The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.
Inclusion of the instantaneous Kerr nonlinearity in the FDTD framework leads to implicit equations that have to be solved iteratively. In principle, explicit integration can be achieved with the use of anharmonic oscillator equations, but it tends to be unstable and inappropriate for studying strong-field phenomena like laser filamentation. In this paper, we show that nonlinear susceptibility can be provided instead by a harmonic oscillator driven by a nonlinear force, chosen in a way to reproduce the polarization obtained from the solution of the quantum mechanical two-level equations. The resulting saturable, nonlinearly-driven, harmonic oscillator model reproduces quantitatively the quantum mechanical solutions of harmonic generation in the under-resonant limit, up to the 9th harmonic. Finally, we demonstrate that fully explicit leapfrog integration of the saturable harmonic oscillator is stable, even for the intense laser fields that characterize laser filamentation and high harmonic generation.
Potassium dihydrogen phosphate (KDP) and its deuterated analog (DKDP) are unique nonlinear optical materials for high power laser systems. They are used widely for frequency conversion and polarization control by virtue of the ability to grow optical-quality crystals at apertures suitable for fusion-class laser systems. Existing methods for freeform figuring of KDP/DKDP optics do not produce surfaces with sufficient laser-induced–damage thresholds (LIDT’s) for operation in the ultraviolet portion of high-peak-power laser systems. In this work, we investigate fluid jet polishing (FJP) using a nonaqueous slurry as a sub-aperture finishing method for producing freeform KDP surfaces. This method was used to selectively polish surface areas to different depths on the same substrate with removals ranging from 0.16 μm to 5.13 μm. The finished surfaces demonstrated a slight increase in roughness as the removal depth increased along with a small number of fracture pits. Laser damage testing with 351 nm, 1 ns pulses demonstrated excellent surface damage thresholds, with the highest values in areas devoid of fracture pits. This work demonstrates, for the first time, a method that enables fabrication of a waveplate that provides tailored polarization randomization that can be scaled to meter-sized optics. Furthermore, this method is based on FJP technology that incorporates a nonaqueous slurry specially designed for use with KDP. This novel nonaqueous FJP process can be also used for figuring other types of materials that exhibit similar challenging inherent properties such as softness, brittleness, water-solubility, and temperature sensitivity.
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