Relative-phase ambiguities in measurements of ultrashort pulses with well-separated multiple frequency components (original) (raw)
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Journal of The Optical Society of America A-optics Image Science and Vision, 1993
We recently introduced a new technique, frequency-resolved optical gating (FROG), for directly determining the full intensity I(t) and phase p(t) of a single femtosecond pulse. By using almost any instantaneous nonlinearoptical 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. Gate pulse, E(t-c) Signal pse , o Rejeclef o (45-degee polariation)
Optics Letters, 2003
We describe a method of characterizing ultrashort optical pulses that is based on the technique of spectral phase interferometry for direct electric-field reconstruction and is capable of simultaneously measuring the amplitude and the phase of the electric field of a sub-10-fs pulse at kilohertz acquisition rates on a single-shot basis. Use of this technique results in a dramatic increase (.503) in acquisition rate compared with that of existing diagnostics for full E-field characterization and opens the door to a range of new experiments in which shot-to-shot phase and amplitude f luctuations are studied at kilohertz rates.
Optics Letters, 1993
We introduce a new technique, frequency-resolved optical gating, for measuring the intensity I(t) and the phase 0(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 -0(t).
Measuring ultrashort pulses in the single-cycle regime using frequency-resolved optical gating
Journal of the Optical Society of America B, 2008
We present a single-shot frequency-resolved optical gating setup for measurements of ultrashort pulse intensity and phase down to single-optical-cycle durations. Several issues stemming from short durations and extreme bandwidths are addressed. We show that after using spectral response correction, the regular FROG algorithm yields reliable pulse retrievals. We demonstrate measurement of pulse widths down to 4.9 fs.
2006
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.
Analysis of a method of phase measurement of ultrashort pulses in the frequency domain
IEEE Journal of Quantum Electronics, 1991
We perform a detailed analysis of our method of phase measurement of ultrashort light pulses; we show that the output pulse of a zero dispersion compressor with a mask consisting of a narrow slit is a wide pulse delayed an amount equal to the phase derivative of the field spectrum with respect to frequency. We also state criteria to know whether the approximations are valid. The method is not affected by artifacts coming from diffraction effects in the slit or by the fact that only correlations are measured. The effects of the errors in positioning the elements are considered and minimized in the construction of the experimental apparatus. We describe a novel technique for measurement of the derivative of the cross correlation, and we employ it to locate the delayed output pulse.
Complete retrieval of the field of ultrashort optical pulses using the angle-frequency spectrum
Optics Letters, 2008
We propose an experimental technique that allows for a complete characterization of the amplitude and phase of optical pulses in space and time. By the combination of a spatially resolved spectral measurement in the near and far fields and a frequency-resolved optical gating measurement, the electric field of the pulse is obtained through a fast, error-reduction algorithm.
Recent progress toward real-time measurement of ultrashort laser pulses
IEEE Journal of Quantum Electronics, 1999
Frequency-resolved optical gating (FROG) is a technique that produces a spectrogram of an ultrashort laser pulse optically. While a great deal of information about the pulse can be gleaned from its FROG trace, often it is desirable to obtain all of the pulse information immediately, in real time. Quantitative information about the pulse is not readily obtainable from its spectrogram without the use of a two-dimensional phase retrieval algorithm. While current algorithms are quite robust, retrieval of all the pulse information can be slow. In this paper, I describe a recently developed FROG trace inversion algorithm called Principal Component Generalized Projects that is fast, robust, and can invert FROG traces in real time. A femtosecond oscilloscope based on second-harmonic generation FROG is also described that uses this new algorithm to rapidly (up to 2.3 Hz) and continuously display the intensity and phase of ultrashort laser pulses. Index Terms-Phase retrieval, pulse measurement, ultrafast lasers, ultrashort pulses.
Quantitative investigation of optical phase-measuring techniques for ultrashort pulse lasers
Journal of the Optical Society of America B, 1996
We have performed a quantitative investigation into the capabilities and the limitations of two phasemeasuring techniques: second-harmonic-generation frequency-resolved optical gating and direct optical spectral phase measurement. In particular, we have studied the reproducibility and the accuracy of these techniques in measuring the frequency-dependent phase of ultrashort pulses with varying amounts of cubic and quadratic phase. We find that both of these techniques are accurate to within 5% in measuring phase distortions in optical pulses.