This PDF file contains the front matter associated with SPIE Proceedings volume 7430, including the Title Page, Copyright information, Table of Contents, Introduction, and the Conference Committee listing.

The design of beam-shaping pupil filters most commonly employs the scalar theory of diffraction, which does not accurately describe the focal field distribution under high numerical aperture focusing. To account for the full vector character of the field, we have developed computational algorithms for designing phase-only pupil filters that incorporate the electromagnetic theory of diffraction. These algorithms use the method of generalized projects or particle swarm optimization to generate phase-filter solutions based on a targeted focal field irradiance distribution. Computational results are presented that demonstrate how these procedures can be used to design phase filters that reshape the transverse beam, or achieve axial super-resolution for a single focused spot. The methods can be applied in the design of beam-shaping and superresolving optics used for imaging, direct laser writing, and lithography.

The task of providing the same conditions of intensity profile transformation for a broad spectral bandwidth can be solved by refractive beam shaping optics with achromatic design. This solution is important for various scientific and industrial applications including confocal microscopy, biomedical fluorescence techniques, some industrial technologies and many tasks based on short pulse lasers where a bandwidth of up to hundreds of nm is to be provided. The design of achromatic refractive beam shapers is based on applying of materials of different dispersion characteristics and provides necessary intensity distribution transformation simultaneously for laser beams in wide spectral range. These achromatic beam shapers keep the resulting intensity distribution over a long distance, operate with collimated and divergent beams and provide easy adaptation to specifications of real lasers. This paper will describe some design examples of achromatic beam shapers optimized to be used with short pulse lasers like Ti:Sapphire or Yb:KGW ones in infrared and ultraviolet spectrum. There will be presented results of applying achromatic laser beam shapers with short pulse lasers in such applications as irradiating the cathode of Free Electron Lasers, processing of photovoltaic materials.

As photolithographic tools are pressed to print the ever shrinking features required in today's devices, complex off-axis illumination is taking an ever increasing role in meeting this challenge. This, in turn, is driving tighter, more stringent requirements on the diffractive elements used in these illumination systems. Specifically, any imbalance in the poles of an off-axis illuminator will contribute to reductions in the ultimate imaging performance of a lithographic tool and increased complexity in tool-to-tool matching. The article will focus on improvements to the manufacturing process that achieve substantially better pole balance. The modeling of the possible process contributors will be discussed. Challenges resulting from the manufacturing methodology will be shared. Finally, the improvement in manufacturing process performance will be reported by means of a pole balance capability index.

Laser applications that demand a high quality with long coherence length are limited by the Gaussian profile of the fundamental TEM00 mode. Many of these applications require a uniform irradiance profile with a flat phase-front. In holography, both phase and intensity are critical to the process. Near-field beam shaping optics, also called beam transformers, re-map an input Gaussian profile to a top-hat profile. The top-hat profile is created at some working distance away from the shaping element where a corrector element has traditionally been placed in order to flatten the phase of the top-hat profile and allow it to propagate as a nominally collimated beam. This paper will discuss the theory to support the use of a diffractive optical element in holography and other applications where the phase is important. Two different geometric beam shapes will be explored, round and square profiles.

Polynomial Gaussian beams, which are laser beams with Gaussian envelops and complex bivariate polynomial prefactors, provide us with a tractable means to investigate the evolution of optical vortices. A formalism for the propagation of such beams allows one to determine how the coefficients of the polynomial transform during propagation. This formalism is used to proof that global topological charge is conserved, provided that the Gaussian envelope of the beam is rotationally symmetric. For astigmatic Gaussian beams the global topological charge is not conserved and can change during propagation in steps of 2 when one of the optical vortices undergoes topological charge inversion. The global topological charge is bounded by the order of the polynomial prefactor. One can also investigate the behavior of vortices in random vortex fields by modelling them as polynomial Gaussian beams. The phase functions that exist in the vicinity of the annihilation of a vortex dipole are similar, regardless of the type of beam in which the vortices exist. One can therefore use polynomial Gaussian beams to find a way to force vortices in random vortex fields to annihilate. The number of optical vortices that can exist in a polynomial Gaussian beam depends on the reducibility of the polynomial prefactor. During propagation the reducibility of the prefactor is generally destroyed. However, if the morphologies of the vortices of a fully reducible prefactor are all the same, the reducibility is maintained during propagation. The results obtained from the analyses of polynomial Gaussian beams are confirmed by numerical simulations.

We present a method to calculate the 2-dimensional complex angular spectrum required to produce a Helmholtz- Gauss (HzG) beam with an arbitrary intensity profile. Using an iterative Fourier transform algorithm, we find numerical solutions for several instances of spectra and we reproduce the corresponding beams by encoding the resulting on a spatial light modulator. We verify the experimental results and compare them to the computer model of their propagation to excellent agreement. We quantitatively asses the fidelity of the produced beams and their expected extended propagation properties as HzG beams. Our method can be used to produce an arbitrary beam with the same extended invariance range characteristic of HzG beams.

In this paper we present a mechanism for the generation of the superposition of higher-order Bessel beams, which implements a ring slit aperture and spatial light modulator (SLM). Our experimental technique is also adapted to generate nondiffracting speckle fields. We report on illuminating a ring slit aperture with light which has an azimuthal phase dependence, such that the field produced is a superposition of two higher-order Bessel beams. In the case that the phase dependence of the light illuminating the ring slit aperture is random, a nondiffracting speckle field is produced. The experimentally produced fields are in good agreement with those calculated theoretically.

Non-diffracting beams, such as Bessel and Mathieu beams, offer a wide range of potential applications in the fields of bio-photonics, micromanipulation and spectroscopy. One of the main features of these beams is their self-healing behavior where the beams reconstruct after an obstacle. Higher order versions of these beams incorporate non-diffracting optical singularities or vortices propagating together with the beams in a straight line. Vortices are ubiquitous in many parts of physics and their dynamics, especially their creation and annihilation processes are very important in fundamental physics. Newly demonstrated Airy beams represent a different class of non-diffracting beams that do not propagate in a straight line but exhibit a constant transversal acceleration. The self-healing properties of these Airy beams together with their transversal acceleration can be used to optically clear entire regions of microparticles. These Airy beams are created using a spatial light modulator that encodes a cubic phase front on an incident Gaussian beam. Using the same method and suitable computer generated holograms we are able to generate Airy like beams that include optical vortices. In this paper, we study the creation and evolution of Airy beam accelerating vortices from the theoretical and experimental perspective.

An analysis of the diffraction of plane waves by an apodized finite-radius circular spiral phase plate (SPP) with integer and fractional topological charge and with variable transmission coefficients inside and outside of the plate edge is presented. We introduce a sinusoidal apodization function at the edge of the plate to allow for a continuous transition between the transmission coefficients, and between the spiral and uniform phase distributions inside and outside of the plate edge. The interference between the light crossing the SPP and the light which undergoes no phase alteration at the aperture plane, and the presence of an apodization at the edge of the plate, cause some interesting phenomena previously unobserved in this widely known problem.

A new type of Bessel-like optical beams, which is distinguished by the dependence on the cone angle from the longitudinal coordinate, is investigated. Such beams have the properties of Bessel beams (ring-spatial spatial spectrum) as well as Gaussian beams (keeping the transverse profile at any distances). This new type of beams can be obtained in optical system composed of lens axicon doublet and conical lens. An experimental set-up for producing such beams is realized. It is shown that depending on its parameters the scheme allows one to produce z-dependent Bessel-like beams, whose spatial spectra change from Bessel function to shifted Gaussian one. It is establish theoretically and confirmed experimentally that on-axial intensity of z-dependent Bessel-like beam could be higher than that of incident Gaussian beam.

Linear and nonlinear processes of transferring optical singularities from anisotropic crystals onto the wavefront of Bessel light beams (BLBs) are investigated. The generation of high-order vortices at the propagation of BLBs along the optical axes of crystals was studied. Particularly, a nonlinear frequency doubling of Bessel vortices in the conditions of new type synchronism (full conical phase-matching) is considered. This scheme of three-wave interactions of BLBs based on that the spatial frequency cones of BLBs coincide with phase-matching cones of uniaxial crystals. New type of frequency doubling of Bessel vortices has been experimentally realized in uniaxial crystals.

The orbital angular momentum (OAM) of a vortex beam depends on the selection of its rotation axis. Therefore, the associated OAM spectrum is subject to the alignment of beam axis as well. It has been demonstrated that a slight misalignment can cause a large change in OAM spectrum. By investigating the relationship between misalignment and the resultant OAM spectrum change, we propose a method of measuring the titling angle and displacement to the reference axis. This approach can be used in correcting the alignment of free-space optical communication system.

We present a dynamic laser beam shaper based on MEMS technology. We show a prototype of a dynamic diffuser made of single crystal silicon. A linearly deformable silicon micromembrane is used to diffuse a laser beam in one dimension. Resonance frequencies of the membrane can range from 1 kHz to 100 kHz. Diffusing angle can be tuned by adjusting the driving voltage. We measured a diffusing angle of 0.16° for an actuation voltage of 20 V.

Laser manufacturing of microstructures using a single focus is a well known technology. Multi-spot optics are applied for process parallelizing if the demand on throughput in mass production rises or large areas of material have to be processed. Diffractive optical elements (DOEs) are used for parallel laser processing of a repetitive structure. These elements split the beam into a periodic spot pattern, where each spot shows the same shape and energy. This allows simultaneous manufacturing of several equal shaped structures at the same time. For patterning a surface this is state of the art and the appropriate technique to reduce processing time while maintaining a high lateral resolution as well as a good relative positioning of the structure due to the DOE. We investigate the usage of microlens arrays as multifunctional elements for forming an arbitrary shaped laser beam into a spot-, a ring-spot- or a line-array pattern. It can be shown that the intensity distribution of each spot is equal to the intensity distribution of all other spots in the whole pattern. The shape of the spots is defined by the angular distribution of the incident beam. We demonstrate that besides other optical properties the output beam profile strongly depends on the Fresnel-Number and is influenced by diffraction and interference effects. We present important design rules which consider geometrical and physical optics. The properties of the spot arrays, like spot diameter, Rayleigh length and beam divergence in dependency of beam and system properties are investigated. Finally we will show some laser micro structuring and micro drilling results in different materials.

Coherent beam shaping can be performed inside laser resonators by filtering the amplitude or the phase of the circulating wave. Along with providing a designer-shaped output, these methods can improve laser performance by suppressing higher-order modes and extracting maximum gain. Under certain conditions, phase filtering is shown to improve modal discrimination by separating modes into bound (low-loss) modes and unbound (high-loss) modes. Mode shapes in resonator arrays are shown to depend on the architecture of the array. In some cases, these architectures can be designed to improve modal discrimination or increase the tolerance to resonator path-length errors.

In this paper we present the analytical and numerical analyses of two new resonator systems for generating flat-top-like beams. Both approaches lead to closed form expressions for the required cavity optics, but differ substantially in the design technique, with the first based on reverse propagation of a flattened Gaussian beam, and the second a metamorphosis of a Gaussian field into a flat-top beam. We show that both have good convergence properties, and result in the desired stable mode.

In this paper we present results on improved paint stripping performance with an intra-cavity generated Flattened Gaussian Beam (FGB). A resonator with suitable diffractive optical elements was designed in order to produce a single mode flat-top like laser beam as the output. The design was implemented in a TEA CO₂ laser outputting more than 5 J per pulse in the desired mode. The FGB showed improved performance in a paint stripping application due to its uniformity of intensity, and high energy extraction from the cavity.

We consider the promising properties of very simple Diffractive Optical Elements (DOE) for reshaping the intensity profile of a laser beam. The first type of DOE that we have considered is a phase aperture which consists in a transparent plate with a circular relief introducing a π phase shift in the central region of the incident beam. The phase aperture is able to convert a Gaussian beam into a super-Gaussian, a ring-shaped or a doughnut profile. The second DOE that has been considered is a phase step which is able to transform a TEM₀₀ beam into a TEM₁₀ or TEM₀₁ beam depending on its orientation. These beams have been used to generate radial polarization.

X-ray imaging technology is highly developed to meet the needs of high-energy physics and diagnostics of inertial confinement fusion. In this paper, we describe the design of a non coplanar toroïdal mirrors microscope. It consists of three off-axis revolution concave toroïdal mirrors working at grazing incidence. Non-periodic W/SiC multilayer coatings have been deposited on each mirror, in order to increase until 10 keV the bandpass of reflectivity of the microscope. These super mirrors have been designed to work at 0.6° grazing incidence angle and display a reflectivity better than 40% in the entire energy range 2-10 keV. Concerning the imaging performances, we have almost achieved 5 μm of spatial resolution in a field of 500 μm. Regarding to these results, this prototype of microscope, the so-called "Plasma Imageur X pour les Experiences Laser Mega Joule" (PIXEL), will be used for 2D spatial and 1D time resolved imaging of dense plasmas produced during inertial confinement fusion experiments at the future Laser Mega Joule French facility (LMJ).

The progress of immersion lithography toward the 22nm production node is putting more stringent requirements on the diffractive optics that are used for off-axis illumination. Tighter tolerances on pole balance, stray light, zeroth order, optical transmission, and matching of the far field output pattern to the design specification are in-turn requiring more accurate and repeatable optical testing. This paper will report on preliminary results from Tessera's new excimer diffractive optics test stand, including gauge capability and sources of variation, ending with a comparison of measurement capability to the required specifications.

One of the key tasks of a laser systems field service engineer is to determine where and why an optical system is not performing to specification or why it has failed prematurely. On most occasions, the field service engineer is faced with a completely failed optical system and is left to isolate how and where the failure occurred and if the rest of the system was affected, if at all. Failure modes are the manner whereby the failure itself is observed. Generally speaking, an "optical failure mode" describes the way in which the optical failure happens and its impact on an entire optical system. Optical failure modes of diffractive optical beam shapers must be determined according to each components performance standards as identified through its design and testing. Optical performance standards must be quantified if they are to be upheld. Quantifiable performance standards are more precise than qualitative standards, but each have a role in determining overall performance. If an optical designer or engineer is incapable of specifying precisely, the optical / functional performance they want from the diffractive optical beam shaper, then it is difficult, if not near impossible, to make a field service and maintenance engineer responsible for maintaining optical performance or to identify the possible different failure modes and mechanisms. Performance can be a function of the placement of optics due to routine maintenance or general wear and tear, but there needs to be established means of identifying both circumstances. Diffractive optical element failure mechanisms are straightforward; defined simply as the physical, chemical or other processes that led to the failure of the diffractive optical element itself. This paper outlines schematically the various (Highest Ranked) failure modes and mechanisms encountered by a standard industrial diffractive optical beam shaper operating at 355 nm in an industrial environment. Furthermore, an overview of field data including optical lifetime averages, metrological image data of failed optical elements and methods to prevent premature failure will be shared.

Applications may vary with time, and so may the technical realization of these applications. Lasers change and consequently application wavelengths, due to requirements imposed by material changes, power constraints, scaling of lateral features, or other parameters and specifications. In applications where diffractive optical elements (DOEs) are employed a change in laser or wavelength usually demands not only a new fabrication batch but a redesign of the diffractive structure. This is almost always the case in the special application of laser beam shaping where a DOE is designed to redistribute the energy of a specific laser beam profile, generally into a flat-top intensity profile (either round or square). In this paper we will describe how a mono-mode beam shaping DOE design for 355 nm was adapted to compensate a wavelength change to 532 nm. A preliminary telescope is necessary to ensure that the input beam retains the initial properties of beam waist and beam diameter. In this case, the original DOE design can be maintained with some minor compensation in phase depth for the wavelength change and in positioning of the elements to compensate the scaled diffraction angles. Further data will be shared showing a side by side comparison of testing results of the 355 nm and 532 nm designs.

Accessibility to fresh clean water has determined the location and survival of civilizations throughout the ages [1]. The tangible economic value of water is demonstrated by industry's need for water in fields such as semiconductor, food and pharmaceutical manufacturing. Economic stability for all sectors of industry depends on access to reliable volumes of good quality water. As can be seen on television a nation's economy is seriously affected by water shortages through drought or mismanagement and as such those water resources must therefore be managed both for the public interest and the economic future. For over 50 years ultraviolet water purification has been the mainstay technology for water treatment, killing potential microbiological agents in water for leisure activities such as swimming pools to large scale waste water treatment facilities where the UV light photo-oxidizes various pollutants and contaminants. Well tailored to the task, UV provides a cost effective way to reduce the use of chemicals in sanitization and anti-biological applications. Predominantly based on low pressure Hg UV discharge lamps, the system is plagued with lifetime issues (~1 year normal operation), the last ten years has shown that the technology continues to advance and larger scale systems are turning to more advanced lamp designs and evaluating solidstate UV light sources and more powerful laser sources. One of the issues facing the treatment of water with UV lasers is an appropriate means of delivering laser light efficiently over larger volumes or cross sections of water. This paper examines the potential advantages of laser beam shaping components made from isostatically micro molding microstructured PTFE materials for integration into large scale water purification and sterilization systems, for both lamps and laser sources. Applying a unique patented fabrication method engineers can form micro and macro scale diffractive, holographic and faceted reflective structures into fused and semi-fused PTFE materials and compounds for use in UV Reactors. The materials unique attributes provide an unusual but effective hybrid element, by combining Lambertian diffusion and spectral reflective attributes. This paper will provide examples of the applications where this technology could be applied and typical constructions. An overview of UV sources commonly used in water treatment, including high power UV lasers and solid state UV light sources will be discussed. The paper will summarize how beam shaping elements produced in PTFE materials would provide further benefits to the emerging water disinfection or treatment market.

Airy beams are of great interest as a result of their unusual characteristics, they are non-diffracting and also propagate along a parabolic path due to the presence of a transversal acceleration component. In this paper the generation of a white light Airy beam is presented, an investigation is also carried out to determine how the properties of an Airy beam change with the wavelength and spatial coherence of the source. A supercontinuum source is used in conjunction with a spatial light modulator to produce the Airy beams. The wavelength dependence study of the Airy beam parameters was carried out by inserting interference filters into the supercontinuum beam path to select each wavelength. The parameters investigated are the deflection coefficient of the Airy beam, b₀, this quantifies the parabolic path traveled by the beam; the characteristic length, x₀, which is related to the lobe spacing, and lastly the aperture coefficient, a₀. The deflection coefficient and the characteristic length were both found to be wavelength dependent. The aperture coefficient did not alter as a result of wavelength, however it was found to be dependent on the spatial coherence, and therefore on the M² value, of the beam. The other parameters, b₀ and x₀, are unaffected by the spatial coherence of the source.

During propagation of high-power femtosecond laser pulse in air dynamic balance between Kerr self-focusing and laser plasma defocusing results in high localization of the energy in a hundred microns region. Stable long laser filament forms. For systems of atmospheric optics it is important to control high fluence of the filament. We investigated numerically the influence of pulse duration and atmospheric aerosol particles scattering on energetic characteristics of the filamented laser pulse. It was shown that in the conditions of pulse energy remaining the same increase of pulse duration results in considerable increase of filament length and high-fluence energy transporting by pulse. It is demonstrated that scattering on atmospheric aerosol particles causes high-fluence energy losses but doesn't prevent further filament propagation.

In this work we design and construct a pulse compressor with volume transmission holographic gratings, to compensate the second order dispersion in femtosecond laser pulses emitting at 794 nm with a spectral broadband of 10 nm. The gratings (730 lines/mm) are recorded in PFG-04 dichromated gelatine emulsion with a wavelength of 532 nm, reaching enough index modulation to use the gratings illuminated with 800 nm light source with high efficiency (around 80% of efficiency in each grating). This efficiency is expected to be increased with an antireflection coating. We measure the factor of compression as a function of the grating distance using an autocorrelator, finding a good agreement with theoretical curve. A dispersed pulse (580 fs) is reduced to the bandwidth limited value of 106 fs with the grating pair separated by 27 mm.

We study the problem of shaping the transverse propagation invariant intensity pattern of an optical beam to induce a photonic lattice for trapping and propagating spatial optical solitons in a stable elliptic motion with varying rotation rate. The transverse pattern is described by a suitable superposition of helical Mathieu beams, the natural family of nondiffracting beams in elliptic cylindrical coordinates. We discuss the properties of the lattice and the novel dynamics of propagation allowed by it.

In this paper we report on two resonator systems for producing LDBLBs with arbitrary initial parameters. First resonator system is based on doublet of divergence and convergence lenses with spherical aberration. Second resonator system is based on doublet of axicon and axicon-lens. For both resonator systems the LDBLB is output of fundamental mode, but the spectral properties of obtaining LDBLBs are different.

The spectrum of spatial frequencies (SFS) of Bessel beams properties emerging at their spatial localization is investigated. The case, when limiting aperture has a circular shape and a center at any distance from the optical axis, was studied. The Bessel beam local SFS was discovered to be radically changing at shifting the localization zone. Namely, a full ring transforms into a light arcs pair and its angular dimensions monotonically decreases as shift growth. The axis orientation of the spectrum maximal intensity coincides with the diaphragm shifting direction. The numerical modeling results agree well with the experiments.

We design a free-form lens, which can reshape a Gaussian green laser beam into a top-hat irradiance distribution over the target plane. We measure the laser beam profile of every part of this green laser beam shaping module. The divergence angle of the green laser module is not wide enough for laser level system. We can get a wider divergence angle of the green laser beam system when adding the beam shaper and the cylindrical lens. The divergence angle of the green laser level system is about 120° and the uniformity of the green laser level system is about 91.08%.

We study the propagating and shaping characteristics of the novel Whittaker-Gaussian beams (WGB). The transverse profile is described by the Whittaker functions. Their physical characteristics are studied in detail by finding the 2n-order intensity moments of the beam. Propagation through complex ABCD optical systems, normalization factor, beamwidth, the quality M² factor and its kurtosis parameter are derived. We discuss its behavior for different beam parameters and the relation between them. The WGBs carry finite power and form a biorthogonal set of solutions of the paraxial wave equation (PWE) in circular cylindrical coordinates.

We propose a temperature sensor based on dispersion shifted long period fiber grating (LPFG) fabricated with the fattening method, using electric arc discharges from a commercial fusion splicer machine. The fattened LPFG are centered at 1524 and 1550 nm, respectively. A temperature characterization in terms of the transmitted spectrum is realized with a pumped Er+3 doped fiber as the light source. The less than 3 mm in length fattened LPFG reached a sensitivity of 72 pm/°C between a temperature range of (25-500°C). Temperature stability was observed among the temperature range of (25-200°C), result in agreement with our previous studies. From up to 200°C sensing is observed as temperature increases. To apply this LPFG as a temperature sensor, sensing was measured as voltage signal outputs with repeatable results. This sensor is a high temperature resistant device because non deterioration of its properties was observed, and can find useful applications when temperature stability may be needed or the sensing requirements are desirable.

The diffraction properties of ultrashort pulsed by the volume gratings with arbitrary boundaries are studied based on the extended two-dimensional coupled wave theory for volume grating readout by ultrashort pulsed beam. The intensity distributions of the diffraction and transmitted pulsed beams in spectral and temporal domains are given. And the total diffraction efficiency is also presented. Our study presents a possibility of shaping a broad band UPB by controlling the boundary of the local volume hologram grating.

This paper was presented at the SPIE conference indicated above but inadvertently published by SPIE subsequent to its publication in another journal (Optics Letters). The paper has therefore been withdrawn from the SPIE Proceedings by the author and the publisher. The journal paper can be accessed at http://dx.doi.org/10.1364/OL.34.002730.

Laser beam shaping is an active discipline in optics owing to its importance to both illumination and detection processes. The formation of single or multiples optical vortices in a laser beam has taken on recent interest in areas ranging from electron and atom optics to astronomy. An optical vortex is characterized as a point node of destructive interference around which the phase varies by an integer multiple of 2 times π. Here we describe our efforts to create localized vortex cores using only the interference of several Gaussian profile laser beams, a method that may be particularly suited to the application of vortex modes to intense femtosecond laser pulses.