Self-referenced measurement of the complete electric field of ultrashort pulses Pablo Gabolde and Rick Trebino

Pablo.Gabolde@physics.gatech.edu

This page is a summary of a paper we published in the online journal Optics Express: P. Gabolde and R. Trebino, Self-referenced measurement of the complete electric field of ultrashort pulses, Opt. Express 12, 4423-4428 (2004). Optics Express articles are available at no cost to the reader: download a PDF copy of our paper at http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4423.

Introduction

Techniques to measure femtosecond (10^-15 s) laser pulses have dramatically improved over the last decade. Obtaining the intensity and phase of a the electric field of a femtosecond laser pulse is now a routine experiment in most optics laboratories. However, these measurements usually yield the intensity and phase as a function of time (or frequency) only. The variation of the electric field with the spatial coordinates is often limited to the appreciation of the quality of the spatial profile of the beam, performed as an independent measurement.

Although this approach works well for clean pulses, it fails to detect spatiotemporal couplings such as spatial chirp and pulse-front tilt. Higher-order spatiotemporal distortions are similarly ignored. To overcome these limitations, we have developed a method to measure the intensity and phase of the electric field E(x,y,t) of a femtosecond laser pulse, both in space and time. This measurement is performed at a particular location z = z₀ on the optical axis. Numerical back-propagation of this field is possible, allowing our method to effectively measure the four-dimensional complex field E(x,y,z, t).

Our device relies on the combination of digital holography and frequency-resolved optical gating (FROG). It is self-referenced, which means that no additional pre-characterized pulse is required in order to measure an unknown pulse.

Method

We obtain the electric field E(x,y,t) of a femtosecond pulse by measuring the intensity and phase of its different frequency components. Each component is obtained by passing the pulse through a tunable band-pass filter, so that its spatial amplitude (beam profile) and phase (wavefront) can be simultaneously reconstructed using digital holography. We use an off-axis geometry where two beams cross at an angle α (see Fig. 1). The resulting interferogram, recorded by a CCD camera, is called a digital hologram and well-established algorithms are used to reconstruct the spatial amplitude and phase of the selected frequency component.

Fig. 1 Schematic of the experiment: (a) 4-prism second-order spectral phase control; (b) 2-prism spatial chirp control; M, mirror; BS, beam-splitter; TF, tunable band-pass filter; P, pinhole; FM, flip-mirror to perform the FROG measurement.

Several digital holograms are recorded and analyzed in this fashion as the band-pass filter is tuned to the different frequencies present in the beam. Then, an additional measurement is performed with a GRENOUILLE on a small spatial portion of the beam to obtain the spectral phase, so that the phase of the different frequency components can be adjusted. Finally, an inverse Fourier transform is applied to yield the electric field in the time domain, E(x,y,t).

Results

The amount of information thus obtained is sufficient to completely characterize the intensity and phase of the electric field E(x,y,t). We have successfully applied this technique to pulses suffering from spatial chirp and pulse-front tilt, two common spatiotemporal distortions. On Fig. 2 we represent the intensity and the instantaneous optical frequency (derived from the phase) of a pulse exhibiting temporal chirp, spatial chirp, and pulse-front tilt, in the format of a movie. Quite intuitively, the coordinates x and y of the movie correspond to the physical coordinates x and y of the pulse, and the time evolution of the movie corresponds to the time evolution of the pulse. Brightness represents the intensity of the electric field, while color represents the instantaneous optical frequency.

Fig 2. (AVI movie, 3.1 MB) Time-resolved intensity-and-phase measurement of the electric field of an ultrashort pulse. Brightness represents the intensity (dark is zero), and color the instantaneous wavelength (blue is 775 nm, red is 797 nm). To help visualize pulse-front tilt, a contour plot of the intensity has been superimposed (dotted white lines). Note also the presence of spatial chirp and temporal chirp.