Lma optical fiber with an annular depressed-index region in the core

Abstract

An active Large Mode Area (LMA) optical fiber for mitigating Transverse Mode Instability (TMI) effects is provided. The active LMA optical fiber includes a core and one or more claddings surrounding the core. The core has a core diameter and an annular depressed-index region in a transverse plane of the LMA optical fiber. The annular depressed-index region has an outer diameter smaller than the core diameter and its local refractive index is lower than in the remainder of the cross-sectional area of the core. The core has a core glass composition including one or more rare-earth dopants and at least one co-dopant. The core glass composition defines a radial refractive index profile in the core of the active LMA fiber, the profile including a depression along the annular depressed-index region.

Description

[0001] LMA OPTICAL FIBER WITH AN ANNULAR DEPRESSED-INDEX REGION IN THE CORE

[0002] TECHNICAL FIELD

[0003] The technical field generally relates to active Large Mode Area optical fibers, and more particularly concerns fibers having a core with a radial refractive-index profile that mitigates Transverse Mode Instability effects.

[0004] BACKGROUND

[0005] Transverse Mode Instability (TMI) is a phenomenon that takes place in active Large Mode Area (LMA) optical fibers once the heat load in the fiber exceeds a certain threshold. These optical fibers are often used in optical amplifiers and they have a core doped with rare earth ions such as ytterbium. The heat load is generally understood to originate from the quantum defect of the radiative transition coming from the laser inversion in the core material initiated by optical pumping, but also from background losses and photodarkening in the fiber. The instability unfolds as an undesired refractive-index grating is formed in the fiber core following the spatial intensity pattern caused by the interference of the fundamental transverse mode (LP01) with the first higher-order mode (LP11) and causing the former to shed some energy to the latter. The mode coupling taking place beyond the given threshold is responsible for beam distortions and pointing fluctuations in the amplifier output, thus limiting the use of these fibers for several applications.

[0006] The occurrence of TMI is known in the art as a serious obstacle to attempts at scaling the power of lasers based on active fibers beyond a few kilowatts, as shown in FIG. 1 (PRIOR ART). LMA fibers are known to support higher-order transverse modes in addition to the fundamental transverse mode. Indeed, LMA fibers with core diameters as large as 50 times the wavelength of the light propagating therein may not be considered singlemode, even with the most special designs known in the art. Such large core diameters are needed to reduce the optical intensity in the fiber core and to avoid distortions induced by nonlinear effects such as Stimulated Raman Scattering. On the other hand, TMI may be prevented by using fibers with smaller core diameters, such that they may support only the fundamental mode, if possible.

[0007] Various strategies for mitigating TMI effects have been reported in the art. For example, U.S. Patent No. 9,214,781 (Honea et al.) discloses an apparatus and method for suppressing modal instabilities in fiber-amplifier systems. The apparatus involves a hybrid fiber with a smaller core in the initial length where the thermal loads are the highest, followed by a larger-core fiber. U.S. Patent No. 9,972,961 (Sipes et al.) shows a fiber optic amplifier system including two stages made up of fibers with different core / cladding diameters, the stages being connected via a double mode adapter. Active methods to inhibit the onset of TMI have also been disclosed in the art, for example in U.S. Patent No. 9,235,106 (Jauregui Misas et al.) and in U.S. Patent Appl. Pub. No. 2017 / 0299900 (Montoya et al.). U.S. Patent No. 9,325,151 (Fini et al.) and U.S. Patent No. 10,263,383 (Headley) disclose TMI mitigation methods with specific layouts for fiber spooling in laser systems. Finally, U.S. Patent Appl. serial No. 17 / 836.153 (Roy et al.) discloses active LMA optical fibers having a core configured to mitigate TMI effects. The core has a center core region and a peripheral core region which are doped so that the radial refractive-index profile of the core is generally continuous while the temperature coefficient of the core material is lower in the peripheral region than in the center region.

[0008] There remains a need in the art for TMI mitigation strategies that provide at least some improvements on the prior art.

[0009] SUMMARY

[0010] In accordance with one aspect, there is provided an active Large-Mode-Area (LMA) optical fiber for mitigating Transverse Mode Instability (TMI) effects, the active LMA optical fiber comprising: - a core; and

[0011] - one or more claddings surrounding said core; wherein the core has a core diameter and comprises an annular depressed- index region in a transverse plane of the LMA optical fiber, the annular depressed-index region having an outer diameter smaller than the core diameter, the core having a core glass composition comprising one or more rare-earth dopants and at least one co-dopant, the core glass composition defining a radial refractive index profile in the core of the active LMA fiber, said radial refractive index profile comprising a depression along the annular depressed-index region.

[0012] In some implementations, the at-least one co-dopant comprises one or more index-lowering co-dopant provided in the annular depressed-index region and absent from said core outside of the annular depressed-index region.

[0013] In some implementations, the at-least one co-dopant comprises one or more index-lowering co-dopant is provided in the core in a concentration higher in the annular depressed-index region than outside of the annular depressed-index region.

[0014] The one or more index-lowering co-dopant may comprise at least one of fluorine and boron. In some implementations, the at least one co-dopant may comprise one or more index-raising co-dopant provided outside of the annular depressed- index region and absent from the depressed-index region. In some implementations, the at least one co-dopant may comprise one or more indexraising co-dopant provided in the core in a concentration higher outside of the annular depressed-index region than in the annular depressed-index region. The one or more index-raising co-dopant may comprise at least one of aluminum, phosphorus and germanium. In some implementations, the depression in the radial refractive index profile has a tapered side edge outwardly of the core.

[0015] In some implementations, the depression in the radial refractive index profile has a tapered side edge inwardly of the core.

[0016] In some implementations, the depression in the radial refractive index profile has a uniform depth.

[0017] In some implementations, the core has a center region inwardly of the annular depressed-index region, and the radial refractive index profile within said center region is uniform or non-uniform. In some variants, a refractive index difference between the center region of the core and the annular depressed-index region may be lower than a refractive index difference between the center region of the core and an innermost one of said one or more claddings. In some variants, the core may have an outer region extending between the depressed-index region and the one or more claddings, and wherein a refractive index within said outer region differs from a refractive index in the center region.

[0018] In some implementations, the core diameter dcorehas a value lower than 100 pm.

[0019] In some implementations, the core has a numerical aperture NA lower than 0.10.

[0020] In some implementations, a width of the annular depressed-index region has a value ranging from about one time to about ten times a wavelength of light propagating in the core.

[0021] In some implementations, a depth of the depression in the radial refractive index profile has a value between about 10’4and about 10’3. In some implementations, the active LMA optical fiber further comprises stress applying members extending longitudinally within the one or more claddings alongside the core.

[0022] In some implementations, the one or more rare-earth dopants are concentrated in the center region of the core and comprise at least one of ytterbium, erbium, thulium, neodymium, holmium, and praseodymium.

[0023] Other features and advantages will be better understood upon reading of detailed embodiments with reference to the appended drawings.

[0024] BRIEF DESCRIPTION OF THE DRAWINGS

[0025] FIG. 1 (PRIOR ART) is a graph of the laser slope efficiency beyond the TMI threshold, as measured using a conventional polarization-maintaining 20 / 400 LMA optical fiber.

[0026] FIGs. 2A and 2B respectively show the schematic cross-sectional area and the radial refractive-index profile of an active LMA optical fiber according to one embodiment.

[0027] FIGs. 3A and 3B respectively show the schematic cross-sectional area and the radial refractive-index profile of an active LMA optical fiber according to one embodiment in which the fiber is polarization-maintaining.

[0028] FIG. 4 (PRIOR ART) is a graph of the ratio of the LPn and LP01 mode field areas for a step-index optical fiber as a function of the normalized frequency V.

[0029] FIGs. 5A to 5H are examples of radial refractive-index profiles of the core of LMA optical fibers having annular depressed-index regions with various depths and widths. FIGs. 6A and 6B are graphs respectively showing the radial intensity distributions of the LP01 (FIG. 6A) and LPi 1 (FIG. 6B) modes for a 35-pm core fiber with a stepindex profile (dash-dotted line) and a 45-pm core fiber with an annular depressed- index region (solid line).

[0030] FIG. 7 is a graph of the ratio of the LP11 and LP01 mode field areas for a step-index fiber (dashed line) and an LMA optical fiber having a core with a radial refractive index profile such as shown in FIG. 5A (solid line), as a function of the normalized frequency V. The normalized frequency of LMA optical fibers such as disclosed herein is determined from the parameters of the equivalent step-index fiber with the depth of the annular depressed-index region ranging from 0 to 8x1 O’4(filled diamonds).

[0031] FIGs. 8A to 80 illustrate radial refractive-index profiles of LMA optical fibers according to various embodiments of multi-cladding fibers.

[0032] FIG. 9 shows an example radial refractive-index profile of the core of an LMA optical fiber having an annular depressed-index region, the rare-earth dopants (depicted herein by the gray shaded area) being concentrated in the center region of the core.

[0033] DETAILED DESCRIPTION

[0034] In the following description, similar features in the drawings have been given similar reference numerals. In order not to unduly encumber the figures, some elements may not be indicated on some figures if they were already mentioned in preceding figures. It should also be understood herein that the elements of the drawings are not necessarily drawn to scale and that the emphasis is instead being placed upon clearly illustrating the elements and structures of the present embodiments. The terms “a”, “an” and “one” are defined herein to mean “at least one”, that is, these terms do not exclude a plural number of items, unless stated otherwise. Terms such as “substantially”, “generally” and “about”, that modify a value, condition or characteristic of a feature of an exemplary embodiment, should be understood to mean that the value, condition or characteristic is defined within tolerances that are acceptable for the proper operation of this exemplary embodiment for its intended application.

[0035] Unless stated otherwise, the terms “connected” and “coupled”, and derivatives and variants thereof, refer herein to any structural or functional connection or coupling, either direct or indirect, between two or more elements. For example, the connection or coupling between the elements may be mechanical, optical, electrical, logical, or any combination thereof.

[0036] In the present description, the terms “light” and “optical”, and variants and derivatives thereof, are used to refer to radiation in any appropriate region of the electromagnetic spectrum. The terms “light” and “optical” are therefore not limited to visible light, but can also include, without being limited to, the infrared or ultraviolet regions of the electromagnetic spectrum. Also, the skilled person will appreciate that the definition of the ultraviolet, visible and infrared ranges in terms of spectral ranges, as well as their boundaries, may vary depending on the technical field or the definitions under consideration, and are not meant to limit the scope of applications of the present techniques.

[0037] To provide a more concise description, some of the quantitative expressions given herein may be qualified with the term "about". It is understood that whether the term "about" is used explicitly or not, every quantity given herein is meant to refer to an actual given value, and it is also meant to refer to the approximation to such given value that would reasonably be inferred based on the ordinary skill in the art, including approximations due to the experimental and / or measurement conditions for such given value. In the present description, the term “about” means within an acceptable error range for the particular value as determined by one of ordinary skill in the art, which will depend in part on how the value is measured or determined, i.e. the limitations of the measurement system. It is commonly accepted that a 10% precision measure is acceptable and encompasses the term “about”.

[0038] In the present description, when a broad range of numerical values is provided, any possible narrower range within the boundaries of the broader range is also contemplated. For example, if a broad range value of from 0 to 1000 is provided, any narrower range between 0 and 1000 is also contemplated. If a broad range value of from 0 to 1 is mentioned, any narrower range between 0 and 1 , i.e. with decimal value, is also contemplated.

[0039] In accordance with some aspects, there is provided an active Large-Mode-Area (LMA) optical fiber having a core with a refractive index profile that mitigates Transverse Mode Instability (TMI) effects.

[0040] Referring to FIGs. 2A and 2B, the schematic cross-sectional area of an active LMA optical fiber 20 according to one embodiment and the corresponding radial refractive index profile 26 are shown. The profile 26 of FIG. 2B thus depicts how the local refractive index of the optical fiber evolves along any given radial line passing through the center position of the cross-sectional area of the fiber.

[0041] The active LMA optical fiber 20 includes a core 22 and one or more claddings 40a, 40b, ... , surrounding the core 22. In some variants, the active LMA optical fiber 20 may have a single cladding 40a. In other embodiments, the active LMA optical fiber 20 may be a multi-clad optical fiber including two or more claddings 40a, 40b, .... A polymer jacket or other coating (not shown) may be provided around the outermost cladding 40b, as well known in the art. While the example illustrated in FIG. 2A shows a double-clad fiber including a first cladding 40a and a second cladding 40b, it will be readily understood that a greater number of claddings may be provided in other embodiments. Multi-clad fibers may for example be used to amplify light in devices such as fiber lasers and amplifiers. Such devices are used in a wide range of applications in fields such as medicine and surgery, scientific instrumentation, semiconductor device manufacturing, military technology, and industrial material processing.

[0042] In some variants, such as for example shown in FIGs. 3A and 3B, the active LMA optical fiber may include stress-applying members 42a, 42b extending longitudinally within at least one of the one or more claddings 40a, 40b, ... , alongside the core 22 so as to maintain the polarization of light in a linear state. In the embodiment illustrated in FIG. 3A, the stress-applying members 42a, 42b extend within the first cladding 40a. Optical fibers provided with stress-applying members are generally known in the art as panda or bow-tie polarizationmaintaining fibers. Such specialty fibers are used in fiber lasers and amplifiers in some of the fields listed above, for instance when a specific application requires the light to be linearly polarized. For example, the generation of laser frequency harmonics using nonlinear optical crystals is one instance in which linearly- polarized light is required, chirped-pulse amplification using grating pair pulse compressors in ultrafast lasers being another instance.

[0043] Parameters of the active LMA optical fiber 20 such as the respective composition, size and configuration of the core 22 and of the one or more claddings 40a, 40b, ... , may be selected in view of the intended use of the fiber. As known in the art, the core 22 is configured to support the propagation of a light beam to be amplified in a fundamental core mode of the typically few-mode active LMA optical fiber 20, while the claddings 40a, 40b, ... , are configured to confine the light beam within the core 22. When the active LMA optical fiber 20 is used in a cladding-pumped implementation, at least one of the claddings 40a, 40b, ... , may also be configured to support and guide an optical pump beam in one or more cladding modes. Referring back to FIGs. 2A and 2B, the core 22 has a core diameter dcore. The core 22 includes an annular (ringlike) depressed-index region 24 in any given transverse plane P of the LMA optical fiber 20, corresponding to the plane of the page in the representation of FIG. 2A. The annular depressed-index region 24 is sketched in black in FIG. 2A. As better seen in FIG. 2B, the local refractive index in the region 24 is lower than in the remainder of the cross-sectional area of the core 22. The annular depressed-index region 24 has an outer diameter dring_out and an inner diameter dnng n, their half difference then defining a width tring of the region 24. In typical implementations, the outer diameter dring_out of the annular depressed- index region 24 is smaller than the core diameter dcore while the inner diameter dringjn is greater than zero. The core therefore has a center region 23 inwardly of the depressed-index region 24, and an outer region 25 extending between the depressed-index region 24 and the one or more claddings 40.

[0044] The core 22 has a core glass composition including a glass host such as silica glass, and one or more rare-earth dopants such as ytterbium (Yb3+), neodymium (Nd3+), erbium (Er3+), thulium (Tm3+), praseodymium (Pr3+) and holmium (Ho3+). As will be readily understood by one skilled in the art, the rare-earth dopants provide for the amplification of light propagating in the core when pumped by an optical pump beam of appropriate energy, defining the “active” characteristic of the active LMA optical fiber 20. By way of example, light of wavelength ranging from about 1020 nm to about 1080 nm may be amplified from stimulated emission of radiation initiated by 976-nm optical pump light with a numerical aperture (NA) less than 0.46 and launched in one or more of the claddings prior to being absorbed in the core of the active LMA optical fiber (doped with ytterbium in this example).

[0045] In some implementations, the rare-earth dopants may be confined within the center region 23 of the core 22. This is done for instance to increase gain saturation by the fundamental mode and minimize the overlap of the higher-order modes with the rare-earth dopants. The rare-earth dopants may be circumscribed for instance to the region bounded by the annular depressed-index region 24. This means that the portion of the cross-sectional area of the core doped with rare earths is delimited by a diameter ddopants that may be smaller than the outer diameter dring_out while being larger than the inner diameter dring n. By way of example, FIG. 9 shows an example of a radial refractive index profile 27 of the core of an LMA optical fiber in which the rare-earth dopants (gray-shaded) are concentrated in the center region 23 of the core. It will be readily understood that in other variants the region of the core in which the rare-earth dopants are concentrated extends either in or out of the annular depressed-index region 24.

[0046] Referring to FIGs. 2A, 2B, 3A and 3B, the core glass composition further includes at least one co-dopant, which may for example be embodied by aluminum, phosphorus, fluorine, or combinations thereof. The rare-earth dopant(s) and the at least one co-dopant have respective concentrations and distributions determining the radial refractive index profile 27 of the core 22, that is, the portion of the whole radial refractive index profile 26 of the active LMA optical fiber 20 which is located within the core 22. As explained further below, the radial refractive index profile 27 of the core 22 includes a depression 28 along the annular depressed-index region 24.

[0047] Values of the molar refractivities of dopants are reported in the scientific literature and are most often quoted with respect to the oxide species (e.g., AI2O3, P2O5, ... ). In the present description, the rare-earth dopants and the co-dopants may be referred to using the chemical element name of the corresponding oxide. For instance, one can refer to “aluminum” or “phosphorus” co-dopants, and to “ytterbium” dopant. One skilled in the art will understand that such elements are present in the optical fiber in their oxide form. Hence, the terms “aluminum” and “aluminum oxide” co-dopant can be used interchangeably. Similarly, the terms “phosphorus” and “phosphorus oxide” co-dopant can be used interchangeably. Regarding the rare earth dopants, such as ytterbium for instance, one will use the terms “ytterbium”, “Yb3+”, “ytterbium oxide”, and “Yb2O3” interchangeably. As mentioned above, TMI takes place in active LMA optical fibers when the heat load in the optical fiber exceeds a certain threshold. In accordance with one aspect, the structure and composition of the core of the LMA optical fiber disclosed herein may be configured to increase this threshold to greater output powers, and therefore mitigate or prevent the onset of TMI. In some implementations, this may be achieved by tailoring the radial refractive index profile of the active LMA optical fiber 20 to substantially reduce the transverse spatial overlap of the linearly- polarized LP11 mode with the linearly-polarized LP01 mode guided by the LMA optical fiber, and further with the gain region in embodiments wherein the rare earths are confined at the center of the core.

[0048] For illustrative purposes only, the ratio ALP11 / ALP01of the mode field areas of the LP11 and LP01 modes may be used to show the influence of the physical parameters of the LMA optical fiber on the spatial overlap between these modes. Referring to FIG. 4 (PRIOR ART), this ratio is plotted for step-index fibers with respect to the normalized frequency V defined as

[0049] V = dcoreNA / A. where dcoreis the core diameter, as mentioned above, NA is the core numerical aperture and is the wavelength of light in vacuum. The ratio ALP11 / ALPQ1is seen to decrease to the asymptotic value of about 1.3 as the normalized frequency V increases. The ratio ALP11 / ALPQ1does not change appreciably as V exceeds 4. As a result, reducing the spatial overlap between the LPn and LP01 modes (or increasing the ratio ALP11 / ALP01) in LMA fibers with core diameters dcoregreater than about 20 pm is challenging.

[0050] As mentioned above and as shown in both FIGs. 2B and 3B, the core glass composition is such that the radial refractive index profile 27 of the core includes a depression 28 along the annular depressed-index region in the embodiments of the active LMA optical fibers described herein,. In some implementations, the at least one co-dopant may include one or more index-lowering dopant(s) provided in the annular depressed-index region and absent from the remainder of the core or present in smaller concentrations. In another variant, the at least one co-dopant may include one or more index-raising dopant(s) introduced outside of the annular depressed-index region or provided in smaller concentrations in the annular depressed-index region than in the remainder of the core. In some implementations, the index-raising dopants may be chosen from aluminum, phosphorus and germanium, whereas the index-lowering dopants may be chosen from fluorine and boron.

[0051] FIGs. 5A to 5H show examples of the radial refractive index profile 27 of the core according to various implementations. All of the radial refractive index profiles depicted in FIGs. 5A to 5H pertain to optical fiber structures that may be assumed to have rotational symmetry about the core center position located at X = 0. The vertical axis of each of these figures corresponds to the incremental refractive index An relative to the refractive index of the first cladding 40a immediately surrounding the core 22. This choice then means that each radial refractive index profile decreases down to zero at the outer edges of the core.

[0052] The depression 28 in the radial refractive index profile 27 of the core may be narrow or wide, depending on the core diameter dcoreand core numerical aperture NA. In some instances, the width tnng of the index depression 28 may be as small as a few times the wavelength of light, e.g., for small core diameters, while in other instances the width of the depression 28 may be as large as ten times the wavelength of light, even more for very large cores.

[0053] The depression 28 may also be shallow or deep, again depending on the core diameter dcoreand core NA. The depth of the index depression 28 may be n the range of about 10’4to 10’3. In some implementations, the depression 28 may have a uniform depth, such as for example shown in FIGs. 5A, 5E, 5F and 5G. In other implementations, the depression may have a radially varying depth defining a tapered side edge 30a or 30b, either inwardly, outwardly, or both (see for example FIGs. 5B, 50, 5D and 5H). Furthermore, the refractive index in the center region 23 of the core may be uniform (see FIGs. 5A to 5E and 5H), or it may assume a non-uniform profile such as for example a step (or staircase) profile (see FIG. 5F) or a dome-shaped profile (see FIG. 5G). The index contrast or difference between the center region of the core and the annular depressed-index region is preferably lower than the index contrast between the core center region and the first cladding. Accordingly, the refractive index in the outer region of the core may differ from that in the center region.

[0054] In some implementations, the index contrast between the outer region 25 of the core 22 and the annular depressed-index region 24 may be adjusted to avoid excessive propagation loss for the LP01 mode when bending the fiber, while effectively reducing the spatial overlap of the LPn mode with the LP01 mode. This is generally possible if the refractive index of the outer region 25 is lower than that of the center region 23, such as shown for example in FIGs. 5E to 5H. A tradeoff is met at some point, i.e., while the spatial overlap between the LPu and LP01 modes is getting smaller as the refractive index of the outer region 25 is about the same as that of the center region 23, the bend-induced propagation losses of the LP01 mode are also increasing (and the other way around as the refractive index of the outer region 25 is set much below that of the center region 23).

[0055] The embodiments shown in FIGs. 5A to 5H all have a same core diameter dcore= 45 pm whereas the index contrast between the core and the cladding is adjusted so they have a mode field area of 550 pm2. As a comparison, a step-index fiber with a core diameter dcoreof 35 pm and a core NA of 0.065 (index contrast of about 1.5x10-3) would yield the same mode field area. It will be readily understood that the specific numbers mentioned herein are meant to serve as an example. In some embodiments, the active LMA optical fiber 20 may have a core diameter dcorepreferably lower than about 100 pm. Likewise, the active LMA optical fiber 20 may have a core NA preferably lower than about 0.10. Still referring to the embodiments shown in FIGs. 5A to 5H, the index contrast between the annular depressed-index region and the center region of the core is shown, by way of example, at about 3x1 O’4to 5x1 O’4for a core diameter of about 45 pm. In some implementations, this refractive index difference could be lower or higher for different core diameters and core NA. In some variants, the difference in the refractive indices of the depressed-index region and the of center region of the core may be selected so as to minimize the spatial overlap of the LP01 mode with the LPi 1 mode. In a step-index fiber, the mode field corresponding to the LPn mode extends further away from the center region of the core than the mode field corresponding to the LP01 mode. In active LMA optical fibers having a depressed- index region such as described herein, the mode field corresponding to the LPn mode stretches even further away from the center, whereas the mode field corresponding to the LP01 mode gets more confined. This can be observed for example on the graphs of FIGs. 6A and 6B showing the radial intensity distributions of the LP01 (FIG. 6A) and LPi 1 (FIG. 6B) modes for a 35-pm core fiber with a stepindex profile (dash-dotted line) and a 45-pm core fiber with an annular depressed- index region (solid line).

[0056] In some implementations, the mid-diameter dringof the annular depressed-index region 24 may also be adjusted so as to minimize the spatial overlap of the LP01 and LPi 1 modes. For illustrative purposes only, the ratio dring / dcorehas been set to about 0.65 for the embodiments illustrated in FIGs. 5A to 5H. This ratio may be tailored according to the core diameter dcoreand core NA. The ratio dring / dcorewill assume a smaller value as the LP01 and LPn modes are further confined toward the center region of the core, i.e. , as the core diameter dcoreand / or the core NA are set larger than 45 pm and / or 0.065, respectively. On the other hand, if the core diameter dcoreand / or the core NA are smaller than 45 pm and / or 0.065, the ratio dring / dcorewill take on a larger value. In general, it may be said that an unduly high ratio dring / dcorewill bring little benefit, while an unduly low ratio dring / dcore will cause distortions on the intensity distribution of the LP01 such that the laser beam at the output of the fiber may not be considered diffraction-limited anymore.

[0057] By way of example, the evolution of the ratio of the mode field areas ALP11 / ALPQ1is illustrated in FIG. 7 for the specific embodiment shown in FIG. 5A (solid line) as a function of the depth of the depressed-index region, all other parameters remaining unchanged. The ratio ALP11 / ALPQ1is seen to exceed almost twice the ratio obtained for step-index fibers (dashed line). Similar results (not shown) may be obtained for the other embodiments shown in FIGs. 5B to 5H. Likewise, optical fibers with cores having depressed-index regions different from the ones illustrated in FIGs. 5A to 5H may yield similar results.

[0058] The normalized frequency V for the solid curve plotted in FIG. 7 was calculated assuming the core diameter deqand core numerical aperture NAeqof the equivalent step-index fiber, i.e. , a step-index fiber with a LP01 mode having the same effective index and the same mode field diameter as for the fiber having the radial refractive index profile shown in FIG. 5A. The normalized frequency determined according to the parameters of the equivalent step-index fiber discussed above decreases as the depth of the depressed-index region increases, as shown in FIG. 7. A trade-off may therefore be expected as smaller normalized frequencies are reached, since the mode field area also decreases as the fiber comes closer to the single-mode cutoff.

[0059] Active LMA optical fibers as described herein may be fabricated according to known methods and techniques. The addition of index-lowering co-dopants in the annular depressed-index region or, likewise, the addition of index-raising codopants outside of the annular depressed-index region may be made in proportion to the molar refractivity of the index-lowering (or index-raising) co-dopant(s), given the core NA and the molar concentrations of the other dopants and co-dopants present in the optical fiber preform. The tailored refractive index profiles contemplated herein may require good control of the fiber fabrication process. More specifically, in core regions where the refractive index is not uniform the molar concentrations of co-dopants change according to a predefined radial gradient. The gradient of the concentration is first calculated according to the refractive index profile and the molar refractivity of the dopants. In polarizationmaintaining embodiments such as shown in FIG. 3A, stress birefringence may for example be induced in the active LMA optical fiber by introducing boron-doped rods alongside the core prior to fiber drawing. Birefringence ranging from 1 xi O’4to 4x1 O’4may be achieved in this way provided that the boron-doped stress rods are dimensioned accordingly.

[0060] As mentioned above, the active LMA optical fiber as described herein may have multiple claddings 40 surrounding the core. FIGs. 8A to 8C show examples of radial refractive index profiles 26 of active LMA optical fibers according to various multi-clad embodiments. In some implementations, the innermost (first) cladding has a refractive index 32 lower than the mean refractive index of the core 34, with the core NA governed by the index contrast between the core and the innermost cladding. The outermost cladding is generally made up of a fluorinated acrylate polymer having a refractive index 36 of about 1.37 and a numerical aperture of 0.46 or higher. The outermost cladding may sometimes consist of fluorine-doped silica glass, in which case the refractive index 36 is about 1.43 and the resulting numerical aperture is 0.22 or higher. Any intermediate cladding(s) (see FIG. 8B) may have refractive indices 39 either higher or lower than the refractive index 32 of the first cladding. For instance, the intermediate cladding(s) may be made of pure silica glass or of silica glass doped with at least one of an index-raising dopant and / or one of an index-lowering dopant. The inner edge of the outer cladding may delineate a circle having a diameter ranging from 80 pm to 600 pm.

[0061] Of course, numerous additional modifications could be made to the embodiments described above without departing from the scope of protection as defined in the appended claims.

Claims

CLAIMS1 . An active Large-Mode-Area (LMA) optical fiber for mitigating Transverse Mode Instability (TMI) effects, the active LMA optical fiber comprising:- a core; and- one or more claddings surrounding said core; wherein the core has a core diameter and comprises an annular depressed- index region in a transverse plane of the LMA optical fiber, the annular depressed-index region having an outer diameter smaller than the core diameter, the core having a core glass composition comprising one or more rare-earth dopants and at least one co-dopant, the core glass composition defining a radial refractive index profile in the core of the active LMA fiber, said radial refractive index profile comprising a depression along the annular depressed-index region.

2. The active LMA optical fiber according to claim 1 , wherein the at-least one codopant comprises one or more index-lowering co-dopant provided in the annular depressed-index region and absent from said core outside of the annular depressed-index region.

3. The active LMA optical fiber according to claim 1 , wherein the at-least one co- dopant comprises one or more index-lowering co-dopant is provided in the core in a concentration higher in the annular depressed-index region than outside of the annular depressed-index region.

4. The active LMA optical fiber according to claim 1 or 2, wherein the one or more index-lowering co-dopant comprises at least one of fluorine and boron.

5. The active LMA optical fiber according to any one of claims 1 to 3, wherein the at least one co-dopant comprises one or more index-raising co-dopant providedoutside of the annular depressed-index region and absent from the depressed- index region.

6. The active LMA optical fiber according to any one of claims 1 to 3, wherein the at least one co-dopant comprises one or more index-raising co-dopant provided in the core in a concentration higher outside of the annular depressed-index region than in the annular depressed-index region.

7. The active LMA optical fiber according to claim 5 or 6, wherein the one or more index-raising co-dopant comprises at least one of aluminum, phosphorus and germanium.

8. The active LMA optical fiber according to any one of claims 1 to 7, wherein the depression in the radial refractive index profile has a tapered side edge outwardly of the core.

9. The active LMA optical fiber according to any one of claims 1 to 8, wherein the depression in the radial refractive index profile has a tapered side edge inwardly of the core.

10. The active LMA optical fiber according to any one of claims 1 to 7, wherein the depression in the radial refractive index profile has a uniform depth.

11. The active LMA optical fiber according to any one of claims 1 to 10, wherein the core has a center region inwardly of the annular depressed-index region, and the radial refractive index profile within said center region is uniform.

12. The active LMA optical fiber according to any one of claims 1 to 10, wherein the core has a center region inwardly of the annular depressed-index region, and the radial refractive index profile within said center region is non-uniform.

13. The active LMA optical fiber according to claim 11 or 12, wherein a refractive index difference between the center region of the core and the annular depressed-index region is lower than a refractive index difference between the center region of the core and an innermost one of said one or more claddings.

14. The active LMA optical fiber according to claim 11 or 12, wherein the core has an outer region extending between the depressed-index region and the one or more claddings, and wherein a refractive index within said outer region differs from a refractive index in the center region.

15. The active LMA optical fiber according to any one of claims 1 to 14, wherein the core diameter dcorehas a value lower than 100 pm.

16. The active LMA optical fiber according to any one of claims 1 to 15, wherein the core has a numerical aperture NA lower than 0.10.

17. The active LMA optical fiber according to any one of claims 1 to 16, wherein a width of the annular depressed-index region has a value ranging from about one time to about ten times a wavelength of light propagating in the core.

18. The active LMA optical fiber according to any one of claims 1 to 17, wherein a depth of the depression in the radial refractive index profile has a value between about 10’4and about 10’3.

19. The active LMA optical fiber according to any one of claims 1 to 18, further comprising stress applying members extending longitudinally within the one or more claddings alongside the core.

20. The active LMA optical fiber according to any one of claims 11 to 19, wherein the one or more rare-earth dopants are concentrated in the center region of the core and comprise at least one of ytterbium, erbium, thulium, neodymium, holmium, and praseodymium.

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