Frequency-resolved optical gating with electro-optic sampling

Abstract

Abstract.We have demonstrated a new pulse characterization technique, cross-correlation frequency-resolved optical gating with electro-optic sampling. Sub-single-cycle mid-infrared pulses were characterized with the absolute carrier-envelope phase values by using the method.Frequency-resolved optical gating (FROG) [1] is an important general technique to determine the intensity and phase evolution of an arbitrary ultrashort pulse. However, determination of its carrierenvelope phase (CEP) [2] was not possible with the method. On the other hand, electro-optic sampling (EOS) [3] is a method to obtain full information of the electric field including the absolute value of the CEP. Since the upper limit of the detectable frequency of the technique is the inverse of the pulse duration of the reference pulse, EOS has been used for characterization of the ultrashort pulses in rather low frequency region, specifically, from terahertz to mid-infrared region [4][5][6].In this contribution, we propose a new pulse characterization scheme which is a combination of FROG and EOS. The method enables us to characterize an ultrashort pulse with the information of the absolute CEP value by using a reference pulse whose pulse duration is much longer than the period of the carrier-wave of the target pulse.The time-averaged intensity of the delayed superposition of the fields of the reference pulse (E ref (t− τ)) and the difference frequency between the reference and test pulses (E test (t)) is written as follows,where denotes time average and α is a complex constant proportional to the nonlinear susceptibility of the difference frequency generation assumed as an instantaneous process. The first term is independent of the delay time. The second term is the intensity cross-correlation signal between the test pulse and the reference pulse. The spectrally resolved second term corresponds to a cross-correlation FROG signal (XFROG) [7]. The third term is the interference term, i.e., the EOS signal. If it is possible to assumeas a delta function, the term becomes E test (τ), which provides the complete information of the electric field of the test pulse. Otherwise, the term is spectrally filtered with the Fourier transform of I ref (t).If we simultaneously measure the XFROG and EOS signals, i.e., the second and the third terms in eq. (1), the absolute value of the CEP obtained with EOS can be used for determining the CEP of the characterized pulse with XFROG. Thus, this technique permits us to completely retrieve an electric field which has too high frequency components to detect with EOS. In other words, the technique dramatically relaxes the requirement of the reference pulse for the full characterization of the target electric field. This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Carrier-envelope phase of ultrashort pulses generated by optical rectification process

“…On the other hand, when ω 0 0, the real output field can be written as ω 0 E (t)E * (t) cos(ω 0 t + Δφ + π/2). In this case, the CEP of the field is Δφ + π/2, which means the relative phase between the two input pulses directly affect the CEP of the output pulse.To experimentally investigate the CEP variation, we have generated phase-stable mid-infrared (MIR) pulses by using four-wave mixing (ω 1 + ω 1 − ω 2 → ω 0 ) through filamentation [3] and characterized the pulse including CEP information by measuring FROG and electro-optic sampling [4]. Figure 1(a) and (b) shows waveforms and spectral phases of the MIR pulses at different relative phases of the input pulses, respectively.…”

“…To experimentally investigate the CEP variation, we have generated phase-stable mid-infrared (MIR) pulses by using four-wave mixing (ω 1 + ω 1 − ω 2 → ω 0 ) through filamentation [3] and characterized the pulse including CEP information by measuring FROG and electro-optic sampling [4]. Figure 1(a) and (b) shows waveforms and spectral phases of the MIR pulses at different relative phases of the input pulses, respectively.…”