Analytical modeling with segmented quasi-phase matching LiNbO3 for voltage-controlled second harmonic generation spectra

We present a theoretical investigation of electro-optic modification of second-harmonic generation (SHG) in a three-segment quasi-phase-matched (QPM) lithium niobate (LiNbO₃) device with a fixed total crystal length of 57 mm. We analyze a segmented architecture in which an externally applied electric field modifies the refractive index of the central segment through the linear electro-optic effect, enabling dynamic tuning of the SHG response. A generalized analytical formulation for the SHG amplitude and intensity is developed for a three-segment structure. The derived expression remains valid for both equal and unequal segment-length configurations, thereby extending the mathematical description beyond fixed-ratio length. Numerical simulations at a fundamental wavelength of 1653 nm demonstrate how variations in segment-length ratios influence SHG intensity modulation, spectral shift, and tuning range. The proposed theoretical framework establishes a systematic basis for segment-length engineering in voltage-controlled nonlinear optical QPM devices.