Patent Publication Number: US-2023161108-A1

Title: Optical fiber structures and methods for varying laser beam profile

Description:
RELATED APPLICATIONS 
     This application claims the benefit of and priority to U.S. Provisional Patent Application No. 62/318,959, filed Apr. 6, 2016, the entire disclosure of which is hereby incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     In various embodiments, the present invention relates to laser systems, specifically laser systems with controllable beam profiles, e.g., variable beam parameter products. 
     BACKGROUND 
     High-power laser systems are utilized for a host of different applications, such as welding, cutting, drilling, and materials processing. Such laser systems typically include a laser emitter, the laser light from which is coupled into an optical fiber (or simply a “fiber”), and an optical system that focuses the laser light from the fiber onto the workpiece to be processed. The optical system is typically engineered to produce the highest-quality laser beam, or, equivalently, the beam with the lowest beam parameter product (BPP). The BPP is the product of the laser beam&#39;s divergence angle (half-angle) and the radius of the beam at its narrowest point (i.e., the beam waist, the minimum spot size). That is, BPP=NA×D/2, where D is the focusing spot (the waist) diameter and NA is the numerical aperture; thus, the BPP may be varied by varying NA and/or D. The BPP quantifies the quality of the laser beam and how well it can be focused to a small spot, and is typically expressed in units of millimeter-milliradians (mm-mrad). A Gaussian beam has the lowest possible BPP, given by the wavelength of the laser light divided by pi. The ratio of the BPP of an actual beam to that of an ideal Gaussian beam at the same wavelength is denoted M 2 , which is a wavelength-independent measure of beam quality. 
     In many laser-processing applications, the desired beam spot size, divergence, and beam quality may vary depending on, for example, the type of processing and/or the type of material being processed. This is particularly true for industrial lasers in material processing applications. For example, a lower BPP value, i.e., a better beam quality, may be preferred for cutting a thin metal, while a larger BPP (i.e., a worse beam quality) may be preferred for cutting through thicker metals. In order to make such changes to the BPP of the laser system, frequently the output optical system or the optical fiber must be swapped out with other components and/or realigned, a time-consuming and expensive process that may even lead to inadvertent damage of the fragile optical components of the laser system. Thus, there is a need for alternative techniques for varying the BPP of a laser system that do not involve such adjustments to the laser beam or optical system at the output of the optical fiber. 
     SUMMARY 
     Various embodiments of the present invention provide laser systems in which the BPP of the system (i.e., of its output laser beam) is varied via manipulation of the numerical aperture (NA) and the spot size (D) of the laser system while minimizing or substantially eliminating optical power losses. Embodiments of the invention involve coupling of the laser beam into a multi-clad optical fiber herein termed a “step-clad fiber.” One exemplary step-clad fiber includes, consists essentially of, or consists of a center core, a first cladding disposed around the center core, the first annular core disposed around the first cladding, and a second cladding disposed around the first annular core. Step-clad fibers in accordance with embodiments of the invention are not limited to having only a single annular core and two claddings—one or more additional annular cores and associated claddings may be disposed around the second cladding. As utilized herein, the term “annular core” is defined as a ring-shaped region having a higher refractive index than both the inner and outer layers adjacent thereto. Layers other than the center core and the annular core(s) are typically claddings in a step-clad fiber. Such claddings have lower refractive indices than at least one layer adjacent thereto. 
     When conventional optical fibers are utilized in laser systems, laser power is typically intended to be only coupled into the cores. Any power “over-spray” on the claddings results in a loss of power and/or becomes a harmful factor to the optics downstream to the fiber. In contrast, laser systems utilizing step-clad fibers in accordance with embodiments of the present invention intentionally have partial or full laser power coupled into at least the first cladding, which is specifically designed with a higher refractive index and larger diameter than those of an internal cladding layer of a conventional multi-clad fiber. For example, the diameter of a first cladding in accordance with embodiments of the invention may range from about 140 μm to about 180 μm for a fiber having a central core diameter of 100 μm, compared to only 110 μm to 120 μm for conventional standard or multi-clad 100-μm-core optical fiber. In various embodiments, the thickness of the first cladding layer may range from, e.g., approximately 40 μm to approximately 100 μm, or approximately 40 to approximately 80 μm. 
     In embodiments of the invention, utilization of the step-clad fiber enables the variation of laser-system BPP based on not only the diameters of the cores and the power ratios in the cores, but also the thickness and refractive index of the first cladding and the power ratios in the first cladding (and/or in additional claddings, if present). The laser power coupled into the first cladding of the step-clad fiber is confined by the first annular core and enables a high degree of BPP variation. Moreover, coupling into the annular core(s) in accordance with embodiments of the invention enables the formation of output beams having uniform profiles without “gaps” or areas of low or no laser power therein; in contrast, conventional techniques in which coupling into cladding layers is impossible and/or actively avoided generally result in output beams having gaps (e.g., annular gaps) in the output beam profile. While embodiments of the invention may be utilized to produce output beam profiles that vary as a function of radius or diameter, even areas between high-intensity areas typically contain laser beam intensity (and are thus not “empty”), and/or any low-intensity or empty regions are very limited in spatial extent, particularly in comparison to output beams produced by conventional techniques. 
     Embodiments of the invention even include variations in which substantially no power is coupled into the one or more annular core regions of the step-clad fiber. Embodiments of the present invention typically vary BPP of the laser system via variation of both the output spot size D and NA and therefore provide a larger range of BPP variation than conventional techniques. For a given BPP variation range, embodiments of the present invention enable use of a step-clad fiber having a much smaller diameter of the first annular core than would be needed in conventional systems; thus, embodiments of the invention generate high-BPP laser beams of much smaller spot size with much less diluted power density. That is, a smaller change in the spot size D is needed in accordance with embodiments of the invention to vary the BPP (since the NA may also be simultaneously varied), thereby leading to less dilution of power density. For example, the diameter of a first annular core in accordance with embodiments of the invention may range from approximately 300 μm to approximately 400 μm (e.g., approximately 360 μm). The thickness of a first annular core in accordance with various embodiments may be, for example, approximately 60 μm to approximately 150 μm, approximately 80 μm to approximately 120 μm, approximately 90 μm to approximately 110 μm, or approximately 100 μm. 
     Herein, “optical elements” may refer to any of lenses, mirrors, prisms, gratings, and the like, which redirect, reflect, bend, or in any other manner optically manipulate electromagnetic radiation, unless otherwise indicated. Herein, beam emitters, emitters, or laser emitters, or lasers include any electromagnetic beam-generating device such as semiconductor elements, which generate an electromagnetic beam, but may or may not be self-resonating. These also include fiber lasers, disk lasers, non-solid state lasers, etc. Generally, each emitter includes a back reflective surface, at least one optical gain medium, and a front reflective surface. The optical gain medium increases the gain of electromagnetic radiation that is not limited to any particular portion of the electromagnetic spectrum, but that may be visible, infrared, and/or ultraviolet light. An emitter may include or consist essentially of multiple beam emitters such as a diode bar configured to emit multiple beams. The input beams received in the embodiments herein may be single-wavelength or multi-wavelength beams combined using various techniques known in the art. 
     Embodiments of the invention may be utilized with wavelength beam combining (WBC) systems that include a plurality of emitters, such as one or more diode bars, that are combined using a dispersive element to form a multi-wavelength beam. Each emitter in the WBC system individually resonates, and is stabilized through wavelength-specific feedback from a common partially reflecting output coupler that is filtered by the dispersive element along a beam-combining dimension. Exemplary WBC systems are detailed in U.S. Pat. No. 6,192,062, filed on Feb. 4, 2000, U.S. Pat. No. 6,208,679, filed on Sep. 8, 1998, U.S. Pat. No. 8,670,180, filed on Aug. 25, 2011, and U.S. Pat. No. 8,559,107, filed on Mar. 7, 2011, the entire disclosure of each of which is incorporated by reference herein. Multi-wavelength output beams of WBC systems may be utilized as input beams in conjunction with embodiments of the present invention for, e.g., BPP control. 
     In an aspect, embodiments of the invention feature a laser system that includes, consists essentially of, or consists of a beam source for emission of an input laser beam, a step-clad optical fiber having an input end and an output end opposite the input end, an in-coupling mechanism, and a controller. The step-clad optical fiber includes, consists essentially of, or consists of (i) a central core having a first refractive index, (ii) surrounding the central core, a first cladding having a second refractive index, (iii) surrounding the first cladding, an annular core having a third refractive index, and (iv) surrounding the annular core, a second cladding having a fourth refractive index. The first refractive index is larger than the fourth refractive index. The third refractive index is larger than the fourth refractive index. The second refractive index is smaller than the first refractive index and larger than the fourth refractive index. The in-coupling mechanism receives the input laser beam and directs the input laser beam toward the input end of the step-clad optical fiber, whereby the input laser beam is in-coupled into the step-clad optical fiber and emitted from the output end of the step-clad optical fiber as an output beam. The controller controls the in-coupling mechanism to direct the input laser beam onto one or more in-coupling locations on the input end of the step-clad optical fiber, whereby at least one of a beam parameter product or a numerical aperture of the output beam is determined at least in part by the one or more in-coupling locations. 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. At least one of the in-coupling locations may at least partially overlap the central core. At least one of the in-coupling locations may at least partially overlap the first cladding. At least one of the in-coupling locations may at least partially overlap the annular core. At least one of the in-coupling locations may at least partially overlap the second cladding. At least one of the in-coupling locations may at least partially overlap two or more of the central core, the first cladding, the annular core, or the second cladding. The in-coupling mechanism may include, consist essentially of, or consist of an optical element for focusing the input laser beam toward the input end of the step-clad optical fiber. The optical element may be movable (e.g., translatable, rotatable, and/or tiltable), in response to the controller, along (i) an axis substantially parallel to a propagation direction of the input laser beam and/or (ii) one or more axes substantially perpendicular to the propagation direction of the input laser beam. The in-coupling mechanism may include, consist essentially of, or consist of a reflector for receiving the input laser beam and reflecting the input laser beam toward the step-clad optical fiber. The optical element may include, consist essentially of, or consist of one or more lenses, one or more mirrors, and/or one or more prisms. The in-coupling mechanism may include, consist essentially of, or consist of a reflector for receiving the input laser beam and reflecting the input laser beam toward the step-clad optical fiber, the reflector being rotatable in response to the controller. The in-coupling mechanism may include an optical element for receiving the input laser beam from the reflector and focusing the input laser beam toward the step-clad optical fiber. The optical element may be movable (e.g., translatable, rotatable, and/or tiltable), in response to the controller, along (i) an axis substantially parallel to a propagation direction of the input laser beam and/or (ii) one or more axes substantially perpendicular to the propagation direction of the input laser beam. The optical element may include, consist essentially of, or consist of one or more lenses, one or more mirrors, and/or one or more prisms. 
     The beam source may be responsive to the controller. The controller may be configured to direct the input laser beam onto a plurality of different in-coupling locations without modulating an output power of (e.g., modulating the intensity of or switching off) the input laser beam as the input laser beam is directed between the different in-coupling locations. The controller may be configured to direct the input laser beam onto at least one in-coupling location at least partially overlapping the first cladding, whereby beam energy in-coupled into the first cladding forms at least a portion of the output beam. Beam energy in-coupled into the first cladding may be confined within the step-clad optical fiber at the interface between the annular core and the second cladding. The second refractive index may be smaller than the third refractive index. The second refractive index may be approximately equal to the third refractive index. The third refractive index may be smaller than the first refractive index. The third refractive index may be greater than the first refractive index. The beam source may include, consist essentially of, or consist of one or more beam emitters (each and/or collectively) emitting a plurality of discrete beams, focusing optics, a dispersive element, and a partially reflective output coupler. Each of the discrete beams may have a different wavelength. The focusing optics may focus the plurality of beams onto the dispersive element. The dispersive element may receive and disperse (i.e., wavelength disperses) the received focused beams. The partially reflective output coupler may be positioned to receive the dispersed beams, transmit a portion of the dispersed beams therethrough as the input laser beam, and reflect a second portion of the dispersed beams back toward the dispersive element. The input laser beam may be composed of multiple wavelengths. The dispersive element may include one or more diffraction gratings (e.g., a transmissive grating and/or a reflective grating). 
     In another aspect, embodiments of the invention feature a method of adjusting a beam parameter product and/or a numerical aperture of a laser beam. A step-clad optical fiber having an input end and an output end opposite the input end is provided. The step-clad optical fiber includes, consists essentially of, or consists of (i) a central core having a first refractive index, (ii) surrounding the central core, a first cladding having a second refractive index, (iii) surrounding the first cladding, an annular core having a third refractive index, and (iv) surrounding the annular core, a second cladding having a fourth refractive index. The first refractive index is larger than the fourth refractive index. The third refractive index is larger than the fourth refractive index. The second refractive index is smaller than the first refractive index and larger than the fourth refractive index. An input laser beam is directed onto one or more in-coupling locations on the input end of the step-clad optical fiber, whereby (i) the input laser beam is in-coupled into the step-clad optical fiber and emitted from the output end of the step-clad optical fiber as an output beam, and (ii) at least one of a beam parameter product of a numerical aperture of the output beam is determined at least in part by the one or more in-coupling locations. 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. At least one of the in-coupling locations may at least partially overlap the central core. At least one of the in-coupling locations may at least partially overlap the first cladding. At least one of the in-coupling locations may at least partially overlap the annular core. At least one of the in-coupling locations may at least partially overlap the second cladding. At least one of the in-coupling locations may at least partially overlap two or more of the central core, the first cladding, the annular core, or the second cladding. The input laser beam may be directed onto a plurality of different in-coupling locations to produce a single output beam or multiple output beams having different numerical apertures and/or beam parameter products. The output power of the input laser beam may not be modulated (e.g., decreased or switched off) as the input laser beam is directed between the different in-coupling locations. At least one of the in-coupling locations may at least partially overlap the first cladding, whereby beam energy in-coupled into the first cladding forms at least a portion of the output beam. Beam energy in-coupled into the first cladding may be confined within the step-clad optical fiber at the interface between the annular core and the second cladding. The second refractive index may be smaller than the third refractive index. The second refractive index may be approximately equal to the third refractive index. The third refractive index may be smaller than the first refractive index. The third refractive index may be greater than the first refractive index. The input laser beam may be emitted by a beam source. The beam source may include, consist essentially of, or consist of one or more beam emitters (each and/or collectively) emitting a plurality of discrete beams, focusing optics, a dispersive element, and a partially reflective output coupler. Each of the discrete beams may have a different wavelength. The focusing optics may focus the plurality of beams onto the dispersive element. The dispersive element may receive and disperse (i.e., wavelength disperses) the received focused beams. The partially reflective output coupler may be positioned to receive the dispersed beams, transmit a portion of the dispersed beams therethrough as the input laser beam, and reflect a second portion of the dispersed beams back toward the dispersive element. The input laser beam may be composed of multiple wavelengths. The dispersive element may include one or more diffraction gratings (e.g., a transmissive grating and/or a reflective grating). 
     In yet another aspect, embodiments of the invention feature a method of adjusting at least one of a beam parameter product or a numerical aperture of a laser beam. A step-clad optical fiber having an input end and an output end opposite the input end is provided. The step-clad optical fiber includes, consists essentially of, or consists of (i) a central core having a first refractive index, (ii) surrounding the central core, a first cladding having a second refractive index, (iii) surrounding the first cladding, an annular core having a third refractive index, and (iv) surrounding the annular core, a second cladding having a fourth refractive index. The third refractive index is larger than the fourth refractive index. The third refractive index is larger than the second refractive index. An input laser beam is directed onto one or more in-coupling locations on the input end of the step-clad optical fiber, whereby (i) the input laser beam is in-coupled into the step-clad optical fiber and emitted from the output end of the step-clad optical fiber as an output beam, and (ii) at least one of a beam parameter product or a numerical aperture of the output beam is determined at least in part by the one or more in-coupling locations. At least one of the in-coupling locations at least partially overlaps the first cladding, whereby beam energy in-coupled into the first cladding forms at least a portion of the output beam. 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. At least one of the in-coupling locations may at least partially overlap the central core. At least one of the in-coupling locations may at least partially overlap the annular core. At least one of the in-coupling locations may at least partially overlap the second cladding. At least one of the in-coupling locations may at least partially overlap two or more of the central core, the first cladding, the annular core, or the second cladding. The input laser beam may be directed onto a plurality of different in-coupling locations to produce a single output beam or multiple output beams having different numerical apertures and/or beam parameter products. The output power of the input laser beam may not be modulated (e.g., decreased or switched off) as the input laser beam is directed between the different in-coupling locations. The input laser beam may be emitted by a beam source. The beam source may include, consist essentially of, or consist of one or more beam emitters (each and/or collectively) emitting a plurality of discrete beams, focusing optics, a dispersive element, and a partially reflective output coupler. Each of the discrete beams may have a different wavelength. The focusing optics may focus the plurality of beams onto the dispersive element. The dispersive element may receive and disperse (i.e., wavelength disperses) the received focused beams. The partially reflective output coupler may be positioned to receive the dispersed beams, transmit a portion of the dispersed beams therethrough as the input laser beam, and reflect a second portion of the dispersed beams back toward the dispersive element. The input laser beam may be composed of multiple wavelengths. The dispersive element may include one or more diffraction gratings (e.g., a transmissive grating and/or a reflective grating). 
     These and other objects, along with advantages and features of the present invention herein disclosed, will become more apparent through reference to the following description, the accompanying drawings, and the claims. Furthermore, it is to be understood that the features of the various embodiments described herein are not mutually exclusive and may exist in various combinations and permutations. As used herein, the term “substantially” means±10%, and in some embodiments, ±5%. The term “consists essentially of” means excluding other materials that contribute to function, unless otherwise defined herein. Nonetheless, such other materials may be present, collectively or individually, in trace amounts. Herein, the terms “radiation” and “light” are utilized interchangeably unless otherwise indicated. Herein, “downstream” or “optically downstream,” is utilized to indicate the relative placement of a second element that a light beam strikes after encountering a first element, the first element being “upstream,” or “optically upstream” of the second element. Herein, “optical distance” between two components is the distance between two components that is actually traveled by light beams; the optical distance may be, but is not necessarily, equal to the physical distance between two components due to, e.g., reflections from mirrors or other changes in propagation direction experienced by the light traveling from one of the components to the other. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the drawings, like reference characters generally refer to the same parts throughout the different views. Also, the drawings are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles of the invention. In the following description, various embodiments of the present invention are described with reference to the following drawings, in which: 
         FIG.  1 A  is a schematic diagram of a conventional double-clad fiber and optical rays transmitted into the core and a cladding thereof; 
         FIG.  1 B  is a schematic diagram of refractive indices of the various layers of the fiber of  FIG.  1 A ; 
         FIG.  1 C  is a plan view of a typical laser beam emanating from the fiber of  FIG.  1 A ; 
         FIG.  2 A  is a schematic diagram of a step-clad fiber in accordance with various embodiments of the invention and optical rays transmitted into the center core and first cladding thereof; 
         FIG.  2 B  is a schematic diagram of refractive indices of the various layers of the step-clad fiber of  FIG.  2 A  in accordance with embodiments of the invention; 
         FIG.  2 C  is a plan view of a laser beam emanating from the step-clad fiber of  FIG.  2 A  in accordance with embodiments of the invention; 
         FIG.  3 A  is a schematic diagram of a step-clad fiber in accordance with various embodiments of the invention; 
         FIG.  3 B  is a schematic diagram of refractive indices of the various layers of the step-clad fiber of  FIG.  3 A  in accordance with embodiments of the invention; 
         FIG.  4 A  is a schematic diagram of portions of a laser system utilizing a step-clad fiber in accordance with embodiments of the invention; 
         FIG.  4 B  is a graph of variation in output BPP as a function of reflector tilt for the laser system of  FIG.  4 A  in accordance with embodiments of the invention; 
         FIG.  4 C  is a graph of variation of output NA as a function of reflector tilt for the laser system of  FIG.  4 A  in accordance with embodiments of the invention; 
         FIGS.  5  and  6    are schematic diagrams of portions of laser systems utilizing a step-clad fiber and adjustable lenses in accordance with embodiments of the invention; and 
         FIG.  7    is a schematic diagram of a wavelength beam combining laser system that may be utilized to supply the input beam for laser systems in accordance with various embodiments of the invention. 
     
    
    
     DETAILED DESCRIPTION 
       FIG.  1 A  shows a conventional double-clad fiber  100  having a center core  105 , an interior cladding  110 , an annular core  115 , and an exterior cladding  120 . The radius of each layer (core or cladding) of the fiber  100  is represented by R 1 , R 2 , R 3 , or R 4 , as shown in  FIG.  1 B . In conventional double-clad fiber  100 , the two cores  105 ,  115  typically have the same higher refractive index, N H , and the two claddings  110 ,  120  typically have the same lower refractive index, N L , as shown in  FIG.  1 B , and, therefore, the two cores  105 ,  115  have the same NA of sqrt(N H   2 −N L   2 ). 
       FIG.  1 A  also depicts the transmission of three representative light rays in the fiber  100 . Ray  125  is coupled into the center core  105 , is confined by the center core  105 , and exits from the center core  105  at the same angle as that which it entered the center core  105 . Ray  130  and ray  135  are transmitted into the interior cladding  110 , propagate within the entire fiber area, and are confined by the exterior cladding  120 . Since the exit surface (the right edge of the fiber  100  in  FIG.  1 A ) contains regions having two different refractive indices, ray  130  coupled into the interior cladding (which has a low refractive index) and exiting from the low refractive index region at the exit surface will typically have an exit angle equal to the input angle. Ray  135  coupled into the interior cladding and exiting from the higher refractive index region at the exit surface will typically have an exit angle larger than the input angle, as shown in  FIG.  1 A . 
       FIG.  1 C  is an image of an output profile  140  observed at a distance from the exit surface of conventional double-clad fiber  100  when a laser beam is transmitted into both the center core  105  and the interior cladding  110 . As shown, output profile  140  contains two well-separated areas of beam intensity, a round central area  145  and an outer-ring area  150 . Areas  145 ,  150  correspond to collections of two groups of rays belonging to two clusters of exiting angles from the fiber  100 , as detailed above. The rays similar to ray  125  and ray  130  will exit at angles equal to their input angles and will contribute to the central round area  145 , while the rays similar to ray  135  will exit at angles larger than their input angles and, therefore, form the outer-ring area  150 . To a first approximation, if not considering any NA degradations due to fiber bending and non-uniformity, the NA of the central round area beam is typically the same as the laser input NA. However, the NA of the outer-ring beam  150 , calculated by sqrt(NA F   2 +NA IN   2 ), is substantially larger than the input NA (NA IN ) and also larger than the fiber NA (NA F ), where NA F =sqrt(N H   2 −N L   2 ). 
     The interior cladding  100  of double-clad fiber  100  is relatively thin and is not intended for the in-coupling of laser energy. For 100 μm-core conventional double-clad fiber  100 , the diameter of the first cladding will be normally be in the range of approximately 110-120 μm, i.e., a layer thickness of about 5-10 μm. However, the beam power entering the interior cladding of the fiber  100 , as represented by the rays  130 ,  135  in  FIG.  1 A , will necessarily spread over to the outer cladding  120  and is typically either removed by mode strippers or transmitted through the fiber  100  with the majority forming the outer-ring area  150  shown in  FIG.  1 C . The former may post a great risk of burning the mode strippers and the fiber  100 , and the latter nay damage the optics downstream of the fiber  100  due to the large NA of the outer-ring beam  150 . 
     Embodiments of the present invention include laser systems utilizing step-clad optical fibers, as illustrated in  FIG.  2 A . In accordance with various embodiments, a step-clad fiber  200  includes, consists essentially of, or consists of a center core  205 , a first cladding  210 , an annular core  215 , and a second cladding  220 . Advantageously, various properties of the first cladding  210  enable BPP variation based at least in part on the power coupled into the first cladding  210 .  FIG.  2 C  depicts an exemplary output profile  225  for laser beam energy coupled into the step-clad fiber  200 . As shown, output profile  225  includes a central round area  230  and an outer-ring area  235  if observed at a distance from the fiber  200 . However, the outer-ring area  235  shown in  FIG.  2 C  typically has a much smaller NA than the corresponding area  150  depicted in  FIG.  1 C ; thus, energy in area  235  may be safely accepted by the optics downstream to the fiber  200 . For example, the outer-ring area  235  may have an NA of less than 0.18, less than 0.17, less than 0.16, or even less than 0.15 for an input laser NA of 0.1. In contrast, the corresponding area  150  may have an NA of at least 0.24 for an input laser NA of 0.1. In various embodiments, the NA of any outer-ring area  235  may be less than approximately 180% of the NA of the input laser, less than approximately 170% of the NA of the input laser, less than approximately 160% of the NA of the input laser, or even less than approximately 150% of the NA of the input laser. In various embodiments, the difference between the NA of any outer-ring area and the NA of the input laser may be less than approximately 0.08, less than approximately 0.07, less than approximately 0.06, or even less than approximately 0.05. In various embodiments, the difference between the NA of any outer-ring area and the NA of the input laser may be at least approximately 0.005, or even at least approximately 0.01. In various embodiments, the difference between the NA of any outer-ring area and the NA of the step-clad fiber may be less than 0.04, less than 0.03, less than 0.02, or less than 0.01. In various embodiments, the difference between the NA of any outer-ring area and the NA of the step-clad fiber may be at least 0.001, or even at least 0.005. 
     As depicted in  FIG.  2 A , a ray  240  transmitted into the center core  205  will typically be confined by the center core  205 . Rays  245 ,  250  transmitted into the first cladding  210  will generally be confined by the first annular core  215 . Ray  240 ,  245  will typically exit at angles equal to their corresponding input angles and will form the central round area  230  shown in  FIG.  2 C , while ray  250  will exit at a slightly larger angle than its corresponding input angle and will form the outer-ring area  235 . In stark contrast with fiber  100  described above, rays emitted into the first cladding  210  generally will not reach the outer cladding  220  and, therefore, will not pose a risk of damaging (e.g., burning out) the fiber  200  or its associated optics. In various embodiments of the present invention, the step-clad fiber  200  is configured for the in-coupling of all or part of the input laser power into the first cladding  210 . Such in-coupled power will be not be lost or pose a risk of damaging the fiber  200 ; rather, it may be a major contributor to BPP variation of the output beam. 
       FIG.  2 B  depicts the refractive index and radius of each layer of the step-clad fiber  200 . In contrast with the refractive indices of fiber  100  shown in  FIG.  1 B , the refractive index (N M ) of the first cladding  210  of the fiber  200  has a value between a high index N H  (not necessarily the high index of  FIG.  1 B ) and a low index N L  (not necessarily the low index of  FIG.  1 B ), so that the center core  205  will have a smaller NA, given by sqrt(N H   2 −N M   2 ), than the NA of the annular core  215 , given by sqrt(N H   2 −N L   2 ). While  FIG.  2 B  depicts the indices of refraction of the center core  205  and the annular core  215  as being approximately equal to each other, in various embodiments the index of refraction of the annular core  215  may be different from (i.e., either less than or greater than) the index of refraction of the center core  205 ; however, in general, the index of refraction of the annular core  215  remains larger than the index of refraction of the first cladding  210 . 
     For a given laser input NA (NA IN ), the difference between indices of refraction N H  and N M  will at least partially define the NA of the outer-ring beam  235  shown in  FIG.  2 C , and this NA is given by sqrt(N H   2 −N M   2 +NA IN   2 ). The smaller the index difference between N H  and N M , the smaller will be the outer-ring NA. However, reducing the index difference of N H  and N M  will typically also decrease the NA of the center core  205  and, therefore, may result in more rays escaping from the center core  205 . Although such rays will be confined by the annular core  215 , the rays escaping from the center core  205  may degrade the best possible BPP, i.e., may result in a higher initial BPP value for the output beam. 
     In various embodiments, the NA of center core  205  of the step-clad fiber  200  ranges from approximately 0.07 to approximately 0.17, or even from approximately 0.09 to approximately 0.14. In various embodiments, the effective NA of the first cladding  210  is larger than approximately 0.09, or even larger than approximately 0.12. In various embodiments, the refractive index of the first annular core  215  is equal or smaller than the refractive index of the center core  205 . 
     In various embodiments, the first annular core has the same refractive index as the first cladding, as shown in  FIGS.  3 A and  3 B , in which the first annular core from  FIG.  2 A  has merged into the first cladding. As shown, such a step-clad fiber  300  includes, consists essentially of, or consists of a center core  305 , a first cladding  310 , and a second cladding  315 . As shown in  FIG.  3 B , the refractive index (N M ) of the first cladding  310  is between the refractive indices of the center core (N H ) and the second cladding (N L ). (All refractive index values are not necessarily the same as values depicted in  FIGS.  1 B and  2 B .) In various embodiments, the NA of the center core  305  of step-clad fiber  300  ranges from approximately 0.07 to approximately 0.17, or even from approximately 0.09 to approximately 0.14. In various embodiments, the NA of the first cladding  310  of the step-clad fiber  300  is larger than approximately 0.09, or even larger than approximately 0.12. 
     As mentioned herein, step-clad fibers in accordance with embodiments of the invention may have substantially all or all of the laser power coupled into the first cladding. More power coupled into the first cladding will generally lead to larger BPP. In various embodiments, the diameter ratio of the first cladding and the center core is larger than 1.2, e.g., between 1.2 and 3, or even between 1.3 and 2. 
     The maximum BPP obtainable with a step-clad fiber in accordance with embodiments of the invention may be dependent on the diameter of the first annular core (or the diameter of the first cladding if the first annular core is absent). Therefore, in various embodiments, the diameter ratio of the first annular core (or the first cladding if the first annular core is absent) and the center core ranges from approximately 1.5 to approximately 6.5, or even from approximately 2 to approximately 5. 
     Structurally, optical fibers in accordance with embodiments of the invention may include one or more layers of high and/or low refractive index beyond (i.e., outside of) the second cladding without altering the principles of the present invention. Such additional layers may also be termed claddings and annular cores, but may not guide light. Such variants are within the scope of the present invention. In accordance with various embodiments of the invention, the various core and cladding layers of step-clad fibers may include, consist essentially of, or consist of glass, such as substantially pure fused silica and/or fused silica doped with fluorine, titanium, germanium, and/or boron. 
     An exemplary laser system  400  for varying BPP using a step-clad fiber  200  in accordance with embodiments of the invention is depicted in  FIG.  4   . (Such systems may alternatively utilize step-clad fiber  300  in accordance with embodiments of the invention.) As shown, the laser system  400  includes an adjustable reflector  405  (e.g., a tip-tilt adjustable mirror) to redirect an incoming input laser beam  410  to a fiber coupling optical element  415  (e.g., one or more lenses), which focuses the beam  410  toward the step-clad fiber  200 . As shown, the region of the input face of step-clad fiber  200  at which the beam  410  is in-coupled is at least partially defined by the configuration (e.g., the position and/or angle) of the reflector  405 . For the best starting beam quality (i.e., the smallest BPP), the step-clad fiber  200  is typically located at the focal spot of the optical element  415 . 
     The configuration of the reflector  405  may be controlled via a controller  420  and/or one or more actuators (not shown) operatively connected to the reflector  405 . Thus, the reflector  405  and/or the one or more actuators may be responsive to controller  420 . The controller  420  may be responsive to a desired target radiation power distribution and/or BPP or other measure of beam quality (e.g., input by a user and/or based on one or more properties of a workpiece to be processed such as the distance to the workpiece, the composition of the workpiece, topography of the workpiece, etc.) and configured to angle reflector  405  to cause the beam  410  to strike the input face of the step-clad fiber  200  such that the output beam output from the step-clad fiber  200  has the target radiation power distribution or beam quality. The output beam thus produced may be directed to a workpiece for processes such as annealing, cutting, welding, drilling, etc. The controller  420  may be programmed to achieve the desired power distribution and/or output BPP and/or beam quality via a particular reflector tilt as detailed herein. 
     The controller  420  may be provided as either software, hardware, or some combination thereof. For example, the system may be implemented on one or more conventional server-class computers, such as a PC having a CPU board containing one or more processors such as the Pentium or Celeron family of processors manufactured by Intel Corporation of Santa Clara, Calif., the 680x0 and POWER PC family of processors manufactured by Motorola Corporation of Schaumburg, Ill., and/or the ATHLON line of processors manufactured by Advanced Micro Devices, Inc., of Sunnyvale, Calif. The processor may also include a main memory unit for storing programs and/or data relating to the methods described herein. The memory may include random access memory (RAM), read only memory (ROM), and/or FLASH memory residing on commonly available hardware such as one or more application specific integrated circuits (ASIC), field programmable gate arrays (FPGA), electrically erasable programmable read-only memories (EEPROM), programmable read-only memories (PROM), programmable logic devices (PLD), or read-only memory devices (ROM). In some embodiments, the programs may be provided using external RAM and/or ROM such as optical disks, magnetic disks, as well as other commonly used storage devices. For embodiments in which the functions are provided as one or more software programs, the programs may be written in any of a number of high level languages such as FORTRAN, PASCAL, JAVA, C, C++, C #, BASIC, various scripting languages, and/or HTML. Additionally, the software may be implemented in an assembly language directed to the microprocessor resident on a target computer; for example, the software may be implemented in Intel 80x86 assembly language if it is configured to run on an IBM PC or PC clone. The software may be embodied on an article of manufacture including, but not limited to, a floppy disk, a jump drive, a hard disk, an optical disk, a magnetic tape, a PROM, an EPROM, EEPROM, field-programmable gate array, or CD-ROM. 
     Simulation results of the output BPP and NA of the laser system  400  are depicted in  FIGS.  4 B and  4 C , respectively. In  FIGS.  4 B and  4 C , the optical element  415  has a 30 mm focal length, and the step-clad fiber  200  has diameters of 100 μm, 160 μm, 360 μm, and 400 μm for the center core, the first cladding, the first annular core, and the second cladding, respectively. The NAs of the center core and the first annular core are 0.12 and 0.22, respectively. As shown in  FIG.  4 B , the BPP ranges from approximately 4 mm-mrad and reaches a maximum at approximately 20 mm-mrad at reflector tilt of about 1.2 mrad. The BPP variation is a combined result of output spot size (D) change and NA change. As the reflector tilt gradually increases from its initial zero position, more power is coupled into the first cladding, which effectively enlarges the output spot size (D) and the NA and thus the BPP. Further increases of reflector tilt (above approximately 1.2 mrad) result, in this example, in smaller NA due to decreased power coupled into the first cladding.  FIG.  4 C  indicates that the output NA decreases back to its initial smallest NA (obtained at 0 reflector tilt) when the reflector tilt is larger than approximately 2.2 mrad, at which point all the power is coupled into the first annular core. As evident from  FIGS.  4 B and  4 C , the power coupled into the first cladding is not lost, but instead plays a major role in BPP variation. 
     In addition, the maximum BPP of approximately 20 mm-mrad for this exemplary embodiment is obtained with a step-clad fiber in which the diameter of the first annular core is 360 μm. For the same BPP range, conventional techniques would require a double-clad fiber having a first annular core diameter of 500 μm, which would result in an almost two-times lower power density at the laser focal spot than in the exemplary embodiment of the present invention. Thus, as indicated, embodiments of the invention advantageously generate larger BPP with increased NA, which is generally desired for large-BPP applications (to, e.g., generate and maintain higher power density of the output beam). 
       FIG.  5    depicts a laser system  500  in accordance with embodiments of the invention with a step-clad fiber ( 51 ). In laser system  500 , the controller  420  directly controls the optical element  415 , which is adjustable (i.e., translatable) in the directions (i.e., x and y as shown in  FIG.  5   ) orthogonal to the input propagation direction of input beam  410  (i.e., z as shown in  FIG.  5   ). For example, the controller  420  may control a lens manipulation system (e.g., one or more motorized stages or actuators movable in two or three dimensions) to control the movements of optical element  415  and thereby adjust the in-coupling position of the input beam  410  on the input surface of step-clad fiber  200  (and, thus, the BPP of the output beam emerging from the step-clad fiber  200 ). As with laser system  400 , the relative amounts of the input beam  400  coupled into the various regions of step-clad fiber  200  results in a controllable variable BPP and/or NA of the output beam.  FIG.  6    depicts a similar laser system  600 , in which the optical element  415  is adjustable in the direction parallel to the input propagation direction of input beam  410  (i.e., z as shown in  FIG.  6   ) via, e.g., one or more motorized stages or actuators. Translation of the optical element  415  with respect to the step-clad fiber  200  alters the amount of the beam that propagates to, and is in-coupled into, the various regions of step-clad fiber  200 . As with laser system  400 , laser systems  500 ,  600  may be utilized with step-clad fiber  300  in addition to or instead of step-clad fiber  200 . Laser systems in accordance with embodiments of the invention may also combine translation of optical element  415  (as in  FIGS.  5  and  6   ) with adjustment of reflector  405  (as in  FIG.  4   ) to controllably adjust the BPP and/or NA of the beam output from the step-clad fiber. 
     Laser systems  400 ,  500 ,  600  may be utilized to alter the BPP and/or NA of a laser beam in a continuous fashion without the need to power down (i.e., switch off) the input laser beam as the beam is swept across the input face of the step-clad fiber such that different portions of the beam are in-coupled into different regions of the fiber. Because the step-clad fibers  200 ,  300  are configured such that beam energy propagating to a cladding region (e.g., the first cladding) is confined and will not lead to damage to the fiber or optics (e.g., optical elements) associated therewith, the input beam need not be switched off as it or a portion thereof strikes the cladding(s) of the step-clad fiber. 
     Embodiments of the present invention may also utilize systems and techniques of BPP variation as described in U.S. patent application Ser. No. 14/632,283, filed on Feb. 26, 2015, U.S. patent application Ser. No. 14/747,073, filed on Jun. 23, 2015, U.S. patent application Ser. No. 14/852,939, filed on Sep. 14, 2015, and U.S. patent application Ser. No. 15/188,076, filed on Jun. 21, 2016, the entire disclosure of each of which is incorporated by reference herein. 
     Laser systems and laser delivery systems in accordance with embodiments of the present invention and detailed herein may be utilized in and/or with WBC laser systems. Specifically, in various embodiments of the invention, multi-wavelength output beams of WBC laser systems may be utilized as the input beams for laser beam delivery systems for variation of BPP as detailed herein.  FIG.  7    depicts an exemplary WBC laser system  700  that utilizes one or more lasers  705 . In the example of  FIG.  7   , laser  705  includes a diode bar having four beam emitters emitting beams  710  (see magnified input view  715 ), but embodiments of the invention may utilize diode bars emitting any number of individual beams or two-dimensional arrays or stacks of diodes or diode bars. In view  715 , each beam  710  is indicated by a line, where the length or longer dimension of the line represents the slow diverging dimension of the beam, and the height or shorter dimension represents the fast diverging dimension. A collimation optic  720  may be used to collimate each beam  710  along the fast dimension. Transform optic(s)  725 , which may include or consist essentially of one or more cylindrical or spherical lenses and/or mirrors, are used to combine each beam  710  along a WBC direction  730 . The transform optics  725  then overlap the combined beam onto a dispersive element  735  (which may include, consist essentially of, or consist of, e.g., a reflective or transmissive diffraction grating, a dispersive prism, a grism (prism/grating), a transmission grating, or an Echelle grating), and the combined beam is then transmitted as single output profile onto an output coupler  740 . The output coupler  740  then transmits the combined beams  745  as shown on the output front view  750 . The output coupler  740  is typically partially reflective and acts as a common front facet for all the laser elements in this external cavity system  700 . An external cavity is a lasing system where the secondary mirror is displaced at a distance away from the emission aperture or facet of each laser emitter. In some embodiments, additional optics are placed between the emission aperture or facet and the output coupler or partially reflective surface. The output beam  745  is a thus a multiple-wavelength beam (combining the wavelengths of the individual beams  710 ), and may be utilized as the input beam in laser systems detailed herein and/or may be coupled into a step-clad optical fiber as detailed herein. 
     The terms and expressions employed herein are used as terms of description and not of limitation, and there is no intention, in the use of such terms and expressions, of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the invention claimed.