Mathematical and Numerical Explanation of the Nonlinear Acoustic Wave Interaction in Acousto-Optical Cells
Received: 6 July 2024 | Revised: 29 July 2024 and 6 August 2024 | Accepted: 11 August 2024 | Online: 29 August 2024
Corresponding author: Abbes Ourahmoun
Abstract
In addition to a recently acousto-optical deflector that has been the subject of both theoretical and experimental analysis, this work presents the successful processing of two acousto-optical deflectors that have been orthogonally positioned using two frequency-modulated ultrasonic waves. A comprehensive theoretical analysis is conducted, based on the Collins integral and the ABCD matrix formalism, to explain how the positions of the diffracted orders oscillate in two dimensions as a function of time. The numerical simulation of the derived formula demonstrates the potential for steering a laser beam along Lissajous trajectories. The trajectories in question are observed to exhibit a variety of shapes and velocities. They are sometimes linear with sinusoidal velocities, sometimes circular with constant velocities, and often elliptical with variable velocities. The noteworthy aspect is that all these diffracted orders traverse the spatial domain with an identical sweep frequency, despite the heterogeneity of their trajectories and velocities. Furthermore, these trajectories can be shaped by controlling the phase shift value. This technique can be employed in metrology for rotation measurements based on the Doppler effect. Additionally, it can be used to develop a spatial display that enables tracing Lissajous trajectories, rather than relying on an oscilloscope.
Keywords:
ultrasonic wave, laser beam steering, Lissajous trajectories, acousto-optic deflectorDownloads
References
A. Boulaouad, A. Ourahmoun, and T. Serrar, "Analysis of a Frictionless Electro Viscoelastic Contact Problem with Signorini Conditions," Engineering, Technology & Applied Science Research, vol. 12, no. 5, pp. 9224–9228, Oct. 2022.
S. Dupont, J. C. Kastelik, and F. Causa, "Wide-band acousto-optic deflectors with high efficiency for visible range fringe pattern projector," Review of Scientific Instruments, vol. 78, no. 10, Oct. 2007, Art. no. 105102.
S. Dupont and J. C. Kastelik, "Demonstration of a tunable two-frequency projected fringe pattern with acousto-optic deflectors," The Review of Scientific Instruments, vol. 79, no. 5, May 2008, Art. no. 056101.
S. H. Dupont, J.-C. Kastelik, and M. Pommeray, "Structured Light Fringe Projection Setup Using Optimized Acousto-Optic Deflectors," IEEE/ASME Transactions on Mechatronics, vol. 15, no. 4, pp. 557–560, Aug. 2010.
A. H. Mack, M. K. Trías, and S. G. J. Mochrie, "Precision optical trapping via a programmable direct-digital-synthesis-based controller for acousto-optic deflectors," The Review of Scientific Instruments, vol. 80, no. 1, Jan. 2009, Art. no. 016101.
T. Scussiato, W. H. Ito, J. Ramis, and P. I. B. de Queiroz, "A Numerical Model for Heat and Moisture Transfer in Porous Media of Building Envelopes," Engineering, Technology & Applied Science Research, vol. 12, no. 5, pp. 9239–9246, Oct. 2022.
A. E. Wallin, H. Ojala, E. Hæggström, and R. Tuma, "Stiffer optical tweezers through real-time feedback control," Applied Physics Letters, vol. 92, no. 22, Jun. 2008, Art. no. 224104.
R. V. Brooks et al., "Preparation of one 87Rb and one 133Cs atom in a single optical tweezer," New Journal of Physics, vol. 23, no. 6, Jun. 2021, Art. no. 065002.
Y. Bao et al., "Fast optical transport of ultracold molecules over long distances," New Journal of Physics, vol. 24, no. 9, Sep. 2022, Art. no. 093028.
A. Guessoum and I. Y. Bouderbala, "Generation of an Optical Spatial Array Oscillating According to Tunable Trajectories and Velocities," Acoustical Physics, vol. 70, no. 2, pp. 248–258, Apr. 2024.
I. Y. Bouderbala, A. Guessoum, S. Rabhi, O. Bouhlassa, and I.-E. Bouras, "Optical band-diagram, Urbach energy tails associated with photoluminescence emission in defected ZnO thin films deposited by sol–gel process dip-coating: effect of precursor concentration," Applied Physics A, vol. 130, no. 3, Feb. 2024.
T. Wang, C. Zhang, A. Aleksov, I. Salama, and A. Kar, "Effect of large deflection angle on the laser intensity profile produced by acousto-optic deflector scanners in high precision manufacturing," Journal of Laser Applications, vol. 28, no. 1, Dec. 2015, Art. no. 012012.
S. N. Antonov and Yu. G. Rezvov, "Acousto-Optic Control of the 2D Energy Profile of Laser Beam," Technical Physics, vol. 66, no. 9, pp. 1078–1084, Sep. 2021.
Y. V. Pichugina, S. V. Garnov, and Y. N. Bulkin, "2D scanning system of the acousto-optical deflector with high diffraction efficiency," Journal of Physics: Conference Series, vol. 2091, no. 1, Nov. 2021, Art. no. 012013.
E. R. V. Reddy and S. Thale, "A Novel Efficient Dual-Gate Mixed Dilated Convolution Network for Multi-Scale Pedestrian Detection," Engineering, Technology & Applied Science Research, vol. 13, no. 6, pp. 11973–11979, Dec. 2023.
T. Mamee, W. Anukool, N. Thaicharoen, N. Chattrapiban, and P. Sompet, "Heuristic compactness maximization algorithm for two-dimensional single-atom traps rearrangement," Journal of Physics: Conference Series, vol. 2145, no. 1, Dec. 2021, Art. no. 012024.
G. J. Evans, P. A. Kirkby, K. M. N. S. Nadella, B. Marin, and R. A. Silver, "Development and application of a ray-based model of light propagation through a spherical acousto-optic lens," Optics Express, vol. 23, no. 18, pp. 23493–23510, Sep. 2015.
B. K. A. Ngoi, K. Venkatakrishnan, B. Tan, P. Stanley, and L. E. N. Lim, "Angular dispersion compensation for acousto-optic devices used for ultrashort-pulsed laser micromachining," Optics Express, vol. 9, no. 4, pp. 200–206, Aug. 2001.
A. Guessoum, N. Laouar, and K. Ferria, "Theoretical and experimental study of the light deflection by a frequency modulated ultrasonic wave," Optics & Laser Technology, vol. 97, pp. 260–267, Dec. 2017.
A. Guessoum, "Scanning Velocity Measurement of an Acousto-Optic Deflector," Optics and Spectroscopy, vol. 126, no. 4, pp. 443–449, Apr. 2019.
S. A. Collins, "Lens-System Diffraction Integral Written in Terms of Matrix Optics," Journal of the Optical Society of America (JOSA), vol. 60, no. 9, pp. 1168–1177, Sep. 1970.
J. Goodman, Introduction to Fourier Optics, 3rd edition. Englewood, Colorado, USA: Roberts and Company Publishers, 2004.
Y. Ohtsuka, Y. Arima, and Y. Imai, "Acoustooptic 2-D profile shaping of a Gaussian laser beam," Applied Optics, vol. 24, no. 17, pp. 2813–2819, Sep. 1985.
Y. Ohtsuka and A. Tanone, "Acousto-optic intensity modification of a gaussian laser beam," Optics Communications, vol. 39, no. 1, pp. 70–74, Sep. 1981.
A. Guessoum, "Convexity and Concavity Control of Laser Beam Using a Frequency Modulated Acoustic Wave," Acoustical Physics, vol. 68, no. 6, pp. 542–548, Dec. 2022.
A. Guessoum, "Laser beam Steering According to Linear Trajectories Using an Acousto-Optic Cell," Acoustical Physics, vol. 69, no. 1, pp. 53–57, Feb. 2023.
A. Guessoum, "Acousto-Optic Scanning of a Laser Beam Along a Reconfigurable Circular Trajectory," Acoustical Physics, vol. 69, no. 4, pp. 487–491, Aug. 2023.
A. Guessoum and A. Bencheikh, "Laser beam array spot steering customized trajectories using the acousto-optic effect," Applied Optics, vol. 62, no. 25, pp. 6585–6592, Sep. 2023.
A. Guessoum and I. Y. Bouderbala, "Spatial representation of Lissajous trajectories by an optical method," Applied Physics A, vol. 130, no. 7, Jun. 2024, Art. no. 472.
Downloads
How to Cite
License
Copyright (c) 2024 Abbes Ourahmoun, Amir Guessoum
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.