EP2721385A1

EP2721385A1 - Device and method for characterizing a light beam

Info

Publication number: EP2721385A1
Application number: EP12731176.9A
Authority: EP
Inventors: Fabien Quere
Original assignee: Commissariat a lEnergie Atomique CEA; Commissariat a lEnergie Atomique et aux Energies Alternatives CEA
Current assignee: Commissariat a lEnergie Atomique et aux Energies Alternatives CEA
Priority date: 2011-06-14
Filing date: 2012-06-08
Publication date: 2014-04-23
Also published as: US20140098367A1; WO2012172463A1; FR2976663B1; FR2976663A1; US9243957B2

Abstract

Method of characterizing a light beam (FL) comprising the steps consisting in: a) disposing the input ends (EE1 - EE11) of N > 3 optical fibres (F01 - F011) on the path of said light beam, in such a way that a respective portion of said beam is coupled and propagates in each optical fibre and is emitted from its output end (ES1 - ES11) so as to form a respective secondary beam; b) introducing an angular spectral dispersion into said secondary beams by means of at least one dispersive element (RD); c) propagating the dispersed secondary beams in such a way that they overlap to form an interferogram; d) acquiring an image of said interferogram; and e) extracting from said image of said interferogram an item of information relating to the spatial variation of the phase of said light beam at a plurality of wavelengths. Device for the implementation of such a method.

Description

DEVICE AND METHOD FOR CHARACTERIZING A BEAM

LIGHT

The invention relates to a device and a method for characterizing a light beam, and in particular a laser beam. The device and the method of the invention make it possible in particular to determine the spatio-temporal properties of a light beam and in particular of a pulsed laser beam, comprising one or more laser pulses of picosecond or femtosecond duration. More generally, the device of the invention can be used to measure the spectral cross-density of a light beam, even a non-pulse beam.

The invention will be described more particularly in relation to its applications to the characterization of ultra-short laser pulses having spatio-temporal couplings, although these uses are not exclusive.

The term "ultra-short laser pulse" means a picosecond pulse (duration between 0.1 and 100 ps approximately) or femtosecond (duration less than or equal to 100 fs = 0.1 ps). The durations are halfway up the intensity profile. These pulses necessarily have a relatively wide spectral band, in a manner well known per se.

Ultra-short laser pulses have many scientific and technological applications; they can be amplified to energies of several joules and form beams ("pulse beams") whose diameter ranges from a few millimeters to several centimeters depending, in particular, their power.

In general, the temporal properties of the electromagnetic field of a pulse beam may vary spatially or, equivalently, the spatial properties may be time dependent. For example, the pulse duration may depend on the position (x, y) in the beam (hereinafter, unless otherwise indicated, we will always consider a beam propagating in a direction "z", the axes "x", "Y" and "z" forming a direct orthonormal mark).

When such a dependence exists, the field E (x, y, t) can not be put into the form E (x, y, t) = E _t (t) EEs (x, y), where E _t ( t) is a function of the time and E _E s (x, y) a function of space. It is said that the beam has a spatio-temporal coupling ("CST" or "STC" of the English "Space-Time Coupling").

The spatio-temporal couplings can lead in particular to a distortion of the intensity front of a pulse beam, illustrated with the aid of FIGS. 1A and 1B. The electromagnetic energy of an ultra-short pulse beam is, in the ideal case, distributed in a very thin disk (Figure 1A) of diameter D and thickness cT, where c is the speed of light and T the duration of the pulse; in the example of Figure 1A, D = 8 cm and cT = 10 μηι, which corresponds to a pulse duration of about 33 fs. In order to maximize the light intensity achieved in the home, which is generally desired, this disc must be as "flat" as possible. To characterize this spatial distribution of energy, we speak of the "intensity front" of the laser (not to be confused with the "wavefronts", which depend on the wavelength).

In practice, and particularly in the case of high-power lasers with a large beam diameter, the intensity fronts may not be flat, but distorted as illustrated in FIG. 1B. Consequently, the peak of the pulse may to be reached at different times in the different points of the section of the beam in the plane (x, y), and the pulse duration can also vary from one point to another.

Other types of spatio-temporal coupling are also possible, such as for example a rotation of the wave fronts in time. For a general discussion of the theory of spatio-temporal couplings one can refer to the article by S. Akturk et al. "The general theory of first-order spatio-temporal distortions of Gaussian pulses and beams", Optics Express Vol. 13, No. 21, pages 8642-8661.

Methods for measuring these couplings have been proposed, but they remain limited in their performances and complex to implement, which means that they are not widely used.

The "SPIDER-2D" technique comes from the SPIDER (Spectral Phase Interferometry for Direct Electric Field Reconstruction) method, ie phase spectral interferometry for the direct reconstruction of the electric field. , introduced in 1998 to measure the temporal structure of an ultra-short pulse at a point in space. It combines spectral shift interferometry (usual SPIDER technique) and spatial shift interferometry to reconstruct the spectral phase φ (χ, ν, ω) along a spatial direction (ω being the angular frequency, linked to the wavelength λ by the relation λ = 2πο / ω). In practice, this technique consists in acquiring an image of an interferogram on the sensor of a CCD camera; the dimensions of this image correspond on the one hand to the frequency ω, and on the other hand to a spatial coordinate. This spatial coordinate can be either the x coordinate or the y coordinate of the (x, y) plane perpendicular to the propagation direction of the beam.

This technique requires a complex assembly to produce several replicas of the initial beam and manipulate them using, among other things, a non-linear crystal. Therefore, its implementation is difficult and expensive. In addition, since one of the coordinates of the interferogram corresponds to a spatial coordinate transverse to the beam, this technique only allows the characterization of relatively small beams of smaller diameter than the CCD sensor of the camera (typically 1 cm or less). In the case of larger diameter beams (eg from a high power source), it is necessary to reduce their size by means of a telescope, which is likely to induce spatio-temporal couplings. parasites. Another disadvantage is that the principle of the technique makes it necessary to perform the measurement according to a single transverse spatial coordinate, x or y.

The so-called "STRIPED FISH" technique exploits a measure of the spatial interferences between the beam to be characterized and a so-called reference beam, for a set of frequencies in the spectrum of the beam to be characterized. The reference beam must have a spectrum that encompasses that of the beam to be characterized, and have a phase q> ₀ (x, y, co) known at all points and for all frequencies. The interferograms make it possible to compare, for a set of frequencies ω ,, the phase cp (x, y, (o) of the beam to be characterized, with that (po (x, y, co) of the reference beam, which is known. This technique is much simpler to implement than the SPIDER-2D, and a single measurement allows to characterize the beam in the two transverse directions x and y.But, the diameter of the beam must be small relative to the size of the CCD sensor used to acquire the interferogram images; this limitation of the beam size is even more restrictive than in the case of SPIDER-2D.

The closest state of the art is constituted by a third technique, called "SEA TADPOLE", which is described in US Pat. No. 7,817,282 and in Bowlan et al.'S article "Directly measuring the spatiotemporal electric field of focusing ultrashort". Optics Express, 10219 (2007). As illustrated in FIG. 2, this technique consists of collecting the light at different points of the beam to be characterized FL with a monomode fiber F1. This collection of light in the unknown beam can be done either at the focus of a focusing optic, or on an unfocused beam. An auxiliary beam FA, of spectral phase cp _a ux (a>), is injected into a second monomode fiber F2. The exit ends of the two fibers are placed next to each other; a convergent lens L1 deflects the beams leaving the fibers in such a manner that they overlap spatially, thereby producing spatial interferences which are resolved spectrally by means of an SPM spectrometer comprising a diffraction grating RD and a cylindrical lens L2 ( the reference FE identifies the entrance slot of the spectrometer, perpendicular to the dispersion direction of the latter). An interferogram S (co, X) is obtained, where X is the spatial coordinate normal to the dispersion direction of the spectrometer, an image of which is acquired by means of a CCD type sensor, identified by the reference Cl.

This interferogram can be used to determine the spectral phase difference between the pulses injected into the two fibers. The intensity S (o, X) measured on the CCD sensor of the spectrometer as a function of ω and X is given by:

S (J, X) = S _to {) + Si _nc ) + 2- / S {u) If _nc {u) cOs (2u S \ 6X C + 'inc {^) -

(1) where Saux and Sine are respectively the spectral intensities of the auxiliary pulses and to be characterized injected into the fibers, φ _3υ χ and q _mc their spectral phases at the fiber output, Θ is the half-angle between the beams, 6 = atan (d / (2L)), where d is the distance between the fibers and L the distance between exits fiber and detector. An example of an interferogram S (co, X) is shown in FIG. 3A.

The interference term of equation (1), which will be noted by ϋ (ω, Χ), contains information on the phase difference Δφ (ω) = φ _ίηο - _pales between the pulses that have been collected. by the two fibers. To extract this information, the procedure used consists of calculating the Fourier transform of this function with respect to the variable X (TF1 D: one-dimensional Fourier transform). As shown in FIG. 3B, this Fourier transform comprises three components in the (ω, k) plane. The central component, which includes only low frequencies, corresponds to the term Saux + Sinc of equation (1). The other two components correspond to the two complex exponentials of the following decomposition of the interference term:

with φ = 2cosin9-X / c + φίηο (ω) -φ _3υ χ (ω).

If only one of these components is selected, for example by multiplying the Fourier transform by a suitable filter, in particular a super-Gaussian filter, and performing an inverse Fourier transform, the following function is obtained:

whose phase φ is:

φ = 2cosin6 X / c + φίηο (ω) -

The first term (p _g eo (<") (" geometric ") is simply induced by the angle used to generate spatial fringes. represents the difference in spectral phase between the beams at the output of the two fibers, ie between a point of the beam to be characterized (corresponding to the input end of the first fiber) and the auxiliary beam. We proceed as follows:

The interferogram S (œ, X) is measured and the above processing is carried out for a given position (xo.yo) of the first fiber in the beam to be characterized. We deduce <p ₀ = 2œsin0-X / c + φ (ω, χο, ν ₀ ) - (Daux (o); The interferogram S (co, X) is then measured and the above processing is carried out for a set of positions (X 1, y) of the fiber 1 in the beam to be characterized. + φ (ω, Χί, Υ _ί ) - 9aux (). We always subtract the phase φο measured during the first shot. We obtain This phase is independent of X, and can be averaged along this axis to improve the signal-to-noise ratio. By doing so, we compare all the points of the beam at the point (xo, yo), using the auxiliary beam as an intermediate.

- One can then perform a SPIDER type of measurement or FROG (the English "Frequency Resolved Optical Gating", ie optical cutting resolved in frequency) at the point (xo, yo). to determine the frequency dependence (o) of φ (ω, χο, γο) - We then have all the information necessary to reconstruct the field E (Xi, yi, t) of the laser beam, by a Fourier transform compared at co, this with a near-term term, a term which is almost independent of ω and which, as will be discussed later, is introduced by the optical fibers.

This technique requires a relatively simple assembly to achieve and inexpensive, and can be applied to large beams. On the other hand, since the phase is determined point by point, the characterization of a beam requires a large number of laser shots. This results in a significant acquisition time and sensitivity to fluctuations and time drifts of the laser source, vibrations and positioning defects of the input ends of the optical fibers.

Another limitation of the SEA TADPOLE technique is that the optical fibers introduce random phase fluctuations, which can not be measured (this point was briefly mentioned above). This means that the electric field of the beam E (x, y, t) can not be reconstructed completely, but only unless there is an unknown phase term _cft (i, Yi, ω). If the information thus obtained makes it possible, for example, to determine the intensity fronts (thanks to the hypothesis, confirmed by experience, that the effect depends does not depend on the frequency co), the phase fronts can not not be rebuilt. The invention is an improvement of the SEA TADPOLE technique, and aims to solve at least some of the aforementioned drawbacks.

A first idea underlying the invention is to use a plurality (N> 3) of optical fibers to collect light at several points of the beam simultaneously, and compare their phases using a similar assembly to that from SEA TADPOLE. In this way, the beam can be characterized by using fewer laser shots, which makes it possible to relax the conditions on its stability; at the limit, a "single-shot" characterization becomes possible. Moreover, it is not necessary to have an auxiliary beam.

Thus, an object of the invention is a method of characterizing a light beam comprising the steps of:

a) arranging the input ends of N> 3 optical fibers, preferably monomode, on the path of said light beam, such that a respective portion of said beam is coupled and propagates in each optical fiber and is emitted from its output end to form a respective secondary beam, each of said portions corresponding to a different point of the cross section of said light beam;

b) introducing an angular spectral dispersion onto said secondary beams by means of at least one dispersive element;

c) propagating the scattered secondary beams in such a manner that they overlap to form an interferogram;

d) acquiring an image of said interferogram; and e) extracting from said image of said interferogram information relating to the spatial variation of the phase of said light beam at a plurality of wavelengths.

We speak of "information" relating to the spatial variation of the phase because, in certain embodiments of the invention, this spatial variation of the phase is not completely determined, in particular because of the aforementioned phase fluctuations introduced. by the optical fibers.

It is important to note that, if no special precautions are taken, the fact of multiplying the number of optical fibers, and therefore of points acquisition of light is likely to cause serious difficulty. Indeed, several pairs of fibers can form similar interference patterns, whose Fourier transforms overlap (so-called "degeneracy"). In this case, it becomes impossible to extract the phase differences from the interferogram. To overcome this difficulty, it is proposed, in particular, to adjust the optical paths of the portions of the beam to be characterized acquired by different fibers, so that they are not all equal to each other. There are other possibilities for suppressing degenerations, for example by acting on the positions of the output ends of the optical fibers, but they are less flexible and more difficult to implement.

According to a preferred embodiment of the invention, the optical paths of said portions of the light beam can be adjusted by adjusting the position of the input ends of said optical fibers in the direction of propagation of said beam. Alternatively or in addition, it would be possible to use optical fibers of different lengths.

The data processing operations applied to the image of the interferogram must also be modified with respect to that known from the aforementioned publications relating to the SEA TADPOLE method. In particular, said step e) can comprise:

e1) calculating a two-dimensional Fourier transform of said image of said interferogram;

e2) identifying at least N-1 peaks of said two-dimensional Fourier transform, each of which is representative of the interference between two, and only two, spectrally dispersed secondary beams; and

e3) for each of said peaks, and for a plurality of wavelengths, determining the phase difference between the two corresponding secondary beams, each said phase difference being corrected for said differences between the optical paths.

Like the conventional SEA TADPOLE technique, the method of the invention can also provide steps consisting of: f) measuring the spectral phase of said light beam at a point of said light beam (for example by one of the methods SPIDER or FROG); and

g) from the information extracted in step e) and from the spectral phase measured in step f), obtaining information relating to the spectral phase of said portions of said light beam.

In particular, step f) may include measuring the spectral phase of said light beam at a point corresponding to the input end of one of said optical fibers.

As a variant, it is possible to proceed as follows: a reference pulse, whose spectral phase is known, is injected into an additional monomodal optical fiber, said pulse being emitted by an output end of said fiber to form a beam additional secondary;

introducing an angular spectral dispersion on said additional secondary beam by means of said or each said dispersive element;

said additional spectrally dispersed secondary beam is propagated so that it is superimposed with said secondary beams, so as to contribute to the formation of said interferogram;

from said image of the interferogram and the known spectral phase of said reference pulse, information relating to the spectral phase of said portions of said beam of light is determined.

A method according to a particular embodiment of the invention may also comprise the following steps:

h) injecting into said optical fibers, simultaneously with said light beam, a reference light beam, shifted spectrally with respect to said light beam and whose spatio-spectral (or temporal space-time) properties are known, to form a second interferogram and to acquire an image; i) determining, from the image of said second interferogram, phase fluctuations introduced by said optical fibers; and

j) use the phase fluctuations thus determined to correct the information extracted in step e).

These three additional steps make it possible to obtain a complete reconstruction of the beam to be characterized, including its phase edges, by avoiding random phase fluctuations introduced by the optical fibers. This is a major advantage over the conventional SEA TADPOLE technique.

According to various particular embodiments of the invention:

The method may also comprise a calibration step by means of a reference light beam, the spatio-spectral properties of which are known and whose spectrum preferably includes that of the light beam to be characterized.

The output ends of said optical fibers may be aligned in a direction perpendicular to a spectral dispersion direction of said dispersive element.

The input ends of said optical fibers may be arranged along a line, or in a two-dimensional pattern.

The positions of the output ends of said optical fibers and the introduced delays may be chosen such that, by representing each optical fiber by a point in a position-delay plane, a polygon or "V" pattern is obtained.

Said light beam may be a laser beam comprising at least one picosecond or femtosecond laser pulse.

Another object of the invention is a device for characterizing a light beam comprising:

N 3 singlemode optical fibers each having an input end and an output end;

a first support for positioning the input ends of said optical fibers on the path of said light beam, such that a respective portion of said beam is coupled and propagates in each optical fiber, said first medium including means for adjusting the position of the input ends of said optical fibers in the propagation direction of said beam;

a spectrometer comprising a dispersive element;

a second support for positioning the output ends of said optical fibers such that secondary beams emitted by said output ends are angularly dispersed by said dispersive element and overlap to form an interferogram; and

a sensor for acquiring an image of said interferogram. According to different embodiments of such a device:

Said second support is adapted to align the output ends of said optical fibers in front of an entrance slot of said spectrometer and parallel to said slot.

Data processing means may be provided for extracting from said image of said interferogram information relating to the spatial variation of the phase of said light beam at a plurality of wavelengths. The data processing means may advantageously be constituted by or comprise a computer programmed in a timely manner.

Other characteristics, details and advantages of the invention will emerge on reading the description given with reference to the accompanying drawings given by way of example and which represent, respectively:

FIGS. 4A and 4B, respectively, an interferogram obtained with the assembly of FIG. 2 and its two-dimensional Fourier transform;

FIGS. 5A and 5B, respectively, an interferogram obtained with the assembly of FIG. 2 and its two-dimensional Fourier transform, a delay x ₀ having been introduced between the two interfering beams;

Figure 6, a device according to one embodiment of the invention; Figure 7 is a detail view of the device of Figure 6 showing a mechanical support for holding the input ends of the optical fibers;

FIGS. 8A and 8B, respectively, an interferogram obtained with the assembly of FIG. 2 and its two-dimensional Fourier transform, illustrating the problem of degenerations;

Figure 9, a first arrangement of the optical fiber input ends of the device of Figure 6, to solve the problem of degeneration;

Figs. 10A and 10B, respectively, an interferogram obtained with the arrangement of Fig. 9, and its two-dimensional Fourier transform, showing no degeneration;

Figure 11, a second arrangement of the input ends of the optical fibers of the device of Figure 6, to partially solve the problem of degeneration;

Figs. 12A and 12B, respectively, an interferogram obtained with the arrangement of Fig. 10, and its two-dimensional Fourier transform, showing a partial lift of degenerations; and

Figure 13, a double interferogram obtained after the addition of a reference beam.

To describe in detail the invention, it is appropriate to return to the simple case in which only two optical fibers F1 and F2 are used, the input ends of which are arranged in the path of a light beam and whose ends are output are arranged opposite the entrance slot of a spectrometer to form an interferogram whose intensity distribution is given by equation (1):

and shown in Figure 4A.

Instead of performing a one-dimensional Fourier transform of the function S (co, X) with respect to co, as in the case of the SEA TADPOLE technique, it is advantageous to perform a transform Fourier bidinnensional ("TF2D"), which we will express Q (x, k). As shown in FIG. 4B, the function Q (x, k) essentially consists of three peaks: a central peak Po, which corresponds to the envelope of the interferogram, and two lateral peaks P.-i, P ₊ i which correspond to the fringes and contain the desired phase information. In the (x, k) plane, the peaks P_i, P ₀ , Pi are aligned along the axis k.

Now, a delay or time shift x _{0 1,} for example 200 fs, between the so-called "secondary" beams originating from two fibers is introduced. This delay can be generated simply by translating the input end of one of the two fibers relative to the other, along the direction of propagation of the beam, so that the paths traveled by the light in the air, before entering the fibers, are slightly different.

In this case, the expression of the interferogram S (co, X) becomes:

S (w, ήη θΧ / α + ωτ ₀ + φ _{ίη (} . (Ω) -φ _αΜΧ (ω))

As illustrated in FIG. 5A, with respect to the case without delay, the fringes turned in the plane (ω, Χ). In other words, the fringes are no longer simply spatial, but "spatio-spectral".

When calculating the two-dimensional Fourier transform Q (x, k) of this interferogram, the result illustrated in FIG. 5B is obtained. Due to the rotation of the fringes in the plane (ω, Χ), the peak P + i is displaced in (x, k) = (x ₀ , 2cusin9 / c), and the peak Pi at the symmetric point with respect to originally. Qualitatively, the positions of these peaks correspond to the vector (x, d) connecting the output ends of the fibers in a space (t, r), where r is the transverse spatial coordinate in the plane of exit of the fibers, and at its opposite . By playing on the delay between the two fibers, we can translate the peaks corresponding to the interference in the Fourier plane, along the x axis.

The beam to be characterized may be a pulse beam, characterized by a pulse duration at the femtosecond scale. However, the pulse is stretched by the dispersive element of the spectrometer; therefore, the delay xo may be greater than said pulse duration. As will become clear later, these considerations are important for the understanding of the invention.

FIG. 6 shows a very schematic representation of a device according to the invention. This device comprises N = 11 monomodal optical fibers F01-F011, whose input ends EE1-EE11 are carried by a first mechanical support SM1, an embodiment of which is represented in FIG. 7. As shown in this figure, the support SM1 comprises a plate PO, adjustable by means of micrometric screws VM, in the manner of a mirror support; the plate is intended to be positioned on the path of the beam FL to be characterized, its surface being oriented perpendicular to the direction (z) of propagation of the latter. Individual supports SI are fixed to the surface of the plate to maintain the input end of an optical fiber FO oriented perpendicularly to said surface, so as to allow the coupling of a respective portion of the beam to be characterized. VR screws make it possible to finely adjust the distance between the input end of each fiber and the surface of the plate, and to introduce delays between the different portions of the beam. Typically, the delays introduced will be between a few tens of femtoseconds and a few picoseconds; therefore, the individual supports will have to allow forward or backward optical fibers along the z axis of several tens or hundreds of microns, with a tolerance of the order of a micrometer.

The optical fibers F01 - F011 ideally have identical lengths; however, the inevitable dispersion of their lengths can be compensated for by acting on the longitudinal position of the input ends during a preliminary calibration step.

To characterize pulses of very short duration (less than 10 fs), or more generally very broadband beams, it is possible to use photonic crystal fibers instead of conventional optical fibers.

The output ends ES1 - ES11 of the fibers F01 - F011 are placed next to each other along a line, held in place by a second mechanical support SM2. In the embodiment of the figure 6, they are very close to each other (distance between closest neighbors of the order of 100 pm), so that the "secondary" beams (from the fibers) overlap spatially; Alternatively or additionally one could use a lens - as in the case of Figure 2 - or even a concave mirror to ensure such a recovery.

Ends ES1 - ES11 are aligned in front of the entrance slot of an SPM spectrometer (or are themselves such a slot), comprising a dispersive element RD which angularly disperses the secondary beams coming from the optical fibers. As in the case of the SEA TADPOLE technique, the scattered beams form an interferogram, an image of which is acquired by means of a CCD sensor, identified by the reference C1. A data processing means MTD, such as a programmed computer of In a timely manner, extract the image from the interferogram for processing as will be described hereinafter.

The observed interferogram is much more complex than in SEA TADPOLE, because of the presence of N fibers instead of just two. FIG. 8A shows such an interferogram in the case where the delay τ ₀ is zero (the input ends of the fibers are therefore on a plane perpendicular to the z axis), and FIG. 8B is its two-dimensional Fourier transform.

With N = 11, we should be able to identify N (N-1) + 1 = 111 peaks in the Fourier plane (x, k): a central peak corresponding to the envelope of the signal, and N (N-1) = 110 peaks corresponding to interference between the N (N-1) / 2 = 55 distinct pairs of fibers (because there are two peaks in the Fourier plane for each interference term). Now, in FIG. 8B, only P = 21 peaks (a central peak and ten pairs of lateral peaks) can be distinguished.

This case illustrates the problem of "degeneration" already mentioned above. Indeed, all neighboring pairs of neighboring fibers are at the same distance from each other and therefore give fringes of the same periodicity; in the Fourier transform of Figure 8B, this results in the superimposition of 10 peaks - as many as neighboring first pairs. The same phenomenon occurs for the second neighbors, and so on. Therefore, all the peaks observed in Figure 8B correspond to a superposition of several interference terms, except the two end peaks, which correspond to the interference between the two farthest fibers (because only two fibers are located at this distance from each other). Under these conditions, it is not possible to determine the relative phases of the portions of the beam to be characterized associated with the different fibers, since the two-dimensional Fourier transform of the interferogram can not be filtered independently the peaks corresponding to each term of the interference between pairs of secondary beams. To do this, it is necessary to lift, at least in part, the degeneracies, by ensuring that the smallest possible number of pairs of fibers are separated by vectors (Δτ, Αή equal or neighboring in the plane (t, r).

A first way of proceeding is to arrange the fiber exit ends in the space (radial coordinate r in the plane of exit of the fibers, introduced previously) of more complex way, so that never two pairs of fibers are to the same distance from each other. However, this condition is very difficult to satisfy.

Another possibility, much more practical to implement, is to exploit the whole Fourier plane (x, k), which is two-dimensional, instead of being restricted to one line. It will thus be possible to separate the N (N-1) interference terms much more easily, and to prevent them from overlapping even partially. To achieve this, it suffices to introduce a delay between the outputs of the different fibers. In practice, as already emphasized, this can be done very simply by translating the input ends of the fibers along the direction of propagation of this beam (z direction of Figure 1). Alternatively or in addition, it would be possible to use fibers of different lengths, but this presupposes that these lengths are controlled very accurately.

It has been shown above that the effect of the introduction of such a delay is to induce a rotation of the fringes in the plane (ω, Χ), and thus a translation of the associated peak along the axis τ in the Fourier plane (x, k). We can therefore use this parameter to move the interference peaks in the plane (-c, k), and thus avoid degeneration. It is then sufficient to find a spatial arrangement of the fibers (spatial coordinate r in the plane of the fiber output ends) and in time τ, such that all pairs of fibers (or at least a sufficient number of these pairs) are separated by different vectors (Δτ, ΔΓ).

An example of such an arrangement is shown in Figure 9, for N = 11 fibers. Each fiber may be represented by a point of a plane whose coordinates are the delay τ and the position of its output end, r. In the plane (x, r), these points form a polygon. More specifically, the output ends of the fibers are arranged regularly along a line, every 100 microns. Delays τ follow the law:

i- (i) = (-l) V _m ^ l - [2 (t - 1) / (N - 1) - l] ² where i (= 1 to N) is the fiber index, and T _ma x the maximum delay between the first fiber and all the others (2750 fs in this case). When N is odd, this configuration can lift all the degeneracies, as will be shown below. When N is even, some degenerations remain.

This arrangement gives the interferogram of FIG. 10A, which is extremely complex because of the large number of interference terms involved. Its two-dimensional Fourier transform, shown in FIG. 10B, has N (N-1) +1. = 1 1 1 well separated peaks: N (N-1) = 1 10 peaks corresponding to the interferences between the N (N-1) / 2 = 55 distinct pairs of fibers, and 1 central peak corresponding to the envelope of the signal. Any degeneration is thus avoided thanks to the delays introduced between the fibers.

Other arrangements of the fibers in the (x, r) plane are also possible, such as that shown in Figure 1 1. In this case, the delay between the fibers is given by the formula:

where i = 1 to N is the fiber index, with here β = 1.2 and τ ₀ = 180 fs. As in the previous case, the output ends of the fibers are regularly spaced along a line in space, which allows for a very simple assembly to achieve. On the other hand, in the plane (τ, χ), the points representing the different fibers form now a curved "V" (when β ≠ 1) instead of a polygon. The corresponding interferogram and its two-dimensional Fourier transform are shown in Figures 12A and 12B, respectively. Note that in this case there remains degenerations, for example between second neighbors (second lines above and below the central point in Figure 12B). But this is not a problem because the information contained in the interferogram is redundant, since all the fibers are "compared" with all the others. In particular, there is no degeneration between first neighbors (first lines above and below the central point), which makes it possible to completely determine the phase differences between all the fibers: all phase differences Δφ are known _ί + ι = φ _{ί +} ι (ω) -φ _ί (ω) for i = 1 to N-1. So knowing φι (ω), for example, (determined by a local FROG or SPIDER measurement, at the collection point of the fiber 1), we can determine all φ, (ω) for i = 1 to N.

From a more general point of view, it is assumed that the measurement makes it possible to separate 2P peaks in the two-dimensional Fourier transform from the interferogram, and thus to measure P phase differences between the N fibers. The goal is to determine, from these measurements, the N spectral phases φκ (ω) (k = 1 to N) at the output of all the fibers, assuming that it is simply known to be one of them, φι (ω) . It is therefore necessary to determine N unknowns by means of P + 1 data (the P measured differences and the phase φι (ω), assumed to be known). The problem is linear, and it is therefore necessary (but not sufficient) to have P + 1≥N, hence P≥N-1, that is to say to have a number of isolated peaks in the plane Fourier greater than 2 (N-1), in addition to the central peak.

It is assumed that this condition P> N-1 is fulfilled. We thus have P≥N-1 measured data Acp _k (k = 1 to P), which are related to the unknowns φ, (ω) by the elementary equation Δφκ = φί (ω) -φ ₎ (ω). Among the P measured data, we can choose N-1 to write a system of linear equations to find the unknown N φ, (ω). This system can be put into a matrix form. For this we define the data vector of length N, D = ((pi (co), Δφκ (ω)), where k = 1 to N-1 is an index listing the N-1 data measured thanks to the interferogram For every k, we have a pair of fiber index p and q such that Δφ (ω) = φ (ω) -φ _ς (ω) We define the vector of unknowns of length N, Ι = (φ, (ω)) (i = 1 to N). The system of equations to be solved can thus be written D = MI, where M is a matrix N x N whose elements are:

Mii = 1

(k + i) _P = 1

(K + l) = q -1

M _{(k +} i ₎ i = 0 for i outside the set (p, q)

This system has a unique solution if and only if the matrix M can be inverted, and therefore if its determinant is not zero (Det M ≠ 0). From a more physical point of view, it is understood that this condition is verified if each of the (N-1) fibers contributes to at least one of the N-1 selected peaks.

Thus, for the P data extracted from the interferogram to be sufficient to reconstruct the spatio-spectral phase of the laser beam, it is necessary and sufficient that we can extract an N-1 number of data, such that the matrix M can be reversed (Det M ≠ 0). It is quite possible that, in some cases, several subsets of data satisfy this condition. There is then a redundancy of information, which can be exploited either to improve the signal-to-noise ratio, or to test the consistency of the measurement.

The input ends of the fibers (apart from their relative offset in the z direction) can be arranged in a straight line, which allows a characterization of the light beam in one dimension. Alternatively, they may be arranged in a two-dimensional pattern (regular or not), so as to characterize the beam in two spatial dimensions with a single interferogram.

Before measurements can be made, the multifiber interferometer of Figure 6 must be calibrated or calibrated, which requires a well-characterized source. The simplest possibility is to use a monomode fibro laser source with a "large" spectral width, which makes it possible to obtain a reference image in the Fourier plane. The beams that will then be characterized with this system will be compared by comparing the interferogram obtained in the Fourier plane with this reference. This reference source can also be used to adjust the delays between fibers, so as to compensate for errors due to tolerances on fiber lengths. Once the sensor is calibrated, it is used to measure an interferogram obtained from the source to be characterized. By analyzing the figure obtained in the Fourier plane, and comparing it with the reference image, we obtain the spatial variation of the phase φ (χ, γ, ω) at the N measurement points (Χί, ν,), for all frequencies ω of the beam. Spatial variations of the spectrum | E (x, y, co) | are also extracted from these measurements, which are also needed to reconstruct the beam.

At this stage, we do not yet know the variation with ω of φ (χ, γ, ω). We have only compared the structure of the pulse (and its arrival time) in different points: it is only a measure in relative. This is also sufficient if one simply wants to determine the spatial variations of the beam. To obtain a better characterization, it is necessary to determine the spectral phase φ (χ, γ, ω) in at least one point. This can be done by performing a SPIDER or FROG measurement for example, at a point of the beam, corresponding to one of the points of collection by the fiber network.

Another possibility is to provide a (N + 1) ^th fiber whose output end is likewise disposed in front of the spectrometer entrance slit, and injecting into its inlet end a reference pulse whose spectral phase is known. This results in up to 2N additional peaks in the two-dimensional Fourier transform of the interferogram. By applying the treatment method described above, the spectral phase of the secondary beams from the other fibers is compared with that of the reference pulse. It is therefore not necessary to use SPIDER or FROG type measurements (except to characterize the reference pulse, but this is a calibration operation that need not be repeated for each measurement).

In theory, this should make it possible to reconstruct the beam E (x, y, t) in three dimensions, by carrying out a Fourier transform of E (x, y, ω) = | E (x, y, ω) | β ^{ίφ (χ} · ^ν ' ^ω) on the variable o.

In reality, this is not usually the case because propagation in the optical fibers introduces random phase fluctuations, which are variable over time. The measurement process described above does not Thus, it is possible to determine the phase φ (χ, γ, ω) only at a term pfi _uc t (x, y, co). Since this unknown term <Pfi _uc t (x, y, a>) can generally be considered independent of the frequency ω, this is already sufficient for some applications (for example, to determine the intensity fronts), but not for all. This problem arises in a similar way in the context of the invention as in that of the conventional SEA TADPOLE technique.

One possible solution consists in simultaneously injecting into the fibers a second so-called reference light beam of the same spatial extent as the unknown, but spectrally shifted, beam of known spatial properties and typically free of spatio-temporal couplings. This type of beam can today be produced relatively easily, for example by means of a monomode fibro laser source with a large spectral width.

Two separate interferograms, Si and S2, are then obtained separated in the dispersion direction of the spectrometer, as shown in FIG. 13. The interferogram Si corresponds to the source to be characterized and the interferogram S ₂ corresponds to the reference source. If the reference beam is well characterized (in the simplest case: flat or spherical wave fronts, identical for all the frequencies of the spectrum), the phase <p (x, y, co) which must be measured is known. Any difference is due to phase fluctuations in the fibers. This signal can then be used to determine these fluctuations over the spectral range of the reference. These measured fluctuations can then be extrapolated over the spectral range of the beam to be characterized, assuming that they are independent of the frequency. It has been experimentally verified that this hypothesis is reasonable.

This correction can apply to either the SEA method

Conventional TADPOLE, either to the method of the invention. In both cases, the approach to correct the fluctuations is the same. The difference is that in one case the fluctuations are corrected over time, while the fiber is displaced, whereas in the other one corrects the random phase fluctuations between N fibers.

The device and method of the invention have been described with reference to their application to the characterization of pulsed laser beams, but this application is not exclusive. Indeed, more generally, this device and this method give access to the quantity known under the name of "cross spectral density function" (in English, "cross-spectral density function") of the studied beam, that is to say to the function two spatial variables xi and x ₂ and the frequency ω:

where Ε (χ, ω) is the (complex) spectrum of the field at point x and "*" indicates the complex conjugation operation. The device of the invention makes it possible to sample this function for all pairs of points (Xj, Xj) of the beam associated with pairs of fibers which correspond to a non-degenerate peak in the two-dimensional Fourier transform of the interferogram.

The function \ Λ / (χι, χ ₂ , ω) is important because it contains all the information about the spatial and temporal coherence properties of the second order of the beam. It is related to the degree of spectral coherence μ (χι, χ ₂ , ω), of module between 0 and 1, by the relation:

μ (χ ₁ , χ ₂ , ω) = / [W XLXLCO) W (x _1, x _2, œ)] ² Thus, the device of the invention enables a simultaneous measurement of consistency at several points of the beam. For example, such a device can be used in combination with a broad-spectrum incoherent source to determine the "spatio-spectral" response of complex optical systems.

Claims

A method of characterizing a light beam (FL) comprising the steps of:

a) arranging the input ends (EE1 - EE1 1) of IM> 3 optical fibers (F01 - F011) on the path of said light beam, such that a respective portion of said beam is coupled and propagated in each fiber optic and is emitted from its output end (ES1 - ES11) to form a respective secondary beam, each of said portions corresponding to a different point of the cross section of said light beam;

b) introducing an angular spectral dispersion onto said secondary beams by means of at least one dispersive element (RD);

c) propagating the spectrally dispersed secondary beams in such a manner that they overlap to form an interferogram;

2. The method of claim 1, wherein the optical paths of said portions of said beam of light are adjusted so that they are not all equal to each other.

3. The method of claim 2 wherein the optical paths of said portions of the light beam are adjusted by adjusting the position of the input ends of said optical fibers in the propagation direction of said beam.

4. Method according to one of claims 2 or 3, wherein said step e) comprises:

5. Method according to one of the preceding claims also comprising the steps of:

f) measuring the spectral phase of said light beam at a point of said beam of light; and

6. Method according to one of claims 1 to 4 wherein: - a reference pulse, whose spectral phase is known, is injected into an additional monomodal optical fiber, said pulse being emitted by an output end of said fiber for form an additional secondary beam;

from said image of the interferogram and the known spectral phase of said reference pulse, information relating to the spectral phase of said portions of said light beam is determined.

7. Method according to one of the preceding claims also comprising the following steps:

h) injecting into said optical fibers, simultaneously with said light beam, a reference light beam, spectrally offset with respect to said beam of light and whose spatial properties are known, to form a second interferogram (S ₂ ) and acquire an image;

i) determining, from the image of said second interferogram, phase fluctuations introduced by said optical fibers; and

8. Method according to one of the preceding claims, also comprising a calibration step by means of a reference light beam, the spatial properties of which are known.

The method according to one of the preceding claims, wherein the output ends of said optical fibers are aligned in a direction perpendicular to a spectral dispersion direction of said dispersive element.

10. Method according to one of the preceding claims, wherein the input ends of said optical fibers are arranged along a line.

11. Method according to one of claims 1 to 9, wherein the input ends of said optical fibers are arranged in a two-dimensional pattern.

12. Method according to one of the preceding claims, wherein the positions of the output ends of said optical fibers and the introduced delays are chosen such that, by representing each optical fiber by a point in a position-delay plane, we obtain a polygon or "V" pattern.

13. Method according to one of the preceding claims, wherein said light beam is a laser beam comprising at least one picosecond or femtosecond laser pulse.

14. A device for characterizing a light beam comprising:

N> 3 singlemode optical fibers (F01 - F011) each having an input end (EE1 - EE11) and an output end (ES1 - ES11); a first support (SM1) for positioning the input ends of said optical fibers on the path of said light beam, such that a respective portion of said beam is coupled and propagates in each optical fiber, said first medium comprising means (VR) for adjusting the position of the input ends of said optical fibers in the propagation direction of said beam;

a spectrometer (SPM) having a dispersive element; a second support (SM2) for positioning the output ends of said optical fibers such that secondary beams emitted by said output ends are angularly dispersed by said dispersive element and overlap to form an interferogram; and

a sensor (C1) for acquiring an image of said interferogram.

15. Device according to claim 14, wherein said second support is adapted to align the output ends of said optical fibers in front of an inlet slot of said spectrometer and parallel to said slot.

16. Device according to one of claims 14 or 15, also comprising data processing means for extracting from said image of said interferogram information relating to the spatial variation of the phase of said light beam at a plurality of wavelengths. .