I described in the prologue how an octave spanning femtosecond laser can generate any electromagnetic frequency through wave-mixing or multiphotonic processes. The scientific applications of such a universal light source depend on one’s ability to control the wave-mixing or multiphotonic process. That control is achieved through spectral phase manipulation with a pulse shaper. Pulse shaping was in the minds of scientists well before femtosecond lasers were demonstrated. Initial research involved simple pulse compression. During those early days, nonlinear optical processes, such as second harmonic generation, were being studied for fundamental curiosity and also because they could be considered for optical switching. Therefore, scientists were exploring how pulse shaping affected second harmonic generation. One of the interesting findings was that a highly dispersed pulse could be made to generate much higher second harmonic signal by blocking some portions of the spectrum using a pulse shaper. This finding seemed to defy intuition because it appeared that attenuating the input light by blocking some of its spectrum increased the intensity of the output second harmonic signal (Figure 15.1). The explanation for this finding was that some frequencies seemed to be interfering with others and that blocking the interfering frequencies caused the observed higher second harmonic signal. In the example included here (Figure 15.1), Gaussian pulses (dashed line) stretched 50 times their original duration by a quadratic phase (black). The peak intensity of the pulse and SHG intensity induced by this pulse drops by a factor of 50 times because of the longer pulse duration. When the spectral components that are out of phase are blocked by setting their amplitude to zero, the pulses are compressed and the SHG intensity recovers to about 15% that of transform-limited pulses. The lower row presents results for binary-phase compressed pulses, where the out-of-phase components are rephased by applying a pi step. This time, the pulse compression is much better and a peak intensity of ~0.4 is achieved. Notice the time profiles of the TL pulse (dashed) and the binary compressed pulses (red), which are very close to one another, with pulse and duration of the binary compressed pulse practically equal to the duration of the TL pulse. From these figures, we learn that phase compression is more efficient than amplitude modulation because one is able to turn destructive interference into constructive interference.