Different beam shaping techniques to obtain the flat-top focus in one-dimension have been compared. It's shown that the smallest flat-top focus can be achieved with no loss by changing the polarization of the incident beam in a spatially inhomogeneous pattern. This spatially variant polarization manipulation adds a new degree of freedom in beam shaping and predicts better and more efficient results than conventional methods.

Generating or shaping a light pulse requires complete knowledge of all the parameters of the complex pulse amplitude. But they are not directly available to us. Our gathered data is only proportional to the square modulus of the EM fields as reported to us by various detectors (including non-linear processes). These detector responses are "colored" by their unique quantum "preferences". EM fields are not directly observable to us. They do not operate on (interfere with) each other either. Classical optics recognizes that light beams of different frequencies and of orthogonal polarizations do not "interfere" with each other. The success of Michelson's Fourier Transform spectrometry relies on this non-interference of different frequencies. Yet, beat signal is a result of simultaneous actions of different frequencies on a fast detector. We are promoting the hypothesis of non-interference of light beams as a generalized principle irrespective of the similarities or dissimilarities of their parameters. All superposition effects can become manifest only when the interacting medium is capable of summing all the induced stimulations simultaneously. Accordingly, an array of CW beams with multiple frequencies cannot create temporal pulses as implied by the time-frequency Fourier theorem in free space or in a medium that does not interact with the fields. Dipole undulations induced by the superposed EM fields within appropriate media are always at the root of creating laser pulses, and this brings conceptual congruence between the processes in generating pulses whether they are due to spiking or mode-locking. To illustrate our position, we present a series of experiments: (i) Simple superposition of three coherent frequencies did not generate mode locking. (ii) A series of ordinary CW He-Ne laser beams can produce mode-lock like current pulses by a high speed detector. (iii) A Q-switched ps diode laser shows 100fs train of autocorrelation spikes but it is not mode locked.

Many analytical techniques exist to explore the propagation of certain laser beams in free space, or in a linearly absorbing medium. When the medium is nonlinearly absorbing the propagation must be described by an iterative process using the well known Kirchoff-Fresnel diffraction equation. In this paper Gaussian and super-Gaussian beam shapes are propagated both through free space, and through a nonlinearly absorbing medium. The results show that shape invariance during propagation is dependent on the medium under consideration, and we find that super-Gaussian fields are shape invariant in certain nonlinearly absorbing media.

For the baseline design of future gravitational wave detection interferometers, use of optical cavities with nonsphericalmirrors supporting flat-top ("mesa") beams, potentially capable of mitigating the thermal noise of the mirrors, has recently drawn a considerable attention. To reduce the severe tilt-instability problems affecting the originally conceived nearly-flat, "Mexican-hat-shaped" mirror configuration, K. S. Thorne proposed a nearly-concentric mirror configuration capable of producing the same mesa beam profile on the mirror surfaces. Subsequently, Bondarescu and Thorne introduced a generalized construction that leads to a one-parameter family of "hyperboloidal" beams which allows continuous spanning from the nearly-flat to the nearly-concentric mesa beam configurations. This paper is concerned with a study of the analytic structure of the above family of hyperboloidal beams. Capitalizing on certain results from the applied optics literature on flat-top beams, a physically-insightful and computationally-effective representation is derived in terms of rapidly-converging Gauss-Laguerre expansions. Moreover, the functional relation between two generic hyperboloidal beams is investigated. This leads to a generalization (involving fractional Fourier transform operators of complex order) of some recently discovered duality relations between the nearly-flat and nearly-concentric mesa configurations. Possible implications and perspectives for the advanced Laser Interferometer Gravitational-wave Observatory (LIGO) optical cavity design are discussed.

We demonstrate the application of deterministic microlens diffusers to generate Lambertian scatter in transmission with high efficiency. Two identical surface diffuser elements are used in tandem to spread light with constant radiance. Design methods are discussed and experimental demonstration is presented.

A flattened Lorentzian irradiance profile, which was introduced by Brenner in 2003, offers prospects for analytic design of beam shaping optics when transforming a Gaussian beam into a soft-flat-top profile. It is shown that for the flattened Lorentzian profile the output power integral and the ray mapping function are analytic functions. This paper presents a systematic derivation of the flattened Lorentzian profile from the super-Lorentzian profile and exploration of properties of the flattened Lorentzian profile and compares its behavior to the super-Gaussian, flattened Gaussian, and Fermi-Dirac profiles. Details are presented for evaluation of the FL profile normalization, profile matching conditions, ray mapping function, and M².

In the present paper it is suggested to use micro-relief on the waveguide's end face for effective excitation of selected mode. The strategy of the search of mode with intensity distribution close to the illuminating beam intensity distribution is suggested to be used. Corresponding numerical procedure is described. Computer simulation results as well as some experimental results are presented.

An optical system is described which is capable of variable resizing of a round flat-top light distribution of a highly coherent and collimated laser beam at a certain, fixed working distance. It contains cylindrical and spherical optics. First-order optics is used to analyze the system, and the second-order moments method is used to describe the beam properties. The analysis indicates the existence of an "image-mode" regime, allowing a dynamic range, or a zoom range of about (13 - 15) : 1 for resizing the diameter of the round, flat-top distribution in the target plane, by rotating one cylindrical element. Experiments using as incoming beam a collimated Ar-laser TEM₀₀ gaussian beam reshaped to a collimated flat-top with 6.8 mm in diameter, confirm the approach, by obtaining at the target plane spot sizes with diameters continuously variable between 1.0 mm and 13.6 mm and with flat-top profiles.

Since the beginning of micro-optics fabrication most of the used technologies have been adapted from or are related to semiconductor fabrication techniques. These are widely known and the special microelectronics fabrication tools, especially lithography machines, are available at numerous places. Besides the fact that therefore micro-optics was able to took advantage of the steady development of semiconductor technology this tight linkage has also a lot of drawbacks. The adaptation of element properties to the fabrication limits given by the available technologies is very often connected with compromises in optical performance. In nowadays micro-optics fabrication has reached a level which justifies the development of fabrication tools specialized to its own demands. In the article the special demands of optical microstructures on the fabrication technologies are discussed and newly developed mico-optics fabrication tools are introduced. The first one is an electron-beam lithography machine for use with up substrates up to 300mm large and 15mm thick achieving a very high overlay accuracy and writing speed. The second one is a laser-lithography system capable to expose micro-optical structures onto non-planar substrates.

The new GaN lasers represent a unique combination of compactness, reliability, energy efficiency, and short wavelength. With respect to the previous state of the art in direct laser write lithography, based on gas lasers, this is resulting in a breakthrough, and is opening the way to real desktop micropatterning. The field of diffractive optics can immediately benefit by the availability of a new breed of pattern generators, based on such sources, mainly for fast turnaround device development. This paper presents the technical advantages involved in the use of 405 nm GaN lasers for one-step multilevel patterning. Beam modulation, exposure control and overall process strategy are discussed. In order to evaluate the effectiveness of the new solution, a sample fabrication of beam shapers is also presented.

The fabrication of diamond-based optical elements for high-power CO₂ lasers is of particular interest because of the low optical absorption coefficient of this material in combination with its very high thermal conductivity and the weak temperature dependence of refractive index. Recent advances in gas-phase synthesis have made it possible to fabricate polycrystalline CVD diamond films (DF) whose optical and thermal properties are close to those of single crystal diamond material, whereas they are far cheaper. As a result, these sophisticated materials are applied more and more to tasks dominated till now by other materials. Such examples for this are windows for high-power CO₂ lasers in the 5 - 20 kW domain¹ and beam-splitters². Recently new techniques have been proposed for antireflective structuring of DF surface^3,4 as well as for generation of phase microrelief to manufacture diamond diffractive optical elements (DOEs) for the far IR range^{5-8, 10}. The realisation of DOE by UV-laser ablation has been considered ^5-8. Using of ion-chemical etching⁹ and plasma etching10 is considered later. The present paper is devoted to further development of considered approaches^5,9. The realization of diamond diffractive optical elements (DOEs) is considered, able to focus an incoming CO₂ laser beam into certain pregiven focal domains. Results of experimental investigation of designed DOEs are presented and discussed.

Function testing of diffractive optics is a straight forward procedure when dealing with single elements or discrete systems of optics on an optical bread board. As the volumes of a particular diffractive optical device increase to production levels approaching hundreds to thousands of optics, the testing task can quickly become arduous and mind-numbing. At this level of production, data collection and quality monitoring is required to close the feedback loop to the manufacturing process. In this paper, a description of a prototype semi-automated diffractive optics testing platform used to measure performance, map quality and confirm working distances of a two element diffractive beam shaper system will be given. The testing system architecture and operation will be outlined and each subsystem will be described including software. A wafer map, consisting of data from an array of beam shapers, representing performance and etch depth from each diffractive optic within the wafer will be presented. An example of how data is compiled from a tested wafer and then interlaced with external sources of topographic data for ease of analysis and interrogation will be explained. Methods for beam analysis will be disclosed including multiple profilometer techniques. Further information will be shown on how the data from the system can be interpreted to identify defects on specific optics, manufacturing defects and non-linearity effects due to grayscale lithography and etch processes.

A high efficiency diffractive optic is created by the combination of high-quality design and a suitable fabrication process that can actually realize the design. Between design and fabrication is the tooling, in this case a photo mask. It is this tooling that is critical. Choosing, Binary or Grayscale methods to fabricate the structures that represent the design can be a daunting task. In many cases, grayscale design doesn't always provide the best solution or cost benefit during product development. This paper will compare and contrast the design and performance of a 1 to 24 beam, two dimensional; beam splitter fabricated using a fifty (50) phase level grayscale and a five (5) phase level binary fabrication methods. Optical modeling data will be presented showing both designs and the performance expected prior to fabrication. An overview of the optical testing methods used will be discussed including the specific test equipment and metrology techniques used to verify actual optical performance and fabricated dimensional stability of each optical element. Presentation of the two versions of the splitter will include data on fabrication dimensional errors, split beam-to-beam uniformity, split beam-to-beam spatial size uniformity and splitter efficiency as compared to the original intended design performance and models. This is a continuation of work from 2005, Laser Beam Shaping VI, where a 2 level binary design was compared to the grayscale design.

We studied the spatial beam profile of a high peak power, ultra-short laser pulse passing through a diffractive beam shaping system. In theoretical simulation, we considered the effects of both group velocity dispersion and nonlinear self-phase modulation on the reshaped beam profile. The output spatial and temporal intensity profile of a 100-fs laser pulse at different energy levels is calculated. We also present the experimental result of the fluence profile at the beam shaping system's target plane for a 1-mJ, 100-fs near infrared laser pulse which is generated from a multi-pass laser amplification system.

We have developed a second-harmonic-generation (SGH) microscope to observe the three-dimensional molecular orientation with three-dimensional high spatial resolution using a polarization mode converter. The mode converter consists of a parallel-aligned nematic-liquid-crystal spatial-light-modulator (PAL-SLM) and quarter-waveplates, and converts a incident linearly polarized beam to orthogonal linearly polarized beams or radially polarized beam. We combined the mode converter with SHG microscope to obtain the local information of the three-dimensional molecular orientation. We demonstrated the detection of three-dimensional molecular orientation of collagen fiber in human Achilles' tendon. For high precision three-dimensional molecular orientation measurement, we propose a technique to calibrate the dependence of SHG detection efficiencies on molecular orientation using a liposome.

Optical micro-manipulation has seen a resurgence of interest in recent years which has been due in part to new application areas and the use of tailored forms of light beams particularly using holographic optical tweezers technology. Optical landscapes using evanescent waves can hold large arrays of particles (~1000) and may be enhanced using surface plasmon interactions or a dielectric resonator. Dynamics in a static 2D landscape of a Bessel beam can lead to optically induced separation.

Flip chip bonding of integrated circuits to chip carrier packaging requires ultra precise placement. Maintaining the parallelism of the IC chip's ball grid array interconnect to the carrier packaging bond pads is of most concern. The bonding tool vacuum pick and place tip which carries the IC, must guarantee that the solder balls that form the interconnect ball grid array are flat and parallel to the mating pads on the carrier. During assembly operations where thousands of IC's are assembled per hour, continuous measurement must be fed back to small motion actuators which can adjust the position of the IC before bonding. This paper describes the design and implementation of a diffractive beam shaper optic into a displacement measurement sensing device. Testing of various beam shapes and conditions allowed for improvements in sensing resolution and dynamic range. A prototype was constructed to allow real time feedback of micro displacements of an IC surface including Z Axis offset, pitch and roll. The sensor assembly design, prototype performance and resulting test data will be presented. Test data includes measurement data, diffractive beam shaper design and its impact on sensor measurement resolution and range.

High aspect ratio line shapes can be generated using a diffractive remapping beam shaper and a refractive cylinder lens. A typical line shape is 10 mm in the long uniform axis and 0.05 mm or less in the Gaussian axis. The use of a TEM₀₀ allows for a diffraction limited short axis focus while expanding to sizes of greater than 100 mm in the uniform direction. In applications that require scanning, the Gaussian axis is perpendicular to the scan direction and the uniform axis is parallel to the scan direction resulting in a uniform (time averaged) illumination in both axis. Many laser users throw away > 50 % of their laser power to achieve these line shapes, while using this diffractive/refractive hybrid approach > 90 % of the total input energy can be utilized.

Percussion drilling and trepanning are two laser drilling methods. Circular laser spots are generally used in conventional laser drilling. Annular laser beams provide a new laser drilling mechanism. When an annular beam is focused on the workpiece surface, the material around the annulus laser spot is heated, melted, vaporized and removed, leading to the formation of a hole. This process, which we refer to as optical trepanning, does not involve any rotating optics or rotating workpiece. Based on the ray tracing technique, an optical lens system using axicon lenses has been designed to transform a Gaussian circular laser beam into an annular laser beam. Both theoretical and experimental results of irradiances of the annular beam along the optical system were analyzed. Optical trepanning experiments were conducted on stainless Steel- 316. Some geometrical and metallurgical characteristics during optical trepanning were investigated.

Relay mirrors offer a method of extending the range and efficacy of laser weapons systems by providing a platform that can relay the high power beam from the source to a target at a lower cost than building more laser weapons. Most laser weapons' platforms use a Cassegrain aperture telescope to project the high-power beam to a target. Diffraction causes power in the projected beam to move out beyond the edge of the receiving aperture and into the central obscuration of the receiving Cassegrain telescope. This paper presents a method of increasing the power coupling between a projected beam and a receiving telescope by warping the phase of the projected beam and shows that the spatial frequency and amplitude of the phase aberration is consistent with being integrated with the adaptive optics control loop on the source beam projector.

Laser brightness is a parameter often used to compare high power laser beam delivery from various sources, and incorporates both the power contained in the particular mode, as well as the propagation of that mode through the beam quality factor, M². In this study a cross Porro prism resonator is considered; crossed Porro prism resonators have been known for some time, but until recently have not been modeled as a complete physical optics system that allows the modal output to be determined as a function of the rotation angle of the prisms. In this paper we consider the diffraction losses as a function of the prism rotation angle relative to one another, and combine this with the propagation of the specific modes to determine the laser output brightness as a function of the prism orientation.

A novel method for tuning the orbital angular momentum (OAM) content of a vortex beam is presented. This approach makes use of the shaping of the odd and even components of the helical phase profile associated to the vortex. A relative azimuthal shift of the components results in the harmonic variation of the magnitude of the OAM density of the beam. We calculate the OAM content and show that for a beam with a vortex of topological charge m, the OAM per photon per unit length can be tuned continuously from (formula available in manuscript). We also observe the experimental propagation of the beam and compare the propagation parameters to our theoretical predictions.

The experimental generation of vector Bessel beams of different orders with TE and TM polarizations is demonstrated in the optical frequencies domain and in free space by means of a Mach-Zehnder interferometer. For the zero order beams, these modes correspond to the well known azimuthal and radial polarization states, whereas higher order versions become vector vortices, thus carrying orbital angular momentum. The case of the lowest order TE and TM vector vortices, corresponding to a topological charge of l=1, is particularly interesting due to their off-axis location and the non-null intensity at the beam center, unlike the case of topological charges l>1. The polarization and angular momentum properties of these waves are thoroughly analyzed and discussed for different cases.

In this work the mode structure of a resonator with Bessel-Gauss transverse mode distribution was investigated. Under some configuration of like resonators, we have found that diffraction losses in high mode number are less when compared with losses of low number of modes.

We review the three types of laser beams - Hermite-Gaussian (HG), Laguerre-Gaussian (LG) and the newly discovered Ince-Gaussian (IG) beams. We discuss the helical forms of the LG and IG beams that consist of linear combinations of the even and odd solutions and form a number of vortices that are useful for optical trapping applications. We discuss how to generate these beams by encoding the desired amplitude and phase onto a single parallel-aligned liquid crystal display (LCD). We introduce a novel interference technique where we generate both the object and reference beams using a single LCD and show the vortex interference patterns.

In this work we present a detailed analysis of the tree families of generalized Gaussian beams, which are the generalized Hermite, Laguerre, and Ince Gaussian beams. The generalized Gaussian beams are not the solution of a Hermitian operator at an arbitrary z plane. We derived the adjoint operator and the adjoint eigenfunctions. Each family of generalized Gaussian beams forms a complete biorthonormal set with their adjoint eigenfunctions, therefore, any paraxial field can be described as a superposition of a generalized family with the appropriate weighting and phase factors. Each family of generalized Gaussian beams includes the standard and elegant corresponding families as particular cases when the parameters of the generalized families are chosen properly. The generalized Hermite Gaussian and Laguerre Gaussian beams correspond to limiting cases of the generalized Ince Gaussian beams when the ellipticity parameter of the latter tends to infinity or to zero, respectively. The expansion formulas among the three generalized families and their Fourier transforms are also presented.

Anew set of superresolution pupil filter which consists of two parallel polarizers and a rotationally symmetric birefringent element is introduced in this paper, and the pupil function of it is deduced with Jones method. It is shown that such filter can be adapted to realize transverse superresolution simply just by selecting the angle θ between either of the two polarizers and the radial birefringent element. When θ=π/4, the superresolution parameter G which is the ratio between the first zero position of the superresolution pattern and the first zero position of the Airy spot is 0.8, the other parameter Strehl ratio which is the ratio between the intensity of the superresolved pattern and the intensity of the Airy spot is 0.4. The advantage of such filter used in superresolution technique is that the nature of superresolution can be changed by changing the angle between polarizer axis and the principle axis of the radial birefringent element. Furthermore, such filter is relatively simple to construct as it requires no phase changes and low cost replication is possible.

In this paper, a new focusing method adopting an axicon for the demand of the plasma measurements in inertial confinement fusion (ICF) drivers is presented. In order to improve the performance of this element, annular-aperture and Super-Guassian apodization are introduced to remove the on-axis oscillations. Meanwhile, the lateral width is optimized through choosing appropriate radius ratio of the inner ring to outer ring of the element. Furthermore, the feasibility is conformed by numerical evaluation of Fresnel diffraction integral .The results obtained are accordant with our designed intention. At last, as an example and for specific application, we designed an axicon, which has almost unchanged axial intensity, a focal depth more than 3mm, beam size smaller than 100μm and the maximal relative intensity of side lobe less than 2%. The performance of this element satisfies the requirements of plasma measurements in ICF drivers.

A new technique for ultrashort pulsed beams (UPBs) shaping that uses volume holographic gratings (VHGs) recorded in anisotropic crystals by modulating the polarization states of the input UPBs is proposed and analyzed. Our approach is based on the investigation that when a VHG recorded in anisotropic crystals is illuminated by a UPB, the spectral and temporal widths and the shapes of the diffracted and transmitted pulsed beams vary with the polarization state of the input UPB, based on the extended coupled wave theory of Kogelnik which combines with the dispersion effect of the crystal materials. By using this approach, the modulation ranges of the spectral and temporal widths of the output UPB can be controlled by the parameters of the grating. Moreover, the diffraction efficiency of the volume holographic grating is analyzed, which also varies with the polarization state of the input UPB. An example of using this approach is given that a linearly polarized Gaussian-shaped UPB with duration of 30fs is effectively shaped with a transmission volume holographic grating recorded in photorefractive LiNbO3 crystals.

Superdiffraction emitting, i.e. far-field spot compression without energy loss in main lob, in space laser communication can increase the main lob energy density. A smaller far-field spot in conjunction with a higher main lob energy density can improve the detection accuracy greatly, and enhance the communication capability of space laser communication system as a result. So superdiffraction emitting is of great significance to space laser communication. In most of the spot compression approaches, the main lob will suffer considerable loss of energy caused by the compression. Aiming at the superdiffraction emitting in space laser communication, we propose two schemes to obtain far-field spot compression without energy loss in main lob. One scheme is based on SA algorithm. We first design the intensity distribution in the far-field receiving plane to meet the particular requirement of space laser communication. According to the desired intensity distribution, we obtain the phase profile of the diffractive phase element (DPE) using the SA algorithm. Placing the designed DPE on the emitting plane, the superdiffraction emitting is achieved. The other scheme is based on YG algorithm. By using the algorithm, we convert the Gaussian beam into an appropriately designed high quality uniform beam in emitting plane. Using the high quality uniform beam as the emitting beam, we then gain far-field spot compression without energy loss in main lob. By means of the two schemes we proposed, the superdiffracion emitting in space laser communication is obtained.

The diffraction behavior of an ultrashort optical pulse with Gaussian-profile both in time and space diffracted by a volume grating is numerically investigated using two-wave first-order coupled wave theory, which elegantly expressed the theory of volume holography by Kogelnik. Simple analytical expressions for the spectrum and spatial profiles of the transmitted and diffracted beams in the near field are obtained. The total diffraction efficiency is also presented. Detailed diffraction characteristics for the ultrashort pulsed Gaussian beams are investigated. The analysis and diffraction characteristics presented in this paper are important for the ultrashort pulse shaping and volume grating applications.

In the final optics assembly of Inertial Confinement Fusion (ICF) driver, Diffractive Optical Elements (DOEs) are applied to achieve some important functions, such as harmonic wave separation, beam sampling, beam smoothing and pulse compression etc. However, in order to optimize the system structure, decrease the energy loss and avoid the damage of laser induction or self-focusing effect, the number of elements used in the ICF system, especially in the final optics assembly, should be minimized. The multiple exposure method has been proposed, for this purpose, to fabricate BSG and CSG on one surface of a silica plate. But the multiple etch processes utilized in this method is complex and will introduce large alignment error. Error diffusion method that based on pulse-density modulation has been widely used in signal processing and computer generated hologram (CGH). In this paper, according to error diffusion method in CGH and partial coherent imaging theory, we present a new method to design coding mask of combine CSG-BSG element with error diffusion method. With the designed mask, only one exposure process is needed in fabricating combined element, which will greatly reduce the fabrication difficulty and avoid the alignment error introduced by multiple etch processes. We illustrate the designed coding mask for CSG-BSG element with this method and compare the intensity distribution of the spatial image in partial coherent imaging system with desired relief.

A low power carbon dioxide CW laser @10.6μm has been designed and built for a clean and efficient production and treatment of high tech ceramic materials. The laser beam optical properties have been characterized from integral and differential beam profile measurements, and the power distributions, at the TEM₀₀ and TEM₁₀, modes were measured. Laser processing and treatment typical results on nanostructure ceramic materials (Yttria-Stabilized Zirconia and Silicon Carbide) are presented in this work. Laser irradiation effects were observed and studied using AFM, XPS, and FTIR techniques performed on irradiated samples and compared with non-treated probes results.

We present a study of the total internal reflection of a Helmholtz-Gauss beam at a plane interface between two dielectric media. The derivation is based on the decomposition of the Helmholtz-Gauss beams in terms of its constituent plane waves components. We determine the shift predicted by the classical theory of the Goos- Hänchen shift and analyze the transverse intensity patterns of the reflected waves for a variety of Helmholtz-Gauss beam including Bessel-Gauss and Cosine-Gauss beams.

The vector Mathieu-Gauss beams of integer order are examined as the solutions of the vector paraxial wave equation in elliptical coordinates. The propagation of the vector components and the three-dimensional intensity distribution of focused vector Mathieu-Gauss beams are analyzed for a variety of polarizations. Conditions in which the linearly polarized Mathieu-Gauss beams can be approximated by the scalar solutions of the paraxial wave equation are also discussed.