on linear dependence of electrical field in piezoceramics from laplasian of corresponding mirror deformation. Exact locating of the electrodes is the second part of the algorithm and is performed during iterative procedure. During the procedure relative root mean square deviation of computed mirror profile from the demanded one is minimized. To calculate mirror deformation on every iteration step we use a specially developed finite element model of the bimorph mirror. By using the developed algorithm, we demonstrate possibility to increase quality of reproducing various phase profiles, for example those, corresponding to human eye aberrations and even to form vortex beam.

Effects of material dispersion are considered for the case of an aspheric lens pair which transforms a collimated laser beam to a collimated beam with a different transverse irradiance profile. When the lenses are used at a wavelength other than the design wavelength, wavefront aberration is the primary consequence, with distortion of the output profile being a minor effect. Using geometric optics, we derive simple expressions for the effects of dispersion on the output wavefront, which depend only on dispersion and the beam shaping transformation under consideration, but which do not require the solution of the full lens design equations. As an example, detailed results are shown for a practical beam shaping design.

Infra-red laser beam shaping has the inherent difficulty that simple ray tracing methods often yield anomalous results, due primarily to the propagation effects at longer wavelengths. Techniques based on diffraction theory have been developed to overcome this, with associated parameters to determine when one approach is needed versus another. In this paper, infra-red (IR) beam shaping by diffractive methods is investigated and compared to refractive methods. Theoretical results on the beam shapers are calculated through a combination of analytical and numerical techniques, and using both ideal and non-ideal inputs. We show that the diffractive optical element (DOE) is remarkably resilient to input errors of wavelength and beam quality, while the refractive shaper is found to be difficult to model. Optical elements based on the two approaches were designed, and then fabricated from ZnSe. A comparison between the fabricated elements and the designed elements is presented, and some of the findings on practical problems in having such elements fabricated are highlighted.

Performance of diffractive optics is influenced partly by fabrication; however the design and modeling of the diffractive optics prior to fabrication play a significant role in the ultimate performance results. When designing completely new diffractive optics, the tendency is to design, model, fabricate and then hope for the best. Many companies who look to source diffractive optics come face to face with the reality of this dilemma since diffractive optic suppliers tend to provide their services on a "best effort basis". In short this means, if the vendor does not get it right the first time, the client will need to place a second order. At which point the diffractive optic vendor will try to make it better the second time around, but no guarantee. This paper will examine and compare the design methods used to generate diffractive optical structures and performance models as well as the micro machining processes used for the fabrication of a diffractive fan out or splitter element. Examples of computer software for design and modeling will be described showing how various approximation and encoding methods compare. An overview of the optical testing methods used will be discussed including the specific test equipment and metrology techniques used to verify performance and dimensional stability. The paper will demonstrate a real world application by showing the analysis of a series (same design) of a one dimensional splitters with varying etch depths and geometries. Presentation of data will include fabrication dimensional errors, splitter beam uniformity and beam efficiency as compared to the original intended design performance and models. Finally a summary of helpful guidelines will be outlined for engineers seeking to develop prototype diffractive optics.

The design of refractive beam shaping elements can be done by the geometrical-optical approach based on ray optics. This means one has to find a map transformation, which transforms an input to a desired output distribution and can additionally be realized by an element with a continuous surface. Easy procedures to find transformations, fulfilling both of these conditions at the same time, exist only for one-dimensional and for special two-dimensional signals, e.g. separate or circular distributions. To realize completely arbitrary two-dimensional signal distributions only iterative methods, based on the wave nature of light, are applicable, e.g. the Iterative Fourier-Transform Algorithm (IFTA). However, they can not be used to design elements with a continuous surface since they usually introduce phase dislocations to the signal distribution. We present an algorithm, which uses both geometrical and wave optical methods to find a most suitable, refractive solution for two-dimensional beam shaping problems. An Iterative Mesh-Adaption Algorithm (IMA), based on the geometrical-optical domain, is used to find a map transformation to describe the energy rearrangement. An IFTA, working in the wave optical domain, is used to refine the mesh. The IFTA produces phase dislocations in the beam shaping element, but nevertheless its output can be used to change parts of the mesh. Both algorithms are used in an alternating fashion. We present the design, fabrication and characterization of beam shaping elements, realized with the help of this method.

Single-mode diode lasers are well-established light sources for a huge number of applications but suffer from astigmatism, beam ellipticity and large manufacturing tolerances of beam parameters. To compensate for these shortcomings, various approaches like anamorphic prism pairs and cylindrical telescopes for circularization as well as variable beam expanders based on zoomed telescopes for precise adjustment of output beam parameters have been employed in the past. The presented new approach for both beam circularization and expansion is based on the use of microlens arrays with chirped focal length: Selection of lenslets of crossed cylindrical microlens arrays as part of an anamorphic telescope enables circularization, astigmatism correction and divergence tolerance compensation of diode lasers simultaneously. Another promising application of chirped spherical lens array telescopes is stepwise variable beam expansion for circular laser beams of fiber or solid-state lasers. In this article we describe design and manufacturing of beam shaping systems with chirped microlens arrays fabricated by polymer-on-glass replication of reflow lenses. A miniaturized diode laser module with beam circularization and astigmatism correction assembled on a structured ceramics motherboard and a modulated RGB laser-source for photofinishing applications equipped with both cylindrical and spherical chirped lens arrays demonstrate the feasibility of the proposed system design approach.

An annular beam provides a new laser drilling mechanism, that we refer to as "optical trepanning". Based on ray tracing techniques, a refractive axicon system has been designed to transform an input Gaussian laser beam into an annular beam with an appropriate irradiance profile. The properties of the resulting annular beam are investigated in this paper. The diffraction patterns were measured, showing that a collimated annular beam can be obtained using a refractive axicon system. However, due to spherical aberration effects, the focused annular beams possess altered irradiance profiles with different focusing lenses. The effects of spherical aberration on the focused annular beam are also investigated.

Optical trepanning is a new laser drilling method using an annular beam. The annular beams allow numerous irradiance profiles to supply laser energy to the workpiece and thus provide more flexibility in affecting the hole quality than a traditional circular laser beam. The refractive axicon system has been designed to generating a collimated annular beam. In this article, calculations of intensity distributions produced by this refractive system are made by evaluating the Kirchhoff-Fresnel diffraction. It is shown that the refractive system is able to transform a Gaussian beam into a full Gaussian annular beam. The base angle of the axicon lens, input laser beam diameter and intensity profiles are found to be important factors for the axcion refractive system. Their effects on the annular beam profiles are analyzed based on the numerical solutions of the diffraction patterns.

The problem of design of a two-mirror optical systems for reshaping the irradiance distribution of a laser beam in a prescribed manner is considered. These designs are developed under the geometrical optics approximation. The novelty is that our method is not limited to input and/or output radiance profiles which are rotational or rectangular symmetric. Moreover, the method leads to two beam-shaping systems for one of which the first mirror is concave and the second is convex.

A design of multi-step diffractive optical element (MDOE) is developed for the high power laser output smoothing. A hybrid algorithm is presented which inserts a quasi-optimum process in every iterative loop. This method of MDOE design saves the computing time tremendously. The top profile error (TPE) is about 8.4%, which looks inferior to what we have gotten in the earlier years with using continues profile design, but very easy in manufacture to match the design data. Now this MDOE with 16 steps on the surface of K9 glass can be realized with four masks' etching facility. The maximum etching error of the depth is 10-80nm, which is receivable with tolerance analyze in our design. The MDOE has 70mm diameter, and uniform illumination area is an Φ600μm spot. With using expanding 1.064 μm beam, the smoothing pattern in focus plane is measured. The result shows that the TPE is about 19%. It is believable that with the influence by the interaction of second hot electron and time domain smoothing this result is acceptable.

Recent experiments demonstrated high conversion efficiency in the process of Orientational Stimulated Scattering (OSS) in nematics. This fact makes OSS attractive for beam combining and clean-up. We consider a scheme for such application and study it by numerically modeling the process. As the process of energy transfer goes, the reverse transfer also begins. However, the region of the back-transfer moves inside the cell with constant velocity in ⁺z direction and given sufficient time, leaves the cell. By modeling the OSS of diffracting one-dimensional beams we show the possibility to obtain a maximum 94% fidelity and 96% power transfer in a numerical experiment with 6 individual overlapping pump beamlets. This means that 90% of the total pump power may be converted into the diffraction-limited output. Remarkably, this output suffers very little cross-phase modulation.

In a recent work it was demonstrated that efficient laser mode selection can be accomplished by replacing one of the laser mirrors by a bi-prism-like (flat-roof) reflector. In that work the objective was to generate a pure "dark beam" (a laser beam with a dark central region) for high resolution metrological applications. With the same objective in mind, in this work we present a new approach that leads to significant improvement of laser performance. This approach is based on an earlier work where a narrow amplitude mask over the middle of a conventional laser mirror was used to suppress the zero-order mode to facilitate oscillation of the first-order mode possessing the required characteristics. Starting from a similar configuration, in the present work we show that the performance can be optimized by combining a partially transmitting amplitude mask with a bi-prism-like reflector. Numerical simulations predict mode selectivity enhancement of at least a factor of 3 as compared to laser resonators with bi-prism-like reflectors alone.

We theoretically demonstrate 2-dimensional beam shaping through adaptive feedback in two adjacent and orthogonally oriented acousto-optic devices with electrical feedback using experimentally determined parameters. Cases of positive and negative feedback from undiffracted and diffracted orders are investigated. In addition, we demonstrate the dependence of the final value of the induced grating strength in the acousto-optic cell on the feedback parameters.

We have recently demonstrated how holographic optical tweezers can be used to build and dynamically manipulate extended 3-D structures. Although successful trapping can be maintained even when a large number of traps are simultaneously manipulated, in general a gradual degradation of trap quality is observed as the number of traps increased. This degradation is partly attributed to the increased 3-D size of the structures. To build and control such large structures the high numerical aperture focusing objective lens has to operate away from its design conjugate for most of the traps, and therefore aberrations will be significant even for high quality objective lenses. A second effect is the decreasing efficiency of the liquid crystal spatial light modulators as they are required to display holograms that contain high spatial frequencies. However these factors do not appear to account fully for the observed weakening of the traps, and it is likely that a reduction of contrast in the trapping optical field also plays an important role. We examine the effects individual optical traps have on each other when they are in close proximity. Techniques that may be used to mitigate the reduced contrast will also be discussed.

A variety of strategies have been utilised for prevention and treatment of chronic wounds such as leg ulcers, diabetic foot ulcers and pressure sores¹. Low Level Laser Therapy (LLLT) has been reported to be an invaluable tool in the enhancement of wound healing through stimulating cell proliferation, accelerating collagen synthesis and increasing ATP synthesis in mitochondria to name but a few². This study focused on an in-vitro analysis of the cellular responses induced by treatment with three different laser beam profiles namely, the Gaussian (G), Super Gaussian (SG) and Truncated Gaussian (TG), on normal wounded irradiated (WI) and wounded non-irradiated (WNI) human skin fibroblast cells (WS1), to test their influence in wound healing at 632.8 nm using a helium neon (HeNe) laser. For each beam profile, measurements were made using average energy densities over the sample ranging from 0.2 to 1 J, with single exposures on normal wounded cells. The cells were subjected to different post irradiation incubation periods, ranging from 0 to 24 hours to evaluate the duration (time) dependent effects resulting from laser irradiation. The promoted cellular alterations were measured by increase in cell viability, cell proliferation and cytotoxicity. The results obtained showed that treatment with the G compared to the SG and TG beams resulted in a marked increase in cell viability and proliferation. The data also showed that when cells undergo laser irradiation some cellular processes are driven by the peak energy density rather than the energy of the laser beam. We show that there exist threshold values for damage, and suggest optimal operating regimes for laser based wound healing.

In the advancing field of gravitational wave interferometry, the desire for greater sensitivity leads to higher laser powers to reduce shot noise. Current detectors[1] such as LIGO and GEO 600 operate with continuous wave lasers at 10-15 W powers, however future versions will operate at 200 W. One of the major challenges of higher power operation is the creation of thermal lenses in optical components, caused by from the absorption of laser light, yielding optical path deformation and concomitant beam aberrations. This effect is especially problematic in transmissive optical components even at very low levels of absorbed power. In environments that restrict the ability to move optical components (such as gravitational wave detectors), this effect can be used for beneficial purposes, specifically for providing adjustable beam-shaping. The method employs an additional laser having a wavelength strongly absorbed by the substrate and can create an aberration-free parabolic lens can be created provided that the heating beam mode is substantially larger than the transmitted beam mode. The resulting focal length varies inversely with the heating laser power. This idea forms the basis for an adaptive optical telescope. We present experimental and theoretical results on a laser adaptive mode-matching system that uses an argon laser absorbed in a color glass filter. We characterize the dynamic focal range of the lens and measure the resulting aberrations in the transmitted Nd:YAG beam. Our results are in good agreement with a theoretical model incorporating the temperature distribution of the lens and the relevant thermo-optic parameters.

Mirror thermal noise is one of the fundamental factors limiting the sensitivity of gravitational wave interferometric detectors. Classical Gaussian beams "interrogate" only a small fraction of the mirror surface, and therefore are not well suited to average out fluctuations and minimize the thermal noise. It has been calculated that flat beam profiles would be better suited to average over thermal fluctuations and would allow sensitivity improvements that would more than double the "reach" of GW interferometric detectors. Non-spherical mirrors, shaped to support flat beam profile beams, have been designed and fabricated. A dedicated interferometer has been built to test the performance of these mirrors. We report on the status of this development.

We have measured the r_c (effective electrooptical coefficient) of pure and doped Ferroelectric Lithium Niobate (LN) using a single beam, null detection polarimeter. The polarimeter is adjustable between two adaptive optics configurations--an iris hard stop beam pattern on the one hand and a diffractive optics generated top-hat beam on the other. We clearly show the need to control thermal heating of LN due to the transmitted laser beam. The required heating control has been implemented using a fabricated metallic heat sink called a "Cold Finger." In addition to its electrooptical properties, LN possesses a combination of unique piezoelectric, pyroelectric, and photorefractive properties. These properties make it suitable for applications in optical devices as frequency doublers, modulators, switches, and filters in communication systems and holographic recording medium. We present the classical microscopic anharmonic oscillator description for generating Pockels coefficients, and briefly describe the polarimetry measurement system. Here, the growth of pure and iron doped lithium Niobate is also described using an Automatic Diameter Control Czochralski Design growth technique. The results of growth, electrooptic measurements, adaptive optics implementation and some physical properties are compared and presented.

We show that when a partially coherent beam with a Gaussian intensity distribution is focused by a lens, the intensity distribution near geometrical focus is strongly dependent upon the spatial coherence. Based on this, the desired intensity distribution near the focus can be generated by choosing appropriate form of spatial coherence. It is shown that the partially coherent flat-top intensity distribution near the geometrical focus or a partially coherent bottle beam can be produced by choosing appropriate forms of spectral degree of coherence. The influence of some parameters of the incident beams on the resultant beams near geometrical focus is investigated.

We propose a Fourier transform scaling relation to find analytically, numerically and experimentally the spatial frequency spectrum of a two-dimensional Dirac delta curve from the spectrum of the non-scaled curve, after an arbitrary coordinate scaling. An amplitude factor is derived and given explicitly in terms of the scaling factors and the angle of the forward tangent at each point of the curve about the positive x axis. With this formulation we experimentally obtain the spectrum of an elliptic contour in a circular geometry, thus acquiring non-diffracting beam characteristics. Additionally we include the generalization to N-dimensional Dirac delta curves.

In this paper, the optimal design problem of diffractive optical elements having a functional relationship between phase and amplitude modulations is investigated by using nonlinear optimization methods. Comparative analysis on formulations and performances of three important iterative methods (iterative Fourier-transform algorithm, nonlinear conjugate gradient method, and Gauss-Newton-Levenberg-Marquardt method) is provided. The detailed design equations of each method are described and numerical results are presented. The stable convergences of three investigated algorithms are confirmed. In our design problem, the conventional phase-only modulation is not assumed but the inherent functional relationship between phase and amplitude modulations of real diffractive optical elements are taken into account. It is shown that considering the functional relationship of phase and amplitude modulations in the design of diffractive optical elements leads to improvements in uniformity and diffraction efficiency.

Indirect-drive Inertial Confinement Fusion(ICF) system has two requests: first, it requires incident beam to focus on a small spot with very low circular side-lobe around the edge of the hole; second, when it continue to transmit onto the wall of cavity, it requires uniform illumination. A two-step iteration algorithm aiming at two positions of this system is proposed to match these two requests with using Pure Phase Plate (PPE). Our results show that the circular side-lobe near the target hole has been depressed to about 10^-11 W/cm², and the beam has small top modulation on the target wall.

It is believed that combining the techniques of smoothing by spectral dispersion (SSD) in the time domain and diffractive optical elements (DOE) in the space domain can improve beam uniform illumination. Adding another SSD unit to the combined system in different grating direction can disturb the incidence wave front more confused, thus the number of speckle patterns in the target plane is increased. The intensity in the target plane becomes smoother after a period of accumulation. However, the wave front distortion is limited by the dimension number of grating directions and the intensity distribution in each direction. In this paper we introduce the air turbulence and study its influence on the wavefront. The disturbance on wave front acts as an infinite aggregate in the number of direction dimension and intensity dimension because of the property of turbulence. The numerical calculation indicates that introducing disturbance by air turbulence on amplitude and phase of the light beam that incident to DOE can smooth the distribution on target plane after a period of accumulation.

We study the Ince-Gaussian series representation of the two-dimensional fractional Fourier transform in elliptic coordinates. A physical interpretation is provided in terms of field propagation in quadratic graded index media. The kernel of the new series representation is expressed in terms of Ince-Gaussian functions. The equivalence between the Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian series representations is verified by establishing the relation between the three definitions.

In this paper, we propose a method to fabricate the grating for a laser diode shaper. During the grating recording, a beam that has polarization mode orthogonal to those of two recording beams is added. The intensity of the additional beam is controlled by a spatial light modulator to provide the spatial variation of intensity modulation, which leads to the difference of the saturation diffraction efficiency. As the results of the experiment, the laser beam shaped by the obtained grating has Gaussian desired profile intensity and is not aberration along the propagation.

Considering the fact that holes contained in spatial filters may also serve to isolate ghosts in different areas, we have proposed an optical matrix method for locating the near-axial ghosts in high power laser systems. We also analyze practical criteria for distinguishing real and virtual ghosts. Our model can be used to calculate arbitrary order ghosts of laser amplifier systems.

In this paper we present different intensity distributions produced by an axicon when is illuminated with a particular field. The incident plane beam was modified using masks, cylindrical lens or tilting the axicon. The distributions obtained were analyzed to different distances using a CCD camera.

Bessel beams have gathered much interest of late due to their properties of near diffraction free propagation and self reconstruction after obstacles. Such laser beams have already found applications in fields such as optical tweezers and as pump beams for SRS applications. However, to model the self reconstruction property of Bessel beams, it is necessary to calculate the field at all points in space before and after the obstacle--a computationally intensive task give the large spatial distribution of Bessel beams. In this work we propose a computationally efficient method of calculating the arbitrary propagation of a Bessel beam, which is both fast and accurate. This method is based on transforming the problem to a new co-ordinate system more in line with the conical nature of the wavefronts, and shows excellent agreement with more traditional methods of calculation based on the Kirchoff-Fresnel diffraction theory in cylindrical co-ordinates. The success of the method is shown for the case of Bessel beams and Bessel-Gauss fields passing through non-transparent obstacles, as well as the for case of these fields propagating through a scattering medium.