Fiber laser amplifier including a side pump device.

Abstract

TITLE: Fiber laser amplifier comprising a side pump device. The present invention relates to a fiber optical amplifier, comprising an amplifying optical fiber (1), including a doped core (11), at least one optical cladding (12, 13) and an external coating (14), the optical amplifier also comprising at least one side pump device (2), including a pump optical fiber (21) assembled to the amplifying optical fiber (1) at a junction zone (20). According to the invention, the external coating (14) is made of a material with high thermal conductivity, covers most of the perimeter of the amplifying optical fiber (1) at the segments (101, 102) of this fiber which surround the junction zone (20), and covers part of this perimeter at the segment (103) of this fiber comprising the junction zone (20), so that the external coating (14) extends without interruption over the amplifying optical fiber (1).Abbreviated figure: Figure 2.

Description

Title of the invention: Fiber laser amplifier comprising a side pump device. Scope of the invention

[0001] The present invention relates to laser amplifiers. It relates in particular to fiber laser amplifiers, in which a light beam is amplified during its propagation in an amplifying optical fiber.

[0002] In particular, the invention relates to such fiber laser amplifiers comprising a lateral pump device. Prior Art

[0003] Fiber laser amplifiers are optical devices well known to those skilled in the art, in which light radiation is amplified during its propagation along an amplifying optical fiber.

[0004] Amplifying optical fibers are generally composed of at least one core surrounded by an optical cladding. The core is most often made of a silica matrix that is doped, generally with rare-earth ions, to constitute an optical amplifying medium. This optical fiber core is designed to guide and amplify the light beam to be amplified.

[0005] The core is generally surrounded by an optical cladding (usually referred to by the English term "cladding"), which is often made of silica with a refractive index lower than that of the core it surrounds. This index difference advantageously keeps the light beam to be amplified within the core, preventing it from escaping into the optical cladding.

[0006] The optical cladding is itself capable of guiding a light beam along the amplifying optical fiber. A so-called "pump" light flux is introduced into this optical cladding. As it travels along the optical cladding, this pump light flux passes through the doped core, where its photons are absorbed by the core's doping ions, which then transition to an excited state. These excited doping ions in the core then amplify the light beam to be amplified as it travels through the core.

[0007] The optical cladding surrounding the core of the optical fiber must ensure the guidance of the pump light flux. For this purpose, this optical cladding can be surrounded by another optical cladding, called the outer optical cladding, whose refractive index is lower than that of the optical cladding surrounding the core, so that the index step prevents the pump light flux from escaping from the optical cladding surrounding the core.

[0008] It is also possible that the optical cladding surrounding the core, or a sheath The external optical cladding surrounding the core is surrounded by an external coating, which may, for example, be a reflective coating that helps maintain the pump's luminous flux within the gaining optical fiber. In many cases, this external coating is made of polymers. It generally provides protection for the gaining optical fiber against mechanical stress.

[0009] Increasingly, fiber laser amplifiers are used to obtain high-power laser beams. They can be incorporated into a laser cavity for this purpose, or used to amplify a laser beam previously produced in a cavity.

[0010] This use of fiber laser amplifiers to obtain high-power laser beams, however, encounters difficulties limiting the power of the light beam obtained.

[0011] Thus, optical amplification in a fiber laser amplifier generates nonlinear effects, well known to those skilled in the art, which are highly detrimental to the quality of the amplified light beam or its spectral sharpness. These nonlinear effects increase sharply with the length of the amplifying optical fiber. They therefore require fiber laser amplifiers to use only a limited length of amplifying optical fiber. An increase in the amplification power of a fiber laser amplifier cannot therefore be achieved by an unlimited lengthening of the amplifying optical fiber, but rather requires increasing the amplification power per unit length of the amplifying optical fiber.

[0012] To obtain very high power amplification with a limited length of amplifying optical fiber, a very high power pump light flux must be introduced into the optical cladding of the amplifying optical fiber.

[0013] Conventionally, the pump light flux can be introduced into the optical cladding surrounding the core of the amplifying optical fiber at the ends of this amplifying optical fiber. However, such a pumping method does not allow for the homogeneous distribution of the pump light flux energy along the amplifying optical fiber and requires the introduction of very high optical power at certain points of the amplifying optical fiber.

[0014] To improve the homogeneity of this distribution, it has been proposed to introduce the pump light flux into an amplifying optical fiber by at least one lateral pump device, placed between the two ends of the amplifying optical fiber.

[0015] Such a lateral pump device, which can be complementary to pump devices located at the ends of the amplifying optical fiber, usually comprises a passive pump optical fiber, which conducts a pump optical flux. This fiber The pump optical fiber is assembled, for example by welding, to the optical cladding of the amplifying optical fiber, at a segment of the amplifying optical fiber whose outer coating has been removed. This assembly of the pump optical fiber to the optical cladding is carried out in such a way that the optical flow from the pump optical fiber passes into the optical cladding of the amplifying optical fiber.

[0016] The introduction of a pump light flux by such a lateral pump device is described for example in documents EP2618191B1 or US2015 / 0007615A1.

[0017] The temperature increase in a laser amplifier, linked in particular to heat emission during optical amplification, is known to be a limiting factor in the amplification power of an amplifying optical fiber. Indeed, this temperature increase can lead to a loss of quality of the amplified light beam, or even to the destruction of the laser amplifier.

[0018] In laser amplifiers comprising one or more lateral pump devices, the junction areas between the amplifying optical fiber and the pump optical fibers are particularly prone to temperature rises increasing the risks of degradation of the quality of the laser beam produced or destruction of the laser amplifier.

[0019] Indeed, at these junction zones, the amplifying optical fiber receives a particularly high pumping power, which leads to a particularly strong excitation of the doping ions located in this zone. This excitation, and the subsequent de-excitation, generate a significant amount of heat.

[0020] Furthermore, the junction between a pump fiber and the amplifying optical fiber is traversed by a very high optical power. This optical power is likely to generate heating at any impurities or irregularities that may appear, particularly at the splice between the fibers.

[0021] Finally, the dissipation of thermal energy is generally less efficient at this junction zone between the amplifying optical fiber and the pump fiber. Indeed, this junction is made on a segment of the amplifying optical fiber that is stripped of its external coating, generally made of polymer materials, which contributes to the dissipation of thermal energy from the amplifying optical fiber.

[0022] Such a junction zone between an amplifying optical fiber and a lateral pump device is therefore particularly fragile and sensitive to heating. Consequently, these lateral pump devices are rarely implemented for the amplification of very high-power laser beams. Description of the invention

[0023] The present invention aims to overcome these drawbacks of the prior art.

[0024] In particular, the invention aims in particular to enable the obtaining of very high power light amplification in fiber laser amplifiers.

[0025] A particular objective of the invention is to enable an increase in the power of the light amplification that can be obtained by fiber laser amplifiers equipped with lateral pump devices.

[0026] Another objective of the invention is to reduce the risk of degradation of the qualities of the beams obtained, due to heat, or of destruction by heat of the fiber laser amplifiers equipped with lateral pump devices.

[0027] These objectives, as well as others which will become clearer later, are achieved using a fiber optic amplifier, this amplifier comprising an amplifying optical fiber, itself comprising at least one doped core, at least one optical cladding surrounding the core(s), and an external coating surrounding the optical cladding(s), this optical amplifier comprising at least one lateral pump device, itself comprising a pump optical fiber assembled to the optical cladding of the amplifying optical fiber, or to at least one of these optical claddings, at a junction zone located between the two ends of the amplifying optical fiber, so as to allow the transfer into the optical cladding, or into at least one of the optical claddings, of at least a part of a pump light flux propagating in the pump optical fiber.According to the invention, the external coating is made of a material having a thermal conductivity coefficient greater than 1 W / mK, and covers at least 90% of the perimeter of the amplifying optical fiber, at the level of a first segment of said amplifying optical fiber, located between said junction zone and a first end of said amplifying optical fiber, and at the level of a second segment of said amplifying optical fiber, located between said junction zone and a second end of said amplifying optical fiber.The external coating also covers, according to the invention, a portion of the perimeter of said amplifying optical fiber, at the level of the segment of said amplifying optical fiber comprising the junction zone, and extending between the first segment and the second segment of the amplifying optical fiber, in such a way that the external coating extends without interruption between the first and second segments of the amplifying optical fiber.

[0028] Thus, the external coating of the amplifying optical fiber can effectively distribute and dissipate the heat generated within the amplifying optical fiber, including at the junction zone, which is particularly susceptible to heat damage. This improved heat dissipation at the junction zone advantageously allows for an increase in the amplification power of the fiber optic amplifier without increasing the risk of damage to the amplifying optical fiber.

[0029] Preferably, the external coating fully covers the perimeter of the amplifying optical fiber at the level of the first and second segments of the amplifying optical fiber.

[0030] This situation corresponds to the majority of cases, in which the outer coating surrounds the entire perimeter of an optical fiber. However, the invention can also be applied to situations in which the outer coating does not completely cover the perimeter of the optical fiber.

[0031] It should be noted that, although the first and second segments are located between the junction zone and the ends of the optical fiber, they do not necessarily extend to these ends. Thus, for example, when the fiber optic amplifier includes several lateral pump devices, these first or second segments may be located between the junction zones of two lateral pump devices.

[0032] According to a particularly advantageous embodiment, the external coating is made of a metallic material.

[0033] The term "metallic material" means a metal or a metallic alloy. Such external metallic coatings for optical fibers are known in themselves from the prior art, and the processes for obtaining them are well established. Their application to the amplifying optical fiber of the invention is particularly advantageous due to their very good thermal conductivity, which allows for efficient heat dissipation.

[0034] Advantageously, the assembly of the pump optical fiber to the optical cladding of the amplifying optical fiber is done by welding at the junction area.

[0035] Preferably, the external coating covers at least 50% of the perimeter of the amplifying optical fiber, at the level of the segment of the amplifying optical fiber comprising the junction area and extending between the first segment and the second segment of the amplifying optical fiber.

[0036] Thus, advantageously, the external coating covers at least 50% of the perimeter of the amplifying optical fiber over the entire length of the amplifying optical fiber.

[0037] The entire length of the amplifying optical fiber is thus covered, over a significant part of its diameter, by an external coating allowing thermal dissipation.

[0038] Preferably, the area of ​​the core section, or the sum of the areas of the core sections, is greater than 400 pm2.

[0039] Such cores advantageously allow the propagation of multimode beams. For example, if there is only one core, it can advantageously have a diameter greater than 30 pm.

[0040] Advantageously, the fiber optic amplifier comprises at least two devices of side pump, each of these side pump devices being assembled to the amplifying optical fiber at one of said junction zones.

[0041] The multiplication of such lateral pump devices makes it possible to greatly increase the amplification of the fiber optic amplifier. It is therefore advantageous, on a fiber optic amplifier, to have at least ten lateral pump devices.

[0042] Advantageously, these junction zones are regularly distributed along the length of the amplifying optical fiber.

[0043] According to an advantageous embodiment, the amplifying optical fiber has at least two distinct optical claddings, a first optical cladding surrounding the core(s) and an external optical cladding surrounding the first optical cladding.

[0044] Preferably, the external optical sheath is cut at the junction area(s).

[0045] Such a cut in the external optical cladding allows the assembly of the pump optical fiber to the first optical cladding surrounding the core(s).

[0046] Cutting the cladding at the junction zone can advantageously be carried out by laser ablation. This laser ablation can also cut the outer optical cladding, if necessary.

[0047] Thus, the present invention also relates to a method of manufacturing a fiber optic amplifier as described above, which includes a local laser ablation step of the external coating to form the junction zone, on a portion of the perimeter of said amplifying optical fiber not covering more than 50% of the perimeter of the amplifying optical fiber. Description of the figures

[0048] The invention will be better understood upon reading the following description of preferred embodiments, given by way of simple figurative and non-limiting example, and accompanied by the figures, among which: - Fig. 1 is a schematic cross-sectional view, in an axial plane, of a segment of a fiber laser amplifier according to an embodiment of the invention. - Fig. 2 is a perspective representation of the portion of the fiber optic amplifier represented by Fig. 1. Description of the implementation methods

[0049] Fig. 1 thus schematically represents a cross-sectional view in an axial plane of a segment of a fiber laser amplifier in which light radiation is amplified during its propagation along an amplifying optical fiber 1. This fiber laser amplifier can be included in a laser cavity, or be used to amplify a previously formed laser beam.

[0050] As is well known to those skilled in the art, the amplifying optical fiber 1 comprises a core 11 surrounded by an optical cladding 12. The core 11 is, in a manner known per se, made of a silica matrix doped with rare-earth ions (for example, with ytterbium ions) to constitute an optical amplifying medium. This core of the optical fiber is intended to guide the light beam to be amplified 91. In the embodiment shown, this core has a diameter of approximately 50 µm.

[0051] In other embodiments, the amplifying optical fiber may, in a known manner, have several cores. The present invention applies identically to such multi-core amplifying optical fibers.

[0052] The core 11 is surrounded by an optical cladding 12 (generally referred to by the English term "cladding"), which is, in a manner known per se, made of silica whose refractive index is lower than that of the core 11 it surrounds. This change in index advantageously keeps the light beam to be amplified 91 within the core 11, preventing it from escaping into the optical cladding 12.

[0053] The optical cladding 12 is itself capable of guiding a light beam along the amplifying optical fiber 1. A light flux 92, referred to as the "pump flux," is introduced into this optical cladding 12. As it propagates along the optical cladding 12, this pump flux 92 passes through the doped core 11, where the photons are absorbed by the doping ions of the core 11, which then transition to an excited state. These excited doping ions of the core 11 then amplify the light beam 91 propagating through the core 11.

[0054] The optical cladding 12 surrounding the core 11 of the amplifying optical fiber 1 must ensure the guidance of the pump light flux 92. For this purpose, in the embodiment shown, this optical cladding 12 is surrounded by another optical cladding, called the external optical cladding 13, whose refractive index is lower than that of the optical cladding 12 surrounding the core 11, so that the index step prevents the pump light flux 92 from escaping from the optical cladding 12 surrounding the core 11.

[0055] In the embodiment shown, the external optical sheath 13 surrounding the optical sheath 12 surrounding the core 11 is surrounded by an external coating 14, which prevents any leakage of light flux outside the amplifying optical fiber 1 and contributes to the protection of the amplifying optical fiber 1 against mechanical stresses.

[0056] According to the invention, this external coating 14 is made of a material with high thermal conductivity. This material thus has a thermal conductivity coefficient greater than 1 W / mK, which is higher than that of polymer materials commonly used for external coatings of optical fibers. Preferably, this thermal conductivity coefficient is greater than 2 W / mK. It is particularly advantageous for this thermal conductivity coefficient to be greater than 30 W / mK, which is the case for most metallic materials.

[0057] Thus, the external coating 14 can for example be made of a metallic material, or of another material with high thermal conductivity, such as for example a composite or organic material.

[0058] It is particularly advantageous to make this coating from a metallic material. Such metallic external coatings for optical fibers are known to those skilled in the art. In particular, they are known to exhibit mechanical strength and heat resistance that are superior to those of conventional polymer coatings. In addition to these previously identified characteristics, metallic external coatings exhibit thermal conductivity much higher than that of polymer coatings. They can therefore contribute more significantly to the distribution and dissipation of heat from the amplifying optical fiber 1.

[0059] Such an external coating 14 may, for example, consist of a metal such as gold, aluminum, or copper, which have very high thermal conductivity (generally greater than 200 W / m / K). The manufacturing processes for optical fibers coated with such metallic external coatings are known to those skilled in the art.

[0060] To obtain very high power amplification, a very high power pump luminous flux 92 is introduced into the optical cladding 12 of the amplifying optical fiber 1.

[0061] Part of this pump 92 luminous flux can be introduced into the optical sheath 12 surrounding the core 11 of the amplifying optical fiber 1 at the ends of this amplifying optical fiber 1, according to a conventional technique well known to those skilled in the art.

[0062] In the embodiment shown, at least part of this pump light flux propagating in the amplifying optical fiber 1 is introduced by one or more lateral pump devices 2.

[0063] The fiber laser amplifier segment represented by [Fig. 1] shows such a lateral pump device 2, equipping the amplifying optical fiber 1. The fiber amplifier may, however, comprise a plurality of these lateral pump devices 2, for example distributed along its length, and may also comprise pump devices at the ends of the amplifying optical fiber 1.

[0064] The lateral pump device 2, which is represented in [Fig. 1], comprises a pump optical fiber 21, which conducts a luminous flux 93 produced by a light-emitting diode 22. This pump optical fiber 21 is assembled, for example by welding, to the optical cladding 12 of the amplifying optical fiber 1, at a junction zone 20 where the outer coating 14 of the optical fiber amplifier 1 has been removed. This assembly of the pump optical fiber 21 to the optical sheath 12 is made in such a way that at least part of the luminous flux 93 propagating in the pump optical fiber 21 passes, at the level of the junction zone 20, into the optical sheath 12, to form the pump luminous flux 92.

[0065] In the embodiment shown, the part of the luminous flux 93 which does not pass directly into the optical sheath 12 and which remains in the pump optical fiber 21 is reflected by a mirror 23 placed at the end of the pump optical fiber 21. It can then pass into the optical sheath 12 during a second pass at the junction zone 20.

[0066] The assembly of the lateral pump device on the amplifying optical fiber 1 requires, in a known manner, the removal of the external coating 14 at the level of a portion of this amplifying optical fiber 1.

[0067] In prior art solutions, when the external coating is made of polymers, it is possible to cut this external coating, on a section of the optical fiber, to remove it and thus expose an entire section of the amplifying optical fiber.

[0068] However, according to the invention, a different method is to be implemented to remove the external coating 14 at the level of a portion of the amplifying optical fiber 1. Thus, advantageously, the removal of the external coating 14 is carried out only on the portion of the perimeter of the amplifying optical fiber 1 onto which the pump optical fiber 21 is to be welded, and not on the entire perimeter.

[0069] Figure 2, which shows a perspective view of the portion of the optical fiber amplifier represented by Figure 1, shows such a cut 140 in the outer coating 14. Three successive segments can be distinguished on the portion of the amplifying optical fiber 1 shown. At the first segment 101 of the amplifying optical fiber 1, located on one side of the junction zone 20 (i.e., between this junction zone 20 and a first end of the amplifying optical fiber 1), the outer coating 14 completely covers the amplifying optical fiber 1. Similarly, at the second segment 102 of the amplifying optical fiber 1, located on the other side of the junction zone 20 (i.e., between this junction zone 20 and a second end of the amplifying optical fiber 1), the outer coating 14 completely covers the amplifying optical fiber 1.In contrast, segment 103 of the amplifying optical fiber 1, which extends between the first segment 101 and the second segment 102, corresponds to the portion of the amplifying optical fiber 1 on which the cut 140 is formed in the outer coating. This segment 103 therefore includes the junction zone 20, which is formed in the cut 140 of the outer coating 14. At this segment 103, the outer coating 14 covers only a portion of the perimeter of the amplifying optical fiber 1. This external coating is not, however, completely removed at the junction zone 20, so that it extends without interruption between the first segment 101 and the second segment 102 of the amplifying optical fiber.

[0070] Thus, advantageously, the outer coating 14 surrounding the amplifying optical fiber 1 continues continuously along the amplifying optical fiber 1. Indeed, this outer coating 14 completely surrounds this amplifying optical fiber 1 on both sides of the junction zone 20 of the lateral pump device 2 on this amplifying optical fiber 1, and covers a portion of the perimeter of this amplifying optical fiber 1 at the level of this junction zone 20. Preferably, at the level of this junction zone 20, the outer coating 14 thus covers between 50% and 80% of the perimeter of the amplifying optical fiber 1.

[0071] The removal of the outer coating 14, on the portion of the perimeter of the amplifying optical fiber 1 to which the pump optical fiber 21 is to be welded, can advantageously be carried out by laser ablation of this outer coating 14, which is advantageously limited to the area where the junction is to be made. For this purpose, a laser is focused on the surface to be ablated, and the photons, by heating, remove the material. The displacement of the focal point determines the surface to be ablated.

[0072] Such laser ablation of the outer coating 14 has the advantage of being able to be carried out efficiently, regardless of the material composing the outer coating. Thus, it can efficiently remove coatings, such as certain metallic coatings, which adhere strongly to the optical fiber they surround, and which cannot be easily removed by a mechanical stripping operation.

[0073] On the occasion of this removal of the external coating 14, it may be planned to also cut the external optical sheath 13, when the amplifying optical fiber 1 includes such an external optical sheath 13, in order to allow the welding of the pump optical fiber 21 directly onto the optical sheath 12 surrounding the core 11.

[0074] The presence of the external coating 14 continuously, over at least part of the perimeter of the amplifying optical fiber 1, allows a distribution and dissipation of thermal energy much more efficiently than in previous solutions of lateral pumps of amplifying fibers.

[0075] This solution according to the invention therefore makes it possible to significantly increase the pump power injected into the amplifying optical fiber 1, and thus the amplification power of this amplifying optical fiber 1. The external coating, preferably continuous along the entire length of the fiber, thus allows for heat distribution and dissipation that greatly limits the risk of light beam degradation due to local temperature rise and the risk of destruction of the fiber-based optical amplifier by excessive temperature rise. This good temperature dissipation allows for the introduction of very high pump power, by lateral pump devices 2, which allow a homogeneous distribution of pump energy over the length of the pump.

[0076] The use of the solution according to the invention therefore makes it possible to push back the limits hindering the production of very high power laser beams by amplifying optical fibers.

Claims

Demands

1. Fiber optic amplifier, said amplifier comprising an amplifying optical fiber (1), comprising - at least one doped heart (11), - at least one optical sheath (12, 13) surrounding said core(s) (11), and - an external coating (14) surrounding said optical sheaths (12, 13), said optical amplifier comprising at least one lateral pump device (2), comprising a pump optical fiber (21) assembled to said optical sheath (12) of said amplifying optical fiber (1), or to at least one of said optical sheaths (12, 13) of said amplifying optical fiber (1), at a junction zone (20) located between the two ends of said amplifying optical fiber (1), so as to permit the transfer into said optical sheath (12), or into at least one of said optical sheaths (12, 13), of at least a portion of a luminous flux (93) propagating in said pump optical fiber (21), characterized in that said outer coating (14) - is made of a material with a thermal conductivity coefficient greater than 1 W / mK, - covers at least 90% of the perimeter of said amplifying optical fiber (1), at the level of a first segment (101) of said amplifying optical fiber (1), located between said junction zone (20) and a first end of said amplifying optical fiber (1), and at the level of a second segment (102) of said amplifying optical fiber (1), located between said junction zone (20) and a second end of said amplifying optical fiber (1), - covers a part of the perimeter of said amplifying optical fiber (1), at the level of a segment (103) of said amplifying optical fiber (1) comprising said junction zone (20), and extending between said first segment (101) and said second segment (102) of said amplifying optical fiber (1), in such a way that said outer coating (14) extends without interruption between said first segment (101) and second segment (102) of said amplifying optical fiber (1).

2. Fiber optic amplifier according to the preceding claim, characterized in that said external coating (14) fully covers the perimeter of said amplifying optical fiber (1) at said first segment (101) and second segment (102) of said amplifying optical fiber (1).

3. Fiber optic amplifier according to any one of the preceding claims, characterized in that said external coating (14) is made of a metallic material.

4. Fiber optic amplifier according to any one of the preceding claims, characterized in that the assembly of said pump optical fiber (21) to said optical sheath (12) of said amplifying optical fiber (1) is made by welding at said junction zone (20).

5. Fiber optic amplifier according to any one of the preceding claims, characterized in that said external coating (14) covers at least 50% of the perimeter of said amplifying optical fiber (1), over the entire length of said amplifying optical fiber (1).

6. Fiber optic amplifier according to the preceding claim, characterized in that the area of ​​the cross-section of said core (11), or the sum of the areas of the cross-sections of said cores, is greater than 400 pm2.

7. Fiber optic amplifier according to any one of the preceding claims, characterized in that it comprises at least two side pump devices (2), each of said side pump devices (2) being assembled to said amplifying optical fiber (1) at one of said junction zones (20).

8. Fiber optic amplifier according to the preceding claim, characterized in that said junction zones (20) are distributed regularly along the length of said amplifying optical fiber (1).

9. Fiber optic amplifier according to any one of the preceding claims, characterized in that said amplifying optical fiber (1) has at least two distinct optical sheaths (12, 13), a first optical sheath (12) surrounding said core(s) (11) and an outer optical sheath (13) surrounding said first optical sheath (12).

10. Fiber optic amplifier according to the preceding claim, characterized in that said external optical sheath (13) is cut at said or said junction zones (20).

11. A method for manufacturing a fiber optic amplifier according to any one of the preceding claims, characterized in that it comprises a local laser ablation step of said external coating (14) to form said junction zone (20), on a portion of the perimeter of said amplifying optical fiber (1) not covering more than 50% of the perimeter of said amplifying optical fiber (1).

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