Achromatic phase matching for second harmonic generation of femtosecond pulses

A scheme is proposed by which the phase matching bandwidth can be increased by adjusting higher-order terms in frequency shift in the phase-matching condition. This is achieved by introducing a spectral angular dispersion so that the different spectral components propagate at their phase-matching angles. This is equivalent to canceling the group velocity mismatch. The equations describing the requirements on the angular dispersion are discussed and applied to the particular case of type I phase matching. A possible experimental setup is shown that would meet all the conditions required