Noise and dynamics in acoustoelectric waveguides

Abstract

We present a quantum field theoretic formulation of acoustoelectric interactions in waveguide-like systems of arbitrary cross-section. Building on an open quantum systems approach, we derive a unified description of plasmon-phonon coupling that incorporates dissipation, noise, and the influence of drift currents. Our analysis captures both bulk and surface plasmon modes, highlighting how drift currents Doppler-shift plasmonic resonances and reshape the phonon noise spectrum. The resulting Heisenberg-Langevin equations yield closed-form expressions for frequency shifts, gain, and noise power spectra, enabling direct evaluation of performance metrics such as the noise factor in acoustoelectric amplifiers and oscillators. In the appropriate limits, this framework reproduces known results while extending them to complex geometries.

Figures (4)

• Figure 1: Acoustoelectric scattering processes (a) and phase matching conditions for (b) $v_d<v_m$ and (c) for $v_d>v_m$. Panel (c) shows that when the drift velocity exceeds the speed of sound, a negative lab frame frequency $\omega'$ plasmon can be spontaneously emitted with a phonon. The tails (heads) of the arrows represent the initial (final) state.
• Figure 2: Schematic of acoustoelectric system. The volume $V_{in} (V_{out})$ is the volume formed by $A_{in} (A_{out})$ and the $z$-axis. $A_{in}$ is the cross-section of the region containing the free-carriers.
• Figure 3: Simulation of acoustoelectric gain in an InGaAsP on LiNbO$_3$ waveguide structure based on the analytical results presented here. (a) Waveguide cross-sectional geometry. (b) Displacement magnitude of the $(2\pi)8.519$ GHz guided mechanical mode considered that is utilized for this acoustoelectric gain analysis. (c) Peak acoustoelectric gain for the various plasmon modes. Inset: electric potential for the first four plasmon modes. (d) acoustoelectric gain for phonon mode shown in (b) as a function of applied electric field. The carrier drift velocity is given by $v_d = \mu E$ where the mobility is $\mu = 2000$ cm$^2$/kV. The materials properties of LiNbO$_3$ and InGaAsP used in this analysis are summarized in Appendix \ref{['App: Materials Properties']}.
• Figure 4: Noise figure (solid gray) and single pass (S.P.) acoustoelectric gain/loss (blue) vs. applied field. The dashed line is the noise figure for the system in the absence of acoustoelectric coupling. The system parameters are take from Fig. \ref{['Fig: GAE']} and Tab. \ref{['tab: parameters']}. The device length $z$ is set at $100 \mu$m, the loss per unit length $\alpha$ is set to $3116$ dB/cm, and selected temperature is 300 K.