Abstract:
Apparatus and method for suppressing modal instabilities (MI) in fiber-amplifier systems. In some embodiments, thermal effects drive the MI process, and in some such embodiments, the present invention provides a plurality of options for mitigating these thermal effects. In some embodiments, the present invention provides a hybrid fiber with a smaller core in the initial length where the thermal loads are highest, followed by a larger-core fiber. In some embodiments the length of the smaller-core section is chosen to keep the core heat-per-unit-length of the second section below a critical value for the onset of MI. In some embodiments, the hybrid fiber of the present invention avoids modal instabilities while yielding almost the same performance as compared to conventional fibers with regard to minimizing fiber nonlinearities such as Stimulated Brillouin Scattering (SBS). In some embodiments, the hybrid fiber outputs a signal beam with at least 1 kW of power.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This invention is related to:
         U.S. Pat. No. 7,391,561 issued Jun. 24, 2008 to Fabio Di Teodoro et al., titled “FIBER- OR ROD-BASED OPTICAL SOURCE FEATURING A LARGE-CORE, RARE-EARTH-DOPED PHOTONIC-CRYSTAL DEVICE FOR GENERATION OF HIGH-POWER PULSED RADIATION AND METHOD,”   U.S. Pat. No. 7,768,700 issued Aug. 3, 2010 to Matthias P. Savage-Leuchs, titled “METHOD AND APPARATUS FOR OPTICAL GAIN FIBER HAVING SEGMENTS OF DIFFERING CORE SIZES,”   U.S. Pat. No. 7,876,803 issued Jan. 25, 2011 to Fabio Di Teodoro et al., titled “HIGH-POWER, PULSED RING FIBER OSCILLATOR AND METHOD,”   U.S. Patent Application Publication 2011/0122895 published May 26, 2011 by Matthias P. Savage-Leuchs et al., titled “Q-SWITCHED OSCILLATOR SEED-SOURCE FOR MOPA LASER ILLUMINATOR METHOD AND APPARATUS” (which issued as U.S. Pat. No. 8,934,509 on Jan. 13, 2015),   U.S. Pat. No. 8,441,718 issued May 14, 2013 by Roy D. Mead, titled “SPECTRALLY BEAM COMBINED LASER SYSTEM AND METHOD AT EYE-SAFER WAVELENGTHS,” and   U.S. Pat. No. 8,493,651 issued Jul. 23, 2013 to Yongdan Hu et al., titled “APPARATUS FOR OPTICAL FIBER MANAGEMENT AND COOLING,” each of which is incorporated herein by reference in its entirety.       

     FIELD OF THE INVENTION 
     The invention relates generally to high-power optical fiber amplifiers and lasers and more particularly to methods and apparatus for fiber amplifier systems and methods that suppress modal instabilities. 
     BACKGROUND OF THE INVENTION 
     Fiber lasers are of great current interest for high-power laser applications. Many of these applications utilize the coherence of the laser light and thus require controlled polarization and narrow linewidth output radiation, such as for coherent LIDAR, frequency conversion or beam combining via spectral or coherent combining techniques. The narrow linewidth and polarized output can limit power scaling of the fiber laser output due to a number of effects. 
     The limitations of fiber lasers include nonlinearities (e.g., Stimulated Brillouin Scattering (SBS)) and Modal Instabilities (MI). For example, in some cases, modal instabilities in Large-Mode-Area (LMA) high-power fiber amplifiers limit power scaling from individual fibers. LMA fibers typically support several transverse modes, but are preferentially operated with the majority of the light in the fundamental (LP 01 ) mode to optimize beam quality. The modal instability can transfer power out of the LP 01  mode to a higher order mode, degrading beam quality. In some cases, this transfer to higher order mode(s) may result in light being coupled out of the core into the fiber cladding, limiting output power. With regard to nonlinearities, some of the techniques used to avoid SBS (e.g., larger core size and reduced fiber length) may result in MI. 
     Papers and presentations reporting on modal instabilities in high power fiber amplifiers include A. Smith, J. J. Smith, “ Mode Instability in High Power Fiber Amplifiers ,” Optics Express 19, 10180-10192 (2011) (hereinafter, “A. Smith et al.”); C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “ The impact of modal interference on the beam quality of high - power amplifiers ,” Opt. Express 19, 3258-3271 (2011) (hereinafter, “C. Jauregui et al.”); and J. Edgecumbe, Nufern, “ Single Mode, High Power, Narrow Line - width Fiber Amplifiers,”  2 4th  Solid State and Diode Laser Technology Review (2011) (hereinafter, “J. Edgecumbe”), each of which is incorporated herein by reference in its entirety. Recent reports in the literature such as the papers identified above indicate a possible thermal origin for modal instabilities (e.g., thermal load per unit length of the fiber) and the likely role of induced gratings by interactions between fundamental mode and higher order mode content. 
     Teemu Kooki et al., “ Fiber amplifier utilizing an Yb - doped large - mode - area fiber with confined doping and tailored refractive index profile ,” Proc. SPIE 7580, Fiber Lasers VII: Technology, Systems, and Applications, 758016 (Feb. 17, 2010) (hereinafter, “Kooki et al.”) is incorporated herein by reference in its entirety. Kooki et al. describe power scaling of Yb-doped large-mode-area fibers drives the scaling of the mode area in order to suppress nonlinearities. Two Yb-doped large-mode-area fibers were manufactured using the Direct Nanoparticle Deposition process: one with a step refractive index profile and active ion confinement, and another with a tailored refractive index and active ion confinement. The index tailoring and doping profiles were designed based on literature to enhance the beam quality of the fibers. Both fibers exhibited a mode field diameter comparable to a 40 μm step index fiber with 0.07 NA. The fibers were characterized for their geometries, index profiles, and material composition profiles. Additional testing for beam quality and nonlinearities in pulsed operation was conducted using a power amplifier setup. The beam quality enhancement capability of the tested fibers was inconclusive due to incomparable launching conditions of the signal to the fibers. 
     U.S. Pat. No. 4,829,529 to James D. Kafka (hereinafter, “Kafka”) titled “LASER DIODE PUMPED FIBER LASERS WITH PUMP CAVITY”, issued May 9, 1989, and is incorporated herein by reference in its entirety. Kafka describe a fiber laser having a single mode fiber core of laser material is pumped by a high power coherent laser diode source by providing a multi-mode fiber around the single mode core to define a pump cavity which propagates pump radiation while allowing the pump radiation to couple to the single mode core. Laser diode arrays and extended emitter laser diodes can be used to pump a single mode fiber by inputting the pump radiation into the multi-mode fiber surrounding the single mode fiber core. The multi-mode [sic] fiber has a much greater diameter than the single mode core. 
     U.S. Pat. No. 5,508,842 to Keiko Takeda et al. (hereinafter, “Takeda et al.”) titled “OPTICAL AMPLIFIER”, issued Apr. 16, 1996, and is incorporated herein by reference in its entirety. Takeda et al. describe an optical amplifier for amplifying a signal light by propagating the signal light and a pumping light in a rare earth element doped fiber doped with a rare earth element. A diameter of a rare earth element doped portion of the rare earth element doped fiber is gradually reduced in a direction of propagation of the pumping light. With this construction, an adverse rare earth element doped area which does not contribute to optical amplification, but rather attenuates the pumping light, can be eliminated to thereby provide an optical amplifier having increased amplification efficiency. 
     U.S. Pat. No. 5,708,669 to David John DiGiovanni et al. (hereinafter, “DiGiovanni et al. &#39;669”) titled “ARTICLE COMPRISING A CLADDING-PUMPED OPTICAL FIBER LASER”, issued Jan. 13, 1998, and is incorporated herein by reference in its entirety. DiGiovanni et al. &#39;669 describe a cladding pumped optical fiber laser comprises a length of optical fiber having a rare earth-doped region of diameter d RE &gt;d 01  where d 01  is the mode diameter of the LP 01  mode of the fiber at the laser radiation at wavelength λ. In one embodiment the fiber has a core diameter d c  selected such that the LP 01  mode is the only guided spatial mode of the fiber, and d RE  is greater than d c . In another embodiment the fiber supports at least one higher order guided spatial mode, typically LP 11  or LP 02 , and d RE  is approximately equal to or larger than d c . Currently preferred embodiments comprise a grating-defined laser cavity that comprises a mode-coupling refractive index grating. Cladding pumped lasers according to the invention will typically have efficient conversion of pump radiation to laser radiation, and consequently can typically be shorter than analogous prior art cladding pumped lasers. 
     U.S. Pat. No. 5,864,644 to David John DiGiovanni et al. (hereinafter, “DiGiovanni et al. &#39;644”) titled “TAPERED FIBER BUNDLES FOR COUPLING LIGHT INTO AND OUT OF CLADDING-PUMPED FIBER DEVICES”, issued Jan. 26, 1999, and is incorporated herein by reference in its entirety. DiGiovanni et al. &#39;644 describe light coupled from a plurality of semiconductor emitters to a cladding-pumped fiber via tapered fiber bundles fusion spliced to the cladding-pumped fiber. Individual semiconductor broad stripe emitters can be coupled to individual multimode fibers. The individual fibers can be bundled together in a close-packed formation, heated to melting temperature, drawn into a taper and then fusion spliced to the cladding-pumped fiber. The taper is then overcoated with cladding material such as low index polymer. In addition, a fiber containing a single-mode core can be included in the fiber bundle. This single-mode core can be used to couple light into or out of the single-mode core of the cladding-pumped fiber. 
     U.S. Pat. No. 6,289,027 to Brian L. Lawrence et al. (hereinafter, “Lawrence et al.”) titled “FIBER OPTIC LASERS EMPLOYING FIBER OPTIC AMPLIFIERS”, issued Sep. 11, 2001, and is incorporated herein by reference in its entirety. Lawrence et al. describe ring and linear cavity, fiber optic laser systems employing non-invasive fiber optic amplification technology. A channel overlay waveguide is employed for amplification of optical energy evanescently coupled to the overlay waveguide from the fiber optic. One of two amplification methods can be employed. The first involves inducing stimulated emission with the overlay waveguide and the second uses a second order, non-linear frequency conversion to down-convert a high-power, short-wavelength pump signal into the waveguide to amplify the optical energy coupled thereto. Amplification of optical energy in the channel overlay waveguide can be established within a single beat length of evanescent removal to evanescent return of the optical energy to the fiber optic. Intra-cavity elements can be employed to effect, e.g., wavelength selection, optical isolation, or modulation of the resultant, optical signal propagating in the fiber optic. 
     U.S. Pat. No. 6,324,326 to Matthew J. Dejneka et al. (hereinafter, “Dejneka et al.”) titled “TAPERED FIBER LASER”, issued Nov. 27, 2001, and is incorporated herein by reference in its entirety. Dejneka et al. describe a tapered fiber laser having a multi-mode section, a single-mode section, and either a tapered section or fundamental mode matching junction therebetween. The multi-mode section has a large core to directly receive pump light from a broad stripe laser or diode bar, and a length preferably longer than the absorption length of the pump light (so optical amplification occurs predominantly in the multi-mode section). Doping levels can be increased to reduce the multi-mode length. The taper angle is sufficiently small to produce adiabatic compression of the fundamental mode from the multi-mode to single-mode sections, and acts as a cutoff filter favoring lasing of the fundamental mode within the multi-mode section. Alternately, the step junction may have a mode field diameter matched to the lowest-order mode, with laser light output via the single-mode section. The invention can be applied to waveguides (particularly those having an aspect ratio corresponding to a broad stripe laser source), doped with ytterbium or neodymium ions, and is particularly advantageous as a pump source for an erbium-doped fiber amplifier (EDFA). 
     U.S. Pat. No. 6,970,624 to David J. DiGiovanni et al. (hereinafter, “DiGiovanni et al. &#39;624”) titled “CLADDING PUMPED OPTICAL FIBER GAIN DEVICES”, issued Nov. 29, 2005, and is incorporated herein by reference in its entirety. DiGiovanni et al. &#39;624 describe optical fiber gain devices, such as lasers and amplifiers, wherein losses due to a large step transition between an input section and a gain section are reduced by inserting an adiabatic transformer between the input section and the gain section. In the preferred case the adiabatic transformer comprises a GRadient INdex (GRIN) lens. The lens serves as an adiabatic beam expander (reducer) to controllably increase (reduce) the modefield of the beam as it travels through the step transition. 
     U.S. Pat. No. 7,557,986 to Yoav Sintov (hereinafter, “Sintov”) titled “HIGH POWER FIBER AMPLIFIER”, issued Jul. 7, 2009, and is incorporated herein by reference in its entirety. Sintov describes a high power fiber amplifier including a double clad fiber including a protective outer jacket (41), an outer clad (44), an inner clad (42, 35) and a doped core (43, 34, 32), and a source of pump power coupled to the inner clad through coupling optics (22) and at least one of a side-fiber coupling section and an end-fiber coupling section, wherein the inner clad includes a large diameter core portion (34), operative as a high power amplification stage, capable of absorbing the majority of the pump power, and a small diameter core portion (32), operative as a low power amplification stage, wherein both core portions, pumped through the inner clad (35), are serially connected through an optical interface point (37). 
     U.S. Pat. No. 7,809,236 to Martin H. Muendel (hereinafter, “Muendel”) titled “OPTICAL FIBER HOLDER AND HEAT SINK”, issued Oct. 5, 2010, and is incorporated herein by reference in its entirety. Muendel describes an optical fiber holding device having an optical fiber held therein. The device has a base with a spiral channel in an upper surface holding and housing the optical fiber. The channel has a first location where the fiber enters leading to a plurality of turnings for holding the optical fiber wrapped there-around at another end a second location where the fiber exits the channel wherein the bend radius of the optical fiber housed within the spiral channel is at least 2 cm. The dimensions are such that housing forms a heat sink allowing heat within the fiber to dissipate within the base. The spiral channel is preferably designed to keep the fiber within the channel and to prevent it from inadvertently springing out spring tension of the bent fiber holds the fiber within the groove or channel. 
     Accordingly, there is a need in the art for improved fiber amplifier systems that suppress modal instabilities. 
     SUMMARY OF THE INVENTION 
     In some embodiments, the inventors have found that polarization-maintaining (PM) fibers appear to have much lower power threshold for modal instabilities when compared to non-PM fibers, and the variations observed in experimental measurements are consistent with a thermal origin for the modal instabilities (MI). For example, in some embodiments, the inventors noted MI at around 650 watts (W) in PM 25/400 fiber (i.e., a PM fiber having a 25-micron-diameter core and 400-micron outer-cladding diameter), and no MI observed up to 1070 W output power in non-PM 25/400 fiber. In some embodiments, it was also determined that smaller core fibers have a higher power threshold for MI (e.g., in some embodiments, 20/400 fiber was found to have a higher power threshold for MI than 25/400 fiber). 
     In some embodiments, thermal effects drive the MI process, and in some such embodiments, the present invention provides a plurality of options for mitigating these thermal effects. In some embodiments, the present invention provides a hybrid fiber with a smaller core in the initial length where the thermal loads are highest, followed by a larger-core fiber. In some embodiments, the hybrid fiber of the present invention avoids or minimizes modal instabilities while yielding almost the same performance as compared to conventional fibers with regard to minimizing SBS. 
     In some embodiments, the present invention provides a hybrid-fiber design having a smaller core at the end where the pump light is introduced and a larger core for the remainder of fiber length needed to absorb the pump light. In some embodiments the length of the smaller core fiber is chosen such that the thermal heat load in the larger core fiber is below the heat load that produces modal instabilities. In some embodiments, in an amplifier with the pump and signal light co-propagating, the initial 2-5 meters includes 20/400 fiber and the remaining length includes 25/400 fiber. In some embodiments, the hybrid-fiber design further includes a fiber mandrel design that provides optimized cooling of the fiber, along with a fiber coil diameter that increases from the input to the output of the fiber such that modal distortions are minimized at the output end of the fiber where power levels are maximized. 
     In some embodiments, the present invention optimizes the core/cladding diameter to balance the effects of thermal-load-per-unit-length of fiber (in some embodiments, controlling thermal load helps avoid modal instabilities) and fiber length (in some embodiments, the longer the fiber length, the more increased the potential for SBS). For example, in some embodiments, a 25/400 fiber shows modal instability at 400-700 W output operating at a linewidth of 5 GHz, while a 20/400 fiber does not show any modal instability up to 1000 W of output power, but the 20/400 fiber is limited by SBS to at least 12 GHz of linewidth. In some embodiments, an intermediate core size of 22 microns is used to balance these two effects. 
     In some embodiments, the present invention uses signal wavelengths closer to the pump wavelength to reduce the quantum defect heating. For example, in some embodiments the laser signal wavelength can be chosen to be 1030 nm instead of 1060 nm in order to reduce the heating from 1−976/1060=8% to 1−976/1030=5%. In some embodiments, the present invention uses long-wavelength pumping to reduce the quantum defect heating. For example, in some embodiments, instead of pumping at the peak absorption of 976 nm, the present invention uses pump wavelengths centered around 1010 or 1020 nm. In some embodiments, for a laser with a signal wavelength of 1060 nm, this reduces the heating from 1−976/1060=8% to 1−1020/1060=4% or even 1−1020/1030=1% of the absorbed pump light. In some embodiments, the absorption cross section is reduced for this long wavelength pumping and therefore, in some embodiments, the amplifier includes a smaller cladding diameter and higher-brightness pump diodes to absorb the pump light with a given fiber length. 
     In some embodiments, the present invention pumps from both ends of a fiber amplifier in order to reduce the peak thermal load. In some embodiments, pumping is at a first end of the fiber amplifier and the pump light is reflected at the opposite second end of the fiber amplifier. In some such embodiments, this pump/reflect configuration is used with a lower absorption (i.e. smaller core/cladding ratio) fiber to avoid the modal instability but reduced fiber length (and increase the threshold for nonlinearity) compared to the typical unreflected pump light performance with that core/cladding ratio. In some embodiments, pump light is inserted into the fiber amplifier at multiple points along the length of the fiber, rather than simply the input or output ends of the fiber. In some such embodiments, in order to maintain the same overall fiber length, the cladding diameter is reduced to increase the effective absorption length, and the overall length of the fiber is the same compared to the end-pumped fiber design, but the peak thermal load is reduced. 
     In some embodiments, the present invention provides a fiber with a longitudinally increasing pump-light-absorption value, either by geometry or concentration of rare-earth ion. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       Each of the items shown in the following brief description of the drawings represents some embodiments of the present invention. 
         FIG. 1  is a schematic diagram of a fiber laser system  101 , according to some embodiments of the present invention. 
         FIG. 2  is a graph  201  illustrating the onset of modal instability and increase in the beam quality factor, M 2 , based on experiments conducted using a PM 25/400 fiber for gain fiber  222  of system  201 . 
         FIG. 3  is a graph  301  showing normalized pump absorption (ytterbium 3+ ) versus pump wavelength (nm). 
         FIG. 4A  is a graph  401  showing results of modeling conducted using about 8 meters of a PM 25/400 fiber for gain fiber  222  of system  201 , assuming a Ytterbium (Yb)-ion density of 7.74×10 25  ions/m 3  and a pump-wavelength distribution centered at 970.0 nm. 
         FIG. 4B  is a graph  402  showing results of modeling conducted using about 8 meters of a PM 25/400 fiber for gain fiber  222  of system  201 , assuming a Yb-ion density of 7.74×10 25  ions/m 3  and a pump-wavelength distribution centered at 971.2 nm. 
         FIG. 4C  is a graph  403  showing core heating (W/m) and signal power (W) versus fiber position for a PM 20/400 fiber used as gain fiber  222  of system  201  and a pump distribution centered at 976 nm. 
         FIG. 5A  is a schematic diagram illustrating a fiber geometry  501  used in some embodiments of the present invention. 
         FIG. 5B  is a schematic diagram illustrating a fiber geometry  502  used in some embodiments of the present invention. 
         FIG. 6  is a schematic diagram of a hybrid fiber  601  designed to manage thermal load in order to stay below the threshold for modal instabilities. 
         FIG. 7  is a schematic diagram of a hybrid fiber  701  that includes a tapered design to produce a large mode output fiber for mitigation of fiber nonlinearities while also being designed to manage thermal load in order to stay below the threshold for modal instabilities. 
         FIG. 8  is a graph  801  illustrating heat-load characteristics of hybrid fiber  601  with the pump light and signal co-propagating from first segment  610  to second segment  611 . 
         FIG. 9  is a schematic diagram of a 1-kilowatt hybrid-fiber-amplifier system  901 . 
         FIG. 10A  is a top-view schematic diagram of a spiral-mandrel assembly  1001  configured to provide optimized cooling for a hybrid gain fiber. 
         FIG. 10B  is a cross-sectional-view schematic diagram of spiral-mandrel assembly  1001 . 
         FIG. 11A  is a perspective-view diagram of a fiber-management-and-cooling apparatus  1101 , according to some embodiments of the invention. 
         FIG. 11B  is a top-end-view diagram of fiber-management-and-cooling apparatus  1101 , according to some embodiments of the invention. 
         FIG. 12A  is a graph  1201  of SBS-limited power (W) versus seed linewidth (GHz) for two hybrid-fiber configurations and a 20/400 fiber. 
         FIG. 12B  is a table  1202  of fiber-amplifier data for various hybrid-fiber configurations as a function of 20/400 fiber length. 
         FIG. 12C  is a graph  1203  showing beam quality (M 2  ratio) as a function of output power for the Hybrid 4 configuration of table  1202  in  FIG. 12B . 
         FIG. 12D  is a graph  1204  showing beam quality (M 2  ratio) as a function of output power for the Hybrid 5 configuration of table  1202  in  FIG. 12B . 
         FIG. 12E  is a graph  1205  of observed output power for different lengths of 20/400 PM fiber in a hybrid-amplifier configuration, according to some embodiments of the present invention. 
         FIG. 13A  is a graph  1301  of efficiency data for a baseline 20/400 fiber. 
         FIG. 13B  is a graph  1302  illustrating power-amplifier electro-optic (E-O) efficiency for the hybrid-fiber configurations identified in table  1202  of  FIG. 12B . 
         FIG. 14A  is a graph  1401  illustrating heat-load characteristics of a hybrid fiber configuration that includes 5.9 meters of PM 20/400 fiber and 3.5 meters of PM 25/400 fiber. 
         FIG. 14B  is a graph  1402  illustrating heat-load characteristics of a hybrid fiber configuration that includes 3.9 meters of PM 20/400 fiber and 3.5 meters of PM 25/400 fiber. 
         FIG. 14C  is a graph  1403  illustrating heat-load characteristics of a hybrid fiber configuration that includes 2.9 meters of PM 20/400 fiber and 3.5 meters of PM 25/400 fiber. 
         FIG. 14D  is a graph  1404  illustrating heat-load characteristics of a hybrid-fiber configuration that includes 1.9 meters of PM 20/400 fiber and 3.5 meters of PM 25/400 fiber. 
         FIG. 14E  is a graph  1405  illustrating heat-load characteristics of a hybrid-fiber configuration that includes 1.3 meters of PM 20/400 fiber and 5.5 meters of PM 25/400 fiber. 
         FIG. 14F  is a graph  1406  illustrating heat-load characteristics of a hybrid-fiber configuration that includes 5.5 meters of PM 25/400 fiber (and no 20/400 fiber). 
         FIG. 14G  is a graph  1407  illustrating heat-load characteristics of a hybrid-fiber configuration that includes 5.5 meters of PM 25/400 fiber (and no 20/400 fiber). 
         FIG. 15A  is a graph  1501  showing the signal linewidth associated with one of the hybrid-fiber embodiments of the present invention as measured by a Scanning Fabry Perot spectrometer. 
         FIG. 15B  is a graph  1502  of an 8-hour life test of a hybrid-fiber amplifier system according to some embodiments of the present invention. 
         FIG. 16  is a schematic diagram of a hybrid-fiber configuration  1601  using longitudinal control of core or cladding properties through the collapse or post processing of air holes in the structure, such as those used in photonic-crystal fibers. 
         FIG. 17A  is a perspective view of a land-based defensive system  1701  that uses a high-energy defensive point-able SBC device  1791  that includes a hybrid-fiber configuration, according to one embodiment of the present invention. 
         FIG. 17B  is a perspective view of a mobile land-vehicle-based defensive system  1702  that uses a high-energy defensive device  1791  that includes a hybrid-fiber configuration, according to one embodiment of the present invention. 
         FIG. 17C  is a perspective view of a mobile sea- and/or aircraft-vehicle-based defensive system  1703  that uses high-energy defensive device  1791  and/or  1791 ′ that each include hybrid-fiber configurations, according to one embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Although the following detailed description contains many specifics for the purpose of illustration, a person of ordinary skill in the art will appreciate that many variations and alterations to the following details are within the scope of the invention. Very narrow and specific examples are used to illustrate particular embodiments; however, the invention described in the claims is not intended to be limited to only these examples, but rather includes the full scope of the attached claims. Accordingly, the following preferred embodiments of the invention are set forth without any loss of generality to, and without imposing limitations upon the claimed invention. Further, in the following detailed description of the preferred embodiments, reference is made to the accompanying drawings that form a part hereof, and in which are shown by way of illustration specific embodiments in which the invention may be practiced. It is understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the present invention. 
     The leading digit(s) of reference numbers appearing in the Figures generally corresponds to the Figure number in which that component is first introduced, such that the same reference number is used throughout to refer to an identical component which appears in multiple Figures. Signals and connections may be referred to by the same reference number or label, and the actual meaning will be clear from its use in the context of the description. 
     The power scaling limits of conventional ytterbium (Yb) fiber amplifiers include a threshold power for fiber nonlinearities (e.g., SBS) that is approximated by the ratio of the effective fiber area to the effective fiber length (A eff /L eff ), where the effective fiber length includes contribution from both the Yb-doped gain fiber and the delivery fiber. In addition, SBS generally requires larger linewidth for higher powers, limiting power scaling for narrow line width fiber lasers and amplifiers. For suppression of nonlinearities such as SBS, larger core fibers can provide higher output due to the larger effective mode area and increased absorption per unit length arising from a larger core/cladding ratio. 
     However, in some embodiments, a larger core fiber can have a lower power threshold for modal instabilities compared to a smaller fiber. For example, in some embodiments, fiber amplifiers fabricated from a single length of PM 20/400 fiber (i.e., using a PM fiber having a 20-micron-diameter core and 400-micron outer-cladding diameter) and pumped at 977 nm (with no additional delivery fiber) produce about one kilowatt (1 kW) and have limited SBS at twelve Gigahertz (12 GHz) linewidth, and, in some embodiments, 25/400 fiber of similar nominal materials and fabrication method can operate at a smaller linewidth due to the larger core area and reduced fiber length enabled by the higher absorption-per-unit-length but shows modal instabilities at about 650 W (beam quality degrades at an M-squared value of greater than or equal to about 1.1). This results in a tradeoff in the output power being limited by the modal instability for large core fibers and by SBS for smaller core fibers. In some embodiments, therefore, the present invention provides an increase in the overall power possible from a single fiber by (1) balancing the effects of nonlinearities versus modal instability, and (2) increasing the threshold power for the modal instability by reducing the peak thermal load. 
     In the double-clad embodiments described herein, only the core diameter and a first cladding diameter are specified, but such double-clad embodiments also include a second cladding layer (not shown) outside of the first cladding layer. For example, in some embodiments, a double-clad 20/400 fiber includes a 20-micron diameter core, a 400-micron diameter first cladding, and a 550-micron diameter second outer cladding (in some such embodiments, the second cladding layer includes a low-index polymer inner coating and a protective polymer outer coating). Similarly, for some embodiments using triple-clad fiber, where there is a first and second cladding layer in addition to the core, three numbers specify the diameters of the core, first cladding layer and second cladding layer, but there is also a third cladding layer (not shown) outside of the second cladding layer (e.g., in some embodiments, the outer diameter of the third cladding layer of segment  710  of  FIG. 7  is about 350 microns, and the outer diameter of the third cladding layer of segment  712  of  FIG. 7  is about 750 microns). The Numerical Aperture (NA) of the inner and outer waveguides is determined by the effective refractive index of the materials in the fiber, including the use of air or vacuum filled sections that change the effective index as well as “air clad” designs to provide high NA confinement of pump light. 
       FIG. 1  is a schematic diagram of a fiber laser system  101 , according to some embodiments of the present invention. In some embodiments, experiments conducted using system  101  achieved 1003 W at a twelve-gigahertz (12-GHz) seed linewidth limited by Stimulated Brillouin Scattering (SBS) before the onset of modal instability. In some embodiments, system  101  has a master-oscillator power-amplifier (MOPA) configuration that includes a seed source  105  (the master oscillator) and a power amplifier module  120 . In some embodiments, seed source  105  includes a polarization-maintaining seed diode  106  (in some embodiments, diode  106  is a distributed-feedback laser (DFBL)). In some embodiments, seed source  105  further includes a plurality of optical isolators including isolator  108 , isolator  110 , and isolator  111 , and a plurality of amplifiers including amplifier  109  and amplifier  110 . In some embodiments, element  107  of seed source  105  indicates that the optical fiber is polarization maintaining (PM) fiber. In some embodiments, optical isolator  112  is a 10-W isolator. In some embodiments, amplifier  109  is a polarization-maintaining 0.2-W amplifier and amplifier  111  is a polarization-maintaining 10-W amplifier. 
     In some embodiments, power amplifier  120  includes a plurality of optical pumps  121 , gain fiber  122 , a pump dump  123 , and an output-beam end cap  124 . In some embodiments, each pump port  121  delivers about 220 W. In some embodiments, gain fiber  122  is a polarization-maintaining (PM) ytterbium (Yb)-doped double-clad fiber (DCF). In some such embodiments, gain fiber  122  is a PM 20/400 fiber (i.e., a PM fiber having a 20-micron-diameter core and 400-micron outer-cladding outside diameter), the M 2  ratio (sometimes referred to herein as the beam quality factor) was determined to be less than about 1.1 (e.g., in some embodiments, the M 2  ratio is equal to 1.086/1.082), and the polarization extinction ratio (PER) was determined to be greater than about 15 dB (e.g., in some embodiments, the PER is about 16.3±1.4 dB). In some embodiments, gain fiber  122  is non-PM. 
       FIG. 2  is a graph  201  illustrating the onset of modal instability and increase in the beam quality factor, M2, based on experiments conducted using a PM 25/400 fiber for gain fiber  222  of system  201 . The x-axis of graph  201  represents the output power of system  101  using PM 25/400 fiber in watts (W) and the y-axis of graph  202  represents the M 2  ratio of the beam outputted by the system  101  using PM 25/400 fiber. In some embodiments, the PM 25/400 fiber offers potential for narrower linewidth, but, as shown in graph  202 , in some embodiments, modal instability degrades the beam quality at power levels beyond approximately 640 W (e.g., in some embodiments, the onset of modal instability was determined to occur at powers greater than about 642 W). 
       FIG. 3  is a graph  301  showing normalized pump absorption (ytterbium 3+ ) versus pump wavelength (nm). In some embodiments, as shown in graph  301 , the peak ytterbium 3+  absorption corresponds with a pump-diode wavelength of about 977 nm. In some embodiments, experiments determined that when the pump-diode wavelength is set to within a range of about 975-978 nm, system  201  using PM 25/400 fiber generates a maximum power of less than 300 W prior to the appearance of modal instability. In some embodiments, experiments determined that when the pump-diode wavelength is set to a value about 971 nm, system  201  using PM 25/400 fiber generates a maximum power of about 360 W prior to the appearance of modal instability. In some embodiments, experiments determined that when pump-diode wavelength is set to a value about 970 nm, system  201  using PM 25/400 fiber generates a maximum power of about 640 W prior to the appearance of modal instability. In some embodiments, the thermal load in the core of a fiber depends on pump wavelength, and thus, in some embodiments, the maximum power data referred to above suggests a thermal origin for PM 25/400 modal instability. In some embodiments, the thermal origin for the modal instabilities is a function of the thermo-optical effect (in some such embodiments, the thermo-optical effect is described by the thermo-optic coefficient, d n /d T , where n is the refractive index and T is the temperature). The examples shown here are for a Ytterbium-doped fiber but for those with ordinary skill in the art, the results are applicable to other laser systems where thermally induced MIs may limit power scaling, including other rare earth doped fibers and Raman fiber amplifiers. 
     Analysis of Experiments with PM 25/400 Gain Fiber Identifies Thermal Onset of MI 
       FIG. 4A  is a graph  401  showing results of modeling conducted using about 8 meters of PM 25/400 fiber for gain fiber  222  of system  201 , assuming a Ytterbium (Yb)-ion density of 7.74×10 25  ions/m 3  and a pump-wavelength distribution centered at 970.0 nm. In some embodiments, the pump-wavelength distribution is centered at 970.0 nm in order to reduce the effective absorption relative to the peak at about 977 nm. In some embodiments, the values for graph  401  were chosen to simulate the experiment used to produce the data shown in graph  201  of  FIG. 2 . The x-axis of graph  401  indicates the position along the gain fiber in meters (m), the left-hand y-axis of graph  401  indicates the core heat in watts/meter (W/m), plotted with the dotted curve, and the right-hand y-axis of graph  401  indicates the signal power (W) produced by the gain fiber at a signal wavelength of 1060 nm, plotted as the solid-line curve. The modeling in  FIG. 4A  shows that the detuned pump wavelength and assumed Yb concentration produces an output power up to about 700 W at a peak core heat loading of about 15 W/m. The modeling results suggest that, in some embodiments, the MI threshold occurs at a core heat load of about 15 W/m. 
       FIG. 4B  is a graph  402  showing results of modeling conducted using about 8 meters of a PM 25/400 fiber for gain fiber  222  of system  201 , assuming a Yb-ion density of 7.74×10 25  ions/m 3  and a pump-wavelength distribution centered at 971.2 nm. In some embodiments, the pump wavelength chosen for the modeling shown in graph  402  is closer to the peak absorption wavelength than the value used in the  FIG. 4A  model, and, in some embodiments, this results in a higher effective absorption-per-unit-length. The x-axis of graph  402  indicates the position along the gain fiber in meters (m), the left-hand y-axis of graph  402  indicates the core heat load in watts/meter (W/m), plotted with the dotted curve, and the right-hand y-axis of graph  402  indicates the signal power (W) produced by the gain fiber at a signal wavelength of 1060 nm, plotted as the dashed curve. The modeling in  FIG. 4B  shows that the pump wavelength of 971.2 nm and assumed Yb-concentration produces an output power of about 350 W at a peak core heat loading of about 15 W/m. The modeling inputs for the results in  FIG. 4B  are chosen to match experimental measurements of the threshold power for the onset of modal instabilities. The modeling results shown in  FIGS. 4A and 4B  suggest that, in some embodiments, the modal-instability threshold occurs at a core heat load of about 15 W/m with different pump conditions and different output powers and represents a maximum core heat load for the PM 25/400 fiber in some embodiments. 
       FIG. 4C  is a graph  403  showing core heating (W/m) and signal power (W) versus fiber position for a PM 20/400 fiber used as gain fiber  222  of system  201  and a pump distribution centered at 976 nm. The x-axis of graph  403  indicates the position along the length of the fiber in meters, the left-hand y-axis of graph  403  indicates the core heat load (W/m), and the right-hand y-axis indicates the signal power (W) produced by the fiber at a signal wavelength of 1060 nm. In some embodiments, it was determined that 28 W/m does not lead to modal instabilities for the PM 20/400 configuration illustrated by graph  403 . In some embodiments, the PM 20/400 gain fiber of  FIG. 4C  showed a higher threshold for modal instabilities as compared to the PM 25/400 gain fiber of  FIGS. 4A-4B , even for a thermal load that caused modal instabilities in the PM 25/400 fiber. For example, in some embodiments, the PM 20/400 fiber of  FIG. 4C  was determined to be at least two times (2×) more stable against modal instabilities when compared to the PM 25/400 fiber represented by  FIGS. 4A-4B . In some embodiments, it was determined that the results obtained for the PM 20/400 fiber are pump power limited or limited by the onset of nonlinearities such as Stimulated Brillouin Scattering, as opposed to being limited by modal instabilities. 
     Methods to Overcome Thermal Threshold 
     In some embodiments, two primary methods are used to manage the thermal threshold related to modal instabilities: (1) modifying the pump-diode wavelength (see, e.g.,  FIG. 3  and its corresponding description), and (2) modifying the fiber geometry (e.g., modifying the core/clad ratio; see, e.g.,  FIGS. 5A-5B  and their corresponding description). 
       FIG. 5A  is a schematic diagram illustrating a fiber geometry  501  used in some embodiments of the present invention. In some embodiments, geometry  501  includes a PM 20/400 fiber (i.e., a PM fiber having a 20-micron-diameter core and 400-micron outer-cladding outside diameter). In some embodiments, geometry  501  includes a non-PM fiber. 
       FIG. 5B  is a schematic diagram illustrating a fiber geometry  502  used in some embodiments of the present invention. In some embodiments, geometry  502  includes a PM 25/400 fiber (i.e., a PM fiber having a 25-micron-diameter core and 400-micron outer-cladding outside diameter). In some embodiments, geometry  501  is characterized by a lower heat load for fixed pump wavelength and geometry  502  is characterized by a higher heat load for fixed pump wavelength. In some embodiments, the PM 20/400 fiber represented by geometry  501  works at 1 kilowatt (kW), but requires about 12 gigahertz (GHz) or larger linewidth. In some embodiments, the PM 25/400 fiber represented by geometry  502  enables narrower linewidth output, but also has a lower threshold for modal instability. In some embodiments, geometry  502  includes a non-PM fiber. 
       FIG. 6  is a schematic diagram of a hybrid fiber  601  designed to manage thermal load in order to stay below the threshold for modal instabilities. In some embodiments, fiber  601  is a segmented fiber having a first segment  610  that includes 20/400 Yb-doped-core double-clad fiber and a second segment  611  that includes 25/400 Yb-doped-core double-clad fiber (in some such embodiments, first segment  610  is spliced to second segment  611 ). Thus, in some embodiments, the core  615  of fiber  601  has a diameter of 20 microns in segment  610  and a diameter of 25 microns in segment  611 , and the cladding layer  620  has a diameter of 400 microns throughout fiber  601 . In some embodiments, hybrid fiber  601  includes PM fiber. In other embodiments, hybrid fiber  601  includes non-PM fiber. 
     In some embodiments, first segment  610  includes core diameters of about 5 to 30 microns and second segment  611  includes core diameters larger than the core diameter of 610 with the cladding diameters nominally identical. In some embodiments, first segment  610  includes 5/400 Yb-doped-core double-clad fiber and second segment  611  includes 10/400 Yb-doped-core double-clad fiber. In some embodiments, first segment  610  includes 10/400 Yb-doped-core double-clad fiber and second segment  611  includes 15/400 Yb-doped-core double-clad fiber. In some embodiments, first segment  610  includes 15/400 Yb-doped-core double-clad fiber and second segment  611  includes 20/400 Yb-doped-core double-clad fiber. In some embodiments, first segment  610  includes 20/400 Yb-doped-core double-clad fiber and second segment  611  includes 25/400 Yb-doped-core double-clad fiber. In some embodiments, first segment  610  includes 25/400 Yb-doped-core double-clad fiber and second segment  611  includes 30/400 Yb-doped-core double-clad fiber. In some embodiments, first segment  610  includes 5/400 Yb-doped-core double-clad fiber and second segment  611  includes 15/400 Yb-doped-core double-clad fiber. In some embodiments, first segment  610  includes 10/400 Yb-doped-core double-clad fiber and second segment  611  includes 20/400 Yb-doped-core double-clad fiber. In some embodiments, first segment  610  includes 15/400 Yb-doped-core double-clad fiber and second segment  611  includes 25/400 Yb-doped-core double-clad fiber. In some embodiments, first segment  610  includes 20/400 Yb-doped-core double-clad fiber and second segment  611  includes 30/400 Yb-doped-core double-clad fiber. In some embodiments, first segment  610  includes 25/400 Yb-doped-core double-clad fiber and second segment  611  includes 35/400 Yb-doped-core double-clad fiber. In some embodiments, first segment  610  includes 5/400 Yb-doped-core double-clad fiber and second segment  611  includes 20/400 Yb-doped-core double-clad fiber. In some embodiments, first segment  610  includes 10/400 Yb-doped-core double-clad fiber and second segment  611  includes 25/400 Yb-doped-core double-clad fiber. In some embodiments, first segment  610  includes 15/400 Yb-doped-core double-clad fiber and second segment  611  includes 30/400 Yb-doped-core double-clad fiber. In some embodiments, first segment  610  includes 20/400 Yb-doped-core double-clad fiber and second segment  611  includes 35/400 Yb-doped-core double-clad fiber. In some embodiments, first segment  610  includes 25/400 Yb-doped-core double-clad fiber and second segment  611  includes 40/400 Yb-doped-core double-clad fiber. 
     In some embodiments, first segment  610  includes a fiber selected from the group consisting of about 5-micron-core Yb-doped-core double-clad fiber (YbDDCF), about 10-micron-core YbDDCF, about 15-micron-core YbDDCF, about 20-micron-core YbDDCF, about 25-micron-core YbDDCF, about 30-micron-core YbDDCF. In some such embodiments, second segment  611  includes a larger core diameter than the core diameter of the adjoining segment  610 , wherein the second segment  611  has a core diameter selected from the group consisting of about 10-micron-core YbDDCF, about 15-micron-core YbDDCF, about 20-micron-core YbDDCF, about 25-micron-core YbDDCF, about 30-micron-core YbDDCF, and about 35-micron-core YbDDCF. In some such embodiments, first segment  610  and second segment  611  have cladding diameters selected from the group consisting of about 200-micron outer-cladding diameter, about 250-micron outer-cladding diameter, about 300-micron outer-cladding diameter, about 350-micron outer-cladding diameter, about 400-micron outer-cladding diameter, about 450-micron outer-cladding diameter, about 500-micron outer-cladding diameter, about 550-micron outer-cladding diameter and about 600-micron outer-cladding diameter. In some embodiments, first segment  610  and second segment  611  have different outer-cladding diameters. In some embodiments first segment  610  has a smaller outer-cladding diameter compared to that of second segment  611 . 
     In some embodiments, first segment  610  includes a first length and second segment  611  includes a second length, and, in some embodiments, the first and second lengths are configured such that a thermal load of second segment  611  stays below a value at which a modal-instability occurs (e.g., in some embodiments, a thermal load of 15 W/m is the threshold above which modal-instability occurs). In some such embodiments, the first length of first segment  610  is in a range of about 1 to 10 meters and the second length of second segment  611  is in a range of about 1 to 10 meters. In some embodiments, the first and/or second length is about 1 meter, about 1.5 meters, about 2 meters, about 2.5 meters, about 3 meters, about 3.5 meters, about 4 meters, about 4.5 meters, about 5 meters, about 5.5 meters, about 6 meters, about 6.5 meters, about 7 meters, about 7.5 meters, about 8 meters, about 8.5 meters, about 9 meters, about 9.5 meters, about 10 meters, or, in other embodiments, the first length is any one of the above values and the second length is any one of the above values. In some embodiments, the first length is about 1.3 meters and the second length is about 5.5 meters. In some embodiments, the first length is about 1.9 meters and the second length is about 5.5 meters. In some embodiments, the first length is about 2.9 meters and the second length is about 3.5 meters. In some embodiments, the first length is about 3.9 meters and the second length is about 3.5 meters. In some embodiments, the first length is about 5.9 meters and the second length is about 3.5 meters. In some embodiments, the first length is about 1.86 meters and the second length is about 5.5 meters. In some embodiments, the first length is about 1.26 meters and the second length is about 5.5 meters. In some embodiments, in addition to the first length of first segment  610  and the second length of second segment  611 , the hybrid fiber provided by the present invention includes an additional non-pumped length of the second segment  611  (see, e.g., table  1202  of  FIG. 12B ). In some such embodiments, the additional non-pumped length of second segment  611  is about 0.5 meters, about 1.0 meters, about 1.5 meters, or about 2.0 meters. In some embodiments, more than two different types of fibers are used, e.g. second segment  611  becomes first segment  610  for another section of fiber amplifier, with a new second segment  611  of different fiber type. 
     In some embodiments, the configuration of hybrid fiber  601  (e.g., in some embodiments, the combination of core diameters and segment lengths of hybrid fiber  601 ) mitigates Stimulated Brillouin Scattering (SBS) such that the linewidth of the output signal beam produced by hybrid fiber  601  is in a range of about 5-20 gigahertz (GHz). In some such embodiments, hybrid fiber  601  is configured such that the linewidth of the output signal beam is about twenty gigahertz 20 GHz, about 19 GHz, about 18 GHz, about 17 GHz, about 16 GHz, about 15 GHz, about 14 GHz, about 13 GHz, about 12 GHz, about 11 GHz, about 10 GHz, about 9 GHz, about 8 GHz, about 7 GHz, about 6 GHz, or about 5 GHz. 
     In some embodiments a transition fiber or taper is used to transition the desired mode of the signal between segments  610  and  611  to minimize loss or conversion to higher order modes (see, e.g.,  FIG. 7 ). In some embodiments the core in segment  610  may use a confined doping profile and the core in segment  611  may use doping of the rare-earth element through the entire diameter of the core. In some embodiments the core in segment  610  may have a refractive index profile designed to produce a mode that matches that produced by the refractive index profile in the core of segment  611  with other properties tailored to reduce the heat loading in one or the other segments. In some embodiments the concentration of the rare-earth ion is higher in one segment to increase the relative absorption-per-unit-length in that segment. 
     In some embodiments pump light is introduced into segment  610  only and the connection between segments  610  and  611  minimizes pump losses to allow the pump light to be absorbed according to the geometry and absorption coefficient of the individual segments of fiber. In some embodiments pump light is introduced into segment  611  only. In some embodiments, pump light is introduced into both segments  610  and  611 . 
       FIG. 7  is a schematic diagram of a hybrid fiber  701  that includes a tapered design to produce a large mode output fiber for mitigation of fiber nonlinearities while also being designed to manage thermal load in order to stay below the threshold for modal instabilities. In some embodiments, fiber  701  is a segmented fiber having a signal  799  that enters a first segment  710  that includes 10/140/200 triple-clad fiber, a second segment  711 , and a third segment  712  that includes 30/420/600 triple-clad fiber. In some embodiments, fiber  701  includes a core  715 , a first cladding layer  720 , and a second cladding layer  721 . In some embodiments, first cladding layer  720  has a 0.22 numerical aperture (NA) achieved through the use of F-doped silica. In some embodiments, second cladding layer  721  has a 0.46 NA and includes a low-index polymer (e.g., fluoroacrylate). In some embodiments, segment  711  forms an adiabatic up-taper between segment  710  and segment  712  that lowers the pump NA, trapping the pump light in the first cladding layer  720 . In some embodiments, the higher core/clad ratio provided by segment  712  also increases the pump absorption fraction. In some embodiments, hybrid fiber  701  includes PM fiber. In other embodiments, hybrid fiber  701  includes non-PM fiber. 
       FIG. 8  is a graph  801  illustrating heat-load characteristics of hybrid fiber  601  with the pump light and signal co-propagating from first segment  610  to second segment  611 . The x-axis of graph  801  indicates the position along the length of hybrid fiber  601  in meters, the left-hand y-axis of graph  801  indicates the core heat load (W/m), and the right-hand y-axis indicates the signal power (W) produced by hybrid fiber  601 . In some embodiments, as shown in graph  801 , hybrid fiber  601  is configured such that each segment is three (3) meters long (in some such embodiments, as shown in graph  801 , the first 3-meter segment has the 20/400 fiber and the next 3-meter segment has the 25/400 fiber). 
       FIG. 9  is a schematic diagram of a 1-kilowatt hybrid-fiber-amplifier system  901 . In some embodiments, system  901  is designed to be operated in a range of about 10-12 GHz. In some embodiments, system  901  includes a seed diode  906 , a two-stage booster amplifier  909 , a plurality of pump banks  921 , and a combiner  922 . In some embodiments, combiner  922  is a 6+1:1 combiner. In some embodiments, the power of the signal outputted by amplifier  909  is about 10 watts (W). In some embodiments, the output from combiner  922  is operatively coupled to a first gain-fiber segment  931  that includes polarization-maintaining (PM) 20/400 ytterbium (Yb)-doped fiber. In some embodiments, gain-fiber segment  931  is operatively coupled to a second gain-fiber segment  932  via a hybrid splice  935 . In some embodiments, gain-fiber segment  932  includes PM 25/400 Yb-doped fiber. In some embodiments, gain-fiber segment  931  and/or gain-fiber segment  932  include non-PM fibers. In some embodiments, the hybrid-fiber portion of system  901  formed by the splicing of gain-fiber segment  931  to gain-fiber segment  932  is substantially similar to hybrid fiber  601  of  FIG. 6 . In some embodiments, gain-fiber segment  932  is operatively coupled to pump dump  933 . In some embodiments, the output of pump dump  933  is operatively coupled to an endcap  934  via fiber segment  940  (in some such embodiments, fiber segment  940  includes PM 25/400 Germanium (Ge)-doped fiber). In some embodiments, endcap  934  has a face having an angle in a range of about 6 to 8 degrees from a plane perpendicular to the axis of signal propagation (and about 0.5-2 millimeters in diameter). 
     In some embodiments, gain-fiber segment  931  is 3 meters long, gain-fiber segment  932  is 4.5 meters long, fiber segment  940  is 2.5 meters long, and system  901  has the following characteristics: SBS is less than or equal to 20 kW peak pulses, M 2  ratio less than or equal to 1.1, polarization extinction ratio (PER) is greater than or equal to 13 dB. 
     In some embodiments, system  901  provides advantages not available with conventional fiber-amplifier systems including the capability of gain-fiber segment  931  to use pump power which would otherwise create modal instabilities in the PM 25/400 gain-fiber segment  932  if a longer length were used alone, combined with the capability of the right-hand gain-fiber segment  932  to generate high power with increased SBS threshold compared to a PM 20/400 fiber. 
       FIG. 10A  is a top-view schematic diagram of a spiral-mandrel assembly  1001  configured to provide optimized cooling for a hybrid gain fiber. In some embodiments, assembly  1001  includes a plate  1005  having a plurality of spiral channels  1010  in which fiber can be held (in some embodiments, plate  1005  is substantially similar to the optical fiber holder described in U.S. Pat. No. 7,809,236 to Muendel, which is incorporated herein by reference). In some embodiments, as shown in  FIG. 10B , spiral channels  1010  are all in the same plane. In some embodiments, plate  1005  is configured to hold the hybrid-fiber portion of system  901  and the length of gain-fiber segment  931  held within channels  1010  of plate  1005  is long enough to prevent or minimize instabilities in gain-fiber segment  931  (e.g., in some embodiments, the length of gain-fiber segment  931  is about 3.5 meters). In some such embodiments, the splice between gain-fiber segment  931  and gain-fiber segment  932  is located within the portion of hybrid fiber contained in the spiral channels  1010  of plate  1005 . In some embodiments, plate  1005  is configured to hold approximately 10 meters of fiber in a low-profile package. In some embodiments, assembly  1001  includes a star coupler  1020 . In some embodiments, star coupler  1020  is operatively coupled to one signal fiber and six pump fibers (not shown) on the input (left) side of coupler  1020 , and coupler  1020  is operatively coupled to gain-fiber segment  931  on the output (right) side of coupler  1020 . 
     In some embodiments, a hybrid-fiber configuration is wrapped around two or more mandrels such as mandrel assembly  1001  of  FIG. 10A . In some embodiments, for example, gain-fiber segment  931  of  FIG. 9  is wrapped around a first mandrel assembly and gain-fiber segment  932  of  FIG. 9  is wrapped around a second mandrel assembly. In some such embodiments, the splice between gain-fiber segment  931  and gain-fiber segment  932  is located between the two mandrel assemblies and the splice area is heat-sinked to manage thermal load due to splice losses. 
       FIG. 10B  is a cross-sectional-view schematic diagram of spiral-mandrel assembly  1001 . 
       FIG. 11A  is a perspective-view diagram of a fiber-management-and-cooling apparatus  1101 , according to some embodiments of the invention. In some embodiments, guiding-and-cooling apparatus  1101  includes a substantially cylindrical body (or cylinder)  1112  (e.g., in some embodiments, it is made of a thermally conductive metal such as silver, aluminum, or copper, or an alloy of two or more suitable elements) having an outer-facing surface  1111  and an inner-facing surface  117 . In some embodiments, outer-facing surface  111  has an outer-facing-surface radius R.sub.o and inner-facing surface  1117  has an inner-facing-surface radius. In some embodiments, the inner-facing surface  1117  includes a continuous inner groove  1115  that coils (this can alternatively be considered travels, wraps, spirals, or loops) around the inner-facing surface  1117  from the first end  1109  to the second end  1109 ′ of the cylinder  1112 . In some embodiments, the continuous inner groove  1115  spirals around the inner-facing surface  1117  from a first end to a second end in a right-hand-screw clockwise direction and in other embodiments, the continuous inner groove  1115  spirals in the opposite or counter-clockwise direction. In some embodiments, the distance between successive loops of continuous inner groove  1115  is substantially fixed. In some embodiments, the distance is selected such that the successive fiber loops are each in contact with their adjacent fiber-loop neighbors. In other embodiments, the distance is selected such that the successive fiber loops are spaced apart from their adjacent fiber-loop neighbors. In some embodiments, the outer-facing surface  1111  includes a continuous outer groove  1113  recessed into the outer-facing surface  1111  that coils around the outer-facing surface  1111  from the first end  109  of the cylinder  1112  to the second end  1109 ′ of the cylinder  1112 . In some embodiments, the continuous outer groove  1113  spirals around the outer-facing surface  1111  from the second end to the first end in a left-hand-screw clockwise direction (e.g., in the same clockwise direction as the inner spiral but in the opposite screw direction since the direction of successive loops is toward the first end) and in some other embodiments, the continuous groove  1113  spirals in the opposite or counter-clockwise direction. In some embodiments, the bottom of groove  1113  is rounded as shown in the present figures; however, in other embodiments, a V-shaped groove bottom or other shaped grooves are used. 
       FIG. 11B  is a top-end-view diagram of fiber-management-and-cooling apparatus  1101 , according to some embodiments of the invention. 
       FIG. 12A  is a graph  1201  of SBS-limited power (W) versus seed linewidth (GHz) for two hybrid-fiber configurations and a 20/400 fiber. In some embodiments, as shown in graph  1201 , the hybrid-fiber configurations demonstrate superior SBS suppression compared to the 20/400 fiber due to a larger core size and a shorter absorption length. In some embodiments, the 20/400 fiber includes a 11.5-meter-long section that is pumped and a 0.5-meter-long section that is not pumped (e.g., in some embodiments, the 0.5-meter-long section is located in between pump dump  933  and end cap  934  of  FIG. 9 ). In some embodiments, the first hybrid configuration includes a 6-meter-long section of 20/400 fiber spliced to a 3.5-meter-long 25/400 fiber that ends at a pump dump and a 0.5-meter-long section of 25/400 fiber located in between the pump dump and an end cap (e.g., in some embodiments, the 0.5-meter-long section is located in between pump dump  933  and end cap  934  of  FIG. 9 ). In some embodiments, the second hybrid configuration (shown as Hybrid 2 on graph  1201 ) includes a 4-meter-long section of 20/400 fiber spliced to a 3.5-meter-long section of 25/400 fiber that ends at a pump dump and a 0.5-meter-long section of 25/400 fiber located in between the pump dump and an end cap (e.g., in some embodiments, the 0.5-meter-long section is located in between pump dump  933  and end cap  934  of  FIG. 9 ). 
       FIG. 12B  is a table  1202  of fiber-amplifier data for various hybrid-fiber configurations as a function of 20/400 fiber length. In some embodiments, the three fiber lengths shown for each hybrid configuration of table  1202  are the length of the 20/400 fiber, the length of the 25/400 fiber directly spliced to the 20/400 fiber, and the length of unpumped 25/400 fiber (e.g., the length of the 25/400 fiber located in between pump dump  933  and end cap  934  of  FIG. 9 ). In some embodiments, it was determined that the length of the 20/400 fiber for both the Hybrid 4 configuration and the Hybrid 5 configuration was too short because modal instabilities were observed for these two configurations. 
       FIG. 12C  is a graph  1203  showing beam quality (M 2  ratio) as a function of output power for the Hybrid 4 configuration of table  1202  in  FIG. 12B . In some embodiments the 1.86 meter length of 20/400 PM fiber used for graph  1203  resulted in the onset of MI above 1000 W. 
       FIG. 12D  is a graph  1204  showing beam quality (M 2  ratio) as a function of output power for the Hybrid 5 configuration of table  1202  in  FIG. 12B . In some embodiments the 1.26 m length of 20/400 PM fiber used for graph  1204  resulted in the onset of MI above 900 W. 
       FIG. 12E  is a graph  1205  of observed output power for different lengths of 20/400 PM fiber in a hybrid-amplifier configuration, according to some embodiments of the present invention. In some embodiments a length of about 3 m of the 20/400 PM fiber section was sufficient to mitigate MI above the 1000 W level and the output power was then pump limited. In some embodiments, when the PM 20/400 fiber was less than 2 meter long, modal instabilities were observed. 
       FIG. 13A  is a graph  1301  of efficiency data for a baseline 20/400 fiber. 
       FIG. 13B  is a graph  1302  illustrating power-amplifier electro-optic (E-O) efficiency for the hybrid-fiber configurations identified in table  1202  of  FIG. 12B . As used in graph  1302 , the efficiency values are based on an output power of about 500 watts (in some such embodiments, pump bank  3  of optical pumps  921  is operated at about 9 amps of current). In some embodiments, the E-O efficiency for the baseline fiber shown in graph  1302  is based on the efficiency data illustrated in graph  1301  of  FIG. 13A . In some embodiments, as shown in graph  1302 , the E-O efficiency remains high for the hybrid-fiber configurations. 
       FIG. 14A  is a graph  1401  illustrating heat-load characteristics of a hybrid fiber configuration that includes 5.9 meters of PM 20/400 fiber and 3.5 meters of PM 25/400 fiber. In some embodiments, the configuration modeled for graph  1501  showed no modal instabilities. In some embodiments, the modeling for  FIGS. 14A-14G  was based on 7.74×10 25  ions/m 3  and pumping at 977 nm. 
       FIG. 14B  is a graph  1402  illustrating heat-load characteristics of a hybrid fiber configuration that includes 3.9 meters of PM 20/400 fiber and 3.5 meters of PM 25/400 fiber. In some embodiments, the configuration modeled for graph  1402  showed no modal instabilities up to the maximum output power available from the pump diodes. 
       FIG. 14C  is a graph  1503  illustrating heat-load characteristics of a hybrid fiber configuration that includes 2.9 meters of PM 20/400 fiber and 3.5 meters of PM 25/400 fiber. In some embodiments, the configuration modeled for graph  1403  showed no modal instabilities up to the maximum output power available from the pump diodes. 
     In some embodiments it was observed that the use of the 20/400 PM fiber allowed a higher core heating per unit length in the 25/400 PM fiber than the core heating that resulted in modal instabilities for the 25/400 PM fiber amplifier without the hybrid configuration. In some embodiments the 20/400 PM fiber length still played an important role in the onset of modal instability. In some embodiments, based on the data from  FIGS. 14A-14C , it was determined that core heat load in the hybrid-fiber configurations shows a threshold, but that thermal distribution along the fiber, in addition to core heating, is also relevant. 
       FIG. 14D  is a graph  1404  illustrating heat-load characteristics of a hybrid-fiber configuration that includes 1.9 meters of PM 20/400 fiber and 3.5 meters of PM 25/400 fiber. In some embodiments, modal instabilities were observed at about 1030 W, and thus, in some embodiments, it was determined that core heating of 38 W/m leads to modal instabilities, similar to the experimental data shown in graph  1203 . 
       FIG. 14E  is a graph  1405  illustrating heat-load characteristics of a hybrid-fiber configuration that includes 1.3 meters of PM 20/400 fiber and 5.5 meters of PM 25/400 fiber. In some embodiments, modal instabilities were observed at about 930 W, and thus, in some embodiments, it was determined that core heating of 39.5 W/m leads to modal instabilities (a similar heat load to that of the hybrid-fiber configuration experimental data in graph  1204 ). 
       FIG. 14F  is a graph  1406  illustrating heat-load characteristics of a hybrid-fiber configuration that includes 5.5 meters of PM 25/400 fiber (and no 20/400 fiber). In some embodiments, as shown in graph  1406 , a 44 W/meter heat load was observed. In some embodiments, the pump power used for graph  1406  is sufficient to produce about 1 kW of output power. 
       FIG. 14G  is a graph  1407  illustrating heat-load characteristics of a hybrid-fiber configuration that includes 5.5 meters of PM 25/400 fiber (and no 20/400 fiber). In some embodiments, modal instabilities were observed at about 350 W, and thus, in some embodiments, it was determined that 15 W/m leads to modal instabilities. In some embodiments, based on the data from  FIGS. 14A-14C , it was determined that core heat load in the hybrid-fiber configurations shows a threshold, but that thermal distribution along the fiber, in addition to core heating, is also relevant. In some embodiments, the pump power used for graph  1407  is sufficient to produce about 380 W of output power. 
     Summary of Hybrid-Fiber Results 
     In some embodiments, lengths of 2.9 meters or 3.9 meters for the 20/400 fiber of a hybrid-fiber configuration were needed before the 25/400 fiber spliced to the 20/400 fiber suppressed the modal instabilities beyond 1 kW. In other embodiments, lengths of 1.9 meters or 1.3 meters for the 20/400 fiber in a hybrid-fiber configuration showed progressively lower power levels for modal instability onset. 
       FIG. 15A  is a graph  1501  showing the signal linewidth associated with one of the hybrid-fiber embodiments of the present invention as measured by a Scanning Fabry Perot spectrometer. In some embodiments, the characteristics corresponding to graph  1501  include output power of 1050 W, a 5.5 GHz signal linewidth, an M 2  ratio of 1.04, a PER of 14.6 dB, and no delivery fiber. 
       FIG. 15B  is a graph  1502  of an 8-hour life test of a hybrid-fiber amplifier system according to some embodiments of the present invention. In some embodiments, graph  1502  shows the corrected output power (P out ) in watts versus time in minutes (min). In some embodiments, the hybrid-fiber configuration tested in graph  1502  includes a 4-meter-long section of pumped 20/400 fiber spliced to a 3.5-meter-long section of pumped 25/400 fiber and a 0.5-meter-long section of unpumped 25/400 fiber. In some embodiments, the signal linewidth is about 5.5 GHz. In some embodiments, the average PER was determined to be 14.5 dB with a standard deviation of 3.5 dB. In some embodiments, the power fluctuation of graph  1502  was due to cooling limitations of the tested configuration. 
       FIG. 16  is a schematic diagram of a hybrid-fiber configuration  1601  using longitudinal control of core or cladding properties through the collapse or post processing of air holes in the structure, such as those used in photonic-crystal fibers. In some embodiments, configuration  1601  includes a first segment  1610  and a second segment  1611 . In some embodiments, the core  1615  and cladding  1620  of at least one of the fiber segments in configuration  1601  are conventional, except the cladding  1620  has an air-cladding design of a photonic-crystal rod (PCR) that is post-processed, e.g., tapers, air-cladding, and/or post-processing to collapse holes over a region of the fiber (e.g., in some such embodiments, the cladding  1620  in first segment  1610  includes photonic-crystal holes that define a smaller effective core and the cladding  1620  in second segment  1611  includes collapsed holes that define a larger effective core). In some embodiments, configuration  1601  uses an air-cladding design such as described in U.S. Pat. No. 7,391,561, which is incorporated herein by reference. 
       FIG. 17A  is a perspective view of a land-based defensive system  1701  that uses a high-energy defensive point-able SBC device  1791  that includes a hybrid-fiber configuration, according to one embodiment of the present invention. In some embodiments, a laser system  1790  having a plurality of high-power lasers (e.g., in some embodiments, optically pumped rare-earth-doped fiber lasers, as are described in some of the various patents incorporated herein by reference) provides a plurality of very high-power laser beams (e.g., in some embodiments, 10 kilowatt or more each), each having a different wavelength, that are combined using SBC into a single extra high-power output beam. In some embodiments, the single extra high-power output beam is used as a directed-energy beam to protect against incoming missiles  69  or aircraft. In some embodiments, a portion of the single extra high-power output beam, using one or more laser modules, is used as a communications beam to communicate with aircraft, or seacraft, submarines or other vehicles. In some embodiments a portion of the high-power output beam is provided by one or more laser modules that can be configured for sensing applications such as active imaging or LIDAR. In some embodiments, laser system  1790  and SBC device  1791  are housed in a terrestrial building. 
       FIG. 17B  is a perspective view of a mobile land-vehicle-based defensive system  1702  that uses a high-energy defensive device  1791  that includes a hybrid-fiber configuration, according to one embodiment of the present invention. In some embodiments, the single extra high-power output beam is used as a directed-energy beam to protect against incoming missiles or aircraft, or ground-based tanks or other vehicles. In some embodiments, a portion of the single extra high-power output beam, using one or more laser modules, is used as a communications beam to communicate with aircraft, or seacraft, submarines or other vehicles. In some embodiments a portion of the high-power output beam is provided by one or more laser modules that can be configured for sensing applications such as active imaging or LIDAR. In some embodiments, laser system  1790  and SBC device  1791  are housed in a mobile vehicle  99  such as a humvee or tank. 
       FIG. 17C  is a perspective view of a mobile sea- and/or aircraft-vehicle-based defensive system  1703  that uses high-energy defensive device  1791  and/or  1791 ′ that each include hybrid-fiber configurations, according to one embodiment of the present invention. In some embodiments, the single extra high-power output beam is used as a directed-energy beam to protect against incoming missiles or aircraft, or seacraft, submarines or other vehicles. In some embodiments, a portion of the single extra high-power output beam, using one or more laser modules, is used as a communications beam to communicate with aircraft, or seacraft, submarines or other vehicles. In some embodiments a portion of the high-power output beam is provided by one or more laser modules that can be configured for sensing applications such as active imaging or LIDAR. In some embodiments, laser system  1790  and SBC device  1791  are housed in a ship  1713  such as a destroyer, aircraft carrier, or frigate, or in an aircraft  1723  such as a fighter jet or helicopter. 
     In some embodiments, in addition to SBC defense-based systems, the hybrid-fiber configurations of the present invention are used with systems such as coherent LIDAR and frequency conversion. For example, in some embodiments, the hybrid-fiber configurations described herein are used with the laser system of U.S. Pat. No. 8,441,718, which is incorporated herein by reference. 
     In some embodiments, the present invention provides an apparatus that includes an optical-fiber amplifier having a plurality of optically coupled gain-fiber segments including a first gain-fiber segment and a second gain-fiber segment, wherein pump light is guided into the optical-fiber amplifier, wherein the first gain-fiber segment has a first core that has a first core diameter, wherein the first core is surrounded by a first cladding layer having a first outer diameter, wherein the first gain-fiber segment has a first end, a second end, and a first length, wherein signal light of a signal-light wavelength propagates in the first core, wherein the first gain-fiber segment has a first thermal load due, at least in part, to absorption of the pump light over the first length, wherein the second gain-fiber segment has a second core that has a second core diameter, wherein the second core diameter is larger than the first core diameter, wherein the second core is surrounded by a second cladding layer having a second outer diameter, wherein the second gain-fiber segment has a first end, a second end, and a second length, wherein the first end of the second gain-fiber segment is connected to the second end of the first gain-fiber segment, wherein a first amplified version of the signal light is coupled into the second core from the first core in a first direction, wherein the second gain-fiber segment has a second thermal load due, at least in part, to absorption of the pump light over the second length, wherein a second amplified version of the signal light is coupled out of the second core as an output signal beam, and wherein the first and second lengths are configured such that the second thermal load stays below a value at which a modal-instability occurs. 
     In some embodiments of the apparatus, the first length is in a range of about 1 to 10 meters and the second length is in a range of about 1 to 10 meters. In some embodiments, the first and/or second length is about 1 meter, about 1.5 meters, about 2 meters, about 2.5 meters, about 3 meters, about 3.5 meters, about 4 meters, about 4.5 meters, about 5 meters, about 5.5 meters, about 6 meters, about 6.5 meters, about 7 meters, about 7.5 meters, about 8 meters, about 8.5 meters, about 9 meters, about 9.5 meters, about 10 meters, or, in other embodiments, the first length is any one of the above values and the second length is any one of the above values. 
     In some embodiments of the apparatus, the optical-fiber amplifier is configured to produce the output signal beam with at least one kilowatt (1 kW) of power. In some embodiments, e optical-fiber amplifier is configured to produce the output signal beam with any other suitable power. In some embodiments, the optical-fiber amplifier is configured to mitigate Stimulated Brillouin Scattering (SBS) such that the linewidth of the output signal beam is less than twenty gigahertz (20 GHz). In some such embodiments, the optical-fiber amplifier is configured such that the linewidth of the output signal beam is about twenty gigahertz 20 GHz, about 19 GHz, about 18 GHz, about 17 GHz, about 16 GHz, about 15 GHz, about 14 GHz, about 13 GHz, about 12 GHz, about 11 GHz, about 10 GHz, about 9 GHz, about 8 GHz, about 7 GHz, about 6 GHz, or about 5 GHz. 
     In some embodiments of the apparatus, the second gain-fiber segment is spliced to the first gain-fiber segment. In some embodiments, the second gain-fiber segment is fused to the first gain-fiber segment. In some embodiments, the optical-fiber amplifier is drawn at different speeds to form the second core diameter to be larger than the first core diameter. In some embodiments, the second gain-fiber segment is connected to the first gain-fiber segment via a first tapered segment, and wherein the first outer diameter of the first cladding layer is smaller than the second outer diameter of the second cladding layer. 
     In some embodiments of the apparatus, the first core diameter is a first effective core diameter, wherein the second core diameter is a second effective core diameter, wherein the first gain-fiber segment includes photonic-crystal holes configured to define the first effective core diameter, and wherein the second gain-fiber segment includes at least partially collapsed photonic-crystal holes configured to define the second effective core diameter. In some embodiments, the first outer diameter of the first cladding layer is equal to the second outer diameter of the second cladding layer. In some embodiments, the first core diameter is about 5 to 30 microns and the second core diameter is larger than the first core diameter with the cladding diameters nominally identical. 
     In some embodiments, the apparatus further includes a plurality of optical pumps operatively coupled to the optical-fiber amplifier and configured to provide the pump light guided into the optical-fiber amplifier, wherein the pump light has a wavelength that is longer than a peak absorption wavelength of the optical-fiber amplifier. In some embodiments, the apparatus further includes a plurality of optical pumps operatively coupled to inject the pump light in the first direction into the second cladding layer of the second gain-fiber segment such that the pump light co-propagates through the second segment in the first direction of the signal light. In some embodiments, the apparatus further includes a plurality of optical pumps operatively coupled to inject the pump light in a second direction, opposite the first direction, into the second cladding layer of the second gain-fiber segment such that the pump light counter-propagates through the second segment in the second direction that is opposite the first direction of the signal light. In some embodiments, the apparatus further includes a plurality of optical pumps operatively coupled to inject the pump light into the optical-fiber amplifier at a plurality of locations along a length of the optical-fiber amplifier. In some embodiments, the apparatus further includes a plurality of optical pumps operatively coupled to inject the pump light into the optical-fiber amplifier, wherein the first end of the first gain-fiber segment includes a high-reflectivity surface and the second end of the second gain-fiber segment includes a low-reflectivity surface, and wherein the optical-fiber amplifier is configured to reflect the signal light between the high-reflectivity surface at the first end of the first gain-fiber segment and the low-reflectivity surface at the second end of the second gain-fiber segment in order to provide lasing of the signal light. 
     In some embodiments of the apparatus, the first gain-fiber segment has a first pump-light-absorption value per unit length, wherein the second gain-fiber segment has a second pump-light-absorption value per unit length, and wherein the second pump-light-absorption value is greater than the first pump-light-absorption value. 
     In some embodiments of the apparatus, the first core diameter is twenty (20) microns, wherein the second core diameter is twenty-five (25) microns, and wherein a first outer diameter of the first cladding layer of the first gain-fiber segment and a second outer diameter of the second cladding layer of the second gain-fiber segment are both four-hundred (400) microns. In some embodiments, the first gain-fiber segment and the second gain-fiber segment are both polarization-maintaining fibers. 
     In some embodiments, the apparatus further includes a spiral-mandrel assembly configured to cool the optical-fiber amplifier, wherein at least a portion of the first gain-fiber segment and at least a portion of the second gain-fiber segment are configured to wrap around the spiral-mandrel assembly in a low-profile spiral-fiber configuration such that the at least portion of the first gain-fiber segment and the at least portion of the second gain-fiber segment both lie on a single plane. In some embodiments, the apparatus further includes a first spiral-mandrel assembly, wherein at least a portion of the first gain-fiber segment is wrapped around the first spiral-mandrel assembly in a first low-profile spiral-fiber configuration such that the at least portion of the first gain-fiber segment lies on a first single plane; and a second spiral-mandrel assembly, wherein at least a portion of the second gain-fiber segment is wrapped around the second spiral-mandrel assembly in a second low-profile spiral-fiber configuration such that the at least portion of the second gain-fiber segment lies on a second single plane. In some embodiments, the apparatus further includes a mandrel assembly configured to cool the optical-fiber amplifier, wherein at least a portion of the first gain-fiber segment and at least a portion of the second gain-fiber segment are configured to wrap around the mandrel assembly in a cylindrical-profile configuration. 
     In some embodiments, the apparatus further includes a seed source operatively coupled to the optical-fiber amplifier to provide the signal light propagating in the first core, wherein the seed source includes: a polarization-maintaining seed diode, wherein the seed diode is a distributed-feedback laser, a plurality of optical isolators, and a plurality of polarization-maintaining amplifiers; the apparatus further including a plurality of optical pumps operatively coupled to the optical-fiber amplifier and configured to provide the pump light guided into the optical-fiber amplifier; a beam combiner configured to combine the pump light from the plurality of optical pumps and guide the pump light into the optical-fiber amplifier; a pump dump configured to remove excess pump light from the optical-fiber amplifier; and an end cap. 
     In some embodiments, the present invention provides a method that includes constructing an optical-fiber amplifier having a plurality of optically coupled gain-fiber segments including a first gain-fiber segment and a second gain-fiber segment, wherein the constructing of the optical-fiber amplifier includes: forming the first gain-fiber segment to have a first core that has a first core diameter, wherein the first core is surrounded by a first cladding layer having a first outer diameter, wherein the first gain-fiber segment has a first end, a second end, and a first length, and forming the second gain-fiber segment to have a second core that has a second core diameter, wherein the second core surrounded by a second cladding layer having a second outer diameter, wherein the second core diameter is larger than the first core diameter, wherein the second gain-fiber segment has a first end, a second end, and a second length, wherein the first end of the second gain-fiber segment is connected to the second end of the first gain-fiber segment, wherein the method further includes guiding pump light into the optical-fiber amplifier, wherein the first gain-fiber segment has a first thermal load due, at least in part, to absorption of the pump light over the first length, wherein the second gain-fiber segment has a second thermal load due, at least in part, to absorption of the pump light over the second length; propagating signal light of a signal-light wavelength in the first core; coupling a first amplified version of the signal light into the second core from the first core in a first direction; coupling a second amplified version of the signal light out of the second core as an output signal beam; and configuring the first and second lengths such that the second thermal load stays below a value at which a modal-instability occurs. 
     In some embodiments of the method, the coupling of the second amplified version of the signal light includes producing the output signal beam with at least one kilowatt (1 kW) of power. In some embodiments, the coupling of the second amplified version of the signal light includes producing the output signal beam with a linewidth of less than twenty gigahertz (20 GHz). 
     In some embodiments, the method further includes splicing the second gain-fiber segment to the first gain-fiber segment. In some embodiments, the method further includes fusing the second gain-fiber segment to the first gain-fiber segment. In some embodiments of the method, the constructing of the optical-fiber amplifier further includes drawing the optical-fiber amplifier at different speeds to form the second core diameter to be larger than the first core diameter. In some embodiments of the method, the constructing of the optical-fiber amplifier further includes forming a first tapered segment, wherein the second gain-fiber segment is connected to the first gain-fiber segment via the first tapered segment, and wherein the first outer diameter of the first cladding layer is smaller than the second outer diameter of the second cladding layer. 
     In some embodiments of the method, the first core diameter is a first effective core diameter, wherein the second core diameter is a second effective core diameter, wherein the forming of the first gain-fiber segment includes forming photonic-crystal holes that define the first effective core diameter, and wherein the forming of the second gain-fiber segment includes forming at least partially collapsed photonic-crystal holes that define the second effective core diameter. 
     In some embodiments of the method, the forming of the first gain-fiber segment includes forming the first outer diameter of the first cladding layer to be equal to the second outer diameter of the second cladding layer. 
     In some embodiments, the method further includes providing a plurality of optical pumps operatively coupled to the optical-fiber amplifier, wherein the guiding of the pump light includes guiding the pump light from the plurality of optical pumps into the optical-fiber amplifier, wherein the pump light has a wavelength that is longer than a peak absorption wavelength of the optical-fiber amplifier. In some embodiments, the method further includes providing a plurality of optical pumps operatively coupled to the optical-fiber amplifier, wherein the guiding of the pump light includes injecting the pump light from the plurality of optical pumps in the first direction into the second cladding layer of the second gain-fiber segment such that the pump light co-propagates through the second segment in the first direction of the signal light. In some embodiments, the method further includes providing a plurality of optical pumps operatively coupled the optical-fiber amplifier, wherein the guiding of the pump light includes injecting the pump light from the plurality of optical pumps in a second direction, opposite the first direction, into the second cladding layer of the second gain-fiber segment such that the pump light counter-propagates through the second segment in the second direction that is opposite the first direction of the signal light. In some embodiments, the method further includes providing a plurality of optical pumps operatively coupled to the optical-fiber amplifier, wherein the guiding of the pump light includes injecting the pump light from the plurality of optical pumps into the optical-fiber amplifier at a plurality of locations along a length of the optical-fiber amplifier. In some embodiments, the method further includes providing a plurality of optical pumps operatively coupled to the optical-fiber amplifier, wherein the guiding of the pump light includes injecting the pump light from the plurality of optical pumps into the optical-fiber amplifier, wherein the first end of the first gain-fiber segment includes a high-reflectivity surface and the second end of the second gain-fiber segment includes a low-reflectivity surface; and reflecting the signal light between the high-reflectivity surface at the first end of the first gain-fiber segment and the low-reflectivity surface at the second end of the second gain-fiber segment in order to provide lasing of the signal light. 
     In some embodiments of the method, the first gain-fiber segment has a first pump-light-absorption value per unit length, wherein the second gain-fiber segment has a second pump-light-absorption value per unit length, and wherein the second pump-light-absorption value is greater than the first pump-light-absorption value. 
     In some embodiments of the method, the first core diameter is twenty (20) microns, wherein the second core diameter is twenty-five (25) microns, and wherein a first outer diameter of the first cladding layer of the first gain-fiber segment and a second outer diameter of the second cladding layer of the second gain-fiber segment are both four-hundred (400) microns. In some embodiments of the method, the first gain-fiber segment and the second gain-fiber segment are both polarization-maintaining fibers. 
     In some embodiments, the method further includes providing a spiral-mandrel assembly configured to cool the optical-fiber amplifier; and wrapping at least a portion of the first gain-fiber segment and at least a portion of the second gain-fiber segment around the spiral-mandrel assembly in a low-profile spiral-fiber configuration such that the at least portion of the first gain-fiber segment and the at least portion of the second gain-fiber segment both lie on a single plane. In some embodiments, the method further includes providing a first spiral-mandrel assembly; wrapping at least a portion of the first gain-fiber segment around the first spiral-mandrel assembly in a first low-profile spiral-fiber configuration such that the at least portion of the first gain-fiber segment lies on a first single plane; providing a second spiral-mandrel assembly; and wrapping at least a portion of the second gain-fiber segment around the second spiral-mandrel assembly in a second low-profile spiral-fiber configuration such that the at least portion of the second gain-fiber segment lies on a second single plane. In some embodiments, the method further includes providing a mandrel assembly configured to cool the optical-fiber amplifier; and wrapping at least a portion of the first gain-fiber segment and at least a portion of the second gain-fiber segment around the mandrel assembly in a cylindrical-profile configuration. 
     In some embodiments, the method further includes providing a seed source operatively coupled to the optical-fiber amplifier, wherein the propagating of the signal light in the first core includes injecting the signal light from the seed source into the optical-fiber amplifier, wherein the seed source includes: a polarization-maintaining seed diode, wherein the seed diode is a distributed-feedback laser, a plurality of optical isolators, and a plurality of polarization-maintaining amplifiers; wherein the method further includes providing a plurality of optical pumps operatively coupled to the optical-fiber amplifier and configured to provide the pump light; beam combining the pump light provided by the plurality of optical pumps to form a combined pump light and guiding the combined pump light into the optical-fiber amplifier; removing excess pump light from the optical-fiber amplifier; and providing an end cap optically coupled to the optical-fiber amplifier. 
     In some embodiments, the present invention provides an apparatus that includes an optical-fiber amplifier having a plurality of optically coupled gain-fiber segments including a first gain-fiber segment and a second gain-fiber segment; wherein the first gain-fiber segment has a first core that has a first core diameter, wherein the first core is surrounded by a first cladding layer having a first outer diameter, wherein the first gain-fiber segment has a first end, a second end, and a first length; wherein the second gain-fiber segment has a second core that has a second core diameter, wherein the second core surrounded by a second cladding layer having a second outer diameter, wherein the second core diameter is larger than the first core diameter, wherein the second gain-fiber segment has a first end, a second end, and a second length, wherein the first end of the second gain-fiber segment is connected to the second end of the first gain-fiber segment; means for guiding pump light into the optical-fiber amplifier, wherein the first gain-fiber segment has a first thermal load due, at least in part, to absorption of the pump light over the first length, wherein the second gain-fiber segment has a second thermal load due, at least in part, to absorption of the pump light over the second length; means for propagating signal light of a signal-light wavelength in the first core; means for coupling a first amplified version of the signal light into the second core from the first core in a first direction; means for coupling a second amplified version of the signal light out of the second core as an output signal beam; and means for configuring the first and second lengths such that the second thermal load stays below a value at which a modal-instability occurs. 
     It is specifically contemplated that the present invention includes embodiments having combinations and subcombinations of the various embodiments and features that are individually described herein, including the various embodiments described by patent applications and patents incorporated by reference herein (i.e., rather than listing every combinatorial of the elements, this specification includes descriptions of representative embodiments and contemplates embodiments that include some of the features from one embodiment combined with some of the features of another embodiment). Further, some embodiments include fewer than all the components described as part of any one of the embodiments described herein. 
     It is to be understood that the above description is intended to be illustrative, and not restrictive. Although numerous characteristics and advantages of various embodiments as described herein have been set forth in the foregoing description, together with details of the structure and function of various embodiments, many other embodiments and changes to details will be apparent to those of skill in the art upon reviewing the above description. The scope of the invention should be, therefore, determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled. In the appended claims, the terms “including” and “in which” are used as the plain-English equivalents of the respective terms “comprising” and “wherein,” respectively. Moreover, the terms “first,” “second,” and “third,” etc., are used merely as labels, and are not intended to impose numerical requirements on their objects.