Sound Meets Light
When an acoustic wave propagates through a transparent crystal, it creates a periodic modulation of the refractive index — essentially a moving diffraction grating. In the Bragg regime, the acoustic grating is thick enough that only one diffraction order satisfies the phase-matching condition simultaneously. Light incident at the precise Bragg angle experiences constructive interference in the first diffracted order, while all higher orders destructively cancel. This selectivity makes Bragg acousto-optic interaction the foundation of practical devices.
The Klein-Cook Parameter
The transition from thin-grating (Raman-Nath) to thick-grating (Bragg) behavior is governed by the Q parameter: Q = 2πλL/(nΛ²). When Q exceeds approximately 4π (≈12.6), only one diffraction order is significant, and the interaction is well-described by coupled-wave theory. Most practical acousto-optic devices operate deep in the Bragg regime with Q values of 50 or higher, ensuring clean single-order diffraction.
Diffraction Efficiency
The fraction of incident light deflected into the first order depends on the acoustic power density and the material's acousto-optic figure of merit M₂. Efficiency follows a sinusoidal relationship: η = sin²(φ/2), where the phase shift φ is proportional to the square root of acoustic power. At the optimal power, efficiency reaches 100%, but exceeding this causes over-coupling — light diffracts back into the zero order, and efficiency decreases. This oscillatory behavior is a hallmark of Bragg diffraction.
Bandwidth and Speed
The acoustic frequency bandwidth over which efficient diffraction occurs is inversely proportional to the interaction length and the acoustic frequency. Shorter crystals yield broader bandwidths at the cost of requiring more acoustic power. This trade-off between efficiency and bandwidth is fundamental to acousto-optic device design — modulators favor short interaction lengths for speed, while deflectors and filters favor longer lengths for angular or spectral resolution.