  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.
