The exploitation of micro-optical technologies in laser beam shaping and wavefront manipulation
applications has a long and distinguished history. The functional flexibility of high resolution, allglass
phase only microstructures, combined with their relative immunity to laser-induced damage
mechanisms, allows the creation of arbitrary beam profiles from a wide range of different laser
configurations. In this paper, we shall review some of the methods used in the design and fabrication
of laser beam shaping and wavefront manipulation micro-optical components.
A review of the design and analysis of plano-aspheric laser beam shapers is presented. Both the Galilean and
Keplerian configurations of the two aspheric lens laser beam shaper have been used and offer benefits for different
applications. The geometrical optics based design methods of Kreuzer have been used to obtain a uniform output
irradiance distribution with a gradual roll-off from the uniform to null region, which increases the distance over
which the uniform irradiance distribution can be used. The flattened Lorentzian function is used to represent
the shaped beam profile and offers benefits of working with an analytic expression for the ray mapping function
between the two plano-aspheric lenses when using an input Gaussian beam.
This paper presents a systematic discussion of the optical and mechanical tolerances which must be addressed in
order for a laser beam shaper system to perform close to the design criteria. First, a general relationship based
on the intensity law of geometrical optics is presented, which relates the input and output beam profiles, and
particular attention is given to the common Gaussian input beam profile. Next, the impact of collimation errors of
the input beam is addressed. Then, lens mounting errors for a two-lens laser beam shaper are addressed including
lens spacing, decenter, and tilt tolerances. Overall, this paper addresses actual variations of the deterministic
transformation of an input irradiance profile into an output beam profile, whether it employs refractive, reflective
or diffractive optical elements.
We present a graded index (GRIN) design methodology for application in coherent beam shaping within the
confines of geometric optics. In theory, a GRIN structure can be designed to convert a specific but arbitrary incident
wave into any general amplitude and phase distribution. The incident and the desired output waves are converted
into ray distributions where the local ray density is associated with the field amplitude and the ray direction and its
optical path length are associated with the phase front of the waves. A set of ray paths is chosen to achieve the
conversion between the initial and final ray distributions. Intermediate wavefronts are extrapolated from the ray
paths and used to determine the refractive index profile required to effect the gradual evolution of the wave as it
propagates through the structure. Our method is demonstrated by a GRIN structure design that converts a Gaussian
beam into a flattop beam. In addition, several techniques used to reduce the dynamic range of the refractive index in
the structure are examined and a design recipe is developed for this particular application. A ray trace shows that the
resulting structure achieves the desired remapping of rays and produces a flat-top beam from an incident Gaussian
Phase-only spatial light modulators are now ubiquitous tools in modern optics laboratories, and are often used to
generate so-called structured light. In this work we outline the use of a phase-only spatial light modulator to achieve full complex amplitude modulation of the light, i.e., in amplitude and phase. We outline the theoretical concept, and then illustrate its use with the example of the laser beam shaping of Gaussian beams into flat-top beams. We quantify the performance of this approach for the creation of such fields, and compare the results to conventional lossless approaches to flat-top beam generation.
The coherent superposition of propagation-invariant laser beams represents an important beam-shaping technique, and results in new beam shapes which retain the unique property of propagation invariance. Propagation-invariant laser beam shapes depend on the order of the propagating beam, and include Hermite-Gaussian and Laguerre-Gaussian beams, as well as the recently introduced Ince-Gaussian beams which additionally depend on the beam ellipticity parameter. While the superposition of Hermite-Gaussian and Laguerre-Gaussian beams has been discussed in the past, the coherent superposition of Ince-Gaussian laser beams has not received significant attention in literature.
In this paper, we present the formation of propagation-invariant laser beams based on the coherent superposition of Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian beams of different orders. We also show the resulting field distributions of the superimposed Ince-Gaussian laser beams as a function of the ellipticity parameter. By changing the beam ellipticity parameter, we compare the various shapes of the superimposed propagation-invariant laser beams transitioning from Laguerre-Gaussian beams at one ellipticity extreme to Hermite-Gaussian beams at the other extreme.
We put forth an analytical approach to the engineering of quasinondiffracting beams based on a relationship between the circular Radon transform and two-dimensional functions with annular support in Fourier space.
The generation of intra-cavity superpositions of Bessel-Gauss beams in an axicon resonator is studied numerically
by means of a genetic algorithm. The coherent superposition of low order modes is induced by introducing crossed
wires within the simulated cavity. Two different strategies are shown to be equivalent for the generation of the
same superposition of two Bessel-Gauss beams with opposite azimuthal orders. In the first strategy the angle
between a pair of cross-wires is varied for mode selection, the second consists on introducing a number of crosswires
at equally spaced angles in which the number of wires corresponds exactly to the order of the superposed
modes. Our results suggest a direct method for generating experimentally a coherent mode superposition of
Bessel-Gauss beams using an axicon-based Bessel-Gauss resonator. These beams are relevant in areas such as
optical trapping and micromanipulatio
We experimentally generated superpositions of higher-order Bessel beams that possess no global orbital angular momentum (OAM), yet exhibit an angular rotation in their intensity profile as the field propagates. The digital holograms encoded on a spatial light modulator (SLM), used for generating such fields, consist of two annular rings of unequal radial wave-vectors where each ring is encoded with an azimuthal mode of equal order but opposite charge. We present experimentally measured angular rotation rates for some example superposition fields, which are shown to be in good agreement with that predicted theoretically. Introducing a second SLM and a Fourier transforming lens, we demonstrate a simple approach to perform an azimuthal decomposition of our generated optical fields. Bounding the match-filter to an annular ring, of varying radius, we are able to perform a scale-independent azimuthal decomposition of our initial field. From the measured weightings of the azimuthally decomposed modes we show reconstruction of the cross-sectional intensity profile and OAM density of our initial field.
Increasing laser beam qualities make thermal lensing again a hot topic and demand for a thermo-optical simulation for improving classical ray tracing and enabling optimization possibilities for thermally aberrated optical systems. This paper summarizes the approach for coupling FEM and ray tracing using a weighted least squares approximation algorithm and demonstrates the abilities of the coupled simulation in the case of a CO2 laser system for polishing of glass and plastics. It can be demonstrated that the algorithm can be used for the analysis of higher order aberrations, since the application contains a Gaussian to top-hat conversion lens group which suffers from thermal gradients. Finally, the benefits and further developments of analyzing thermal gradients in optical simulation are being discussed.
Rotary comb-drive electrostatic actuators with virtual pivotal point of rotation were designed and fabricated for their application in external cavity tunable lasers in Littman configuration. Silicon on insulator (SOI) wafers with device layer thickness of 50 μm and buried oxide layer of 2 μm were used. The structures were fabricated through bulk micromachining of the device layer followed by release of movable arms through wet etching. Six pairs of comb arms were used to symmetrically distribute electrostatic forces on an interconnected movable arm structure. The movable structure consisting of stiff truss connectors in arc shapes on inner and outer periphery was anchored through three beams. Actuation of the movable arms on a circular profile with a virtual pivotal point was achieved for the designed range of operation. A maximum rotation of ± 1.5 degrees at 190 V was achieved. The dimensions of the movable arm are on the order of 1.2-1.5 mm. The actuators have a physical clearance of up to 2.8 mm from the device structure to the virtual pivot point. The sidewalls of the movable arms are accessible for optical applications. The geometrical configuration of the fabricated structures supports the stringent requirements of optical path alignments in external cavity lasers. The fabricated structures can be reliably operated in the kilohertz range
A Gaussian to top-hat beam homogenizer has been designed and fabricated for a UV laser illumination system used in the manufacture of integrated circuit substrates. An important part of the system is a “coherence buster” which is used for minimizing interference effects, normally encountered when using microlens array homogenizers together with a coherent light source. The coherence buster is a diffraction grating, which introduces a time delay across the beam. If this time delay is sufficiently large in comparison to the pulse length, it can be so arranged that beams, which would normally interfere, now arrives at different times and therefore add incoherently. The theory behind the coherence reduction is described, as well as the design of the grating. The irradiance uniformity of the manufactured homogenizer has been measured, and shown to be free from interference fringes.
Proc. SPIE 8490, Examination and optimizing of a liquid crystal display used as spatial light modulator concerning the fringing field effect, 84900H (15 October 2012); https://doi.org/10.1117/12.929707
Due to the small pixel sizes of modern LC-based microdisplays the crosstalk between adjacent pixels has to
be taken into account when considering the performance of LCDs used as spatial light modulators in optical
setups. This crosstalk effect is called fringing field effect. Measurements show that this effect is anisotropic and
therefore has different influences on the diffraction efficiencies of vertical and horizontal gratings. Because such
microdisplays are employed in many different holographic applications it is desirable to improve the diffraction
efficiency as much as possible. Recently a simulation model of an LCD which takes the fringing field effect
into account has been presented. Using this model optimization of blazed gratings is realized to improve the
A five element zoomable anamorphic beam expander is designed and fabricated for a laser illumination system used in the manufacture of patterned micro-circuit substrates. The beam expander is the front end of a Gaussian to top-hat beam shaping illuminator. The tightly toleranced optical system downstream of the beam expander should not be readjusted with changes to the input beam. The job of the beam expander is to maintain, independent of the input beam, a constant diffraction limited output beam size as well as a specific waist location. A high power quasi-CW laser at 355 nm is employed for high throughput. The specifications of the laser allow for a range of x,y-beam diameters (ellipticity), x,y-waist locations (astigmatism), and x,y-divergence. As the laser’s frequency tripling crystal is exposed to high fluence over time, the beam parameters will change. At some point the laser is exchanged for a new one, and a new set of beam parameters is presented to the beam expander. Movable cylindrical lenses enable the independent adjustment of x- and y-beam parameters. The mounting cells are motorized to enable adjustments remotely. We present the optical design approach using Gaussian beam ray tracing and discuss the mechanical implementation.
Applying of the refractive beam shapers in real research optical setups as well as in industrial installations requires very often manipulation of a final laser spot size. In many cases this task can be easily solved by using various imaging optical layouts presuming creating an image of a beam shaper output aperture. Due to the unique features of the refractive beam shapers of field mapping type, like flat wave front and low divergence of the collimated resulting beam with flattop or another intensity profile, there is a freedom in building of various imaging systems with using ordinary optical components, including off-the-shelf ones. There will be considered optical layouts providing high, up to 1/200×, de-magnifying factors, combining of refractive beam shapers like πShaper with scanning systems, building of relay imaging systems with extended depth of field. These optical layouts are widely used in such laser technologies like drilling holes in PCB, welding, various micromachining techniques with galvo-mirror scanning, interferometry and holography, various SLM-based applications. Examples of real implementations and experimental results will be presented as well.
Adaptive beam shaping is a critical part of multiple Laser Guide Stars (LGS) for Multiple Conjugate Adaptive Optics (MCAO) for ground-based astronomical telescopes. There are two kinds of Laser Guide Stars: Na Laser Guide Stars (at 589 nm and 92 km altitude) and Rayleigh Laser Guide Stars (at
532 nm and 20 km altitude). Multiple Conjugate Adaptive Optics (MCAO) corrects for each "layer" of atmosphere independently. Multiple Laser Guide Stars are being developed to achieve a measure of tilt and increase the isoplanatic patch. Multiple Laser Guide Stars are being combined with Multiple Conjugate Optics in the Large Binocular Telescope (LBT): more than one Laser Guide Star (4-5) and two different wavelengths: 589 nm and 532 nm. Other observatories have multiple Laser Guide Stars but only one wavelength: 589 nm or 532 nm. Because Laser Guide Stars are launched into the atmosphere, adaptive beam shaping will be carried out before the laser is launched and will be different depending on which laser is being used, presumably to effect the tightest beam which can be achieved
at the power level which is required to provide the requisite return to gound-based wavefront sensors.
A complete range of devices are used. Beam attenuation and divergnece will take place. Multiple Laser Guide Stars of major observatories (SOR, LBT, MMT, ESO VLT and Gemini South) will be evaluated for effective adaptive beam shaping and impact on performance
In this work, the development of a laser scanning system for ophthalmology with micrometric positioning precision is presented. It is a semi-automatic scanning system for retina photocoagulation and laser trabeculoplasty. The equipment is a solid state laser fully integrated to the slit lamp. An optical system is responsible for producing different laser spot sizes on the image plane and a pair of galvanometer mirrors generates the scanning patterns.
The thermal effect of an Yb-doped fiber laser with fattening is numerically investigated. We have identified two principal sources of thermal sensitivity: The temperature dependence of the cross-section of the pump and signal radiations, and modifications of the numerical aperture (NA) due to changes in temperature. We have found that the first factor affects principally the thermal response of the fiber laser with fattening and this sensitivity can be modulated according to the fattening ratio. Additionally this thermal response is higher than that found in doped fibers without fattening. Our results are reproducible and contribute with new information for the development of novel temperature fiber laser sensors
We report the numerical investigation of an Yb-doped fiber amplifier with a taper end in order to be used as a thermal sensor. The spectral fluorescence intensity of the Yb-doped fiber is highly modified when the tapered end is subject to different temperatures from 20 to 150°C, and these changes are more sensitive than that presented in untapered doped fibers. This enhanced temperature response is attributed to the taper effects on the temperature dependence of the crosssections of the pump and signal radiations and additional changes of the numerical aperture of the doped tapered core due to temperature. These results can be extrapolated to other doped fibers and contribute with new information for the development of temperature fiber laser sensors.
The ellipsoidal coordinate system has the interesting property that every other orthogonal coordinate system in which the three-dimensional Helmholtz equation is separable, is a special case of it. In this work, we explore the solutions to the wave equation in ellipsoidal coordinates in order to visualize the behavior of optical fields with ellipsoidal geometry. We show several parity properties which allow us to create fundamental modes of vibration with different symmetries around the (x; y), (x; z) and (y; z) planes. We discuss the resonant modes of an ellipsoidal cavity and the traveling waves with ellipsoidal geometry. We propose a method to calculate the second linearly independent solution to the ellipsoidal wave equation
Highly efficient beam splitters are important for a variety of high power laser applications. We prove different approaches like aperture and amplitude splitting for practicability for single- and multimode laser sources. Combining of micro- and macro-optical fabrication technologies allows novel monolithic free form splitting components with implemented segmented or stepless diffractive optical surfaces. The monolithic components are robust, compact and low weight and easy in handling. Here, we present two monolithic components: a segmented free form 1-to-17 beam splitter for fibre coupled lasers and a diffractive 1-to-11 beam splitter for single mode lasers with peak-to-peak pitch of 1.25mm and 0.8mm, respectively. The optical designs, the manufacturing of the prototypes as well as surface and performance measurements are reported. The prototypes from Fused Silica and Calcium Fluoride are designed for 532nm and 1064nm wavelength. Simulations show efficiencies larger than 98% and peak-to-peak non-uniformity below±3.2%. First laboratory results confirm efficiencies of < 95% and peak-to-peak non-uniformity of less than ±5%.