Algorithm for determining the spatio-temporal profile of an ultrashort pulse from an image of a self-referenced interferogram

Abstract

The present invention relates to an algorithm for determining and simulating the spatio-temporal intensity profile of an ultrashort pulse from an image of a self-referenced interferogram which makes it possible to calculate the electromagnetic field of this pulse in the spatio-temporal measurement domain with a very large measurement dynamic range, in particular for measurements of very high-power ultrashort laser pulses carried out by a spatially resolved spectral interferometry device. To this end, the invention relates to a signal processing algorithm comprising several steps making it possible to use detectors with a very large number of pixels while limiting the calculation time and the correction of defects in the measuring apparatus and its method. The determination of the spatial phase of the pulse contained in the interferogram is used to correct these defects.It applies in particular to measurements of ultra-short, ultra-powerful lasers obtained by frequency drift amplification to characterize their defects in temporal and spatio-temporal contrast.

Description

Title of the invention: Algorithm for determining the spatio-temporal profile of an ultrashort pulse from an image of a self-referenced interferogram

[0001] The present invention relates to an algorithm for determining and simulating the spatio-temporal intensity profile of an ultrashort pulse from an image of a self-referenced interferogram which makes it possible to calculate the electromagnetic field of this pulse in the spatio-temporal measurement domain. It applies in particular to ultrashort pulse measurements carried out by a spatially resolved spectral interferometry device. This method makes it possible to determine with great dynamics the key parameters of this type of pulse with very high precision.

[0002] Measurement methods are used to characterize ultrashort pulses, temporally to determine their duration and contrast, but also spatially to precisely determine the amount of energy contained, for example, in the focal spot used to generate secondary radiation. Among the methods used to measure the spatio-temporal profile, many are limited in dynamics.

[0003] A method used primarily for duration characterization exhibits significantly superior dynamic quality. This method, self-referenced spectral interferometry (SRSI), is described in the following documents: a. D. Kaplan, T. Oksenhendler, N. Forget, “Method and device for measuring the spectral phase or combined spectral and spatial phases of ultrashort light pulses”, FR2925956A1 b. T. Oksenhendler, “Self-referenced spectral interferometry theory”, arxiv 1204.4949, 2012.

[0004] This method has been improved to further increase its dynamics and to be able to exploit its capacity to measure spatio-temporal characteristics. These improvements have been described in the following document which describes a new method called SRSLETE and its device: has. T. Oksenhendler, P. Bizouard, O. Albert, S. Bock, U. Schramm, “High dynamic, high resolution and wide range single shot temporal draw contrast measurement”, Optics Express 2017.

[0005] This method makes it possible for the first time to characterize pulses with very high dynamics in a single acquisition. But inherent defects in the device and the method limit its dynamics and deteriorate its spatio-temporal measurement quality.

[0006] However, the determination of the spatio-temporal parameters is essential for determining the peak power and the temporal profile, particularly for ultrashort high-power lasers. Various state-of-the-art spatio-temporal measurement methods are described in the following document: has. SW Jolly, O. Gobert, F. Quéré, “Spatio-temporal characterization of ultrashort laser beams: a tutorial”, Journal of Optics 2020.

[0007] More generally, the ability to identify and analyze faults such as, for example, pre-pulses, post-pulses, a pedestal is essential both for the use and operation of these systems as they are and for their improvement.

[0008] The invention aims to enable such diagnostics by improving and expanding the parameters accessible by an SRSLETE measurement.

[0009] The SRSLETE measurement provides an image which is a spectral interferogram. This interferogram is the result of the spatio-spectral measurement of the spectrum of the interference between a replica of the pulse and a replica filtered by a degenerate third-order non-linear effect such as the generation of cross-polarized waves ("Cross Polarized Wave", XPW). However, to increase its time excursion and its dynamics, an angle is used between the two channels of the interferometer. This angle, as well as the aberration defects between the two channels but also of the spectrometer, deteriorates the result obtained both in dynamics and for its spatio-temporal profile.

[0010] The originality of the invention is to make it possible to determine with greater precision and dynamics the spatio-temporal intensity profile of the pulse but also other characteristics not measured until now.

[0011] To this end, the invention relates to a data processing algorithm for a single measurement on a single pulse, as well as accumulated measurements of several pulses or successive measurements of one or more pulses. After processing each measurement, the temporal dynamics is greatly improved. And, by repeating the measurements, the invention makes it possible to further improve the contrast but also to determine whether the observed contributions are coherent or incoherent, which constitutes key information for identifying their origin. Finally, the time-resolved spectral contents which are also accessible by this method also make it possible to determine the origin.

[0012] The invention has the following main advantages: a. It allows a very high dynamic time profile measurement on a single measurement of a pulse, on a maximum time excursion relative to the detector and the spectral width of the initial pulse, b. It allows a measurement of the spatio-temporal profile with a very high dynamic range of the ultimate performance of the pulse, c. It allows, with some measures, to differentiate between coherent and incoherent contributions, d. It allows to increase the measurement dynamics linearly with the number of measurements.

[0013] Other characteristics and advantages of the invention will appear more clearly in the description which follows and in the appended figures which represent: a. [Fig.l] is a schematic representation of a spatially resolved self-referenced spectral interferometry setup, b. [Fig.2] is a block diagram of a state-of-the-art iterative pulse recovery algorithm, c. [Fig.3] is the result of the measurement obtained by a device of [Fig.l] by the algorithm of [Fig.2], d. [Fig.4] is a functional diagram of the algorithm of the invention, e. [Fig.5] is the result of the measurement obtained by a device of [Fig.l] by the algorithm of [Fig.4], f. [Fig.6] is a functional diagram of the algorithm of the invention resulting in the spatio-temporal profile, g. [Fig.7] is the result of the measurement obtained by a device of [Fig.l] by the algorithm of [Fig.6].

[0014] In the example shown in [Fig.l] [Fig.l], one or more pulse separation devices, designated by S, are included which, from an input pulse, produce two output pulses. There are several devices in the state of the art performing this function. For some of these devices the polarizations of the two output pulses are crossed. The arrangement also uses one or more pulse recombination devices, designated by R, producing from two input pulses, a single output pulse performing a summation of the two input pulses. Some techniques for producing the recombination devices include a selection of polarization of the input pulses.

[0015] In the schematic representation of [Fig.l], the incident pulse to be measured li is first separated into two pulses Is, Irp, of crossed polarizations, respectively s and r, by a device S. The r polarization pulse is designated as the primary reference pulse Irp, and the s polarization pulse as the signal pulse Is. The Irp pulse is then transferred to the input of a device for interaction with a nonlinear medium, DMNL, defined by a predominantly nonlinear third-order interaction producing collinear light with polarization perpendicular to the incident polarization. This type of mechanism is called collinear polarization rotation in French and is designated in the English literature as the XPW effect (cross-polarized wave). The interaction effects of an ultrashort pulse with an XPW effect material are described in the publication A. Jullien, O. Albert, G. Cheriaux, J. Etchepare, S. Kourtev, N. Minkovski and SM Saltiel "Nonlinear polarization rotation of elliptical light in cubic crystals, with application to cross-polarized wave generation", Journal of Optical Society of America B 22, 2635 (2005). The materials that can be used are, for example, fluorides of formula BaF2 and LiF. The DMNL device may include, in addition to the nonlinear material itself, optical focusing components so that the light intensity in the material is optimized for the nonlinear effect. The secondary reference pulse 1rs, leaving the DMNL device, is of s polarization. It is combined with the signal pulse Is, of polarization s, by a suitable recombination device R. A spectrometer type device SPEC measures the spectral intensity of the output pulse of the recombination device R.The optical paths in the signal path S=>R and the reference path S=>DMNL=>R are adjusted so that the two linearly mixed signals Is, 1rs are adequately time and angularly offset for the spatially resolved spectral interferometry measurement. If necessary, a person skilled in the art can add a section introducing a mechanically adjustable delay in order to adjust this time offset. Similarly, a light intensity attenuation device can possibly be added to the signal path to obtain an adequate intensity ratio between the two recombined pulses Is, 1rs, in order to optimize the spectral interferometry measurement. These additions, which are not essential to understanding the operating principle, have not been included in the diagram of [Fig. 1]. Of course, several simultaneous measurement paths could be set up using combinations of several S, R and SPEC elements.

[0016] In the case of measuring an ultrashort laser pulse, we seek to determine the spatio-temporal profile of the pulse. Generally, to fully exploit the extreme power of these pulses, they are compressed as best as possible both temporally with spectral phase corrections and spatially by correcting the spatial phase. Despite the corrections, temporal, spatial and mixing spatio-temporal defects remain. To determine them, we wish to carry out a measurement on the entire pulse both spatially and spectrally. The device of [Fig.l], for which the pulse is focused in the slit of a SPEC imaging spectrometer, then measures the entire integrated profile according to the focused dimension and resolved spatially and spectrally for the other dimensions. The image obtained at the output is then given by the equation: Signal (2, x) = Af | Eo (2, x, y) + ENL (kx, y | dÿ where y is the transverse dimension to the beam and in the plane of the diagram, x the transverse dimension perpendicular, the optical wavelength, A a constant, and Eo represents the spatio-spectral electric field of the initial pulse represented in the form of complex amplitude whose square modulus is the intensity, ENL that of the intensity of the secondary pulse obtained by the non-linear effect of the DMNL device, r the delay and a the angular spatial frequency (a=2irkx where kx is the spatial frequency) introduced between the two channels, co=2jrc / X the angular frequency. This signal is an interferogram which includes fringes which allow the use of a data processing algorithm from which we find the spatio-temporal intensity 70 ( 2, x, y ) = JJ ( 2, x, y ) 12dy This algorithm is illustrated in [Fig.2].

[0017] [Fig.2] illustrates an algorithm which takes as input the spatio-spectral image 10 called spatio-spectral interferogram which is the result of the assembly of [Fig.l]. The image is, in a first step 20, resampled by an interpolation according to the spectral dimension to be according to the spectral dimension on a perfectly regular sampling in optical frequency. This step is very important to guarantee the quality of the signal in the time domain obtained by Fourier transform. The resampled image 30 is therefore transformed, by step 40, according to a Fourier transform according to the two dimensions. The result is a complex signal in the domains of the spatial frequencies kx, and time t (50). Using the amplitude of this signal, the DC components (of spatial frequencies close to 0) and AC (of spatial frequencies close to kx = a / 2ir) are selected and filtered (60).From these two signals 70 are extracted amplitude and phase curves by selecting the spatial frequency line passing through the maximum for each of the two components (80). From these signals (90) is applied the algorithm for spectral phase recovery and reconstruction of the temporal signal described in T. Oksenhendler, “Self-referenced spectral interferometry theory”, arxiv 1204.4949, 2012. The signal obtained is characterized by a very large measurement dynamic range as shown in T. Oksenhendler, P. Bizouard, O. Albert, S. Bock, U. Schramm, “High dynamic, high resolution and wide range single shot temporal puise contrast measurement”, Optics Express 2017. .

[0018] [Fig.3] shows a typical result that can be obtained by this device and this algorithm with a state-of-the-art camera of more than 15 million pixels using for example a Panasonic MN34230 detector or more recent one like a SONY IMX455 detector. The dynamic range of this measurement obtained in a single acquisition from a single pulse is very large, of the order of 109, much higher than other state-of-the-art methods measuring in a single acquisition.

[0019] The present invention proposes a modified algorithm which is illustrated by [Fig.4]. This algorithm brings several innovations to the previous one of [Fig.2]. The first innovation is to limit the number of points during processing and especially during resampling which consumes a lot of power and computing time. This aspect is all the more important since the measurement dynamics is directly proportional to the number of pixels of the detector used. Thus this device must use the latest detectors of 100 million pixels or more to increase its measurement dynamics. But such a number of pixels makes resampling slow. From the image of the spatio-spectral interferogram A10, the new algorithm thus performs a first Fourier transform only according to the spatial dimension (A20). The signal obtained A30 is filtered while retaining only M lines (A40) for each component of the signal.On a typical signal, M is of the order of 100 while the detector has several thousand lines. A gain greater than 10 is easily possible from this step. The reduced signal A50 is then transformed by inverse Fourier transform (A60) to be again in the spatial domain (A70). It is then that the resampling (A80) is carried out by interpolation to be according to the spectral dimension on a perfectly regular sampling in optical frequency (A90). We then apply a Fourier transform according to the two dimensions (A100) to obtain the signal in the spatial frequency and time domains (A1 10). This signal is then filtered around the selected DC and AC peaks and recentered to obtain two signals centered in the spatial frequency domain. During this step (A120), one of the defects of the device which reduces its dynamics, the inclination of the wavefront linked to the angle used a is removed.On the signal obtained A130, the peak of the AC signal is determined. The following processing (A140) is then to subtract the phase errors of this peak for all other times on this AC signal. This operation corresponds to determining the temporal profile of the main pulse perfectly corrected. It corresponds to the optimal operating mode of a pulsed laser on which the spatial profile of the pulse is corrected by a loop. This operation (A140) also corrects the defects of the measuring device in particular the differences in divergences and other aberrations between the two measuring channels. From these DC and AC signals (A 150) are extracted amplitude and phase curves by selecting the spatial frequency line passing through the maximum for each of the two components (A160). From this signal (A170) is applied the algorithm for recovering the spectral phase and the reconstruction of the temporal signal described in T.Oksenhendler, “Self-referenced spectral interferometry theory”, arxiv 1204.4949, 2012. The obtained signal is characterized by a very large measurement dynamic as shown in T. Oksenhendler, P. Bizouard, O. Albert, S. Bock, U. Schramm, . “High dynamic, high resolution and wide range single shot temporal tap contrast measurement”, Optics Express 2017.

[0020] [Fig.5] shows the results obtained from the same spatio-spectral interferogram image by the two algorithms. The innovative algorithm allows both to gain in calculation speed by reducing the resampling part and especially in dynamics in a very significant way.

[0021] Another form of the algorithm illustrated by [Fig.6] allows to find as a result the spatio-temporal intensity of the initial pulse. Indeed, the algorithm is identical to the previous one of [Fig.4] up to the B150 signals. From these signals, by deconvolving the AC signal by iteration by the signal obtained by calculating the XPW signal by the cube of the intensity, we find the B170 signal which corresponds to the spatio-temporal intensity of the focused pulse (or in the far field). This processing allows to eliminate the defects of the device but also to choose certain defects of the pulse itself, it allows to determine what would be the optimal profile of the pulse after correction of the spatial aberrations.

[0022] [Fig.7] shows the result of this measurement obtained in a single acquisition which makes it possible to obtain the spatio-temporal intensity with an extreme dynamic range never reached greater than 1010. The dotted line is that of the profile presented in the CIO figure which makes it possible to appreciate the measurement dynamic range. For the first time this measurement makes it possible to see defects in ultrafast lasers such as defects linked to stretchers and compressors and thus to better understand and improve these laser systems and their applications. Generalization of the invention

[0023] The algorithm presented for temporal characterization can be used for spatial characterization by reversing the roles of the spatial and temporal domains. Access to such significant measurement dynamics is, however, less sought after at present for the spatial domain because the contrasts there are currently much less significant.

[0024] Thus this algorithm can be applied to all types of self-referenced interferometry or interferometry referenced with respect to a suitable reference signal, i.e. covering at least the same spectral band and whose spectral phase content is either known or having a known non-linear filtering relationship with the original pulse.

Claims

Claims

1. Data processing and electromagnetic simulation algorithm, for determining the spatio-temporal optical intensity profile of an ultrashort pulse from a spatio-spectral self-referenced interferogram image (10) characterized in that it comprises at least: a. A Fourier transformation according to a first chosen dimension (A20), b. A determination of the AC components (centered around the spectral frequency corresponding to the first-order phase derivative used to obtain the interferogram) and DC components (centered around the spectral frequencies around 0) according to the spectral frequencies of this dimension, c. A filtering of these AC and DC components in the spectral frequency domain of this dimension (A40), d. A resampling according to the dimension of the other dimension to obtain a regular sampling in spectral frequency of this dimension (A80), e. A Fourier transform along the two dimensions (A100), f. Determination of DC and AC peaks in the spectral frequency domains, their filtering and refocusing in the spectral frequency domain of the first dimension (A120), g. The determination for the AC peak of the phase defects to be corrected for the spectral frequencies according to this same dimension (A 131), h. Subtraction of these defects for all spectral frequencies of the second dimension (A140), i. Obtaining two images (A150) of amplitude and phase, one for the DC peak, the other for the AC peak corrected for phase defects.

2. Algorithm according to claim 1 characterized in that it comprises: a. As the first dimension, the spatial dimension according to the height of the slit of the imaging spectrometer used to obtain the spatio-spectral interferogram image, b. As a second dimension the optical wavelength.

3. Algorithm according to claim 2 characterized in that it comprises: a. Determination of the amplitude and phase profiles for the two pulses constituting the initial interferogram from the images (A150) of the AC and DC peaks in amplitude and phase.

4. Algorithm according to claim 2 characterized in that it comprises: a. Determination of the spatio-temporal images (B 170) of amplitude and phase for the pulse to be measured and corresponding to the interferogram, from the images (B 150) of the AC and DC peaks in amplitude and phase.

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