Frequency-resolved Optical Gating - Basics - Theory

Theory

FROG and autocorrelation share the idea of combining a pulse with itself in a nonlinear medium. Since a nonlinear medium will only produce the desired signal when both pulses are present at the same time (i.e. “Optical Gating”), varying the delay between the pulse copies and measuring the signal at each delay gives a vague estimate of the pulse length. Autocorrelators measure a pulse by measuring the intensity of the nonlinear signal field. Estimating the pulse length requires assuming a pulse shape, and the phase of the pulse electric field cannot be measured at all. FROG extends this idea by measuring the spectrum of the signal at each delay (hence “Frequency Resolved”), instead of just the intensity. This measurement creates a spectrogram of the pulse, which can be used to determine the complex electric field as a function of time or frequency as long as the nonlinearity of the medium is known.

The FROG spectrogram (usually called a FROG trace) is a graph of intensity as a function of frequency and delay . The signal field from the nonlinear interaction is easier to express in the time domain, however, so the typical expression for the FROG trace includes a Fourier transform.

The nonlinear signal field depends on the original pulse, and the nonlinear process used, which can almost always be expressed as, such that . The most common nonlinearity is second harmonic generation, where . The expression for the trace in terms of the pulse field is then:

There are many possible variations on this basic setup. If a well-known reference pulse is available, then it may be used as a gating pulse instead of a copy of the unknown pulse. This is referred to as cross-correlation FROG or XFROG. In addition, other non-linear effects besides second harmonic generation may be used, such as third harmonic generation (THG) or polarization gating (PG). These changes will affect the expression for .