Erik Zeek

Cross-correlation frequency resolved optical gating analysis of broadband continuum generation in photonic crystal fiber: simulations and experiments

Numerical simulations are used to study the temporal and spectral characteristics of broadband supercontinua generated in photonic crystal fiber. In particular, the simulations are used to follow the evolution with propagation distance of the temporal intensity, the spectrum, and the cross-correlation frequency resolved optical gating (XFROG) trace. The simulations allow several important physical processes responsible for supercontinuum generation to be identified and, moreover, illustrate how the XFROG trace provides an intuitive means of interpreting correlated temporal and spectral features of the supercontinuum. Good qualitative agreement with preliminary XFROG measurements is observed.

Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum

Cross-correlation frequency-resolved optical gating with an angle-dithered nonlinear-optical crystal permits measurement of the intensity and the phase of the ultrabroadband (as much as 1200 nm wide) continuum generated from microstructure optical fiber. Retrieval revealed fine-scale structure in the continuum spectrum. Simulations and single-shot spectrum measurements confirmed that the fine structure does exist on a single-shot basis but washes out when many shots are averaged.

Pulse-front tilt caused by spatial and temporal chirp

Pulse-front tilt in ultrashort laser pulses is usually considered equivalent to angular dispersion. We prove, however, that the combination of spatial and temporal chirp also produces pulse-front tilt. We verify this experimentally using a GRENOUILLE.

Relative-phase ambiguities in measurements of ultrashort pulses with well-separated multiple frequency components

Ultrashort-pulse characterization techniques, such as the numerous variants of frequency-resolved optical gating (FROG) and spectral phase interferometry for direct electric-field reconstruction, fail to fully determine the relative phases of well-separated frequency components. If well-separated frequency components are also well separated in time, the cross-correlation variants (e.g., XFROG) succeed, but only if short, well-characterized gate pulses are used.

Measurement of the intensity and phase of attojoule femtosecond light pulses using Optical-Parametric-Amplification Cross-Correlation Frequency-Resolved Optical Gating

We use the combination of ultrafast gating and high parametric gain available with Difference-Frequency Generation (DFG) and Optical Parametric Amplification (OPA) to achieve the complete measurement of ultraweak ultrashort light pulses. Specifically, spectrally resolving such an amplified gated pulse vs. relative delay yields the complete pulse intensity and phase vs. time. This technique is a variation of Cross-correlation Frequency-Resolved Optical Gating (XFROG), and using it, we measure the intensity and phase of a train of attenuated white light continuum containing only a few attojoules per pulse. Unlike interferometric methods, this method can measure pulses with poor spatial coherence and random absolute phase, such as fluorescence.

Simulations of frequency-resolved optical gating for measuring very complex pulses

Frequency-resolved optical gating (FROG) and its variations are the only techniques available for measuring complex pulses without a well-characterized reference pulse. We study the performance of the FROG generalized-projections algorithm for retrieving the intensity and phase of very complex ultrashort laser pulses [with time-bandwidth products (TBPs) of up to 100] in the presence of noise. We compare the performance of three versions of FROG: second-harmonic-generation (SHG) FROG, polarization-gate (PG) FROG, and cross-correlation FROG (XFROG), the last of which requires a well-characterized reference pulse. We found that the XFROG algorithm converged in all cases on the first initial guess. The PG FROG algorithm converged for all moderately complex pulses, for 99% of the pulses we tried, and for more than 95% of even the most complex pulses (TBP~100). The SHG FROG algorithm converged for 95% of the pulses we tried and for over 80% of even the most complex pulses. We found no additional ambiguities in any of these techniques.

Determining error bars in measurements of ultrashort laser pulses

We present a simple and automatic method for determining the uncertainty in the retrieved intensity and phase versus time (and frequency) due to noise in a frequency-resolved optical-gating trace, independent of noise source. It uses the “bootstrap” statistical method and also yields an automated method for phase blanking (omitting the phase when the intensity is too low to determine it).

Measuring very complex ultrashort pulses using Frequency-Resolved Optical Gating (FROG)

For very complex pulses (TBP ~ 100), the XFROG, PG FROG, and SHG FROG pulse-retrieval algorithms converged for 100%, 99%, and 80%, respectively, of the pulses tried in our simulations, which included noise.

Frequency-resolved optical gating: the state of the art

Summary form only given. Frequency-Resolved Optical Gating (FROG) can completely measure ultrashort laser pulses in almost every situation. We have recently introduced a remarkably simple SHG FROG device that overcomes essentially all of the alignment difficulties of pulse-measurement devices. First, we replace the usual beam splitter, delay line, and beam combining optics with a single element, a Fresnel biprism. Second, we use a thick SHG crystal, which not only gives considerably more signal, but also simultaneously replaces the spectrometer. The resulting device, which we call GRating-Eliminated No-nonsense Observation of Ultrafast Incident Laser Light E-fields (GRENOUILLE), has zero sensitive alignment degrees of freedom and hence is extremely simple to align.

Including the nonlinear medium's dispersion in frequency-resolved optical gating

When we measure something, we unavoidably change it, and ultrashort laser pulse measurement is a perfect example. When we measure a pulse, the measurement itself affects the pulses shape. All ultrashort pulse measurement techniques use a nonlinear medium, and this mediums dispersion changes the shape of the pulse as it propagates. For many years, pulse measurers worried obsessively about group-velocity mismatch (GVM), which limited crystal thickness to as little as 5 microns. New frequency-resolved-optical-gating (FROG) variations, such as GRENOUILLE and crystal-angle dithering, either take advantage of GVM effects or avoid them completely, allowing the use of a nonlinear medium more than an order of magnitude thicker than that allowed by GVM considerations. Because nonlinear-optical efficiency scales with thickness, these techniques are considerably more sensitive. On the other hand, the use of such thick crystals allows a usually smaller dispersion effect, group-velocity dispersion (GVD), formerly negligible in all cases, to potentially yield pulse distortions. Fortunately, as we show here, in FROG, we can take advantage of our knowledge of the dispersion and the generality and versatility of the FROG algorithm to precisely remove these adverse effects in angle-dithered FROG and GRENOUILLE devices. This will allow these convenient techniques to measure ever shorter and ever weaker pulses.