We summarize the problem of measuring an ultrashort laser pulse and describe in detail a technique that completely characterizes a pulse in time: frequency-resolved optical gating. Emphasis is placed on the choice of experimental beam geometry and the implementation of the iterative phase-retrieval algorithm that together yield an accurate measurement of the pulse time-dependent intensity and phase over a wide range of circumstances. We compare several commonly used beam geometries, displaying sample traces for each and showing where each is appropriate, and we give a detailed description of the pulse-retrieval algorithm for each of these cases.

We discuss the use of second-harmonic generation (SHG) as the nonlinearity in the technique of frequencyresolved optical gating (FROG) for measuring the full intensity and phase evolution of an arbitrary ultrashort pulse. FROG that uses a third-order nonlinearity in the polarization-gate geometry has proved extremely successful, and the algorithm required for extraction of the intensity and the phase from the experimental data is quite robust. However, for pulse intensities less than-1 MW, third-order nonlinearities generate insufficient signal strength, and therefore SHG FROG appears necessary. We discuss the theoretical, algorithmic, and experimental considerations of SHG FROG in detail. SHG FROG has an ambiguity in the direction of time, and its traces are somewhat unintuitive. Also, previously published algorithms are generally ineffective at extracting the intensity and the phase of an arbitrary laser pulse from the SHG FROG trace. We present an improved pulse-retrieval algorithm, based on the method of generalized projections, that is far superior to the previously published algorithms, although it is still not so robust as the polarization-gate algorithm. We discuss experimental sources of error such as pump depletion and group-velocity mismatch. We also present several experimental examples of pulses measured with SHG FROG and show that the derived intensities and phases are in agreement with more conventional diagnostic techniques, and we demonstrate the highdynamic-range capability of SHG FROG. We conclude that, despite the above drawbacks, SHG FROG should be useful in measuring low-energy pulses.

Two-photon absorption can place a fundamental limitation on waveguide all-optical switching devices. We have derived a general criterion to describe this limitation that must be satisfied by all materials. As a specific example, we have experimentally evaluated this criterion for a lead-glass fiber.

We show that frequency-resolved optical gating combined with spectral interferometry yields an extremely sensitive and general method for temporal characterization of nearly arbitrarily weak ultrashort pulses even when the reference pulses is not transform limited. We experimentally demonstrate measurement of the full time-dependent intensity and phase of a train of pulses with an average energy of 42 zeptojoules (42 x 10(-21) J), or less than one photon per pulse.

We use the algorithmic method of generalized projections (GP's) to retrieve the intensity and phase of an ultrashort laser pulse from the experimental trace in frequency-resolved optical gating (FROG). Using simulations, we show that the use of GP's improves significantly the convergence properties of the algorithm over the basic FROG algorithm. In experimental measurements, the GP-based algorithm achieves significantly lower errors than previous algorithms. The use of GP's also permits the inclusion of an arbitrary material response function in the FROG problem.

We recently introduced frequency-resolved optical gating (FROG), a technique for measuring the intensity and phase of an individual, arbitrary, ultrashort laser pulse. FROG can use almost any instantaneous optical nonlinearity, with the most common geometries being polarization gate, self-diffraction, and secondharmonic generation. The experimentally generated FROG trace is intuitive, visually appealing, and can yield quantitative information about the pulse parameters (such as temporal and spectral width and chirp). However, the qualitative and the quantitative features of the FROG trace depend strongly on the geometry used. We compare the FROG traces for several common ultrashort pulses for these three common geometries and, where possible, develop scaling rules that allow one to obtain quantitative information about the pulse directly from the experimental FROG trace. We illuminate the important features of the various FROG traces for transform-limited, linearly chirped, self-phase modulated, and nonlinearly chirped pulses, pulses with simultaneous linear chirp and self-phase modulation, and pulses with simultaneous linear chirp and cubic phase distortion, as well as double pulses, pulses with phase jumps, and pulses with complex intensity and phase substructure.

We report full characterization of the intensity and phase of 10-fs optical pulses using second-harmonic-generation frequency-resolved-optical-gating (SHG FROG). We summarize the subtleties in such measurements, compare these measurements with predicted pulse shapes, and describe the implications of these measurements for the creation of even shorter pulses. We also discuss the problem of validating these measurements. Previous measurements of such short pulses using techniques such as autocorrelation have been difficult to validate because at best incomplete information is obtained and internal self-consistency checks are lacking. FROG measurements of these pulses, in contrast, can be validated, for several reasons. First, the complete pulse-shape information provided by FROG allows significantly better comparison of experimental data with theoretical models than do measurements of the autocorrelation trace of a pulse. Second, there exist internal self-consistency checks in FROG that are not present in other pulse-measurement techniques. Indeed, we show how to correct a FROG trace with systematic error using one of these checks.

We explore several practical experimental issues in measuring ultrashort laser pulses using the technique of frequency-resolved optical gating (FROG). We present a simple method for checking the consistency of experimentally measured FROG data with the independently measured spectrum and autocorrelation of the pulse. This method is a powerful way of discovering systematic errors in FROG experiments. We show how to determine the optimum sampling rate for FROG and show that this satisfies the Nyquist criterion for the laser pulse. We explore the low-and high-power limits to FROG and determine that femtqjoule operation should be possible, while the effects of self-phase imodulation limit the highest signal efficiency in FROG to 1%. We also show quantitatively that the temporal blurring due to a finite-thickness medium in single-shot geometries does not strongly limit the FROG technique. We explore the limiting time-bandwidth values that can be represented on a FROG trace of a given size. Finally, we report on a new measure of the FROG error that improves convergence in the presence of noise.