Acousto-Optic Lens Design

• Acousto-optic lens design is a technique that uses acoustic waves to modulate the refractive index and dynamically steer, focus, and shape laser beams.
• Recent designs incorporate double-pass acousto-optic deflectors and multi-tone RF signals to achieve precise 3D beam control, reaching focus shifts over 20 Rayleigh ranges at up to 100 kHz.
• These systems are pivotal in quantum technologies and high-resolution microscopy, providing real-time, multi-focal beam modulation through advanced RF control and feedback.

An acousto-optic lens (AOL) is an optical device capable of dynamic, non-mechanical control over the position and focusing of laser beams by exploiting the interaction between coherent light and acoustic waves in a modulated medium. AOLs use the photoelastic effect—where acoustic fields produce refractive index changes—to deflect, focus, or multiplex light, providing highly tunable beam steering and shaping with high speed and precision. Contemporary AOL designs combine acousto-optic deflectors, advanced frequency control, and multiplexing architectures to enable simultaneous multi-dimensional manipulation, opening new possibilities in microscopy, quantum technologies, and real-time laser processing.

1. Fundamental Principles of Acousto-Optic Lensing

The principle underlying acousto-optic lenses is the modulation of the refractive index of an optical medium via a propagating or standing acoustic wave. This modulation creates a dynamic phase grating, and when an incident laser beam interacts with this grating under phase-matching (Bragg) conditions, the beam is diffracted into new spatial orders, each potentially frequency-shifted by integer multiples of the acoustic frequency.

In the Raman–Nath regime (thin grating approximation), the incident field $E_{in}$ is diffracted into multiple orders given by:

$$E_{diff} = E_0 + E_{+1} \, e^{i2\pi (F_A + F_s)t} + E_{-1} \, e^{i2\pi (F_A - F_s)t}$$

where $F_A$ is the introduced frequency shift (e.g., via AOMs) and $F_s$ is the ultrasonic frequency. The acousto-optic efficiency $K_{US}$ quantifies conversion into the $+1$ and $-1$ orders (Jacquin et al., 2012).

Spatially modulating the frequency of the acoustic drive across the medium introduces a controlled phase gradient, shaping the wavefront and acting as a lens. The deflection angle for Bragg diffraction is:

$\sin\theta_B = \frac{\lambda F}{2V}$

with $\lambda$ the optical wavelength, $F$ the acoustic frequency, and $V$ the sound velocity (Schrödel et al., 2023).

2. Three-Dimensional Acousto-Optic Control and Multiplexing

Recent advances extend AOLs to full three-dimensional (3D) beam control by integrating double-pass acousto-optic deflectors (AODs) and diffraction gratings in the Littrow configuration (Picard et al., 9 Oct 2025, Guo et al., 10 Oct 2025). The architecture decouples lateral (x–y) and axial (z) beam manipulation:

• Lateral Control: Standard crossed AODs steer the beam transversely via RF-frequency-tuned angular deflection:

$$\Delta = F_M \cdot \left(\frac{\lambda}{v_A}\right) (f_{RF} - f_0)$$

where $F_M$ is the focusing lens focal length, $v_A$ the acoustic velocity, and $f_{RF}$ the drive frequency.

• Axial Control (Focus Tuning): The double-pass AOD with Littrow grating creates a frequency-tunable lens:

$f_{eff} = \frac{f_{CEL}}{2\tan\theta\tan\phi}$

$$z_s = \frac{F^2}{f_{eff}} = \frac{2F^2\tan\theta\tan\phi}{f_{CEL}}$$

with $f_{CEL}$ the cat’s eye lens focal length, $\theta$ the Littrow angle, and $\phi$ the AOD deflection angle.

By applying multi-tone RF signals, the system can form arbitrary multi-focal 3D beam profiles, enabling reconfigurable optical patterns and rapid focus switching over more than twenty Rayleigh ranges at rates up to 100 kHz (Picard et al., 9 Oct 2025).

3. Experimental Architectures and Dynamic Focal Control

Physical implementations of 3D AOLs (Guo et al., 10 Oct 2025) leverage double-pass AOD modules for axial tuning and independent crossed AODs for lateral displacement. A cat-eye retroreflector ensures path correction and self-cancellation of unwanted transverse deflections during focus shifts. Frequency chirping of the RF drive on the double-pass module produces a spatially varying diffraction angle, yielding a dynamic cylindrical lens effect:

$$F_{AOL} = \frac{v_A^2}{\lambda} \left(\frac{df_{RF}}{dt}\right)^{-1}$$

Chirping both AODs produces a spherical lensing effect, allowing for precise arbitrary 3D trajectories. A critical formula for dynamic focus position:

$$\delta(t) \approx -\frac{2\lambda F_M^2}{v_A^2 M_S^2} \frac{df_{RF}}{dt}$$

where $M_S$ is the telescope magnification (Guo et al., 10 Oct 2025).

Time delays (∼8 μs) occur due to finite acoustic transit times across the beam diameter; high chirping rates may introduce nonlinear acoustic distortion. Typical power losses from double-pass optics are ∼30%. Optimization of RF synthesis and feedback compensates for nonlinearity and delay distortion.

4. Applications in Quantum Technologies and Advanced Imaging

AOLs have transformed neutral atom quantum computing by facilitating fast, flexible 3D shuttling of atoms in optical tweezer arrays. These systems enable fully connected two-qubit gates, efficient rearrangement for error-free array preparation, and mid-circuit measurements by allowing atoms to be shuttled out-of-plane for selective readout (Guo et al., 10 Oct 2025).

In high-resolution microscopy and laser micro-processing, AOLs provide rapid 3D focus scanning, which is essential for volumetric imaging and dynamic beam patterning. Fast switching rates (∼100 kHz) and multiplexing allow simultaneous addressing of multiple focal spots, critical for parallel operation in advanced optical manipulation platforms (Picard et al., 9 Oct 2025).

5. Key Performance Metrics and Limitations

Performance characterization in static and dynamic operation demonstrates:

• Axial focal shift slopes closely tracking theoretical predictions ($\sim$–28 mm/(MHz/μs) measured vs. –33 mm/(MHz/μs) calculated).
• Achievable axial scanning well beyond 20 Rayleigh ranges.
• Switching rates up to 100 kHz, limited by acoustic transit time (τ) and RF bandwidth.
• Crosstalk suppression and intensity isolation are achieved via precise beam shaping and aberration correction (Lim et al., 21 Feb 2024).
• Power losses (∼30%) inherent to double-pass configurations require trade-off analysis against desired dynamic range and speed.

Limitations include acoustic propagation delay, nonlinear distortion at high acceleration chirps, and residual lensing effects during rapid transverse movement, mitigated through advanced RF control and feedback.

6. Future Directions in Acousto-Optic Lens Research

Future research targets include:

• Scaling AOLs to larger aperture deflectors for extended axial control, potentially requiring increased optical demagnification.
• Integration with advanced RF synthesis systems for complex three-dimensional addressing trajectories and motional excitation minimization.
• Real-time feedback systems for compensating nonlinear acoustic dynamics in fast focus trajectories.
• Robust operation in large-scale atomic arrays and deeper integration with quantum logic and error correction protocols in scalable quantum architectures (Guo et al., 10 Oct 2025).
• Extension to ambient air and hybrid photonic platforms for higher power, broader spectral coverage, and damage resistance (Schrödel et al., 2023).

AOLs—leveraging compounded RF-driven acousto-optic modulation, multiplexing, and advanced feedback—are establishing platforms for high-speed 3D beam control across a range of quantum, imaging, and laser engineering applications. The combination of deep theoretical modeling and experimentally validated device architectures outlined in (Picard et al., 9 Oct 2025) and (Guo et al., 10 Oct 2025) marks the emergence of frequency-tunable, dynamically reconfigurable lens systems capable of complex spatial and temporal beam shaping at microsecond timescales.