Coherent control of second harmonic generation using spectrally phase coded femtosecond waveforms

We report the demonstration of coherent control of second harmonic generation (SHG) with over three orders of magnitude contrast in the SHG yield. Under conditions of large group-velocity mismatch and narrow phase matching bandwidth, we show that SHG can serve (in the perturbative limit) as a nonlinear optical but classical analogue for quantum mechanical two-photon transitions in atomic media, with advantages in efficiency and ease of implementation. Our coherent control scheme results in a spectral phase correlator for ultrashort pulse waveforms, which may have applications in novel high-bandwidth optical communication schemes. We demonstrate a set of different waveforms with similar strong control yields by introducing families of binary phase codes taken from communication theory into the coherent control process. The response to these waveforms under certain nonideal situations is also studied.