We present a high-spectral-resolution and experimentally simple version of spectral interferometry using optical fibers and crossed beams, which we call SEA TADPOLE. Rather than using collinear unknown and reference pulses separated in time to yield spectral fringes-and reduced spectral resolution-as in current versions, we use time-coincident pulses crossed at a small angle to generate spatial fringes. This allows the extraction of the spectral phase with the full spectrometer resolution, which allows the measurement of much longer and more complex pulses. In fact, SEA TADPOLE achieves spectral super-resolution, yielding the pulse spectrum with even better resolution. Avoiding collinear beams and using fiber coupling also vastly simplify alignment. We demonstrate SEA TADPOLE by measuring a chirped pulse, a double pulse separated by 14 ps, and a complex pulse comprising two trains of pulses with a time-bandwidth product of ~400.

We present a rigorous, but mathematically relatively simple and elegant, theory of first-order spatio-temporal distortions, that is, couplings between spatial (or spatial-frequency) and temporal (or frequency) coordinates, of Gaussian pulses and beams. These distortions include pulse-front tilt, spatial dispersion, angular dispersion, and a less well-known distortion that has been called "time vs. angle." We write pulses in four possible domains, xt, xomega, komega, and kt; and we identify the first-order couplings (distortions) in each domain. In addition to the above four "amplitude" couplings, we identify four new spatio-temporal "phase" couplings: "wave-front rotation," "wave-front-tilt dispersion," "angular temporal chirp," and "angular frequency chirp." While there are eight such couplings in all, only two independent couplings exist and are fundamental in each domain, and we derive simple expressions for each distortion in terms of the others. In addition, because the dimensions and magnitudes of these distortions are unintuitive, we provide normalized, dimensionless definitions for them, which range from -1 to 1. Finally, we discuss the definitions of such quantities as pulse length, bandwidth, angular divergence, and spot size in the presence of spatio-temporal distortions. We show that two separate definitions are required in each case, specifically, "local" and "global" quantities, which can differ significantly in the presence of spatio-temporal distortions.

We present the first technique for directly measuring (without assumptions) the spatio-temporal intensity and phase of a train of ultrashort pulses at and near a focus. Our method uses an experimentally simple and high-spectral resolution variant of spectral interferometry (SEA TADPOLE). To illustrate our technique, we measured the spatio-temporal electric field in and around the foci of several different types of lenses. To confirm our results, we also simulated these measurements by numerically propagating a pulse through each of the lenses used. From one set of measurements, we made a movie showing a focusing pulse with severe chromatic aberration.

We demonstrate an experimentally simple and high-spectral-resolution version of spectral interferometry (SEA TADPOLE) that can measure complicated pulses (in time) at video rates. Additionally, SEA TADPOLE can measure spatial information about a pulse, and it is the first technique that can directly measure the spatiotemporal electric field ͓E͑x , y , z , ͔͒ of a focusing ultrashort pulse. To illustrate and test SEA TADPOLE, we measured E͑͒ of a shaped pulse that had a time-bandwidth product of approximately 100. To demonstrate that SEA TADPOLE can measure focusing pulses, we measured E͑x , ͒ at and around the focus produced by a plano-convex lens. We also measured the focus of a beam that had angular dispersion present before the lens. We have found that SEA TADPOLE can achieve better spectral resolution than an equivalent spectrometer, and here we discuss this in detail, giving both experimental and simulated examples. We also discuss the angular acceptance and spatial resolution of SEA TADPOLE when measuring the spatiotemporal field of a focusing pulse.

We present a remarkably simple technique for measuring the full spatio-temporal electric field of a single ultrashort laser pulse. It involves capturing a large digital hologram containing multiple smaller holograms, each of which characterizes the spatial intensity and phase distributions of an individual frequency component of the pulse. From that single camera frame, we numerically reconstruct the complete electric field, E(x,y,t), using a direct algorithm. While holography requires a well-characterized reference pulse, this pulse can easily be generated from the pulse itself in most cases, so the technique is self-referencing. We experimentally demonstrate this technique using femtosecond pulses from a mode-locked Ti:Sapphire oscillator.