Rick Trebino

Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating

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.

Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating

The frequency-resolved optical gating (FROG) technique for characterizing and displaying arbitrary femtosecond pulses is presented. The method is simple, general, broadband, and does not require a reference pulse. Using virtually any instantaneous nonlinear-optical effect, FROG involves measuring the spectrum of the signal pulse as a function of the delay between two input pulses. The resulting trace of intensity versus frequency and delay is related to the pulses spectrogram a visually intuitive transform containing time and frequency information. It is proven using phase retrieval concepts that the FROG trace yields the full intensity I(t) and phase phi (t) of an arbitrary ultrashort pulse with no physically significant ambiguities. FROG appears to have temporal resolution limited only by the response of the nonlinear medium. The method is demonstrated by using self-diffraction through the electronic Kerr effect in BK-7 glass and 620-nm, linearly chirped, approximately 200-fs pulses of a few microjoules. >

Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating

We recently introduced a new technique, frequency-resolved optical gating (FROG), for directly determining the full intensity I(t) and phase φ(t) of a single femtosecond pulse. By using almost any instantaneous nonlinear-optical interaction of two replicas of the ultrashort pulse to be measured, FROG involves measuring the spectrum of the signal pulse as a function of the delay between the replicas. The resulting trace of intensity versus frequency and delay yields an intuitive display of the pulse that is similar to the pulse spectrogram, except that the gate is a function of the pulse to be measured. The problem of inverting the FROG trace to obtain the pulse intensity and phase can also be considered a complex two-dimensional phase-retrieval problem. As a result, the FROG trace yields, in principle, an essentially unique pulse intensity and phase. We show that this is also the case in practice. We present an iterative-Fourier-transform algorithm for inverting the FROG trace. The algorithm is unusual in its use of a novel constraint: the mathematical form of the signal field. Without the use of a support constraint, the algorithm performs quite well in practice, even for pulses with serious phase distortions and for experimental data with noise, although it occasionally stagnates when pulses with large intensity fluctuations are used.

Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating

We introduce a new technique, frequency-resolved optical gating, for measuring the intensity I(t) and the phase ø(t) of an individual arbitrary ultrashort pulse. Using an instantaneous nonlinear-optical interaction of two variably delayed replicas of the pulse, frequency-resolved optical gating involves measuring the spectrum of the signal pulse versus relative delay. The resulting trace, a spectrogram, yields an intuitive full-information display of the pulse. Inversion of this trace to obtain the pulse intensity and phase is equivalent to the well-known two-dimensional phase-retrieval problem and thus yields essentially unambiguous results for I(t) and ø(t).

Frequency-resolved optical gating with the use of second-harmonic generation

We discuss the use of second-harmonic generation (SHG) as the nonlinearity in the technique of frequency-resolved 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 high-dynamic-range capability of SHG FROG. We conclude that, despite the above drawbacks, SHG FROG should be useful in measuring low-energy pulses.

Highly simplified device for ultrashort-pulse measurement.

We show that a frequency-resolved optical gating device using (1) a thick nonlinear crystal to replace the usual thin crystal and spectrometer and (2) a Fresnel biprism to replace the beam splitter and delay line yields a remarkably simple single-shot ultrashort-pulse intensity-and-phase measurement device with no sensitive alignment parameters and significantly greater sensitivity.

Cross-correlation frequency resolved optical gating analysis of broadband continuum generation in photonic crystal fiber: simulations and experiments

Numerical simulations are used to study the temporal and spectral characteristics of broadband supercontinua generated in photonic crystal fiber. In particular, the simulations are used to follow the evolution with propagation distance of the temporal intensity, the spectrum, and the cross-correlation frequency resolved optical gating (XFROG) trace. The simulations allow several important physical processes responsible for supercontinuum generation to be identified and, moreover, illustrate how the XFROG trace provides an intuitive means of interpreting correlated temporal and spectral features of the supercontinuum. Good qualitative agreement with preliminary XFROG measurements is observed.

Measurement of the intensity and phase of ultraweak, ultrashort laser pulses

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.

Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum

Cross-correlation frequency-resolved optical gating with an angle-dithered nonlinear-optical crystal permits measurement of the intensity and the phase of the ultrabroadband (as much as 1200 nm wide) continuum generated from microstructure optical fiber. Retrieval revealed fine-scale structure in the continuum spectrum. Simulations and single-shot spectrum measurements confirmed that the fine structure does exist on a single-shot basis but washes out when many shots are averaged.

Comparison of ultrashort-pulse frequency-resolved-optical-gating traces for three common beam geometries

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 second-harmonic 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.