Frequency-resolved optical gating

Frequency-resolved optical gating (FROG) is a general method for measuring the spectral phase of ultrashort laser pulses, which range from subfemtosecond to about a nanosecond in length. Invented in 1991 by Rick Trebino and Daniel J. Kane, FROG was the first technique to solve this problem, which is difficult because, ordinarily, to measure an event in time, a shorter event is required with which to measure it. For example, to measure a soap bubble popping requires a strobe light with a shorter duration to freeze the action. Because ultrashort laser pulses are the shortest events ever created, before FROG, it was thought by many that their complete measurement in time was not possible. FROG, however, solved the problem by measuring an 'auto-spectrogram' of the pulse, in which the pulse gates itself in a nonlinear-optical medium and the resulting gated piece of the pulse is then spectrally resolved as a function of the delay between the two pulses. Retrieval of the pulse from its FROG trace is accomplished by using a two-dimensional phase-retrieval algorithm. Frequency-resolved optical gating (FROG) is a general method for measuring the spectral phase of ultrashort laser pulses, which range from subfemtosecond to about a nanosecond in length. Invented in 1991 by Rick Trebino and Daniel J. Kane, FROG was the first technique to solve this problem, which is difficult because, ordinarily, to measure an event in time, a shorter event is required with which to measure it. For example, to measure a soap bubble popping requires a strobe light with a shorter duration to freeze the action. Because ultrashort laser pulses are the shortest events ever created, before FROG, it was thought by many that their complete measurement in time was not possible. FROG, however, solved the problem by measuring an 'auto-spectrogram' of the pulse, in which the pulse gates itself in a nonlinear-optical medium and the resulting gated piece of the pulse is then spectrally resolved as a function of the delay between the two pulses. Retrieval of the pulse from its FROG trace is accomplished by using a two-dimensional phase-retrieval algorithm. FROG is currently the standard technique for measuring ultrashort laser pulses, and also popular, replacing an older method called autocorrelation, which only gave a rough estimate for the pulse length. FROG is simply a spectrally resolved autocorrelation, which allows the use of a phase-retrieval algorithm to retrieve the precise pulse intensity and phase vs. time. It can measure both very simple and very complex ultrashort laser pulses, and it has measured the most complex pulse ever measured without the use of a reference pulse. Simple versions of FROG exist (with the acronym, GRENOUILLE, the French word for FROG), utilizing only a few easily aligned optical components. Both FROG and GRENOUILLE are in common use in research and industrial labs around the world. 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 ω {displaystyle omega } and delay τ {displaystyle au } . 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 E sig ( t , τ ) {displaystyle E_{ ext{sig}}(t, au )} depends on the original pulse, E ( t ) {displaystyle E(t)} , and the nonlinear process used, which can almost always be expressed as E gate ( t − τ ) {displaystyle E_{ ext{gate}}(t- au )} , such that E sig ( t , τ ) = E ( t ) E gate ( t − τ ) {displaystyle E_{ ext{sig}}(t, au )=E(t)E_{ ext{gate}}(t- au )} . The most common nonlinearity is second harmonic generation, where E gate ( t − τ ) = E ( t − τ ) {displaystyle E_{ ext{gate}}(t- au )=E(t- au )} . 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 E gate ( t − τ ) {displaystyle E_{ ext{gate}}(t- au )} .