LMA fibers for suppression of thermal mode instability

Abstract

An optical fiber, such as in some instances a high-power, diode-pumped, dual-clad, ytterbium-doped fiber amplifier (YDFAs), having a fundamental mode and at least one higher order mode, wherein the higher order mode or modes have mode areas that are substantially larger than a mode area of the fundamental mode.

Claims

1. An optical fiber comprising a core configured to guide light propagating in a fundamental mode and at least one higher order mode, wherein: the higher order mode or modes have physical mode areas that are at least 60% larger than a physical mode area of the fundamental mode, to reduce thermal mode instability between the fundamental mode and the at least one higher order mode; a refractive index profile of the optical fiber comprises a graded-index portion and a step at a core-cladding interface of the optical fiber; and an index difference between a center of the core and a cladding is equal to or greater than 0.00141.

2. The optical fiber of claim 1, wherein the higher order mode or modes have physical mode areas that are each at least 80% larger than the physical mode area of the fundamental mode.

3. The optical fiber of claim 1, wherein the optical fiber comprises a core-diameter to wavelength ratio of at least 20.

4. The optical fiber of claim 1, wherein the optical fiber comprises a numerical aperture that is less than or equal to 0.11.

5. The optical fiber of claim 1, wherein the optical fiber comprises a numerical aperture that is less than or equal to 0.08.

6. The optical fiber of claim 1, wherein the optical fiber comprises a refractive index profile of the core that has a graded index difference measured from the center of the core to an edge of the core, a total index difference between the core and the cladding measured from the center of the core to the cladding, and the graded index difference divided by the total index difference is equal to or less than 0.29.

7. The optical fiber of claim 1, wherein the optical fiber comprises a refractive index profile that has a flat top and a linear graded index portion.

8. The optical fiber of claim 1, wherein the refractive index profile generally decreases from the center of the optical fiber to an edge of the core over a range of less than or equal to 0.0015.

9. The optical fiber of claim 1, wherein the step is greater than or equal to 0.0003.

10. The optical fiber of claim 1, wherein the optical fiber comprises a gain doping region that is smaller than the physical mode area of the fundamental mode.

11. The optical fiber of claim 1, wherein the optical fiber comprises a cylindrical gain doping region centered in the core of the optical fiber, wherein the cylindrical gain doping region is smaller than the physical mode areas of the one or more higher order modes.

12. The optical fiber of claim 11, wherein the optical fiber comprises a core-diameter to wavelength ratio of at least 20 whose intensity overlap with the cylindrical gain doping region is at least 20% smaller for the one or more higher order modes than it is for the fundamental mode.

13. The optical fiber of claim 11, wherein the optical fiber comprises a core-diameter to wavelength ratio of at least 25 whose intensity overlap with the cylindrical gain doping region is at least 10% smaller for the one or more higher order modes than it is for the fundamental mode.

14. The optical fiber of claim 11, wherein the optical fiber comprises a core-diameter to wavelength ratio of at least 45 whose intensity overlap with the cylindrical gain doping region is at least 10% smaller for the one or more higher order modes than it is for the fundamental mode.

15. The optical fiber of claim 11, wherein the optical fiber comprises a core-diameter to wavelength ratio of at least 45 whose intensity overlap with the cylindrical gain doping region is at least 20% smaller for the one or more higher order modes than it is for the fundamental mode.

16. The optical fiber of claim 1, wherein the optical fiber is a doped fiber amplifier in a laser system.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 compares fundamental and higher-order modes of a conventional step-index fiber and a graded-index fiber. FIG. 1(a) shows modes of a conventional step-index fiber that are nearly the same size. In contrast, FIG. 1(b) shows modes of a graded-index fiber that are not of the same size, with higher-order modes being increasingly larger.

(2) FIG. 2 shows various non-limiting alternative fiber core designs with generally decreasing refractive index profile across the core.

(3) FIG. 3 shows a non-limiting example of a fiber core with generally decreasing refractive index profile across the core, and an abrupt step between the outer edge of the core and the cladding.

(4) FIG. 4 compares modes of an example of a cladded linear index graded (CLING) fiber compared to modes of a conventional (step-index) LMA fiber with the same mode area. The refractive index profile of the CLING fiber has a 0.00041 index grade with a 0.001 core-clad index step and is shown as the gray dotted line. The LMA fiber has a 50 μm core diameter with a 0.06 NA and is not shown.

(5) FIG. 5 depicts modes of interest in an example of a CLING fiber with (a) doping density and profile for the equivalent conventional 50 micron fiber, showing options (b,c) with increased doping density (represented by height) but with a narrower profile to provide reduced overlap with the LP.sub.11 HOM.

(6) FIG. 6 shows non-limiting examples of transverse cross sections of optical fibers having tri-fold azimuthal symmetry. The outer cross hatched areas represent the fiber cladding, while the inner cross hatched triangle (A) and circles (B) represents the fiber core(s).

(7) FIG. 7 shows fundamental and nearest HOMs calculated for an example of a triple-core (Trefoil) fiber. The dashed circles indicate the core locations.

(8) FIG. 8 shows examples of Trefoil fibers with spatially localized gain.

(9) FIG. 9 shows fundamental and nearest HOMs calculated for triple-core (Trefoil) fiber. The dashed half-circles indicate the gain regions.

DETAILED DESCRIPTION

(10) In this section, we describe examples of optical fibers that have higher-order modes that are substantially larger than both the fundamental mode, reducing the spatial overlap between the fundamental and higher-order modes, and the region providing the optical gain, reducing the spatial overlap of the heat generation region with those higher-order modes. Such fibers have a significantly increased TMI threshold.

(11) We have designed active optical fibers that have refractive index profiles that generally decrease from the center of the fiber to the edge of the core. The basic physics of this realization is depicted in FIG. 1. In the simplest terms, waveguide modes are well represented by a quantum mechanical potential (i.e., a quantum well) viewed upside down. The eigenvalues (effective indices) are positioned in the “well” at an appropriate “energy level” (location in refractive index space), and the mode size is largely dictated by the location of the edges of the “well” (refractive index boundary). This concept is shown in FIG. 1(a). Note that the modes in this case are approximately the same size and thus have high spatial (intensity) overlap, particularly for highly confined modes.

(12) A detailed calculation of the physical mode area for different LMA fiber diameters is shown in the table below. In this table, the mode size is represented as the physical mode area (an elliptical beam with orthogonal radii represented by the standard deviation of the intensity distribution) and not the nonlinear effective area that is often used to characterize fiber modes for the purpose of evaluating optical nonlinearities. Since a 20 μm LMA fiber only supports two guided modes, the second (LP.sub.11) mode extends far into the cladding. However, as the core expands, the second mode becomes more confined. This physics is well known to those skilled in the art.

(13) TABLE-US-00001 TABLE 1 Mode area for the fundamental (LP.sub.01) and next (LP.sub.11) modes for LMA fiber with 0.06 NA and various core diameters. Ratio of Core diameter LP.sub.01 mode area LP.sub.11 mode area LP.sub.11/LP.sub.01 mode areas 20 μm 259 μm.sup.2 413 μm.sup.2 1.59 25 μm 347 μm.sup.2 494 μm.sup.2 1.42 50 μm 1075 μm.sup.2  1433 μm.sup.2  1.33

Example #1: Expanded HOM Fiber

(14) One new method to reduce the overlap between the modes is to alter the profile of the “well”. Based on the above logic, it is reasonable to assume that if the “well” were tapered (i.e., a graded-index), the second mode would be larger than the fundamental mode. This concept is depicted in FIG. 1(b), and is oversimplified since the changes in n.sub.eff were not taken into account. Nonetheless, the concept of modifying the waveguide profile to affect the mode sizes stands.

(15) Although a linear graded index is shown in FIG. 1, various refractive index designs for accomplishing the desired HOM expansion are also possible, as depicted in FIG. 2. Note that these are all cross-sectional examples. The refractive index profile of a real three-dimensional fiber would vary in accordance with the various shapes as spun about their axis of symmetry (e.g., the center of the fiber).

(16) Variations from the displayed shapes and deviations expected during fabrication do not affect the physics described by these general and non-limiting examples. Note that it is not required that the fiber core be radially symmetric, although symmetric designs are generally simpler to fabricate.

(17) In a preferred embodiment, the core is surrounded by a cladding that has substantially lower refractive index than that at the outer edge of the core. This is exemplified by the non-limiting example shown in FIG. 3. If this example profile is spun about the axis of symmetry (i.e., the center) of a real fiber as it would in practice, then the three-dimensional refractive index shape formed is that of an obtuse cone atop a cylinder. This specific example is a cladded linear index-graded fiber, or CLING fiber.

(18) To demonstrate the effectiveness of one embodiment of the invention, a specific case of the geometry shown in FIG. 3 is calculated and compared to that of a standard step-index LMA fiber. The results are shown in FIG. 4. While the fundamental modes (LP.sub.01) of both fibers are nearly identical, the next mode (LP.sub.11) is clearly substantially wider in the CLING fiber compared to that of the LMA fiber. In this specific non-limiting example, the LP.sub.11 mode is 1.9 times larger (in physical mode area) than the LP.sub.01, which is significantly larger than the LMA cases, as shown in Table 1.

(19) Having a generally decreasing graded index profile provides differing effective radii of confinement for separate lateral modes of the signal light with the fundamental mode being confined to the narrowest region as shown in FIGS. 1-4. The TMI coupling coefficient given in Eqn. 1 shows that the reduced spatial overlap of the fundamental mode with the HOMs is beneficial. In addition, if the HOMs are expanded without expanding the gain region, then the perturbation itself (δn in Eqn. 1 that is generated thermally by the energy efficiency of the gain medium) is also reduced. Therefore, increasing the HOM size by itself results in a double benefit: reducing the overlap of the HOMs with the fundamental mode, and reducing the overlap of the HOMs with the perturbation.

(20) An example of this is given in Table 2, which shows the overlap of the fundamental and closest higher-order mode for LMA fibers with the gain. Note that in all cases, the overlap of the LP.sub.11 mode with the gain is high, and increases as the fiber scales to larger core diameters. Stated another way, the reduction of the LP.sub.11 overlap with the gain relative the LP.sub.01 overlap with the gain is small for standard LMA fiber and decreases rapidly at the core diameter increases.

(21) In contrast, our discovery of increasing the mode size results in significantly lower overlap of the HOMs with the gain. For the CLING fiber example previously calculated, which has a larger fundamental mode than a 50 μm LMA fiber, the HOM-overlap with the gain is 71%, significantly lower than that of standard LMA fiber of any core diameter. Moreover, the reduction of the LP.sub.11 overlap with the gain relative the LP.sub.01 overlap with the gain is quite large, approaching 25%.

(22) TABLE-US-00002 TABLE 2 Intensity overlap of the fundamental (LP.sub.01) and next (LP.sub.11) modes for (i) LMA fiber with 0.06 NA and various core diameters and (ii) the CLING fiber. The final column is the reduction in the overlap of the LP.sub.11 mode relative to the LP.sub.01 mode. LP.sub.01 overlap LP.sub.11 overlap Gain overlap Core diameter with gain with gain reduction 20 μm 0.9265 0.7726 16.6% 25 μm 0.9594 0.8823 8.0% 50 μm 0.9935 0.9829 1.1% CLING 0.9340 0.7111 23.9%

(23) The net result of these two reductions to the mode-coupling coefficient in the TMI threshold is drastic. In the single non-limiting example of the CLING fiber, a 60% increase in the threshold signal power of thermal mode instability for a 50 μm LMA fiber.

(24) The latter concept of reducing the overlap of the higher-order modes with the gain can be taken one additional step further. If the gain that nominally spans the fundamental mode were made smaller than the fundamental mode, then the coupling coefficient given in Eqn. 1 would be even smaller. This concept is shown in a non-limiting case in FIG. 5 for the CLING fiber example. Instead of the gain region filling the area of the fundamental mode as in case (a), it can be made smaller as in case (b) or (c) to further decrease the TMI coupling coefficient. Those skilled in the art recognize that gain can be provided by ionic doping (for example ytterbium, erbium, or thulium), nonlinear processes (for example stimulated Raman scattering), and other means.

(25) It has been shown that in the absence of TMI, making the gain region smaller than the fundamental mode can produce optimal benefits for beam quality (filtering out HOMs) without significantly impacting the efficiency of the amplifier. With the addition of TMI physics, the confined gain region adds an additional benefit in reducing the TMI coupling coefficient, thereby increasing the TMI threshold and allowing higher amplifier output power with stable beam quality.

Example #2: Broken Azimuthal Symmetry Fiber

(26) Another new method to reduce the overlap between the modes is to alter the symmetry of the “well”. By changing the symmetry of the core refractive index profile, it is reasonable to assume that the mode shapes will also change. For example, the LP.sub.11 mode of a round fiber has a mirror symmetry such that the each half of the mode look identical in intensity, albeit opposite in phase. If the symmetry of the core refractive index core is broken such that there is no longer azimuthal symmetry, then the shape and location of the LP.sub.11 mode will necessarily be highly modified. The spatial modification can not only provide lower spatial overlap with the fundamental mode, but also lower spatial overlap with the gain. Both of these factors contribute to reducing the mode-coupling coefficient in Equation (1) and will lead to an increase in the TMI threshold.

(27) One strong method for eliminating the azimuthal symmetry is by using a core with three-fold-only symmetry. Several non-limiting examples of inducing three-fold symmetry into the refractive index profile of the core of an optical fiber are shown in FIG. 6. A triangular core, as shown in FIG. 6(a), represents perhaps the most straightforward conceptualization, however manufacturing of such a core presents fabrication challenges. A simpler fabrication option is to use three separate but closely spaced cores, as shown in in FIG. 5(b). Such a triad of cores maintains the three-fold symmetry while at the same time allowing for simpler fabrication.

(28) The triple-core fiber, which we call Trefoil fiber due to its similarity to the architectural feature of the same name, does indeed significantly shift the spatial distribution of the LP.sub.11 modes. FIG. 7 shows an example of a triple-core fiber, using three standard 25 μm LMA fiber cores arranged in an equilateral distribution. Note that the fundamental (LP.sub.01) mode is largely contained to the innermost region of the three cores, the LP.sub.11 modes are not. In conventional, round, azimuthally-symmetric fibers, the LP.sub.11,a and LP.sub.11,b modes look identical, except for a rotation of 90-degrees. In this new fiber with azimuthally-broken symmetry, the LP.sub.11,a and LP.sub.11,b modes are distinctly different. The LP.sub.11,a mode has one lobe fully occupying one of the three cores, while the other lobe is stretched across the other two cores. The LP.sub.11,b mode only has substantial power in two of the three cores, with the third core carrying very little power. In both cases, the LP.sub.11 modes largely avoid the center of the fiber with their power more concentrated in the middle of the three cores. This is in direct contrast to the LP.sub.01 mode, which has its power concentrated towards the inner edge of the three cores and in the area between the cores. The non-limiting example shown in FIG. 7 clearly demonstrates how breaking the azimuthal symmetry separates the fundamental mode spatially from its nearest neighbor HOMs.

(29) The concept of reduced overlap with the gain also applies to this fiber type, particularly for localizing the gain towards the center of the fiber. In a non-limiting example, FIG. 8 shows spatially localizing the gain in the Trefoil fiber using practical manufacturing methods. In 8(a), two core halves, one with gain and one without, together comprise the core. In 8(b), each core preform has an offset confined gain region. Other configurations are readily obvious to those skilled in the art.

(30) The impact of the particular example in FIG. 8(a) is shown in FIG. 9, where it is readily obvious that the LP.sub.11 modes have significantly lower overlap with the gain region than the fundamental (LP.sub.01) mode. While the LP.sub.01 modes largely resides in the half of each of the cores that contain the gain, the LP11 modes do not. In one of the cores, the LP.sub.11,a only is half in the gain region. For the LP.sub.11,b mode, the majority of the power is clearly not in the gain region.

(31) Table 3 shows the overlap of the gain region with the fundamental and closest higher-order modes for the Trefoil fiber example shown in FIG. 8(a). In particular, the reduction of the LP.sub.11 overlap with the gain relative the LP.sub.01 overlap with the gain is very large, over 24%, which is quite significant particularly when compared to the LMA fiber shown in Table 2.

(32) TABLE-US-00003 TABLE 3 Intensity overlap of the fundamental (LP.sub.01) and next (LP.sub.11) modes for the Trefoil fiber where only the half of each core nearest the center of the fiber contains the gain. The final column is the reduction in the overlap of the LP.sub.11 modes relative to the LP.sub.01 mode. Trefoil fiber mode Intensity overlap with gain Gain overlap reduction LP.sub.01 0.7771 n/a LP.sub.11/a 0.5875 24.4% LP.sub.11/b 0.5515 29.0%

(33) The net result of these two concepts, broken azimuthal symmetry and redistributing the HOMs intensity outside the gain region, specifically using the non-limiting Trefoil fiber example shown in FIG. 8(a), resulted in a simulated 40% increase in the TMI threshold over that of a conventional 50 μm LMA fiber.

(34) It must be noted that in addition to the benefits of increasing the TMI threshold, this new concept of redistributing the HOMs allows for radically new methods for exploiting gain filtering for single-mode behavior even in the absence of TMI.

(35) It will be appreciated that variants of the above-disclosed examples and other features and functions, or alternatives, may be combined into many other different systems or applications. Various presently unforeseen or unanticipated alternatives, modifications, variations, or improvements therein may be subsequently made by those skilled in the art which are also intended to be encompassed by the following claims.