FROG: Frequency Resolved Optical Gating

Ultrafast laser systems, which generate laser pulses with durations of approximately 10 picoseconds or less, have a large number of applications in biochemistry, chemistry, physics, and electrical engineering. Such systems may be used to explore kinetics in proteins or examine carrier relaxation in semiconductors. They are also used as an ultrafast probe in electronic circuits. By using ultrafast diagnostic systems, highly advanced semiconductors, electronic circuitry, and even biomedical products can be developed and tested for commercial applications. Unfortunately, such laser systems are difficult to develop and maintain because few diagnostics are available to characterize the ultrashort laser pulses.

Real ultrafast laser pulses exhibit temporal structure in their amplitude or phase. The most common structure is called chirp. Chirped pulses can be viewed as changing color, say from red at the beginning of a pulse to yellow at the end. This chirp is the result of a change in phase of the light during the pulse that can be induced by dispersion or nonlinear optical processes. Chirped pulses have been used to excite molecules more efficiently and to generate sculpted quantum states. Chirp also increases the length (duration) of a pulse. Ultrafast laser systems require a diagnostic tool that can measure both the intensity (or amplitude) and the phase of an an optical pulse.

Frequency-resolved optical gating, or FROG, characterizes ultrashort laser pulses by interacting one or more pulses in a nonlinear medium. One pulse forms a "gate" that lets a time slice of the other pulse pass to a spectrometer. This signal pulse is spectrally resolved and recorded as a function of the delay between the input pulse and the gate. This record is called a spectrogram or FROG trace. The spectrogram is a plot of signal intensity vs. frequency and time which contains all of the information about the laser pulse. In the chirp example given above, the spectrogram would show that the pulse was red at early times, changing to orange in the middle and yellow at the end of the pulse. The target information, the temporal and spectral profile of the input pulse (intensity and phase), can be obtained from the FROG trace using two-dimensional phase retrieval methods.

Fast analysis of FROG spectrograms

Using a proprietary algorithm, the new VideoFROG software system can perform the phase retrieval in real time. When running on a PIII-based personal computer, update rates of 20 frames per second have been obtained. Now you can tweak up your laser system systems while watching the phase, intensity, and duration of the pulses displayed on a computer screen. The ultrafast oscilloscope has arrived.

resolution) because of the iterative nature of the phase retrieval calculation. Thus, FROG's usefulness as a real-time diagnostic for ultrashort laser pulses depends on the speed and robustness of the phase retrieval algorithm used.

At Mesa Photonics, we use a new inversion algorithm, developed by the founder at Southwest Sciences, called the Principal Component Generalized Projections Algorithm (PCGPA), that is very fast and easy to implement for some common FROG geometries. By combining PCGPA with data acquisition in a multishot second harmonic generation (SHG) FROG device, we have developed a femtosecond oscilloscope that demonstrates real-time pulse measurement, displaying the intensity and phase of the extracted pulse at rates up to 20 Hz. This technology forms the basis for the VideoFROG system.

The following references describe, in detail, the PCGP algorithm and its application to real-time ultrafast pulse measurement:

• "Simultaneous measurement of two ultrashort laser pulses from a single spectrogram in a single shot," D. J. Kane, G. Rodriguez, A. J. Taylor, and T. S. Clement, Journal of the Optical Society of America B, vol. 14, pp. 935-943 (1997). This paper describes the derivation of the PCGP algorithm, discusses generating error bars for FROG inversions, and discusses limitations of blind-FROG retrievals.
• "Real-Time Measurement of Ultrashort Laser Pulses Using Principal Component Generalized Projections," D. J. Kane, IEEE Journal of Selected Topics in Quantum Electronics, vol. 4, pp. 278-284 (1998). This paper derives the fast version of the PCGP algorithm and applies it to the measurement of ultrashort laser pulses in real-time.

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