Frequency-resolved Optical Gating

There are different versions of FROG, which rely on different nonlinear gating mechanisms, generate different kinds of FROG traces (thus requiring different phase retrieval algorithms), and have different strengths and weaknesses:

• Polarization-gated FROG (PG FROG) is the conceptually simplest FROG variant. Here, the gate pulse, polarized under 45° relative to the probe pulse, rotates the polarization of the latter when overlapping it in a χ⁽³⁾ medium (e.g. fused silica), and thus leads to transmission of the probe through a polarizer. As always with FROG, the transmitted probe signal is analyzed with a spectrometer. Advantages of PG FROG are easy alignment, the absence of ambiguities in the retrieval, and the generation of fairly intuitive FROG traces. A problem is that a polarizer with very high extinction ratio is required.
• In self-diffraction FROG (SD FROG), two beams overlapping in a χ⁽³⁾ medium generate a nonlinear refractive index grating, which diffracts both beams into new beams, one of which is used for detection. As no polarizers are required, SD FROG can be applied in various spectral regions, e.g. in the deep UV region. However, relatively high pulse energies are required.
• Transient-grating FROG (TG FROG) also uses a nonlinear refractive index grating, but uses a third pulse with variable delay as the probe which is diffracted at the grating generated by the other two beams. For various reasons, it allows for a much higher detection sensitivity than SD FROG.
• Second-harmonic FROG (SHG FROG) is the most popular FROG variant. It is based on a χ⁽²⁾ nonlinear crystal and can thus reach a much higher sensitivity than is possible with all χ⁽³⁾ versions of FROG. Phase-matching issues have to be carefully treated to avoid distortions for short pulses. There is an ambiguity concerning the direction of time, which can be removed e.g. by performing an additional measurement with some glass piece in the beam path.
• Interferometric FROG (IFROG) [12] uses a collinear geometry, avoiding a loss of temporal resolution via geometric effects (finite beam angles) in the characterization of few-cycle pulses.
• Cross-correlation FROG (XFROG) [7] uses an additional reference pulse, which does not need to be spectrally overlapping with the pulse under investigation. The recorded signal is obtained by sum or difference frequency generation of the two pulses. This method can be very sensitive, and can be applied in different spectral regions.

Beyond these traditional FROG measurement methods, refined versions of FROG have been developed, which can be applied even to very short pulses (with angle dithering of the crystal to remove strong effects of group velocity mismatch in the nonlinear crystal) or to fairly long pulses (where a high spectrometer resolution is required). A particularly compact setup is achieved with the GRENOUILLE geometry [9], which has no moving parts and even allows the measurement of additional features such as spatial chirps. A waveguide as the nonlinear component allows detection at ultralow power levels, and polarization scrambling makes possible polarization-independent measurements, which facilitate e.g. the delivery of pulses via fibers [13].

A possible alternative to frequency-resolved optical gating is spectral phase interferometry for direct electric-field reconstruction (SPIDER), as explained in the article on spectral phase interferometry.

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[3]	FROG tutorial of Rick Trebino's group at the Georgia Institute of Technology, http://www.frog.gatech.edu/tutorial.html
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[9]	P. O'Shea et al., “Highly simplified device for ultrashort-pulse measurement”, Opt. Lett. 26 (12), 932 (2001), doi:10.1364/OL.26.000932
[10]	J. Zhang et al., “Measurement of the intensity and phase of attojoule femtosecond light pulses using Optical-Parametric-Amplification Cross-Correlation Frequency-Resolved Optical Gating”, Opt. Express 11 (6), 601 (2003), doi:10.1364/OE.11.000601
[11]	S. Akturk et al., “Extremely simple device for measuring 20-fs pulses”, Opt. Lett. 29 (9), 1025 (2004), doi:10.1364/OL.29.001025
[12]	G. Stibenz and G. Steinmeyer, “Interferometric frequency-resolved optical gating”, Opt. Express 13 (7), 2617 (2005), doi:10.1364/OPEX.13.002617
[13]	H. Miao et al., “Polarization-insensitive ultralow-power second-harmonic generation frequency-resolved optical gating”, Opt. Lett. 32 (7), 874 (2007), doi:10.1364/OL.32.000874
[14]	X. Liu et al., “Numerical simulations of ultrasimple ultrashort laser-pulse measurement”, Opt. Express 15 (8), 4585 (2007), doi:10.1364/OE.15.004585
[15]	D. Lee et al., “Experimentally simple, extremely broadband transient-grating frequency-resolved-optical gating arrangement”, Opt. Express 15 (2), 760 (2007), doi:10.1364/OE.15.000760
[16]	J. Gagnon et al., “The accurate FROG characterization of attosecond pulses from streaking measurements”, Appl. Phys. B 92, 25 (2008), doi:10.1007/s00340-008-3063-x
[17]	R. Trebino, Frequency-Resolved Optical Gating: the Measurement of Ultrashort Laser Pulses, Kluwer, Boston (2002)

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