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Metrology of few-cycle NIR femtosecond pulses using SEA-SPIDER.

Contents

Introduction

Fig. 1: SEA-SPIDER concept

Ultrashort optical pulses can be used in time-resolved experiments to capture extremely fast events, analogous to flash photography. However, detailed knowledge of the pulse is required for accurate measurements. Unfortunately, a direct measurement of the temporal structure of the pulse is currently not possible because the pulse duration (<<10-13s) is at least an order of magnitude shorter than current detector response times (>10-12s). Such a problem can be overcome by measuring the pulse in the spectral domain (the amplitude of each frequency and their relative phase, i.e. the 'arrival time' of each frequency component). Current detectors are 'slow', measuring the average power of the field, thus it is not possible to measure the phase directly.

The most widely used characterisation methods include frequency resolved optical gating (FROG [1]) and spectral phase interferometry for direct electric-field reconstruction (SPIDER [2]). Although these techniques have been proven characterisation methods in the sub-10-fs range, their application can become very challenging or even impossible under certain conditions. These include the cases when: (1) the spectrum is ultra-broadband (e.g. over an octave), (2) the spectrum is highly modulated, (3) the pulse exhibits space-time coupling (STC), (4) real-time measurement is required for use in a phase compensation feedback system and (5) it is desirable to have single shot acquisition. At Oxford, we have developed a variant of SPIDER which uses a spatially encoded arrangement (SEA-SPIDER [3,4]) which has been optimised for sub-10-fs pulses in the near infrared (NIR) and can overcome the aforementioned issues.

Fig. 2: SEA-SPIDER interferograms. (a) FTL pulse, (b) Positive dispersion, (c) Negative dispersion. Dashed line represents fringe contour = phase gradient.

The difficulties in measuring sub-10-fs pulses lie in the method of encoding the pulse-shape information in conventional FROG and SPIDER. FROG requires a 2D data set that encodes a 1D field. It can operate near the spectral sampling limit (given by the Whittaker-Shannon theorem) and uses an iterative deconvolution algorithm to reconstruct the field. However, a FROG apparatus is usually configured to spectrally and temporally oversample the pulse so that it can measure complex pulse shapes with little adjustment. The size of data and reconstruction time increases nonlinear with the pulse complexity and is not suited for real-time measurement. For an octave spanning spectrum, a non collinear geometry is required, which causes temporal smearing of the FROG trace due to the thickness of the pulse beams. Single shot acquisition can only be accomplished in the absence of STC because the spatial dimension of the beam is used to encode temporal information, the resulting trace can become ambiguous in the presence of STC. Conventional SPIDER records a 1D data set and uses a direct, linear reconstruction algorithm which makes it ideally suited for real-time, single shot acquisition and phase compensation feedback. However, the phase is encoded in the spacing of spectral fringes and thus SPIDER oversamples the spectrum significantly. If the spectral amplitude has regions of low spectral intensity or high structure, then a very high spectral resolution is required in order to resolve the fringes if phase errors are to be avoided. However it is possible to measure STC and perform single shot acquisition simultaneously with rapid reconstruction.


SEA-SPIDER basics

Fig. 1 shows the basic idea for SEA-SPIDER. The pulse to be measured (test pulse) upconverts with two spatially titled, temporally delayed and highly chirped pulses in a type II nonlinear crystal. During the interaction time, this test pulse will see a different quasi-monochromatic frequency from each of the chirped pulses. Thus after the upconversion, two signal pulses are produced which are spectrally shifted replicas of the test-pulse. These two signal pulses are then imaged onto the entrance slit of a 2D imaging spectrometer such that interference between them causes fringes in the spatial domain. The interference pattern can be represented by equation 1. Provided the pulse has no spectral phase, the distance between each fringe would be Kx, where K is the difference in the mean wavevector of each pulse and x is the spatial position. However, if there is any phase on the test-pulse, then the shear Ω between the two signal pulses modulates the fringe pattern and thus allows the test-pulse phase to be recovered. The fringes are induced in the spatial domain, thus the spectrum can be sampled at the Whittaker-Shannon limit, thus a low resolution spectrometer can be used to record ultrabroadband pulses.


Fig. 3: Accuracy of SEA-SPIDER. The test pulse was measured before and after traversing 1cm fused silica. The difference in the phase was compared to the theoretical phase of fused silica.

Experimental Results

Figure 2 to the right shows three experimental SEA-SPIDER interferograms of a sub-10-fs pulse. From equation 1, it is evident that SEA-SPIDER traces can show some intuitive behaviour which allows manual phase compensation / optimisation without the need to reconstruct. This intuitive nature arises from the fact that the contour of the fringes directly map the gradient of the spectral phase, which itself is equal to the dispersion. For example, figure a is the result for a Fourier transform limited (FTL) pulse (i.e. zero phase) - the fringes appear completely horizontal. Figures b and c correspond to positive and negative group velocity dispersion (GVD) respectively. This is shown by the positive or negative slope in the fringe pattern (as shown by the dashed lines.

Figure 3 compares the phase of a glass block as measured by the SEA-SPIDER with the theoretical phase calculated using the Sellmeier coefficients for that glass. The agreement is excellent over the whole spectrum of the pulse, even in regions of low spectral intensity. The phase is recovered over the whole extend of the spectrum, even in the presence of noise on the interferogram. Due to the large spectrum required to support few-cycle pulses, any slight phase can result in significantly stretching the pulse, thus it is critical that the phase is measured over the whole spectral bandwidth with very high accuracy.


Experimental outlook

As SEA-SPIDER measures the spectrum and phase at every position in a slice through the beam, it is possible to measure STC directly (although a complete space-time measurement requires a further measurement). The next step is to use the device on the output of the hollow-core fibre system to measure frequency dependant mode size (FDMS) and spatial chirp. Due to the sensitivity of the device, it should be possible to measure the pulse phase while performing experiments (e.g. high harmonic generation) simultaneously and possibly with single shot acqusition as well.

References

[1] Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating Rick Trebino and Daniel J. Kane, J. Opt. Soc. Am. A - Optics Image Science and Vision, 10 (5), 1101, (1993)

[2] Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulsesC. Iaconis and A. Walmsley, Opt. Lett., 23 (10), 792-794, (1998)

[3] Interferometric technique for measuring broadband ultrashort pulses at the sampling limit Ellen M. Kosik, Aleksander S. Radunsky, Ian A. Walmsley, and Christophe Dorrer, Opt. Lett., 30 (3), 326-328, (2005)

[4] Sub-10-fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric-field reconstruction Adam S. Wyatt, Ian A. Walmsley, Gero Stibenz and Günter Steinmeyer, submitted Opt. Lett. January 2006