Engineering & Science
Acousto-Optic Modulator (AOM) Acoustic Wavelength & Bragg Deflection Angle
Calculate the ultrasonic grating period Lambda = v_a / f_RF (um) and external Bragg angle theta_B ~ (lambda_0 * f_RF) / (2 * v_a) (milliradians) for TeO2 and fused-silica laser acousto-optic deflectors.
Steer and frequency-shift laser beams with RF ultrasound waves inside crystals!
Driving a piezoelectric transducer at radio frequency f_RF (MHz) launches a traveling acoustic compression wave at sound speed v_a (m/s) through a Tellurium Dioxide (TeO2, longitudinal v_a = 4,200 m/s) or fused-silica crystal. That periodic photoelastic strain creates a moving refractive-index diffraction grating of spatial period Lambda = v_a / f_RF!
Entering at the external Bragg incidence angle sin(theta_B) = lambda_0 / (2 * Lambda) = (lambda_0 * f_RF) / (2 * v_a) (with total deflected separation 2 * theta_B between 0th and 1st orders) couples up to 85–90% of a HeNe laser beam (lambda_0 = 632.8 nm) into the frequency-shifted 1st order! At f_RF = 80 MHz in TeO2 (v_a = 4,200 m/s), acoustic grating period Lambda = 52.50 um and external small-angle Bragg angle theta_B = 6.027 mrad (2 * theta_B = 12.053 mrad beam separation); sweeping RF up to 160 MHz doubles theta_B linearly to 12.053 mrad!
| RF Drive Frequency (HeNe 632.8 nm in TeO2, va = 4,200 m/s) | Acoustic Grating Period Lambda (um) | External Bragg Angle thetaB (mrad) | 0th-to-1st Separation 2*thetaB |
|---|---|---|---|
| 80 MHz Standard Carrier | 52.50 um | 6.027 mrad | 12.053 mrad |
| 160 MHz Swept Deflector | 26.25 um | 12.053 mrad | 24.107 mrad |
| Zero RF Frequency or Sound Speed | Guarded Input Error | "Invalid AOM Inputs" | Requires lambda > 0, f_RF > 0, va > 0 |
Ultrasonic Grating Wavelength Lambda (um) = v_a / f_RF_MHz
Since 1 MHz = 10^6 Hz and 1 m = 10^6 um, dividing sound speed v_a (m/s, B3) directly by f_RF (MHz, B4) yields Lambda in micrometers (um)!
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Invalid AOM Inputs", ROUND(B3 / B4, 2))External Acousto-Optic Bragg Angle theta_B (mrad) = ((lambda_nm * 10^-9 * f_MHz * 10^6) / (2 * v_a)) * 1000
Simplifies cleanly to (lambda_nm * f_MHz) / (2 * v_a) in milliradians under the small-angle paraxial approximation.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0), "Invalid AOM Inputs", ROUND((B2 * B4) / (2 * B3), 3))Try the example
Use the original values or change them to test your understanding.