The time-reversed second-harmonic generation in one-dimensional nonlinear photonic crystals has been theoretically studied without the undepleted pump approximation. A simple criterion has been deduced which determines the energy flow. Based on it, two kinds of structures with different symmetries are presented to realize the nonlinear time reversal effect. A completely reciprocal nonlinear response is also found in the same process. Furthermore, a multi-section-cascaded structure is proposed to realize the nonlinear time reversal at any given position.
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