This thesis extends the prior work which produced an exact solution to the four-order acousto-optic (AO) Bragg cell with assumed fixed center frequency and with exact Bragg angle incident light. The extension predicts the model that incorporates the dependencies of both the input angle of light and the sound frequency. Specifically, a generalized 4th order linear differential equation (DE), is developed from a simultaneous analysis of four coupled AO system of DEs. Through standard methods, the characteristic roots, which requires solving a quartic equation, is produced. Subsequently, a derived system of homogeneous solutions, which absorbs the roots obtained using Ferrari's approach, is formalized into a transition matrix operator which predicts the diffracted light orders at the exit of the AO cell in terms of the same diffracted light orders at the entrance. Numerical tests are used to test the hypothesis that the state of transition matrix is unitary. It is shown that this unitary matrix condition is sufficient to guarantee energy conservation. Three different types of tests: normalized space variation, normalized angle variation, and normalized frequency variation, have been used to demonstrate the agreement between analytical solutions and numerical predictions, which validate the formalism. Lastly, all four generated eigenvalues from the four-order acousto-optic differential matrix operator can be expressed simply in terms of Euclid's Divine Proportion.

Date of publication

Spring 5-2-2017

Document Type




Persistent identifier


Committee members

Ron. Pieper, Ph. D., Regan Beckham, Ph.D., Randy Back, Ph. D., Premananda Indic, Ph. D.


Master's of Science in Electrical Engineering