Theory of backward second-harmonic generation of short laser pulses in periodically and aperiodically poled nonlinear crystals

Abstract

We study numerically and analytically the backward second-harmonic generation in periodically and aperiodically poled nonlinear crystals in the quasiphase-matched regime. In our numerical analysis, we apply the optimum control technique based on the shooting method. Due to the fast and efficient numerical technique, we are able to analyze this frequency-conversion process in detail, taking into account various factors -the pump intensity, group-velocity mismatch and dispersion, linear phase mismatch, and "chirp" of nonlinear grating. Also we derive several approximate solutions for the backward harmonic efficiency employed in the undepleted pump approximation.

On theory of second harmonic generation in 2D nonlinear photonic crystals with arbitrary structures

“…for G(1, 0) lattices wave-vector [2,16]. As is seen from the figure, numerical and analytical results correspond to each other with high accuracy for any configuration of NPC.…”

“…It has been shown that harmonic generation with desired (e.g., amplitude and phase) parameters can be obtained by "exactly" designing 1D NPC. Pulse shaping technique via NPC with extremely short domains was also studied previously [16] for backward SHG energy conversion in the non-stationary regime. For this purpose and other tasks of frequency conversion problems, it is necessary to develop mathematical methods for analyzing spectral and temporal responses of 2D NPC at given three-wave interactions.…”

“…(2) Furthermore, one can get the following solution (see also in [10,11]): The phase mismatch of the interacting fundamental frequency and SH can be calculated by using the following formula (see Fig. 2) [2,16]:…”

Simulating optical processes: Monte Carlo photon tracing method

“…Scientific models are presumably accurate because they are usually derived from fundamental equations such as Maxwell and Schrödinger. In practice, however, scientific models make use of several approximations to achieve closed-form formulation or solvability [2],resulting in degraded accuracy. Statistical models rely in part on randomness (statistical laws) to determine a "highly probable outcome" at the expense of less precision.…”

Femtosecond pulse shaping via engineered nonlinear photonic crystals

“…Among them, the optimal control technique, based on Lagrange multipliers and real amplitudes [12][13], was applied to tailor ultra-short SH pulses by spatially varying the size of the nonlinearity. More recently, a similar approach was employed to design QPM gratings for picosecond SHG from femtosecond (fs) input FF pulses [14][15][16][17][18][19].…”