Title : Nonlinear plasma wave excitation in cylindrical semiconductor waveguides
Abstract:
This study investigates the nonlinear excitation of plasma waves produced by the interaction of an electron acoustic pump wave and a hole acoustic sideband wave in a cylindrical semiconductor waveguide. Their coupling generates a low-frequency beat acoustic mode and establishes a resonant three-wave interaction system. A quantum hydrodynamic framework is employed to account for the collective motion of electrons and holes, while the model explicitly incorporates Fermi-degenerate pressure, the Bohm potential, and exchange-correlation effects. Cylindrical confinement is included through the radial eigenmode condition, enabling the derivation of the dispersion relations for the pump, sideband, and excited beat modes. The nonlinear response originates from the second-order convective term in the momentum equation, which acts as a ponderomotive driving mechanism. Under frequency and wave-vector phase-matching conditions, a coupled nonlinear dispersion relation and an analytical expression for the temporal growth rate of the beat wave are obtained. Numerical analysis shows that the beat mode has a lower frequency than its parent waves and can be strongly amplified when the interaction remains resonant. The growth rate increases with electron number density because the enhanced plasma frequency strengthens wave coupling and energy transfer. In contrast, increasing electron temperature reduces the growth rate by weakening the resonance and increasing thermal motion. Greater pump-wave potential supplies a stronger nonlinear driving force, whereas a larger pump wave vector, corresponding to a shorter wavelength, improves phase matching and further enhances amplification. The results identify high carrier density, low temperature, high pump potential, and short-wavelength excitation as favorable conditions for efficient nonlinear energy exchange in semiconductor quantum plasmas. These findings advance the understanding of confined plasma-wave dynamics and may support the optimization of semiconductor waveguides, nonlinear resonators, quantum amplifiers, and parametric oscillators.
