Acousto-optic modulator (AOM)

An acousto-optic modulator consists of a transparent optical material (typically tellurium dioxide TeO$_2$ or fused silica) with a piezoelectric transducer bonded to one face. The transducer launches a high-frequency acoustic wave (typically 80 MHz – 2 GHz) through the crystal, producing a traveling refractive-index modulation via the photoelastic effect. Incident laser light Bragg-diffracts off this index grating, producing one or more diffracted beams.

For Bragg diffraction (the typical operating regime), the geometry satisfies the Bragg condition:

$$\sin\theta_B \;=\; \frac{\lambda}{2 \Lambda} \;=\; \frac{\lambda \, f_a}{2 v_a},$$

where $\theta_B$ is the Bragg incidence angle, $\Lambda = v_a / f_a$ is the acoustic wavelength, $v_a$ is the acoustic velocity, and $f_a$ is the acoustic frequency.

Frequency shift. The diffracted beam is frequency-shifted by the acoustic frequency (the photon "absorbs" or "emits" an acoustic phonon):

$$\omega_\text{diffracted} \;=\; \omega_\text{incident} \pm 2\pi f_a.$$

The sign depends on whether the diffraction is up-shifting (anti-Stokes, +1 order) or down-shifting (Stokes, −1 order).

Diffraction efficiency is controlled by RF drive power to the transducer:

$$\eta \;=\; \sin^2\!\left(\frac{\pi L \sqrt{M_2 \, P_\text{ac}}}{\lambda \cos\theta_B}\right),$$

where $L$ is the interaction length, $M_2$ is the acousto-optic figure of merit, and $P_\text{ac}$ is the acoustic power. Typical maximum efficiency 70 – 95% depending on material and design.

AOM applications:

Use case	Mechanism
Laser intensity modulation	Modulate RF drive amplitude → modulate diffracted-beam intensity
Frequency shifting	The diffracted beam shifts by $f_a$, useful for heterodyne measurement
Beam deflection	Sweep $f_a$ → sweep $\theta_B$ → scan beam
Q-switching	Apply or remove RF drive → switch laser cavity Q (see Q-switching)
Mode locking	Synchronize $f_a$ to cavity FSR → active mode locking
Optical isolators (alternative)	Frequency shift before back-reflection produces frequency mismatch with original — useful where Faraday isolators are impractical
Pulse pickers	Select individual pulses from a high-repetition-rate train by gating the AOM RF

Typical AOM specifications:

Parameter	Telecom / visible (typical)	High-power
Operating wavelength	400 nm – 2 μm	1 μm
Acoustic frequency	80 – 250 MHz	25 – 80 MHz
Maximum diffraction efficiency	80 – 90%	75 – 85%
Rise/fall time	10 – 100 ns	100 ns – 1 μs
Peak power handling	$\sim$ 1 W	$>$ 10 W
Aperture	0.5 – 5 mm	5 – 20 mm

Acoustic transit time sets the modulation rise/fall time:

$$\tau_\text{rise} \;\sim\; \frac{d_\text{beam}}{v_a},$$

where $d_\text{beam}$ is the beam diameter at the AOM. For a 1 mm beam in TeO$_2$ ($v_a = 660$ m/s): $\tau_\text{rise} \approx 1.5$ μs. For faster modulation, tighter focusing reduces this — at the cost of larger diffraction angle and other tradeoffs.

Comparison with electro-optic modulators. AOMs are slower (~ns to μs rise time) but generally higher diffraction efficiency, broader wavelength range, and no requirement for high-voltage electronics. EOMs are faster (~ps to ns) but require higher drive voltage and have narrower spectral acceptance.