Abstract
A visible colored crescent with a bandwidth broader than 220 nm is observed experimentally by loosely focused femtosecond pulses in a bulk quadratic nonlinear crystal (\ensuremath{\beta}-BBO crystal) at certain incident angles. Through the analysis based on a simple collinear phase-matching model, we suggest that the colored crescent might be the coexistence of spontaneous parametric down-conversions (SPDCs) in the infrared range and the corresponding efficient second-order harmonic generations (SHGs) that occur in a wide spectrum. We further provide a possible mechanism for the SHG process in which the phase-mismatching angles of the frequency doubling of SPDCs in \ensuremath{\beta}-BBO crystal are assumed to be compensated by the strong diffraction effect during the self-focusing process of the generated intense SPDC signals.
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