An exact solution to the four-order acousto-optic (AO) Bragg diffraction problem with arbitrary initial conditions compatible with exact Bragg angle incident light is developed. The solution, obtained by solving a 4th-order differential equation, is formalized into a transition matrix operator predicting diffracted light orders at the exit of the AO cell in terms of the same diffracted light orders at the entrance. It is shown that the transition matrix is unitary and that this unitary matrix condition is sufficient to guarantee energy conservation. A comparison of analytical solutions with numerical predictions validates the formalism. Although not directly related to the approach used to obtain the solution, it was discovered that all four generated eigenvalues from the four-order AO differential matrix operator are expressed simply in terms of Euclid’s Divine Proportion.
© 2009 Optical Society of America
Original Manuscript: August 13, 2008
Revised Manuscript: November 20, 2008
Manuscript Accepted: December 5, 2008
Published: January 26, 2009
Ron Pieper, Deborah Koslover, and Ting-Chung Poon, "Exact solution for four-order acousto-optic Bragg diffraction with arbitrary initial conditions," Appl. Opt. 48, C141-C150 (2009)