The goal of the paper is to simplify a simulation of cascaded Fresnel diffraction (CFD) by reducing the number of integrals and giving a solution for arbitrary plane. The simplification becomes possible with a use of CFD theorem. CFD theorem is formulated and proved. CFD theorem for simplification of one-lens model and two-lens model is demonstrated, and their mathematical models are obtained. As a result, the number of integrals describing diffraction and light propagation in lens models is decreased multiple times. We consider the optical field in any plane, making our approach more universal by assuming ideal point spread function. This approach may be applicable to numerical simulations as well as analytical investigations, optimizations, and designs. Our work benefits Fresnel diffraction method for modeling complex optical systems.
Computational study of nanosecond pulse laser radiation in periodically poled LiNbO3 and LiTaO3 crystals reveals the complex spacio-temporal evolution of the 1.064 μm fundamental harmonic (FH) and second harmonic (SH) energy fields with associated temperature fields, leading to the thermal dephasing and inhibition of second harmonic generation (SHG). The investigated range of the laser input power is W0=0.5-50 W (with the pulse energy Q0=0.01-1 mJ/pulse and repetition rate of 50 kHz). For input laser powers W0>10 W the FH and SH energy fields are found to strongly couple with non-uniform temperature field leading to significant thermal dephasing and SHG efficiency loss. Heat generation and temperature distributions also exhibit very significant non-uniformities along and across the laser beam, maximizing at the rear or inside the crystal, depending on the input power. Performed study shows the feasibility of the effective thermal control with temperature gradient along the crystal allowing one to maintain (i) the irradiated zone within the temperature tolerance range and (ii) high SHG efficiency under high input laser powers.