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Direct measurement of spectral phase for ultrashort laser pulses

Vadim V. Lozovoy, Bingwei Xu, Yves Coello, and Marcos Dantus

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Abstract

We present an intuitive pulse characterization method that provides an accurate and direct measurement of the spectral phase of ultrashort laser pulses. The method requires the successive imposition of a set of quadratic spectral phase functions on the pulses while recording the corresponding nonlinear spectra. The second-derivative of the unknown spectral phase can be directly visualized and extracted from the experimental 2D contour plot, without any inversion algorithm or mathematical manipulation.

©2008 Optical Society of America

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Figures (4)
Fig. 1.
Fig. 1. Principle of the method. (a) The unknown ϕ″(ω) function is probed using a set of reference linear chirps represented by the horizontal grid. (b) The maximum SHG intensity for every frequency indicates that the corresponding reference chirp value compensates the unknown function at the position of the maximum. (c) A two-dimensional contour plot mapping the intensity of the SHG as a function of chirp and frequency directly reveals the unknown ϕ″(ω).

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Fig. 2.
Fig. 2. Experimental measurement of a cubic phase obtained by a single chirp scan. The figure is a contour plot of the SHG spectra measured at each value of applied chirp. The feature revealed by the spectral maxima corresponds to the second derivative of the cubic phase introduced. As expected, the second derivative is linear with frequency. The inset shows a magnified portion of the trace.

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Fig. 3.
Fig. 3. Spectral phase measurement. The introduced (red) and measured (green) phase functions agree without adjusting parameter. (a) Shows the second derivative of the spectral phases. (b) Shows the spectral phases. The spectrum of the pulses is also shown (dashed).

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Fig. 4.
Fig. 4. Sinusoidal spectral phase measurement. (a) Shows the experimental trace. The measured second-derivative of the phase can be directly visualized from the feature corresponding to the spectral maxima. (b) Shows the measured second-derivative after a chirp scan (green) and after one measurement-compensation iteration (black). The red curve corresponds to the introduced sinusoidal function.

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Equations (1)

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ϕ ″ ( ω ) − f ″ ( ω ) = 0
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