Design of gradient-index lens systems for laser beam reshaping

Automatic generation of a holographically shaped beam in an actual optical system for use in material laser processing

In-system optimization involves designing a computer-generated hologram (CGH) in an actual optical system. An important advantage of this approach is automatic generation of a target shaped beam with compensation for imperfections in the actual optical system that would degrade the reconstruction performance. We developed a novel in-system optimization method for beam shaping based on our previous research where it had been applied only to generate parallel focused beams. The key point in the application to beam shaping is to accurately express the conditions and coordinates of the actual optical system in the CGH calculation.

Replacing optical surfaces with gradient index functions which preserve ray trajectory

Laws of reflection and refraction between homogeneous media and gradient index (GRIN) ray behavior are both derived from Fermat's principle. Design methods for GRIN can be difficult to analytically develop. This Letter proposes a foundation for complete replacement of refracting and total internally reflecting optical interfaces in existing designs with GRIN distribution. The proposed method can aid in incorporating GRIN into existing optical designs. Refraction in GRIN is specified to match the ray striking and leaving the optical interface in both position and angle. This result is shown for a collection of similar GRIN functions. One GRIN function is analyzed over a full space of attainable ray bend angles. A local arbitrarily oriented planar interface is replaced with GRIN distribution, and ray behavior is maintained.

Implementation of a SVWP-based laser beam shaping technique for generation of 100-mJ-level picosecond pulses

We present implementation of the energy-efficient and flexible laser beam shaping technique in a high-power and high-energy laser amplifier system. The beam shaping is based on a spatially variable wave plate (SVWP) fabricated by femtosecond laser nanostructuring of glass. We reshaped the initially Gaussian beam into a super-Gaussian (SG) of the 12th order with efficiency of about 50%. The 12th order of the SG beam provided the best compromise between large fill factor, low diffraction on the edges of the active media, and moderate intensity distribution modification during free-space propagation. We obtained 150 mJ pulses of 532 nm radiation. High-energy, pulse duration of 85 ps and the nearly flat-top spatial profile of the beam make it ideal for pumping optical parametric chirped pulse amplification systems.

Gradient-index design for mode conversion of diffracting beams

Gradient-index (GRIN) media offer advantages over thin optical elements for beam shaping of strongly diffracting fields. A numerical GRIN design method is presented, where diffraction effects are considered in solving for the refractive index profile. The index profile is found by specifying a desired beam transformation throughout the GRIN volume and solving a series of phase retrieval problems. A Gaussian to flat-top beam shaper and a coherent beam combiner are shown as examples. Reduced beam distortion is demonstrated in comparison to a purely geometric design method.

Deflectometry for measuring inhomogeneous refractive index fields in two-dimensional gradient-index elements

We present a numerical method for calculating inhomogeneous refractive index fields in rectangular gradient-index (GRIN) elements from measured boundary positions and slopes of a collection of rays that transit the medium. The inverse problem is reduced to a set of linear algebraic equations after approximating ray trajectories from the measured boundary values and is solved using a pseudo-inverse algorithm for sparse linear equations. The ray trajectories are subsequently corrected using an iterative ray trace procedure to ensure consistency in the solution. We demonstrate our method in simulation by reconstructing a hypothetical rectangular GRIN element on a  15×15 discrete grid using 800 interrogating rays, in which RMS refractive index errors less than 0.5% of the index range (n(max)-n(min)) are achieved. Furthermore, we identify three primary sources of error and assess the importance of data redundancy and system conditioning in the reconstruction process.

Design and performance of a refractive optical system that converts a Gaussian to a flattop beam

A system of two aspheric lenses is described, which efficiently converts a collimated Gaussian beam to a flattop beam. Departing from earlier designs, both aspheric surfaces were convex, simplifying their fabrication; the output beam was designed with a continuous roll-off, allowing control of the far-field diffraction pattern; and diffraction from the entrance and exit apertures was held to a negligible level. The design principles are discussed in detail, and the performance of the as-built optics is compared quantitatively with the theoretical design. Approximately 78% of the incident power is enclosed in a region with 5% rms power variation. The 8-mm-diameter beam propagates approximately 0.5 m without significant change in the intensity profile; when the beam is expanded to 32 mm in diameter, this range increases to several meters.

Design and optimization of an irradiance profile-shaping system with a genetic algorithm method

We develop a genetic algorithm (GA) optimization method and use it in the design of a refractive-beam profile-shaping system. In this application, we employ the GA to determine the shape of one surface of the primary beam profile-shaping element in our system. The GA is instructed to vary the shape of this surface such that the output intensity profile is flat on a spherical surface some distance away. The GA does this while insuring that only a specified area of the output surface is illuminated. The calculation of the intensity profile is based on geometrical optics and is accomplished exclusively through ray tracing, giving this method broad applicability.

Multiple harmonic generators for improved efficiency of laser-pumped lasers

A multistage system of three second-harmonic-generating crystals has been used to improve the total conversion efficiency from the fundamental at 1.06 mum to the second harmonic at 532 nm. Demagnifying telescopes placed into the path of the residual fundamental light, after chromatic separation of the second harmonic, allow further second-harmonic crystals to be used. More than 97% conversion has been obtained from 207-mJ, Q -switched Nd:YAG laser pulses at 1.06 mum, producing more than 201 mJ at 532 nm. Good agreement is achieved between experiment and theory for the spatial and temporal evolution of the second-harmonic beams at each stage.