Analytic phase solutions of three-wave interactions.

Closed-form analytic phase solutions of three-wave interactions are presented for the first time, to the best of my knowledge. Cases from simple second-harmonic generation to the most general three-wave interactions without any constraints are considered. The phase amplification or deamplification behavior in the phase-sensitive parametric process is illustrated using the results obtained here. The analytic solutions agree with the results from direct numerical integration. The validity range of an approximate phase solution is discussed.

Gaussian curvature and stigmatic imaging relations for the design of an unobscured reflective relay.

We derive the relationship between Coddington's equations and the Gaussian curvature for a stigmatic reflective imaging system. This relationship allows parameterizing off-axis conic optical systems using traditional first-order optics by considering the effective curvature at the center of the off-axis sections. Specifically, we demonstrate parameterizing the system requirements of a 2× achromatic image relay for a terawatt laser system. This system required both collimation (far-field) and pupil imaging (near-field) simultaneously. Long working distances and specific spatial constraints limited the available layout options for the imaging components. By parameterizing these system requirements and packaging constraints, the final specifications could be quickly iterated, while allowing for flexibility in the layout of the system during a multi-year conceptual period.

Chromatic diversity: a new approach for characterizing spatiotemporal coupling of ultrashort pulses.

Two-dimensional chromatic aberrations are characterized by a single-shot scheme based on a simultaneous measurement of chromatically diversified focal spots. The chromatic diversity is introduced by a 2-D grating with holographic defocus terms. The chromatic aberrations in the beam are either subtracted or added by the additional known chromatic aberrations in the grating, depending on the diffraction order. By analyzing the asymmetry in the size of diffracted focal spots, input beam chromatic aberrations can be deduced. Theoretical discussions and experimental results are presented.

Chromatic-aberration diagnostic based on a spectrally resolved lateral-shearing interferometer.

A simple diagnostic characterizing one-dimensional chromatic aberrations in a broadband beam is introduced. A Ronchi grating placed in front of a spectrometer entrance slit provides spectrally coupled spatial phase information. The radial-group delay of a refractive system and the pulse-front delay of a wedged glass plate have been characterized accurately in a demonstration experiment.

Offner radial group delay compensator for ultra-broadband laser beam transport.

Conventional lens-based image relays introduce radial group delay that significantly reduces focal-spot intensity of ultra-broadband short pulses. A direct compensation scheme that can be used with conventional singlet image relays is proposed. The compensation scheme is based on using two negative lenses embedded within an Offner imaging system. The setup allows a single-pass configuration and eliminates the need for polarization switching optics. The performance of this setup is calculated using ray tracing. The compensation improves the spatiotemporal Strehl ratio from 0.02 to 0.97.

Highly accurate wavefront reconstruction algorithms over broad spatial-frequency bandwidth.

New algorithms for reconstructing wavefront from slopes data are developed, which exhibit high accuracy over broad spatial-frequency bandwidth. Analyzing wavefront reconstructors in the frequency domain lends new insight into ways to improve frequency response and to understand noise propagation. The mathematical tools required to analyze the frequency domain are first developed for discrete band-limited signals. These tools are shown to improve frequency response in either spatial-or frequency-domain reconstruction algorithms. A new spatial-domain iterative reconstruction algorithm based on the Simpson rule is presented. The local phase estimate is averaged over 8 neighboring points whereas the traditional reconstructors use 4 points. Analytic results and numerical simulations show that the Simpson-rule-based reconstructor provides high accuracy up to 85% of the bandwidth. The previously developed rectangular-geometry band-limited algorithm in frequency domain is adapted to hexagonal geometry, which adds flexibility when applying frequency-domain algorithms. Finally, a generalized analytic expression for error propagation coefficient is found for different reconstructors and compared with numerical simulations.

A high-resolution, adaptive beam-shaping system for high-power lasers.

A high-resolution, high-precision beam-shaping system for high-power-laser systems is demonstrated. A liquid-crystal-on-silicon spatial light modulator is run in closed-loop to shape laser-beam amplitude and wavefront. An unprecedented degree of convergence is demonstrated, and important practical issues are discussed. Wavefront shaping for the applications in OMEGA EP laser is demonstrated, and other interesting examples are presented.

Spot-shadowing optimization to mitigate damage growth in a high-energy-laser amplifier chain.

A spot-shadowing technique to mitigate damage growth in a high-energy laser is studied. Its goal is to minimize the energy loss and undesirable hot spots in intermediate planes of the laser. A nonlinear optimization algorithm solves for the complex fields required to mitigate damage growth in the National Ignition Facility amplifier chain. The method is generally applicable to any large fusion laser.

On-shot focal-spot characterization technique using phase retrieval.

We present an on-shot focal-spot characterization technique based on a phase-retrieval scheme that retrieves near-field phase from multiplane focal-spot measurements in an experimental target chamber. The technique is easy to implement inside a target chamber and is demonstrated in a multiterawatt laser system. It is also found that phase retrieval can quantitatively detect residual angular dispersion coming from the pulse compressor misalignment.

Band-limited wavefront reconstruction with unity frequency response from Shack-Hartmann slopes measurements.

The analytic frequency responses of the traditional wavefront reconstructors of Hudgin, Fried, and Southwell are presented, which exhibit amplification or attenuation of the original signal at high spatial frequencies. To overcome this problem, a reconstructor with unity frequency response is developed based on a band-limited derivative calculation. The algorithm is both numerically and experimentally confirmed.