WO2009053630A1

WO2009053630A1 - Homogeniser including an optical fibre

Info

Publication number: WO2009053630A1
Application number: PCT/FR2008/051843
Authority: WO
Inventors: Federico Canova; Jean-Paul Chambaret; Stéphane TISSERAND; Fabien Reversat; Christian Hubert
Original assignee: Ecole Polytechnique; Silios Technologies
Priority date: 2007-10-12
Filing date: 2008-10-10
Publication date: 2009-04-30
Also published as: FR2922326A1; FR2922326B1

Abstract

The invention relates to a system for homogenising a laser pulse emitted by a laser source in order to illuminate a target homogeneously. According to the invention, the following elements are disposed between the laser source and the target, namely: a disperser including at least one multi-mode optical fibre intended to generate numerous spatio-temporal modes due to the optical fibre having a delay time Tr such that Tc < Tr < Δt, Tc and Δt representing respectively the temporal coherence and the duration of the laser pulse; and focusing means for imaging the output plane of the optical fibre on the target by superimposing the spatio-temporal modes in a homogeneous spot.

Description

"Optical fiber homogenizer."

The present invention relates to a system for homogenizing a laser pulse emitted by a laser source to homogeneously illuminate a target.

It finds a particularly interesting application in the field of laser pumping of solid media femtosecond intense amplifiers.

Indeed, the homogeneity of the laser pumping of femtosecond amplifiers based in particular on Ti: Saphir technology is an essential parameter, because of the difficulty of efficiently pumping amplifiers (from the point of view of energy extraction), and robust (from the point of view of the damage of the laser material). The threshold of damage of Ti: Saphir, in nanosecond regime, is estimated between 5 and 10J / cm2. This value does not come from a systematic study but from an estimate based on experience. The uncertainty about the value of the threshold forces the "laserists", to preserve the crystals from the risks of damage, to pump the active materials just beyond the saturation fluence, ie U / cm2, with a extraction of energy inefficient (20%).

In the case of pumping at 4J / cm2, for example, the efficiency would be three times greater (60%). In such a case, the damage threshold of the material would be very close to the pumping fluence necessary for a good energy extraction in the power amplifiers, and any inhomogeneity of the pump laser would result in a risk of major damage, therefore to a strong reduction of the reliability or thus to a deterioration of the performances entailing one and the other an important extra cost.

This inhomogeneity is due to pump profiles never completely mastered with the imaging techniques used today. These profiles have modulations or hot spots often important and therefore often lead to the destruction of laser crystals which are excessively expensive, their price reaching several tens of thousands of euros for the largest, and long to grow, until to lan. If one considers that between 60% to 70% of the price of a laser amplifier is due to the pump lasers, it is obvious that one identifies there in the control of the spatial quality of the pump laser beams, a parameter major for the development of more efficient systems. To limit the modulations in the pump profiles, we can think of the fact that when the beam is spread over a few meters, without leaving the Rayleigh area, the modulations are minimal. For example if we consider a pump laser that delivers U / cm ² (at 532nm and at 10Hz) on a Gaussian beam with a diameter of 10mm, the Rayleigh area will have an extension of 140m. But in reality the typical profiles of the pump lasers are closer to a "top-hat" (super-Gaussian) profile than to a Gaussian because this shape is imposed to optimize the frequency conversion and the performances of the source in terms of useful energy. In the case of a super-Gaussian profile, with the other features of the example considered above, already after four meters of propagation only modulations appear and can become dangerous for optics and laser crystals, even if the Rayleigh area is considerably longer. Because of these modulations it is difficult to use in practice a propagation distance greater than 3 - 4 meters. The approach to propagation in the Rayleigh zone therefore implies very strong constraints on the configuration of the amplifiers, because of the small distances over which the beam effectively retains its homogeneity.

Otherwise, to limit the modulations in the pump profiles, one can also use the technique of transporting the near field (supposedly homogeneous) of the pump laser beam, by imaging on the amplifier crystal. But this technique does not protect the latter from any variation in intensity that may occur over time on the pump laser used. We know today that to effectively limit these modulations in the pump profiles, it is necessary to homogenize the source, which implies the complete control of the energy transport, from the pump lasers to the active material. Thanks to this control, it would be possible to pump lasers to high efficiency extraction regimes, but close to the damage threshold and to avoid overcurrents that could damage them. the amplifying crystals. In general, the purpose of a homogenizer is to ensure a homogeneous energy distribution on the amplifier crystal regardless of the initial spatial distributions of the incident beams.

In this context, a refractive homogenizer with microlens matrices is known. Such a refractive sub-pupil homogenizer consists of two parts: a matrix optical element composed of a set of microlenses and a focusing component. Each microlens is a sub-pupil. The microlenses separate the incident beam into several segments, and the focusing component superimposes the projection of each sub-pupil on the focal plane. This technique is based on the low spatial coherence of the laser beam at the input to obtain an averaging effect (sum in intensity) of the contributions of the different sub-elements spread over the entire area to be pumped.

This technique has shown good performance on pumping systems with low spatial coherence. However, on pumping systems that are almost perfectly spatially coherent, the microlens matrix induces modulations of 100%. Even in the case of low spatial coherence beams, the best homogenization performances are obtained outside the focal plane, because this is modulated by the diffraction effects of the periodic structures, known as the Talbot effect. In other words, this Talbot effect prevents the use of energy distribution in the focal plane and requires the use of planes where the energy distribution is not modulated but less close to the ideal "top-hat".

US4521075 describes a system for spatially incoherent laser beam directed to a target. This system comprises between the laser source and the target:

an optical component for introducing a spatial incoherence between several parts of the laser beam, and

a focusing lens for directing the laser beam on the target. This results in interference that limits interference at the target.

However, experience has shown that this system does not allow to homogenize light sources other than those very inconsistent, such as laser diodes and excimer lasers. The present invention aims to overcome the aforementioned drawbacks by proposing a homogenization system eliminating the effects of interference and diffraction.

Another object of the invention is to propose a system capable of guaranteeing a robust and reliable pumping configuration for medium power amplifiers in femtosecond laser systems, implemented in a growing number of installations and intended to achieve peak powers for example beyond the Petawatt.

The present invention also aims at an efficient system from the point of view of energy extraction, for controlling the intensity of the laser beam on the target.

Another object of the present invention is a homogenizer for spatially and temporally strongly coherent pump lasers.

At least one of the above-mentioned objects is achieved with a system for homogenizing a laser pulse emitted by a laser source in order to homogeneously illuminate a target, this system comprising between the laser source and the target:

a disperser comprising at least one multi-mode optical fiber designed to generate numerous spatio-temporal modes from the laser pulse injected at the input; these spatio-temporal modes due to the optical fiber have a delay time Tr such that:

Tc <Tr <Δτ, Tc and Δτ respectively being the temporal coherence and the duration of the laser pulse; and

focusing means for imaging the output plane of the optical fiber on the target by superimposing the spatio-temporal modes in a homogeneous spot.

With the system according to the invention, the pump laser is converted into an incoherent, homogeneous and high-gloss source. Indeed, the multi-mode optical fiber, including index jump, generates several modes that are delayed from each other so that the beam from the optical fiber is inconsistent. Then we transport the near field by imaging on the target. This technique decouples the intensity variations in the pump laser beam (always possible) from the spatial distribution which remains homogeneous on the amplifier crystal. More specifically, multi-mode optical fiber smoothing is a homogenization approach based on reducing the coherence of the laser beams. In fact, the propagation adds a random phase shift to the modes, because of their different paths and imperfections of the fiber, and at the output the beam is composed by several independent spatial modes. Each spatial mode propagates in the fiber with a particular angle, which induces a time delay between the spatial modes. With Tr chooses according to the invention, the number of modes which propagate in the optical fiber is large and the figure of scab at the output, where the modes are superimposed, presents a Gaussian statistic. Scab ("Speckle" in English) is a pattern of random interference. The optical fiber then acts as a disperser and couples the spatial and temporal domain.

The system according to the invention makes it possible to obtain the homogenization of any pump laser for power amplifiers such as those based on titanium-doped sapphire, TkSaphir.

The performances are superior to existing techniques because this approach using optical fiber homogenization eliminates parasitic modulations due to the effects of interference and diffraction (Ta I bot effect).

The system according to the invention is also advantageous in terms of energy extraction, which makes it possible to reduce the necessary number of pump lasers for a given energy, and thus the cost of the overall system. This interest is accompanied by greater reliability by protecting expensive amplifier crystals from any risk of damage.

The system according to the invention also makes it possible to use the length of an optical fiber to increase the distance between the pump laser and the amplifier. In practice, this makes it possible to install the pump laser in one room and the amplifier in another.

Advantageously, each optical fiber has a length L determined by the following relation: L> _c 2.n .c.Tr / θ ^2, with n _c the refractive index of the heart of the fiber, "c" the speed of light and θ the numerical aperture of the optical fiber. The relationship between the delay time and the length of the fiber is linear, which allows to delay scab figures of an arbitrary value, with only limit the duration of the pulse, because if the parts of the beam are too much delayed they will no longer overlap temporally. The plane at the output of the multi-mode optical fiber is the place where all the spatial scabs are superimposed, and by imaging this plane on the crystal amplifier we can take advantage of the maximum delay between the modes and obtain the best smoothing.

According to an advantageous characteristic of the invention, the disperser comprises a matrix consisting of a plurality of said at least one optical fiber; the system further comprising injection means for injecting a partition of the energy of the laser pulse into each of the optical fibers of the matrix.

The injection means may comprise a phase plate consisting of a plurality of sub-pupils capable of generating a plurality of elementary beams each directed towards the input of an optical fiber. A phase information is etched on each sub-pupil so that each elementary beam has an identical given form. This form consists of both a geometric shape and the form "top-hat" in intensity.

At the exit of the matrix, we sum in intensity the different parts of the beam over the entire area to be illuminated. The focusing means are positioned so that the elementary beams from the sub-pupils are superimposed on each other. There is complete recovery of the elementary beams. On the contrary, in the system described in US4521075, the beams may overlap but not overlap.

The optical homogenization system according to the present invention makes it possible to guarantee a repeatability of the spatial profile in intensity on the crystal. This allows for more robust power amplifiers. The robustness is related to the control of the energy distribution, which guarantees to work without modulations and not to damage the optical components. By way of example, each elementary beam has a cylindrical shape whose transverse dimension is substantially smaller than the diameter of the core of each optical fiber.

According to the invention, the focusing means may comprise a convergent lens, called a field lens, arranged in such a way that the target is at the focusing distance of this convergent lens. This convergent lens makes it possible in particular to obtain the far field (the Fourier transform) of the product between the profile of the incident beam and the optical transfer function of the optical fiber. According to one characteristic of the invention, for a desired contrast level r of the homogeneous spot, the delay time Tr is determined by the following relation: Tr ≡ Tc / r ² . In general, contrast can be defined as a statistical measure of the homogeneity of the spatial profile of a laser. It is defined as the ratio between the standard deviation and the mean, ie r = sigma (I) / <I>, where I is the intensity. The reason of a statistical characterization of the homogeneity of a beam comes from the strong spatio-temporal coupling present in the laser pulses, because of the coupling of the modes of the partial coherence spatial and temporal. The statistic governing the contrast is described by the mathematical model of scab figures ("speckle"). The ergodicity theorem is valid and the statistic which describes an instantaneous realization is also valid to describe the evolution in time.

Moreover, for a desired contrast level r of the homogeneous spot, the number N of optical fibers constituting the matrix is determined by the relation: N ≡ 1 / r ² .

In fact N is an integer closest to the value 1 / r ² . The present invention makes it possible to make the link between the intensity of the homogeneous spot, characterized here by its contrast, and the number of optical fibers. Advantageously, said at least one optical fiber has a numerical aperture θ such that: θ ≡ Mλ ₀ / (4a), M being the number of modes that can be generated in this optical fiber in a given direction, where λ ₀ is the length of central wave of the laser pulse, where "a" is the diameter of the core of each optical fiber. Preferably, the laser source is a pump laser and the target is an amplifier solid medium. The target may advantageously be a sapphire crystal doped with titanium. The laser source may advantageously be a frequency-doubled laser chosen from the following lasers: Nd: YAG; Nd: glass,

Nd: YLF, Yb: glass, Yb: YAG.

Advantageously, the disperser (in fact said at least one optical fiber or the optical fiber matrix) may have a length of several meters so that the laser source is offset at a distance of several meters from the target.

The system according to the invention may also comprise several sets arranged in parallel, each set comprising a laser source associated with a disperser; these sets being arranged so that the laser beams from the different sets are superimposed on at least one face of the target. Laser sources can be of different wavelengths. Moreover, when the target is for example an amplifier, the disperser of each of said sets may comprise a plurality of optical fibers, a portion of the optical fibers being arranged to illuminate by a first homogeneous spot one face of the target, and at least one other part being arranged to illuminate by a second homogeneous spot another face of the target.

According to another aspect of the invention, it is proposed an application of the system for pumping amplifying media in a CPA-Ti: Saphir laser chain.

Other advantages and characteristics of the invention will appear on examining the detailed description of a non-limiting embodiment, and the attached drawings, in which: FIG. 1 is a schematic view of the homogenization system an optical fiber according to the present invention;

FIG. 2 is a schematic view of the principle of using a smoothed beam at the output of optical fiber;

FIG. 3 is a schematic view of a homogenizer comprising a matrix of optical fibers according to the invention; Figures 4 to 6 are schematic views illustrating the injection of elementary beams in the face of a matrix of optical fiber bundles;

Fig. 7 is a graph illustrating a time profile before and after propagation in a 30m multi-mode fiber, and

FIG. 8 is an exemplary embodiment of a multi-source system according to the invention.

Although the invention is not limited thereto, the homogenization of a pump laser beam for a Tk Saphir power amplifier will now be described. The Tk Saphir amplifier material has its maximum absorption around 500nm. Virtually all pumping systems for power amplifiers are based on neodymium ion, whether in a YAG or YLF crystal lattice, or in a glass mesh. The choice of this material and its use in triggered mode are dictated by economic and technological considerations. These neodymium systems are excited by flash lamp at repetition rates of several Hz and emit at lμm, and then doubled in frequency to reach the wavelengths of absorption of Tk Saphir. FIG. 1 shows an Nd: YAG 1 pump laser comprising at its output a doubling crystal 2 after amplification. This pump laser 1 emits a laser pulse 3 at about 500 nm to a multi-mode optical fiber 4 jump index. The injection of the pulse into the optical fiber can be done directly, but preferably it is performed by means of a convergent optics (not shown) which focuses the pulse in the optical fiber 4.

The optical fiber 4 generates within it several spatiotemporal modes 5, 6 which are delayed relative to each other, which smooths the laser pulse 3 which becomes incoherent. The different modes of the optical fiber have different propagation angles, and an injection that corresponds to the numerical aperture (typically ON = 0.22) makes it possible to excite them all. The numerical aperture of an index jump fiber is defined from the index of the core n _c and the index of the cladding n _g by θext such that: The basic principle of smoothing is to use a scatterer to separate the wavelengths in space and to transfer a time inconsistency to a spatial incoherence. Optical fiber smoothing is a smoothing technique that uses as a disperser a multi-mode optical fiber. Thanks to the propagation in the optical fiber the spatio-temporal coupling is automatic and no additional component is necessary to achieve the scab, the scab ("Speckle" in English) being a figure of random interference. Scab may also be defined as "hot spots" that is local intensity maxima in a volume where a smoothed beam is focused.

According to the invention, the optical fiber 4 induces a delay time Tr which is longer than the duration of the temporal coherence Tc of the laser pulse 3. This gives an effective smoothing and the space-time modes are added in intensity and not in the field. At the same time, the delay time Tr induced by the disperser is shorter than the pulse duration Δτ, so that the modes still interfere. The conditions on Tr are:

Tc <Tr <Δτ, Tc and Δτ respectively being the temporal coherence and the duration of the laser pulse.

The laser beam 7 emerging from the optical fiber is focused into a homogeneous spot 9 on one face of the amplifier 10. This homogeneous spot 9 has a uniform intensity profile of the "top hat" type.

In FIG. 2, the laser beam 7 emerging from the optical fiber 4 is seen in more detail. It shows the schematic diagram on the use of the smoothed beam at the output of the optical fiber for pumping the amplifier. Such as Ti: Saphir. The output plane of the optical fiber 4, which has the best smoothing, is imaged on the laser crystal Ti: Sapphire to pump. Particular attention is paid to the quality of smoothing in the intermediate planes (reduced planes of smoothing), because in these plans the superimposition of the modes is reduced and the modulations can be important, and to be dangerous for the optical transport of the laser beam . In order to be able to carry interesting energies in a power amplifier, it is planned to use a homogenizer composed of a matrix of multi-mode optical fibers. FIG. 3 shows such a homogenizer according to the invention comprising, for example, 37 optical fibers in order to be able to pump the amplifier 10 with an energy of 10. With 37 optical fibers, it is estimated that it can be injected approximately 70 μm (approximately 20 μm by optical fiber). ), for a total efficiency of the system of about 70% and therefore available energy for pumping 50OmJ.

The characteristics of each optical fiber are given in the table below:

The effective coupling of the energy of the laser pulse 3 in the matrix 11 of optical fibers is obtained thanks to a phase plate 12 which is a diffractive plate which distributes the energy of the incident beam on the entrance surface of each optical fiber. This phase plate thus generates a discrete set of energy profiles distributed in the far field on this input surface. The transverse dimension of each elementary beam coming from the phase plate is slightly smaller than the diameter of the core of the optical fiber. The entire pupil of the incident beam (the laser pulse 3) contributes to each cylindrical profile thus contributing to a first time mixing step.

In other words, this phase plate 12 makes it possible to redistribute the energy of the incident beam (the laser pulse 3) to the focal plane in 37 supergaussian spots ordered in hexagon as can be seen in the diagram of FIG. In FIG. 4 is seen a little more in detail the arrangement of the optical fibers relative to one another as well as the inter-fiber distances. Figure 6 is an image of 37 supergaussian profiles at the focal plane of a 60mm lens.

It is also possible to use other types of injector for distributing the laser pulse 3 in the matrix 11 of optical fibers. Advantageously, a noble gas stream can be used to keep

"Clean" the entrance surface of each optical fiber. This detail ensures a longer life of the surface condition of the fiber because the deposition of dust is reduced.

You can also perform anti-reflection treatment on the faces to reduce Fresnel losses. This solution can further improve performance.

Each sub-pupil (or output surface of each elementary fiber of the matrix 11) illuminates the whole of the useful surface of the amplifier crystal 10. Each of them having become non-coherent with its neighbors, the total illumination on the amplifier crystal 10 is obtained by a summation in intensity (and no longer in amplitude with the associated interferences) of the contributions of each sub-pupil. The modulations are suppressed and in case of upstream fluctuations of the energy in the different sub-pupils the effect is only reflected by an overall variation of the illumination on the pumped crystal.

It is possible to use the lens 8 or an output coupler (not shown) to superimpose in a homogeneous spot 9 all the sub-pupils coming from all the elementary fibers of the matrix 11. Said output coupler can be produced with a lens matrix, to recover the divergence at the output of the optical fibers, and a field lens to image them on the amplifying crystal and obtain a focal spot where the beams superimpose themselves in energy without modulations.

The superposition of energy distributions on the laser crystal of beams from different fibers allows a sum in intensity. The different fibers of the beam are "incoherent" to each other and the contrast r is given by the formula of the type: r =, = with Nf.bres the fiber number of the beam. fibers

The practical advantages of a beam configuration are numerous, because the energy transported can be increased directly, in increasing the number of fibers, and new multipasspass amplifier configurations, with spatial multiplexing of the pulse of the pump laser, become accessible.

In Figure 7, we see a graph illustrating the time profile before and after propagation in a multi-mode fiber 30m. The smoothing effect on the temporal profile depends on the delay induced by the different propagation of the spatio-temporal modes in the optical fiber. In this case, the effect can be quantified with a reduction in peaks of 20% and an increase in the temporal duration of 2ns. With the homogenization system according to the present invention:

- we can deport the pump lasers. From the point of view of the implantation of a laser chain, the possibility of installing the pump lasers in one place differs with respect to the femtosecond part, and to carry the light as in "pipes", makes it possible to envisage a robust installation, well organized and comfortable and generally better accessible for maintenance.

- Lights can be mixed from several sources. This approach makes it possible to average between several sources, to separate them between several beams, and any fluctuation in the pumping performance of one laser compared to the others will be averaged.

FIG. 8 shows an exemplary embodiment in which several laser sources 1a and 1b are used. Each laser source is associated with an injection means 12a and 12b, and with an optical fiber bundle 11a and 11b. Half of the optical fibers of each bundle 11a, 11b is directed on a face 9a of an amplifier 10. The other half of the optical fibers of each bundle 11a, 11b is directed to another face 9b of the amplifier 10. Each 8a, 8b lens converges laser beams from both laser sources la and Ib. These laser beams from the lenses 8a and 8b are respectively superimposed on the face 9a and 9b. Homogenization is obtained on each face 9a and 9b. Thus the amplifier is powered by these two faces. With such an arrangement, the possible failure of a laser source is compensated by the other laser source. Low (single laser source) and high speed (both laser sources) operating modes can be defined. Homogenization with a bundle of optical fibers according to the invention therefore makes it possible, unlike refractive and diffractive sub-pupil techniques, to homogenize a laser source with a strong spatial and temporal coherence. This approach allows complete control of the pumping profile by adapting to all available sources.

Of course, the invention is not limited to the examples that have just been described and many adjustments can be made to these examples without departing from the scope of the invention.

Claims

A system for homogenizing a laser pulse emitted by at least one laser source in order to homogeneously illuminate a target, which system comprises at least between the laser source and the target:

a disperser comprising at least one multi-mode optical fiber designed to generate numerous spatio-temporal modes from the laser pulse injected at the input; these spatio-temporal modes due to the optical fiber have a delay time Tr such that: Tc <Tr <Δτ, Tc and Δτ respectively being the temporal coherence and the duration of the laser pulse; and

2. System according to claim 1, characterized in that the disperser comprises a matrix consisting of a plurality of said at least one optical fiber; the system further comprising injection means for injecting a partition of the energy of the laser pulse into each of the optical fibers of the matrix.

3. System according to claim 2, characterized in that the injection means comprise a phase plate consisting of a plurality of sub-pupils capable of generating a plurality of elementary beams each directed towards the input of an optical fiber. .

4. System according to claim 3, characterized in that a phase information is etched on each sub-pupil so that each elementary beam has an identical given form.

5. System according to claim 4, characterized in that each elementary beam has a cylindrical shape whose transverse dimension is substantially less than the diameter of the core of each optical fiber.

6. System according to any one of the preceding claims, characterized in that the focusing means comprise a convergent lens arranged such that the target is at the focusing distance of the converging lens.

7. System according to any one of the preceding claims, characterized in that for a desired contrast level of the homogeneous spot, the delay time Tr is determined by the following relationship: Tr ≡ Tc / r ²

8. System according to claim 4, characterized in that each optical fiber has a length L determined by the following relationship: L> 2.n _c .c.Tr / θ ² , with n _c the refractive index of the heart of the optical fiber,

"C" the speed of light and θ the numerical aperture of the optical fiber.

9. System according to any one of claims 2 to 8, characterized in that for a desired level of contrast of the homogeneous spot, the number N of optical fibers constituting the matrix is determined by the relation: N ≡ 1 / r ² .

10. System according to any one of the preceding claims, characterized in that said at least one optical fiber has a numerical aperture θ such that: θ ≡ Mλ _o / (4a), M being the number of modes that can be generated in this optical fiber in a given direction, λ ₀ being the central wavelength of the laser pulse, "a" being the diameter of the core of each optical fiber.

11. System according to any one of the preceding claims, characterized in that the laser source is a pump laser and the target is an amplifying solid medium.

12. System according to claim 11, characterized in that the target is a sapphire crystal doped with titanium.

13. The system of claim 11 or 12, characterized in that the laser source is a frequency doubled laser selected from the following lasers: Nd: YAG; Nd: glass, Nd: YLF, Yb: glass, Yb: YAG.

14. System according to any one of the preceding claims, characterized in that a noble gas flow is used to keep the input surface of the optical fiber clean.

15. System according to any one of the preceding claims, characterized in that the disperser has a length of several meters so that the laser source is deported at a distance of several meters from the target.

16. System according to any one of the preceding claims, characterized in that it comprises several sets arranged in parallel, each set comprising a laser source associated with a disperser; these sets being arranged so that the laser beams from the different sets are superimposed on one side of the target.

17. System according to claim 16, characterized in that the target being an amplifier, the disperser of each of said sets comprises a plurality of optical fibers, a portion of the optical fibers being arranged to illuminate by a first homogeneous spot a face of the target, and at least one other part being arranged to illuminate by a second homogeneous spot another face of the target.

18. Application of the system according to any one of the preceding claims, for pumping amplifying media in a CPA-Ti: Saphir laser chain.