Abstract

Ultrafast synchronously-pumped optical parametric oscillators (OPOs) are broadband systems displaying complex dynamics and spectral structures which cannot be approximated using the classical, coupled wave equations. These systems are more readily described by a χ² nonlinear envelope equation (NEE) [1], an analytical technique for studying ultra-broadband χ² interactions. The NEE has shown good agreement with OPOs containing short (≤ 1 mm) nonlinear crystals operating in a low-dispersion regime [2, 3]; however, OPO cavities containing long crystals [4], significant material dispersion [5], or those pumped with highly chirped pulses, result in fields exhibiting much larger time-bandwidth products. Modelling such fields is computationally expensive due to the data required to maintain oversampling in large temporal/spectral windows (space complexity), compounded by the many round-trips needed for complex cavities to achieve steady-state (time complexity). Although evolution of the full field is inherently sequential, independent calculation of all sample points at each time step allows parallel processing to be leveraged for large data sets. Here we demonstrate GPU acceleration of full-field split-step Fourier methods (SSFM) through extreme parallelism, with an adaptive step-size algorithm, leading to more than three orders of magnitude improvement in computation time for long-crystal OPOs.

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