We develop in this paper efficient and accurate numerical schemes based on the scalar auxiliary variable (SAV) approach for the generalized Zakharov system and generalized vector Zakharov system. These schemes are second-order in time, linear, unconditionally stable, only require solving linear systems with constant coefficients at each time step, and preserve exactly a modified Hamiltonian. Ample numerical results are presented to demonstrate the accuracy and robustness of the schemes.
We develop in this paper efficient numerical schemes for solving the micropolar Navier-Stokes equations by combining the SAV approach and pressure-correction method. Our first-and second-order semi-discrete schemes enjoy remarkable properties such as (i) unconditional energy stable with a modified energy, and (ii) only a sequence of decoupled linear equations with constant coefficients need to be solved at each time step. We also construct fully discrete versions of these schemes with a special spectral discretization which preserve the essential properties of the semi-discrete schemes. Numerical experiments are presented to validate the proposed schemes.
We propose a novel, to the best of our knowledge, adiabatic nonlinear optical frequency conversion method based on the electro-optic effect, which can be applied in a plethora of bulky nonlinear crystals. Within our method, an electric field gradient is applied on the crystal, which causes the phase mismatch to also gradually vary in space, thus achieving adiabatic frequency conversion. We demonstrate the validity and feasibility of this new approach by providing a theoretical framework and experimental evidence. In the experiment, the second harmonic generation of 532 nm is conducted in
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. Conversion efficiency approaching 47.2% is achieved, with a corresponding temperature acceptance bandwidth of 4.56°C, which is about 4.3 times the temperature without the external electric field. We argue that the approach based on the electro-optic effect is promising for extending the range of applications of adiabatic frequency conversion and, consequently, for achieving efficient and robust frequency conversion.
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