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Practical formula for the evaluation of high-order multiphoton absorption in thin nonlinear media

We present an analytical formula for the fast and accurate evaluation of nonlinear absorption in materials exhibiting an admixture of different multiphoton processes. This approach is specifically addressed for its use in thin films when the slowly varying envelope approximation applies. The contribution of absorptions of distinct order is conveniently averaged in order to use well-known expressions for a single multiphoton process. In the latter case, therefore, our simple expression is reduced toward the exact solution.