Progress in Analytical Solutions for High Order Harmonic Generation in Semiconductor Superlattice Multipliers

In this study, we address the limitations of previous solutions for modeling high-order harmonics in semiconductor superlattices (SSLs). Earlier research proposed a step function ansatz that effectively modeled high-order even and odd harmonics but introduced numerical noise. An upgrade using a logistic function addressed the noise problem but eliminated high-order odd harmonics. To overcome both limitations, we examined the impact of the y-intercept value in the discontinuity of the step function and proposed a modified logistic function as a new ansatz. The modified logistic function delivers accurate results, preserving high-order odd harmonics up to the 50th order similar to the previous ansatz while also eliminating numerical noise. This research contributes to a more efficient and robust analytical approach for modeling SSLs, notably by avoiding time-consuming numerical solutions and enhancing our understanding of nonlinear phenomena in GHz-THz devices.