Two new transform-limited criteria and their applications in ultrafast optics and soliton systems

We define new parameters for the pulse width and chirp of an optical pulse and its second harmonic generation (SHG) and show how they may be used to test whether a pulse, of arbitrary profile, is transform-limited. Our new transform-limited criteria are based on the product of Laplacian pulse width and rms spectral width of either the pulse or its SHG. We derive a simple equation that may be used to check whether a measurement of pulse amplitude and phase profile is consistent with a measurement of the rms spectral width. We show how the Laplacian pulse width may be measured by autocorrelation and the rms chirp may be obtained from measurements of the Laplacian pulse width and rms spectral width. Our new parameters can lead to simple equations, which can be conveniently used to design devices and systems for ultrafast optics and soliton systems