Theory of noncollinear frequency doubling of transform limited pulses in non-steady-state regime

Noncollinear second-harmonic generation from two ultrashort pulses intersecting in a nonlinear medium is studied in spectral and time domains. We derive analytical expressions for the second-harmonic (SH) amplitude in crystals of finite thickness neglecting diffraction. The contribution from characteristics of the fundamental radiation and interaction geometry to the process is analyzed. In addition, refined phase-matching conditions are obtained. We find that the spectral bandwidth is determined by the intersection angle and can be enlarged. The SH pulse duration can be optimized by varying the fundamental beam size and the intersection angle. It is found that the SH beam excited by a Gaussian fundamental beam becomes elliptical. It is shown that the fundamental pulse duration can be readily characterized with single pulses by means of measuring the ellipticity of the SH beam profile. The approach developed can potentially be used to calculate parametric interactions of fundamental pulses with an arbitrary spectrum.