It is shown analytically that gap solitons can occur in materials with χ⁽²⁾ susceptibility due to cascaded second-order nonlinearities. Families of bright and dard spatial gap solitons are described in the framework of asymptotic expansions that are valid, in particular, for nonzero phase mismatch between the first and second harmonics; effective coefficients of self- and cross-phase modulation are calculated.
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Yuri S. Kivshar (1995) studied this question.
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