Complete retrieval of the field of ultrashort optical pulses using the angle-frequency spectrum

Abstract

We propose an experimental technique that allows for a complete characterization of the amplitude and phase of optical pulses in space and time. By the combination of a spatially resolved spectral measurement in the near and far fields and a frequency-resolved optical gating measurement, the electric field of the pulse is obtained through a fast, error-reduction algorithm.Ultrashort laser pulses are widely used in many laboratories and are routinely adopted for many applications. In past decades, various techniques were developed to measure the electric field of optical pulses as a function of time or frequency. The different approaches belong to two main categories: spectrographic and interferometric techniques. The most known examples of these approaches are frequencyresolved optical gating (FROG) [1] and spectral interferometry for direct electric-field reconstruction (SPIDER), respectively [2]. The first is based on the measurement of the temporally resolved spectrum (spectrogram). An iterative inversion algorithm is applied to the measured spectrogram in order to retrieve the electric field. The second approach consists of the measurement of the interference between a pair of spectrally sheared replicas of the input pulse. A direct inversion of the measured interferogram yields the electric field of the pulse.These techniques have an analog in the spatial coordinate, and are often applied by assuming that temporal and spatial features of pulses are independent. This assumption is no longer valid for situations involving beam focusing [3], pulse shaping using zero-dispersion line [4] and compression [5], or nonlinear interactions (see, e.g., [6,7]) leading to space-time coupling effects. In the past few years some techniques have been proposed to characterize the amplitude and phase profile of pulses both in space and time. Among these, the most interesting are variants of FROG and SPIDER techniques with extension to the spatial dimension characterization. Indeed, in [8] a combination of FROG and digital holography is proposed to characterize the complete (3D) electric field of a train of laser pulses possessing at least one point in space where all the frequencies are present. This method is based on the use of a tunable filter or of a series of bandpass filters. A variation of this technique is proposed in [9], which has the advantage of being a single-shot measurement. The same authors recently proposed a technique that is based on crossed-beam spectral interferometry [10]. By exploiting the coherence between a reference pulse and the one under investigation, this allows for a characterization of the field both in time and space with high spectral resolution, but requires a highresolution scan along the spatial dimension.On the other hand, the extension to the spatial dimension of the SPIDER technique has been proposed in [11][12][13]. Thanks to a direct inversion algorithm, the technique is capable of a fast reconstruction of the electric field as a function of one transverse spatial coordinate and time...

Spatiotemporal Amplitude and Phase Retrieval of Bessel-X pulses using a Hartmann-Shack Sensor

“…pulses whose temporal profile depends on the transverse spatial position. Among these, Spatial Encoded Arrangement for Temporal Analysis by Dispersing a Pair of Light E-fields (SEA TADPOLE) [4,5], Spatially and Temporally Resolved Intensity and Phase Evaluation Device: Full Information from a Single Hologram (STRIPED FISH) [6] and Spa- * Electronic address: daniele.faccio@uninsubria.it tial Encoded Arrangement SPIDER (SEA SPIDER) [7] and, more recently, complete retrieval of the optical amplitude and phase using the (k ⊥ , ω) spectrum (CROAK) [8].…”

Spatio-temporal couplings in ultrashort laser pulses

“…One technique, called CROAK [91], is based on a pair of spatially resolved spectral measurements in both the nearand far-fields and another FROG measurement of the temporal field. There is no analytical formula for the retrieval of the spatio-temporal field.…”

Complete characterization of a spatiotemporally complex pulse by an improved single-frame pulse-measurement technique

“…Beginning with methods that measure the temporal profile using a measured trace that is only one-dimensional (such as spectral interferometry), it is straightforward to extend the measurement using a standard two-dimensional camera to also include one spatial domain, i.e., Ex; t or Ex; ω [26][27][28][29][30][31][32]. The resulting measurement, however, remains incomplete in space (either cropping or averaging over the missed spatial dimension), so assumptions must be made about the spatial homogeneity or cylindrical symmetry-which may not be valid in practice.…”