Full-field characterization of femtosecond pulses by ... - OSA Publishing

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OPTICS LETTERS / Vol. 24, No. 23 / December 1, 1999

Full-field characterization of femtosecond pulses by spectrum and cross-correlation measurements J. W. Nicholson, J. Jasapara, and W. Rudolph Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131

F. G. Omenetto and A. J. Taylor Los Alamos National Laboratory, MS K764, Los Alamos, New Mexico 87545 Received June 21, 1999 We present a practical and accurate technique for retrieving the amplitude and the phase of ultrashort pulses from a nonlinear (second-order) intensity cross correlation and the spectrum that overcomes shortcomings of previous attempts. We apply the algorithm to theoretical and experimental data and compare it with frequency-resolved optical gating.  1999 Optical Society of America OCIS codes: 320.7100, 320.7080, 320.5550.

Generation, handling, and many applications of ultrashort light pulses require the knowledge of both pulse amplitude and phase. Various methods to obtain this information have been developed and analyzed.1 – 5 As few-cycle optical pulses are becoming available, the dispersive properties of the nonlinear optical element used in correlators become critical. Care must be taken to include such effects in the retrieval procedure.6 – 8 That complicates successful reconstruction algorithms such as frequency-resolved optical gating (FROG).4 From an experimental point of view one of the simplest and most practical techniques for pulse retrieval is the measurement of the pulse spectrum and an intensity and (or) interferometric pulse correlation. In fact, one of the first attempts at amplitude and phase retrieval of femtosecond pulses was based on an interferometric cross correlation and spectrum.1 A straightforward field retrieval from the measurement of a linear and second-order interferometric autocorrelation was proposed in Ref. 2, which leaves unresolved only the twofold ambiguity that is due to the sign of chirp and pulse asymmetry. More recently, the pulse intensity was obtained by direct deconvolution of the intensity autocorrelation.9 However, the algorithm failed for certain types of pulse, and those authors suggested that it be used as a seed for a FROG retrieval algorithm. During preparation of the manuscript for this Letter two other groups of researchers reported intensity and phase retrieval from autocorrelation measurements.10,11 We use a second-order intensity cross correlation from an unbalanced Michelson interferometer together with the pulse spectrum to retrieve the complex pulse amplitude. For the cross-correlation measurement, multiphoton current detectors can be applied to overcome difficulties associated with the second-harmonic generation or the Kerr effect of short pulses. The calculation is based on a downhill simplex method12 and results in a robust algorithm that allows for the retrieval of complicated envelope and phase functions. The technique is applicable to both single-shot mea0146-9592/99/231774-03$15.00/0

surements of amplified pulses and analysis of pulses from low-power oscillators. The two data sets needed are the pulse spectrum and a nonlinear intensity cross correlation. The cross correlation is between the original pulse and its replica that has passed through a linear element with known dispersive properties, for example, a slab of fused silica in one arm of a Michelson interferometer. The unbalanced interferometer results in a cross correlation that is sensitive to the sign of the chirp and the asymmetry of the pulse envelope. For convenience a second-order nonlinear process is used for the cross correlation realized by a two-photon current detector.13 The spectral data can be obtained either from an optical multichannel analyzer or by recording of the linear correlation from the second arm of the interferometer. We dub this procedure PICASO: phase and intensity from cross correlation and spectrum only. We start the pulse retrieval by guessing a spectral phase Fini 共v兲. The retrieval speed, but not the results, depends on this initial guess. For most practical purposes the assumption of a quadratic term suff ices. The inverse Fourier transform F 21 of the square root of the measured spectral intensity S共v兲 times the assumed spectral phase function provides a temporal pro˜ 1 共t兲, file of the complex field amplitude A ˜ 1 共t兲 苷 F 21 A

Ωq

æ S共v兲 exp关iFini 共v兲兴 ,

(1)

and of the field that has passed through the dispersive ˜ 2 共t兲, element A ˜ 2 共t兲 苷 F 21 A

Ωq

æ S共v兲 exp关iFini 共v兲兴exp关2iC共v兲兴 . (2)

Here C共v兲 is the phase response of the dispersive element. From the two fields, R the second-order intensity ˜ 1 共t兲j2 jA ˜ 2 共t 2 t兲j2 dt can be cross correlation Ir 共t兲 苷 jA computed. The rms deviation between the normalized retrieved and the measured cross correlations, Ir 共t兲  1999 Optical Society of America

December 1, 1999 / Vol. 24, No. 23 / OPTICS LETTERS

and Im 共t兲, divided by the number of sample points N, provides a measure of the quality of the guess for the spectral phase: 8 91/2 N