Acousto-Optic Deflectors (AODs) are inertialess optical solid state devices that have advantages over conventional mechanically controlled mirror-based deflectors in numerous scientific and industrial applications. These applications include fluorescence microscopy, sensing, variable-focus lens, photolithography and laser materials processing. AODs are currently operated with a single piezoelectric transducer that modulates the refractive index only in one direction. This operating principle limits the performance of AODs to a narrow acoustic bandwidth of the transducer and a small angle of laser deflection governed by the Bragg diffraction. To overcome these two limitations, the operation of AODs with phased array ultrasonic transducers is analyzed in this study. Only the amplitude and frequency of the acoustic waves are modulated in conventional AODs. The phased array mechanism enables modulating the acoustic phase in addition to the amplitude and frequency modulations. The latter two phenomena affect the refractive index variation and its periodicity in the AOD medium, respectively, and the phase modulation produces tilted wavefronts due to diffraction and interference of the ultrasonic waves. Consequently, a tilted phase grating is formed inside the AOD device and the tilt angle automatically modifies the laser incident angle on the grating compared to the original angle of incidence on the AOD device. The acoustic frequency and amplitude are, therefore, modulated to achieve the Bragg diffraction under the new angle of incidence and maximize the diffraction efficiency, respectively. The phase grating can be tilted at any arbitrary angle by steering the ultrasonic beam in different directions. The beam steering can be achieved by operating the transducers with various time delays to generate ultrasonic waves of different phases. Due to the diffraction pattern of the ultrasonic intensity distribution, the refractive index varies both longitudinally and transversely to the beam steering direction, and two-dimensional refractive index modulation occurs when the transducers are very long in the third dimension. The acoustic waves affect the refractive index through the photoelastic effect by inducing mechanical strain waves in the AOD medium. The ultrasonic beam steering and the mechanical strain are determined using a modified Rayleigh-Sommerfeld diffraction integral. This integral represents the mechanical displacement vector field produced by ultrasonic waves in solid media. An analytic expression is obtained for the displacement field and the resulting strain distribution is calculated using this expression. Based on the strain and the photoelastic constants, the two-dimensional variation in the refractive index is determined for single-crystal paratellurite TeO2 which is an excellent AOD material. Conventional two-dimensional coupled mode theory of AOD, which is based on only one-dimensional refractive index modulation, is extended in this study to analyze the effect of two-dimensional index variation on the performance of AODs. The diffraction efficiency and the laser beam deflection angle are determined for both plane waves and Gaussian laser beams by obtaining analytic solutions for the coupled mode equations. The diffraction efficiency is found to be nearly unity over a broad range of the acoustic frequency, and the deflection angle can also be increased by steering the ultrasonic beam at large angles.


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Graduation Date





Kar, Aravinda


Doctor of Philosophy (Ph.D.)


College of Optics and Photonics


Optics and Photonics

Degree Program

Optics and Photonics









Release Date

May 2022

Length of Campus-only Access

5 years

Access Status

Doctoral Dissertation (Open Access)