WO2009088598A1

WO2009088598A1 - Apparatuses and methods for performing gain guiding

Info

Publication number: WO2009088598A1
Application number: PCT/US2008/085565
Authority: WO
Inventors: Tsinghua Her
Original assignee: University Of North Carolina At Charlotte
Priority date: 2008-01-08
Filing date: 2008-12-04
Publication date: 2009-07-16

Abstract

A fiber, such as a photonic bandgap fiber, is provided, the fiber including a core and a cladding. The core can extend longitudinally and can have a gain medium configured to provide laser amplification to signal radiation propagating along the core. For example, the gain medium may include a dopant configured to provide laser amplification, when activated by excitation radiation, to signal radiation propagating along said core. The cladding can be radially exterior to the core, and can be configured to resonantly reflect at least some excitation radiation propagating transversely to the core and to generally transmit signal radiation propagating transversely to the core. The core may have an effective core index of refraction that is lower than an effective cladding index of refraction. Associated methods and apparatuses are also provided.

Description

APPARATUSES AND METHODS FOR PERFORMING GAIN GUIDING

FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT This invention was made with United States Government support under Grant No. W911NF-05-1-0517 awarded by the U.S. Army Research Office, and under Grant No. HROOl 1-08-1-0065 awarded by the Defense Advanced Research Projects Agency. The United States Government has certain rights in the invention.

BACKGROUND

Embodiments of the present invention relate to the guiding of radiation, and more particularly, to apparatuses and method for performing gain guiding. High-power waveguide lasers and amplifiers at eye-safe wavelengths can enable a broad spectrum of military and civilian applications. These include Light Detection And Ranging (LIDAR) for ranging, tracking and target identification; obstacle avoidance systems for unmanned vehicles; improved free-space laser communications (ground-to-air, air-to-air, and inter-satellite); coherent laser radar for wind metrology and vibrometry; pump sources for nonlinear frequency down-conversion for counter-measures; clear-air turbulence analysis; bio-chemical detection and pollution monitoring; and high power laser weaponry. Among various platforms of high-power sources, fiber lasers and amplifiers are particularly attractive for their light weight, high conversion efficiency, and near diffraction-limit beam quality. Referring to Figs. 1 and 2, conventional fiber lasers are often "cladding-pumped," meaning that the fiber 10 has a core 12 surrounded by an inner cladding layer 14, which is then surrounded by an outer cladding layer 16. The core 12 and inner and outer cladding 14, 16 have respective indices of refraction n_& n_ic, n_oc and are chosen such that n_c > n_ic > n_oc. This causes signal radiation propagating through the core 12 to be confined in the core, and excitation or "pump" radiation to be confined by the inner cladding 14 (such that it propagates through both the inner cladding and the core) via total internal reflection. Fibers having cladding configured in this way are referred to as "double-cladding" fibers, and the described mode of radiation propagation is termed "index guiding."

To maximize the obtainable power, both high output power from a single aperture and coherent combining of multiple apertures are desirable. Power scaling of single fiber lasers/amplifiers is limited by optical damage of the host materials and optical nonlinearity, including stimulated Brillouin scattering (SBS), stimulated Raman scattering (SRS), and self-phase modulation (SPM). To increase the throughput of single aperture, large modal area (LMA) and high optical gain are desired, these factors facilitating a reduction in the optical intensity and device length without surpassing the nonlinear threshold. LMA and high gain are also desired for coherent beam combining, since SBS and SRS can also impose noise-like wide band modulation on the amplified beam. In addition, single-polarization and single-mode operation is preferred in order to obtain a predictable interference pattern at the far field. However, in order to obtain single mode operation, it is usually necessary to limit the diameter of the core, thereby limiting the modal area and output power of the fiber.

BRIEF SUMMARY

In one aspect, a fiber is provided that includes a core and a cladding. The core can extend longitudinally and can have a gain medium configured to provide laser amplification to signal radiation propagating substantially longitudinally along the core. For example, the gain medium may include a dopant configured to provide laser amplification, when activated by excitation radiation, to signal radiation propagating along said core. The cladding can be radially exterior to the core, and can be configured to resonantly reflect at least some excitation radiation propagating transversely to the core and to generally transmit signal radiation propagating transversely to the core. The core may have an effective core index of refraction that is lower than an effective cladding index of refraction.

In one embodiment, the core is cylindrical and the cladding radially surrounds said core. In another embodiment, the core is generally planar and said cladding is disposed on opposing transverse sides of said core. The fiber may include a photonic bandgap fiber, wherein the cladding includes an array of longitudinal holes, rods, and/or a series of layers stacked transverse to said core and having alternating respective indices of refraction. The cladding can be configured to establish a nearly complete photonic bandgap. The cladding can be configured to confine therein one or more transverse modes for excitation radiation propagating along the core, and to transmit all transverse modes for signal radiation propagating along the core. The gain medium can be configured to provide laser amplification of sufficient magnitude to signal radiation propagating along the core to compensate for propagation losses in radiation associated with the lowest order mode of propagation and insufficient to compensate for propagation losses in radiation associated with higher order modes of propagation.

In another aspect, an apparatus is provided that includes a fiber having a core and a cladding. The core can extend longitudinally and can have a gain medium configured to provide laser amplification to signal radiation propagating along the core. The cladding may be radially exterior to the core and configured to resonantly reflect at least some excitation radiation propagating transversely to the core and to generally transmit signal radiation propagating transversely to the core. A signal radiation source may be coupled to the core and configured to emit signal radiation to be generally transmitted by the cladding when propagating transversely to the core. An excitation radiation source may also be coupled to the core and configured to emit excitation radiation to be at least partially resonantly reflected by the cladding and absorbed by the gain medium when propagating transversely to the core.

In some embodiments, the apparatus may further include a pump mirror disposed along a longitudinal axis defined by the core. The pump mirror can be configured to be significantly transmissive to excitation radiation and significantly reflective of signal radiation. An output coupler can also be disposed along the longitudinal axis defined by the core and in opposition to the pump mirror, which output coupler can be configured to be partially reflective of signal radiation.

In yet another aspect, a method is provided that includes providing a fiber including a core and a cladding. The core can extend longitudinally and can have a gain medium configured to provide laser amplification to signal radiation propagating along the core. The cladding may be radially exterior to the core and configured to resonantly reflect at least some excitation radiation propagating transversely to the core and to generally transmit signal radiation propagating transversely to the core. Signal radiation may be coupled into the core, the signal radiation being configured such that a portion of the signal radiation associated with transverse modes of propagation is transmitted by the cladding. Excitation radiation may also be coupled into the core, the excitation radiation being configured such that at least some of the excitation radiation associated with transverse modes of propagation is resonantly reflected by the cladding and absorbed by the gain medium.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S) Having thus described the invention in general terms, reference will now be made to the accompanying drawings, which are not necessarily drawn to scale, and wherein: Fig. 1 is a cross-sectional view of a double-cladding fiber; Fig. 2 is a schematic plot of the intensities of both pump and signal radiation as a function of position within the fiber of Fig. 1 ; Fig. 3 is a side view, in partial cross section, of a fiber laser amplifier configured in accordance with an example embodiment;

Fig. 4 is a perspective view of the fiber of the fiber laser amplifier of Fig. 3; Fig. 5 A is a partially exploded perspective view of the fiber of Fig. 4; Fig. 5B is a magnified end view of the portion labeled 5B of the fiber of Fig. 5 A; Fig. 6 is a perspective view of the fiber core of Fig. 5, wherein the fiber core is sectioned to reveal its interior;

Fig. 7 is a side view, in partial cross section, of the fiber laser amplifier of Fig. 3, illustrating the propagation of excitation radiation;

Fig. 8 is a magnified cross-sectional view of the fiber of Fig. 7; Fig. 9 is a side view, in partial cross section, of the fiber laser amplifier of Fig. 3, illustrating the propagation of signal radiation in the absence of excitation radiation; Fig. 10 is a cross-sectional view taken along line 10-10 of Fig. 9; Fig. 11 is a schematic plot of the intensities of both pump and signal radiation as a function of position within the fiber of Fig. 9; Fig. 12 is a side view, in partial cross section, of the fiber laser amplifier of Fig. 3, illustrating the propagation of signal radiation in the presence of excitation radiation; Fig. 13 is a cross-sectional view taken along line 13-13 of Fig. 12; Fig. 14 is a schematic plot of the intensities of both pump and signal radiation as a function of position within the fiber of Fig. 12; Fig. 15 is a perspective view of a fiber configured in accordance with another example embodiment;

Fig. 16 is an end view of the fiber of Fig. 15;

Fig. 17 is a perspective view of the fiber core of Fig. 15, wherein the fiber is sectioned to reveal its interior; Fig. 18 is a cross-sectional view of the fiber of Fig. 15;

Fig. 19 is a perspective view of a fiber configured in accordance with yet another example embodiment;

Fig. 20 is a perspective view of a fiber configured in accordance with yet another example embodiment;

Figs. 2 IA-D are schematic side views of a process for producing a waveguide configured in accordance with an example embodiment;

Figs. 22A-C are schematic side views of another process for producing a waveguide configured in accordance with an example embodiment; and Fig. 23 is a side view, in partial cross section, of a fiber laser configured in accordance with an example embodiment.

DETAILED DESCRIPTION The present inventions now will be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all embodiments of the inventions are shown. Indeed, these inventions may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. Like numbers refer to like elements throughout. Referring to Figs. 3-6, therein is shown a fiber laser amplifier 100 configured in accordance with an example embodiment. The fiber laser amplifier 100 includes a fiber 102 or other elongated structure for guiding waves, a signal radiation source 104, and an excitation or "pump" radiation source 106. The fiber 102 may have a core 108, such as an optical fiber formed, say, of glass or plastic, that extends along a longitudinal direction /. A cladding 110 may be disposed radially exterior to the core 108. For example, the core 108 may be cylindrical, and the cladding 110 may partially or completely radially surround the core, such as by being formed of a "Bragg grating," wherein a series of alternating layers 112a, 112b are stacked transversely to the core (i.e., transversely to the longitudinal direction / defined by the core). The layers 112a, 112b may be respectively composed of materials with alternating indices of refraction n_ci and n_c2.

The core 108 may include a gain medium 114 configured to provide laser amplification to radiation of appropriate wavelength and propagating along the core. In some embodiments, the gain medium 114 may include an optical fiber incorporating a dopant 116 that is configured to provide laser amplification when activated by excitation radiation. Examples of materials that may be used as dopants include, for example, ions of erbium, ytterbium, neodymium, dysprosium, praseodymium, holmium, and/or thulium. These ions may act to absorb radiation (i.e., excitation radiation) of wavelengths appropriate to excite the ions into one or more metastable states, thereby "activating" the gain medium. Once the ions have been excited, incoming radiation of appropriate wavelength may then interact with the excited ions to produce stimulated emission and amplification of the incoming radiation.

The core 108 and cladding 110 can be configured such that radiation propagating transversely through the core (/. e. , propagating along a direction having a non-zero transverse component, such that the radiation is directed at least somewhat towards the cladding) is generally transmitted by the cladding (i.e., the cladding 110 is "leaky"). For example, the core 108 can have an effective core index of refraction n_co that is lower than an effective cladding index of refraction n_cι associated with the cladding 110, where the effective index of refraction is a spatial average index of refraction for the materials making up either the core or the cladding. That is, for either the core or the cladding, the effective index of refraction will be a weighted average of the respective indices of refraction of the constituent materials, with each constituent material contributing to the effective index by an amount proportional to the spatial proportion of that material relative to the whole. In this way, the total internal reflection mechanism for propagating radiation through the core 108 is precluded. Fibers for which the core has a lower index of refraction than the cladding are referred to as "index-antiguided" fibers (or "IAG fibers"). Radiation propagating transversely along the core 108 of the fiber 102 (or any waveguiding strucuture) is said to be associated with a "transverse mode" of propagation. Referring to Fig. 3, the signal radiation source 104 may be, for example, a seed laser that is solid-state, liquid, or gas in nature and that can be continuous wave or pulsed, including, without limitation, fiber lasers, diode laser, dye lasers, gas lasers, etc. The excitation radiation source can be any source configured to emit radiation capable of promoting electrons associated with the dopant ions. For example, flash lamps, light- emitting diodes (LEDs), fiber lasers, and/or diode lasers may be utilized as the excitation radiation source. The excitation radiation source may emit radiation that is not spatially coherent. As described in more detail below, the signal and excitation radiation sources 104, 106 may be configured such that radiation emitted by the radiation sources is received by the fiber 102, with a portion of the radiation being propagated along the fiber. Referring to Figs. 7 and 8, the excitation radiation source 106 can be coupled to the core 108 such that excitation radiation R_e emitted from the excitation radiation source enters the core. For example, the output of the excitation radiation source 106 can be coupled to the core 108 using lenses, mirrors, filters, couplers, and/or other such components used for directing radiation (not shown). The cladding 110 and excitation radiation source 106 may be configured such that some excitation radiation R_e propagating transversely through the core 108 (say, one or more propagation modes) will tend to be resonantly reflected by the cladding. For example, reflections from the interfaces between various layers 112a, 112b in the cladding 110 may constructively interfere with one another, producing reflected radiation R_r. Such resonant reflections can occur when the period of repetition or pitch A of the layers 112a, 112b and the angle of incidence Θ_R of the excitation radiation R_e obey the relationship

Λ = λl2n_r ύn θ_R (1)

where λ is the wavelength of the excitation radiation R_e and n_r is the real part of the effective index of refraction n_cι of the cladding 110 (e.g., the average of the indices of refraction n_cj and n_C2 for the layers 112a, 112b). The reflected portion R_r of the excitation radiation R_e can then interact with and activate the gain medium 114, enabling laser amplification of subsequent incoming radiation. The bandwidth Aλ of the cladding at its resonance is Aλ = λ κ/(πn_ctsmθ_R), where /cis the coupling constant of the grating and is proportional to the difference between alternating indices of refraction n_cι and n_C2. For other angles of incidence of the excitation radiation R_e with respect to the cladding 110, the reflected excitation radiation will not constructively interfere, and such radiation will be essentially transmitted by the cladding 110. As the reflected portion of the radiation R_r propagates along the core 108, it may be somewhat or highly multi-modal.

Referring to Figs. 9-14, the signal radiation source 104 can be coupled to the core 108 such that signal radiation R_s emitted from the signal radiation source enters the core (e.g., enters an input end 120 of the core). For example, a beam splitter 118 can be used to receive signal radiation R_s from one direction and direct the radiation into the core 108 while allowing excitation radiation R_e propagating along another direction to pass through and enter the core. As mentioned above, the core 108 and cladding 110 can be configured, along with the signal radiation source 104, such that the signal radiation R_s is transmitted by the cladding and propagates out of the fiber 102 in a variety of directions (e.g., as where the effective index of refraction of the core n_co is less than that of the cladding n_ci). In other words, the cladding 110 may be leaky with respect to most or all of the propagation modes of the signal radiation R_s. When the excitation radiation source 106 is not emitting excitation radiation R_e into the core 108 (as illustrated in Fig. 9), the intensity of the signal radiation R_s at points along the fiber 102 and spaced from the input end 120 is generally low (see Figs. 10 and 11). The intensity may be fairly uniform in the variety of directions, as shown in Figs. 10 and 11, for cases where the signal radiation R_s activates many propagation modes, or may be nonuniform where only a few propagation modes are active. In either case, the intensity of the signal radiation will be low due to propagation losses. Some of the signal radiation R_s does propagate through the core 108 and is emitted from the output end 122 thereof. However, because much of the signal radiation R₁ has escaped the core 108 before reaching the output end 122, the energy associated with the radiation being emitted at the output end is relatively small compared to that being emitted by the signal radiation source 104 into the input end 120.

When the excitation radiation source 106 is emitting excitation radiation R_e into the core 108 (as illustrated in Fig. 12), the gain medium 114 is activated thereby. Under these conditions, signal radiation R_s propagating along the core 108 interacts with the activated gain medium and is continuously amplified as it advances along the core (this amplified portion of the signal radiation is denoted as R_a in Fig. 12).

For signal radiation R_s propagating substantially parallel to the longitudinal direction / defined by the core 108 (i.e., the lowest order mode of propagation), propagation losses are less than for other (higher order) modes of propagation that are directed transversely to the core (i.e., transverse modes). Therefore, when the amplified signal radiation R_a is ultimately emitted from the output end 122 of the core 108, the intensity associated with the lowest order mode of propagation is increased relative to that associated with higher order modes of propagation (see Figs. 13 and 14). As such, despite the fact that much of the input energy from the signal radiation source 104 has been distributed elsewhere, the intensity of the amplified signal radiation R_a being emitted from the output end 122 is both of acceptable magnitude to allow for signal extraction or other subsequent uses and mainly representative of the lowest order mode of propagation. It is noted that the decay of the signal and/or pump radiation when moving away from the central axis of the fiber 102 can be faster or slower than that depicted in Fig. 14, and Fig. 14 should therefore be understood to be a general representation of radiation intensity. Further, the intensities of the signal and pump radiation need not tend towards zero at the outer radius of the cladding (i.e., when x ~ r_ci), but may tend towards zero outside the outer radius of the cladding (i.e., x > r_ci) or well inside the outer radius of the cladding (i.e., x « r_ci). As mentioned above, signal radiation R_s propagating along the core 108 in a direction substantially parallel with the longitudinal direction / (this corresponding to the lowest order mode of propagation of the signal radiation along the core) ultimately emerges from the output end 122 of the fiber 102 with intensity that is increased relative to that associated with other modes of propagation. As mentioned, radiation associated with all of the modes of propagation will experience amplification, but the propagation losses associated with the higher order modes will be greater than those for the lowest order mode. The gain provided by the gain medium 114 can be tailored to provide amplification sufficient such that the intensity of the radiation associated with the lowest order mode of propagation reaches a useful or non-trivial level while the intensity of the radiation associated with the higher order modes of propagation are at relatively low levels. The lowest order mode of propagation is then said to be "confined" by the cladding 110, while the cladding remains leaky with respect to higher order modes. This amplification- induced discrimination between radiation associated with lower and higher order modes of propagation is referred to as "gain guiding." Further details regarding gain guiding can be found in U.S. Patent No. 6,751,388 to Siegman, which is incorporated herein by reference in its entirety.

The above description can be re-casted in terms of the theory of photonic bandgap (PBG) and optical waveguides. The cladding made of periodic media (e.g., one- dimensional rings or a two-dimensional array of rods/holes), whereby the cladding possesses one or more photonic bandgaps to pump radiation having a certain range of incident angles, such that the pump radiation has a multitude of confined modes in the fiber. The confined modes may propagate along the core of the fiber without much propagation loss other than those due to pumping the gain medium. At the same time, the cladding possesses no photonic bandgaps with respect to the signal radiation, regardless of the incident angle. In addition, the refractive index of the core is smaller than the average of the refractive indexes in claddings to preclude index guiding. As a result, signal radiation has no confined modes in the absence of pump radiation and all the modes are leaky. When the excitation radiation is present, it provides the signal radiation suitable amplification, part of which is used to compensate for the propagation loss and the rest for a net increase in output energy compared to the input. The fiber can be configured to provide a gain that is sufficient to compensate for losses in the lowest order mode, but insufficient to compensate for the propagation loss of the higher order modes, and the fiber thus possesses only single confined mode. Referring to Figs. 15-18, therein is shown a fiber 202 configured in accordance with another example embodiment. The fiber 202 may include a cladding 210 having various layers 212 that surround a core 208 (a fiber with this geometry is sometimes referred to as a "Bragg fiber"). The layers 212 can be solid and/or hollow (and possibly filled with fluid). Descriptions of Bragg fibers having hollow layers are provided by G. Vienne et al., "Ultra-large bandwidth hollow-core guiding in all-silica Bragg fibers with nano-supports," Optics Express, Vol. 12(15), pp. 3500-3508 (2004), which is incorporated herein by reference in its entirety.

The core 208 may be a hollow defined by the fiber 202, for example, by the radially innermost layer 212 of the cladding 210. A fluid 214 may be disposed in the hollow core 208 so as to act as the gain medium. The fluid 214 could be a gas that is capable of acting as the gain medium; examples of such gases include, for example, various alkali atom vapors, such as lithium, sodium, potassium, rubidium, and/or cesium, when dispersed in appropriate buffer gases, such as helium, as described further in U.S. Patent No. 7,286,575 to Payne et al., which is incorporated herein by reference in its entirety. The fluid 214 can also be a solvent containing suspended dyes or doped nanoparticles that are capable of acting as the gain medium. Examples of such particles include, but are not limited to, Nd₂O₃ and/or NdF₃, and are described further in U.S. Patent Application Publication No. 2007/0189351 to Rice et al., which is incorporated herein by reference in its entirety. In other embodiments, the core 208 may be a solid core that includes appropriate dopants to act as the gain medium.

Referring to Fig. 19, therein is shown a fiber 302 configured in accordance with yet another example embodiment. The fiber 302 may again be a "Bragg fiber," with a cladding 310 including various layers 312. A generally planar core 308 may extend along a longitudinal axis / between opposing portions of cladding 310. As such, the cladding 310 may be disposed on the transverse side of the core 308 and may only partially surround the core 308. In other embodiments, the cladding 310 may completely surround the core 308.

The fibers 102, 202, 302 described above and depicted, for example, in Figs. 4, 15, and 19, are examples of PBG fibers. A PBG fiber is a fiber that utilizes photonic bandgap effects to confine radiation propagating therealong. Specifically, periodic dielectric structures of appropriate dimensions tend to affect the propagation of electromagnetic radiation by causing diffraction. This diffraction defines wavelengths of radiation (for a given set of angles of incidence of the radiation) that are either reflected or transmitted by the periodic dielectric structure. It is noted that PBG fibers are also sometimes referred to as "photonic crystal fibers" and/or "microstructured fibers." The example presented above, in which a PBG fiber includes a Bragg grating, is sometimes referred to as a "Bragg fiber."

In some embodiments, other types of PBG fibers may be utilized. For example, referring to Fig. 20, therein is shown a fiber 402 configured in accordance with another example embodiment. The fiber 402 may be a "holey fiber," for which a core 408 extends along a longitudinal direction / and is (at least partially) surrounded by a cladding 410 that includes an array of longitudinal holes 412. For example, the fiber 402 may be a unitary structure, with the holes 412 being formed longitudinally through the fiber and radially around the core 408. The cladding 410 then includes both the holes 412 and areas 413 between the holes where material is present. The effective index of refraction n_cι of the cladding 410 is then an average of the index of refraction associated with the holes 412 (e.g., the refractive index for the material disposed within the holes, such as air, or that associated with vacuum if the holes are empty) and that of the material disposed in the areas 413 between the holes, and is higher than the refractive index of the core 408 (which core may be empty). As with earlier described embodiments, the core 408 may include a gain medium, such as gases (not shown) configured to provide laser amplification to radiation of appropriate wavelength and propagating along the core. It is noted that while the holes 412 are illustrated as being discrete and independent of one another, in some embodiments, the cladding 410 can be configured as a cellular structure, such as a honeycomb structure, that defines a periodic array of holes. An example of such a cladding is provided in G. Bouwmans et ah, "Properties of a hollow-core photonic bandgap fiber at 850 nm wavelength," Optics Express, Vol. 11(14), pp. 1613-1620 (2003), which is incorporated herein by reference in its entirety. In some embodiments, the core 408 may be (at least partially) surrounded by a cladding 410 that includes an array of longitudinal solid rods. For example, each of the holes 412 could instead be full of solid material. The solid rods could be configured such that the average refractive index of the rods and the material disposed among rods is higher than that of the core 408. The core 408 could be made of liquids containing suspending doped nanoparticles or solids containing doped ions or doped nanoparticles to provide amplification. In other embodiments, periodic arrays of solid structures other than cylindrical rods could be utilized as part of the cladding 410.

As with the Bragg fiber of Figs. 4 and 5 A, through appropriate choice of the configuration of the holes/rods 412 and the material of the core 408 and the areas 413 around the holes, the effective index of refraction of the cladding n_cι can be higher than that for the core n_co, thereby precluding total internal reflection for radiation propagating along the core. Further, excitation radiation of appropriate wavelength and direction that is directed into the core 408 can be resonantly reflected by the cladding 410 in much the same way as described above. Finally, the core 408 can include a gain medium, for example, in the form of dopant (for a solid core) or an appropriate fluid (for a hollow core).

Embodiments configured in accordance with the above examples may facilitate single mode, large modal area (LMA) transmission of signal radiation through a fiber. Using an index-antiguiding fiber, radiation associated with higher order modes of propagation tends to be emitted in a variety of directions, and therefore does not contribute appreciably to the output from the fiber. This may facilitate the use of larger diameter fibers, as the ability to discriminate, by embodiments of this method, between the lowest order mode of propagation and higher order propagation modes does not depend exclusively on the diameter of the fiber core (as in many prior devices), but is a function of the gain as well. Additionally, by using a PBG fiber for signal transmission, excitation radiation can be propagated through the fiber, despite its index-antiguiding nature, the excitation radiation inducing the continuous amplification of the lowest order mode of propagation of the signal radiation as it advances along the fiber core. Overall, this waveguiding mechanism can be referred to as "gain-guiding in photonic bandgap fibers" or "GG-PBG."

The bandwidth of the photonic bandgap for a given cladding affects the number of confined modes for the excitation radiation. It is known from conventional double- cladding fibers that as the number of pump modes confined in the inner cladding increases, it becomes easier to couple excitation radiation into the inner cladding, thereby improving the overall pumping efficiency. Embodiments provided herein may support many confined modes for the excitation radiation by employing fibers/waveguides incorporating cladding having a large photonic bandgap. For example, some embodiments may utilize PBG fibers with complete photonic bandgaps that contain excitation radiation from all incident angles. An example of such a PBG fiber is the BeamPath™ fibers available from OmniGuide Inc. of Cambridge, MA. Further discussion of PBG fibers is provided in B. Temelkuran et al, "Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission," Nature, Vol. 420, pp. 650-653 (2002), which is incorporated herein by reference in its entirety.

Referring to Figs. 21 A-D, therein is schematically represented a method for producing a GG-PBG planar waveguide configured in accordance with an example embodiment. A substrate 540a of commercially available phosphate glass, such as active IOG1 glass, can serve as the base material. IOG1 glass is a doped phosphate glass that includes a uniformly high concentration of, for example, Er³⁺ (for example, in order to produce a final dopant density of approximately 10²¹ cm^" ) and Yb³⁺ (for example, in order to produce a final dopant density of approximately 10²⁰ cm^"3). The substrate 540a can be uniformly doped with Na⁺ and/or K⁺ ions, for example, via an ion exchange process, thereby creating a doped region 541a. A mask 542a can then be disposed over the substrate 540a before doping the substrate (in the unmasked areas 544) with Ag⁺. The suitability of IOG1 glass for such applications is discussed further in S. Blaize et. al., IEEE Photon. Technol. Lett., Vol. 15, p. 516 (2003), which is incorporated herein by reference in its entirety. This process results in a PBG fiber 502a having a core 508a, and a surface grating 510a. Ion exchange can produce index differences from 0 to 0.008 for potassium-doped or 0 to 0.015 for silver-doped materials. Ion exchange leads to a graded index profile that is highest on the surface and is gradually reduced towards the substrate until a depth of 5- 8 μm. The index profile can be adjusted by controlling the concentration of the salts, the oven temperature during the ion exchange (between 300-500 ⁰C), and exposure time of substrate in the salt bath. The resulting surface single mode waveguides can be expected to exhibit losses of- 1 dB/cm (K-doped) and ~ 1.2-1.5 dB/cm for Ag-doped. To reduce the propagation loss, an additional field-assisted ion diffusion process can be performed by applying a voltage of approximately 100 V/cm across the substrate 540, which can result in an embedded waveguide. Referring to Figs. 22A-C, therein is schematically represented another method for producing a GG-PBG fiber configured in accordance with an example embodiment. A substrate 540b of commercially available phosphate glass is patterned via reactive ion etching through a mask 542b to form a surface grating 510b. The surface region 541b of the substrate 540b can be co-doped, via ion exchange, with high concentration of, for example, Na⁺/K⁺ ions and Ag⁺ ions. This process results in a PBG fiber 502b having a core 508b, and a surface grating 510b.

Some embodiments of GG-PBG may have the following advantages:

1. Robust single-mode operation with high gain Where an index-antiguided fiber of core diameter 2a that has both an index step An and a power-gain coefficient g in the fiber core with respect to the surrounding cladding, the normalized threshold gains for the onset of bounded LP₀₁ and LP₀₁ modes of are

ΔN and G are the dimensionless index and gain parameters defined by

_{A λr} (2πaλ² (2πa)² ( n_oλλ _m

ΔN ≡ x 2n₀ x An and G ≡ \ x -⁵^- x g {->)

\ λ J _\ λ ) \ 2π J where no is the background index of the cladding and λ is the vacuum wavelength.

Equations (2) are expected to be valid for ΔN < -50, as discussed in A. E. Siegman, "Gain- guided, index-antiguided fiber lasers," J. Opt. Soc. Am. B, Vol. 24(8), pp. 1677-1682 (2007), which is incorporated herein by reference in its entirety. It can be seen that the power threshold of LPn mode remains larger than that of LP₀₁ mode by a factor of 2.54, which indicates potentially strong transverse mode discrimination. To ensure single- transverse mode, the pump gain coefficient g should be kept smaller thang^¹. The modal gain coefficient of the bounded modes, on the other hand, is related to the pump gain coefficient g by g_m » g - g_lh . The maximum modal gain coefficient for pure single-mode operation thus becomes g°'_max = g°_aχ - g"¹ = 1.54 • g% . The threshold gain coefficient of LPoi mode g^ can be made over a wide range of values by controlling the fiber core diameters and the strength of IAG. For example, gJ° _ms>. for fibers with core diameter of 200 wm andΔw ~ -10^~4 is ~ 0.4 cm^"1, which is a fairly large gain for fiber amplifiers. It is interesting to point out that the same threshold gain coefficient can be obtained for a wide range of fiber diameters by carefully controlling the negative index step between the core and the cladding.

2. Single-polarization output

GG-PBG fibers are compatible to all existing techniques to produce single- polarization output in fibers. Photonic-crystal fibers are known to possess the largest form birefringence of all fibers. Placing air holes or high-index rods at location that break the azimuthal symmetry of the fibers will introduce significant structural anisotropy, as discussed in A. Ortigosa-Blanch et. al. , "Highly birefringent photonic crystal fibers," Opt. Lett., Vol. 25, pp. 1325-1327 (2000), which is incorporated herein by reference in its entirety. Alternatively, stress may be induced in LMA-single mode photonic crystal fibers using stress-applying parts, as discussed in J.R. Folkenberg, et. al. , "Polarization maintaining large mode area photonic crystal fiber," Opt. Exp. (2004), which is incorporated herein by reference in its entirety. GG-PBG fibers, therefore, hold promise for strong polarization-maintaining characteristics and the delivery of robust single- polarization operation.

3. Ultra large modal area

Referring to Equations (2) and (3), ultra-LMA may be obtained by controlling An . LMA can be a significant factor in reducing optical nonlinearity for coherent beam combining and power scaling. For example, the threshold power of stimulated Brillouin scattering, P_SBS, for single polarization scales as

21 • (1 + Δ v_ngM, I Δ v_Bnllomn ) ^■ A_{eff (} ._Λ rSBS * ~ ^

^{L •} S SBS where g_SBS is the Brillouin gain coefficient (~ 5xlO^'π m/W), L is the length of the fiber, and A_ef/ is the modal area (assumed here to be 75 % of the core area). For narrow linewidth operation that is desired for coherent beam combining, Av _ug I A v_Brιllomn ~ 0 , and

P_SBS f°^{r a} 200 μm diameter fiber is approximately 64 times greater than that for a conventional LMA fiber with a diameter of 25 μm.

4. High conversion efficiency and short fiber length The necessary length of the fiber can often be reduced by reducing the ratio of the inner cladding diameter to the core diameter. Doing so increases the spatial overlap between pump and signal and therefore the filling factor, which enables more efficient energy transfer therein. High conversion efficiency can also help reduce the required device length (for a fixed total gain) and thus increase the nonlinear threshold. Embodiments of the GG-PBG fiber may have a core dimension that is nearly equal to that of the inner cladding. Thus, GG-PBG may be expected to have a relatively high conversion efficiency and therefore facilitate a reduced device length. Many modifications and other embodiments of the inventions set forth herein will come to mind to one skilled in the art to which these inventions pertain having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. For example, while many of the above described embodiments included reference to a "fiber," it should be understood that the term "fiber," as used herein, can refer to any elongated structure capable of at least partially facilitating the propagation of radiation therealong, optical fibers being but one example. As such, the term "fiber" is often interchangeable with the term "waveguide," and it should be understood that linear or planar waveguides can be utilized in most applications. Also, while many of the above described embodiments have focused on fiber laser amplifier applications, the concepts embodied therein may also be applicable to laser oscillation applications by placing the fibers inside an optical cavity, usually defined between two mirrors. For example, referring to Fig. 23, therein is shown a fiber laser oscillator 600 (or simply "fiber laser") configured in accordance with an example embodiment. The fiber laser oscillator 600 includes a fiber 602 having a gain medium- containing core 608 and a cladding 610, as discussed above. An excitation radiation source 606 can be configured so as to emit excitation radiation R_e and a signal radiation source (not shown) can emit signal radiation R_s.

A pump mirror 650 can be disposed along a longitudinal axis / defined by the core 608. The pump mirror 650 can be configured to be significantly transmissive to excitation radiation R_e while being significantly reflective of signal radiation R_s. An output coupler 652 can be disposed along the longitudinal axis / and in opposition to the pump mirror 650. The output coupler 652 can be configured to be partially reflective of signal radiation R_s, such that signal radiation encountering the output coupler is partially reflected and partially transmitted by the coupler.

As the excitation radiation source 606 emit excitation radiation R_e, the radiation is transmitted by the pump mirror 650 and propagates along the core 608, thereby activating the gain medium contained therein. The signal radiation R_s also propagates along the core 608 and is amplified by the gain medium. The amplified signal radiation R_s is partially reflected and partially transmitted by the output coupler 652. The reflected portion of the signal radiation R_s propagates in the opposite direction along the core 608 until it encounters the pump mirror 650. The signal radiation R_s is reflected by the pump mirror 650 in a direction back along the core 608. As the signal radiation R_s propagates back and forth along the core, it is further amplified by the gain medium. Stable oscillations of the fiber laser oscillator 600 are established when the amplification of the signal radiation R_s for each round trip through the fiber 602 is sufficient to compensate for the energy loss associated with the round trip, most of the loss being related to the partial transmission of signal radiation by the output coupler 652.

Therefore, it is to be understood that the inventions are not to be limited to the specific embodiments disclosed and that modifications and other embodiments are intended to be included within the scope of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.

Claims

THAT WHICH IS CLAIMED:

1. A fiber comprising: a core extending longitudinally and having a gain medium configured to provide laser amplification to signal radiation propagating along said core; and a cladding that is radially exterior to said core and configured to resonantly reflect at least some excitation radiation propagating transversely to said core and to generally transmit signal radiation propagating transversely to said core.

2. The fiber of Claim 1 , wherein said core has an effective core index of refraction, said cladding has an effective cladding index of refraction, and the effective core index of refraction is lower than the effective cladding index of refraction.

3. The fiber of Claim 1 , wherein said gain medium includes a dopant configured to provide laser amplification, when activated by excitation radiation, to signal radiation propagating along said core.

4. The fiber of Claim 1, wherein said core is cylindrical and said cladding radially surrounds said core.

5. The fiber of Claim 1 , wherein said core is generally planar and said cladding is disposed on opposing transverse sides of said core.

6. The fiber of Claim 1 , wherein said gain medium is configured to provide laser amplification of sufficient magnitude to signal radiation propagating along said core to at least compensate for propagation losses in radiation associated with the lowest order mode of propagation and insufficient to compensate for propagation losses in radiation associated with higher order modes of propagation.

7. The fiber of Claim 1 , wherein said cladding is configured to confine therein at least one transverse mode for excitation radiation propagating along said core, and to transmit all transverse modes for signal radiation propagating along said core.

8. The fiber of Claim 7, wherein said cladding is configured to confine therein multiple transverse modes for excitation radiation propagating along said core.

9. The fiber of Claim 1, wherein said fiber includes a photonic bandgap fiber.

10. The fiber of Claim 9, wherein said cladding includes an array of longitudinal holes.

11. The fiber of Claim 9, wherein said cladding includes an array of longitudinal rods.

12. The fiber of Claim 9, wherein said cladding includes a series of layers stacked transverse to said core and having alternating respective indices of refraction.

13. The fiber of Claim 9, wherein said cladding is configured to establish a nearly complete photonic bandgap.

14. An apparatus comprising: a fiber including a core extending longitudinally and having a gain medium configured to provide laser amplification to signal radiation propagating along said core; and a cladding that is radially exterior to said core and configured to resonantly reflect at least some excitation radiation propagating transversely to said core and to generally transmit signal radiation propagating transversely to said core; a signal radiation source coupled to said core and configured to emit signal radiation to be generally transmitted by said cladding when propagating transversely to said core; and an excitation radiation source coupled to said core and configured to emit excitation radiation to be at least partially resonantly reflected by said cladding and absorbed by said gain medium when propagating transversely to said core.

15. The apparatus of Claim 14, wherein said core has an effective core index of refraction, said cladding has an effective cladding index of refraction, and the effective core index of refraction is lower than the effective cladding index of refraction.

16. The apparatus of Claim 14, wherein said gain medium includes a dopant configured to provide laser amplification, when activated by excitation radiation, to signal radiation propagating along said core.

17. The apparatus of Claim 14, wherein said core is cylindrical and said cladding radially surrounds said core.

18. The apparatus of Claim 14, wherein said core is generally planar and said cladding is disposed on opposing transverse sides of said core.

19. The apparatus of Claim 14, wherein said gain medium is configured to provide laser amplification of sufficient magnitude to signal radiation propagating along said core to at least compensate for propagation losses in radiation associated with the lowest order mode of propagation and insufficient to compensate for propagation losses in radiation associated with higher order modes of propagation.

20. The apparatus of Claim 14, further comprising: a pump mirror disposed along a longitudinal axis defined by said core and configured to be significantly transmissive to excitation radiation and significantly reflective of signal radiation; and an output coupler disposed along the longitudinal axis defined by said core and in opposition to said pump mirror, said output coupler being configured to be partially reflective of signal radiation.

21. The apparatus of Claim 14, wherein said cladding is configured to confine therein at least one transverse mode for excitation radiation propagating along said core, and to transmit all transverse modes for signal radiation propagating along said core.

22. The apparatus of Claim 21, wherein said cladding is configured to confine therein multiple transverse modes for excitation radiation propagating along said core.

23. The apparatus of Claim 14, wherein said fiber includes a photonic bandgap fiber.

24. The apparatus of Claim 23, wherein said cladding includes an array of longitudinal holes.

25. The apparatus of Claim 23, wherein said cladding includes an array of longitudinal rods.

26. The apparatus of Claim 23, wherein said cladding includes a series of layers stacked transverse to said core and having alternating respective indices of refraction.

27. The apparatus of Claim 23, wherein said cladding is configured to establish a nearly complete photonic bandgap.

28. A method comprising: providing a fiber including a core extending longitudinally and having a gain medium configured to provide laser amplification to radiation propagating along the core; and a cladding that is radially exterior to the core and configured to resonantly reflect at least some excitation radiation propagating transversely to the core and to generally transmit signal radiation propagating transversely to the core; coupling signal radiation into the core, the signal radiation being configured such that a portion of the signal radiation associated with transverse modes of propagation is transmitted by the cladding; and coupling excitation radiation into the core, the excitation radiation being configured such that at least some of the excitation radiation associated with transverse modes of propagation is resonantly reflected by the cladding and absorbed by the gain medium.