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Exact solution for four-order acousto-optic Bragg diffraction with arbitrary initial conditions

机译：任意初始条件下四阶声光布拉格衍射的精确解

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摘要

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.
机译：针对四阶声光（AO）布拉格衍射问题，开发了一种精确的解决方案，该问题具有与精确的布拉格角入射光兼容的任意初始条件。通过求解四阶微分方程获得的解被形式化为转换矩阵算子，该矩阵根据入口处的​​相同衍射光阶来预测AO单元出口处的衍射光阶。结果表明，转移矩阵是unit的，该this矩阵的条件足以保证能量守恒。分析解决方案与数值预测的比较验证了形式主义。尽管与获取解决方案的方法没有直接关系，但是发现从四阶AO微分矩阵算子生成的所有四个特征值都简单地用Euclid的Divine比例表示。

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