Lawrence Livermore National Laboratory

Nils Petersson (16-ERD-018)

Executive Summary

This project combines laser physics, mathematical methods, asymptotic analysis, computational efficiency and algorithm convergence, and high-performance computing to create an accurate simulation of the effects of imperfect grating stretchers and compressors for beam wavelength tuning on chirped-pulse-amplified lasers. Our research will support the design of high-power, ultrashort-pulse lasers and enable simulations to model how realistic gratings change experimental results.

Project Description

For more than four decades, Lawrence Livermore National Laboratory has been the world leader in the design, construction, activation, and operation of ever-more-complex high-energy inertial-confinement fusion laser drivers, culminating in the 192-beam National Ignition Facility. The foundation for this capability is the unique ability to numerically simulate important physical processes that determine the success and failure of laser operation, which led to the ability to anticipate and avoid potential failure modes and to optimize cost and performance trade-offs. However, the cutting edge of new laser construction has now expanded into ultrashort-pulse lasers, an area in which the Laboratory has considerable expertise but has not kept pace regarding the capabilities needed to simulate their operation and thus optimize their design. We are attempting to close this gap in the area of ultra-intense, short-pulse lasers. One enabling technology for generating ultrashort laser pulses with sufficient energy to be of interest is chirped-pulse amplification, a method by which a spectrally dispersive element, such as a set of diffraction gratings (optical tools for reflecting light), is used to stretch an initial short pulse to nanosecond duration, allowing it to be amplified without damaging the amplifier. The high-energy pulse is then recompressed with another set of diffraction gratings. Approximations for modeling the grating compressor exist, but are not adequate to capture the effect of realistic diffraction gratings. We are developing a method for modeling the interaction of chirped-pulse-amplified laser beams with realistic diffraction gratings. This is challenging because of the enormous spatial and temporal difference in scale among the full-beam description, the time constant of the beam’s spectral content, and the spatial scale of the grating structure. We are combining the Laboratory’s expertise in laser modeling with expertise in multi-scale techniques, mathematical modeling, and high-performance computing to explore a number of approaches to address this challenge.

We are developing advanced mathematical and computational techniques for multiple-wave propagation applications. We are addressing the issues of laser physics, mathematical methods, asymptotic analysis, computational efficiency and algorithm convergence, and high-performance computing with a multi-pronged approach to create an accurate simulation of the effect of realistic, imperfect grating stretchers and compressors on chirped-pulse-amplified laser beams. We intend to examine the application of boundary-element methods accelerated by the fast-multipole method. This technique appears to naturally accommodate high-aspect-ratio spatial discretization, enabling calculations in which grating lines are microscopically resolved in only one dimension, while the longer-scale defects and line-direction anomalies are resolved on the millimeter scales that are natural to their rate of variation. We are also using the analytical results of modeling the wave-optics description of gratings, in which we derive a phase-transfer function that couples space and frequency. Our research will support the design of high-power, ultrashort-pulse lasers at the Laboratory and will enable simulations to model how realistic gratings change the results of experiments. We expect to gain a detailed understanding of (and the ability to simulate) the spatial and temporal coupling introduced by various grating imperfections. By developing this capability, our research will advance the science of laser design.

Mission Relevance

This project aligns with the Laboratory's laser and optical science and technology core competency, which includes the general updating and modernization of laser-simulation capability; specifically, the development, design, and optimization of short-pulse lasers. This research is relevant to the DOE's goal of a more economically competitive, environmentally responsible, secure, and resilient U.S. energy infrastructure through the advancement of science for high-energy, inertial-confinement fusion lasers. It also supports the Laboratory’s core competency in high-performance computing, simulation, and data science by fostering the development of advanced mathematical and high-performance computing techniques.

FY17 Accomplishments and Results

In FY17 we (1) developed a new parallel solver for the electric-field integral equation in the frequency domain based on the Message Passing Interface library for communication across a distributed-memory machine; (2) discretized the integral equation by a boundary-element method using Raviart-Thomas edge elements on a structured quadrilateral mesh, resulting in a linear system of equations that is solved by a preconditioned iterative method (e.g., the generalized minimal residual method), where the fast-multipole method accelerates matrix-vector products; (3) verified the solver for a Gaussian beam (monochromatic electromagnetic radiation that describes the intended output of most lasers) impinging on an inclined plate, and verified the diffraction angles for a sinusoidal grating; and (4) determined that the solver can analyze several frequencies in parallel and that the diffracted beam is available in the time domain after inverse Fourier transformation (a mathematical representation of a signal's frequencies).