Breakdown of the Slowly Varying Amplitude Approximation: Generation of Backward Traveling Second Harmonic Light

By numerically solving the nonlinear field equations, we simulate second-harmonic generation by laser pulses within a nonlinear medium without making the usual slowly-varying-amplitude approximation, an approximation which may fail when laser pulses of moderate intensity or ultrashort duration are used to drive a nonlinear process. Under these conditions we show that a backward-traveling, second-harmonic wave is created, and that the magnitude of this wave is indicative of the breakdown of the slowly-varying-amplitude approximation. Conditions necessary for experimental detection of this wave are discussed. © 2003 Optical Society of America OCIS codes: 190.0190, 190.4160, 350.5500.