Patent Publication Number: US-2017368638-A1

Title: Material processing utilizing a laser having a variable beam shape

Description:
RELATED APPLICATIONS 
     This application claims the benefit of and priority to U.S. Provisional Patent Application No. 62/362,824, filed Jul. 15, 2016, the entire disclosure of which is hereby incorporated herein by reference. This application is also a continuation-in-part of U.S. patent application Ser. No. 15/261,096, filed Sep. 9, 2016, which is (i) a continuation-in-part of U.S. patent application Ser. No. 14/639,401, filed Mar. 5, 2015, which claims the benefit of and priority to U.S. Provisional Patent Application No. 61/948,205, filed Mar. 5, 2014, and (ii) a continuation-in-part of U.S. patent application Ser. No. 15/188,076, filed Jun. 21, 2016, which claims the benefit of and priority to U.S. Provisional Patent Application No. 62/183,210, filed Jun. 23, 2015. The entire disclosure of each of these references is hereby incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     In various embodiments, the present invention relates to the processing (e.g., welding or cutting) of materials utilizing high-power laser devices having shapeable beams and/or variable beam polarizations. 
     BACKGROUND 
     High-power lasers are used in many cutting, etching, annealing, welding, drilling, and soldering applications. As in any materials-processing operations, efficiency can be a critical limiting factor in terms of expense and time; the lower the efficiency, the higher will be the cost and/or the slower will be the operation of the laser deployed to process a given material. The brightness and polarization of the laser beam can influence efficiency, and different materials (such as copper, aluminum, steel, and so forth) respond differently to beam polarization as they are processed. Moreover, the thicknesses of these materials can affect their polarization response. That is, the nature of a cut or weld may vary with the beam polarization depending on the material and its thickness. For example, a linearly polarized processing beam may be absorbed differently depending on the orientation of the beam&#39;s polarization with respect to the cut front. For this reason, laser-processing systems sometimes utilize circularly or randomly polarized laser output in order to avoid directionally dependent polarization responses. While that approach avoids the efficiency-degrading results of unfavorable polarization orientations, it likewise precludes the benefits of favorable orientations. 
     In addition, high-power laser systems often 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). 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). (BPP values disclosed herein are in units of mm-mrad unless otherwise indicated.) 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. 
     While techniques such as WBC have succeeded in producing laser-based systems for a wide variety of applications, materials-processing challenges remain. For example, lasers having beam shapes optimized for cutting a particular material at a particular thickness may not be suitable for different materials, materials having different thicknesses, and materials having variable thicknesses. Welding processes present similar challenges. Moreover, due to the limited spatial extent of conventional, highly focused laser beams, welding processes typically require relative motion between the laser beam and the parts being welded, and such motion may require complex and expensive robotics, movable gantries, and/or other equipment. Techniques utilizing multiple laser systems with movable beams have been developed (see, e.g., U.S. Pat. No. 9,335,551, the entire disclosure of which is incorporated by reference herein), but the use of multiple laser systems is often prohibitively expensive. Therefore, a need exists for individual laser systems capable of a wider variety of materials processes. 
     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. In order to make such changes to the BPP and/or shape of the laser beam, 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. 
     Accordingly, there is also a need for improved systems and techniques for enhancing the efficiency of laser processing operations that exploit the varying responses to beam polarization and/or other beam characteristics (e.g., BPP and/or beam shape) that characterize different materials and material thicknesses. 
     SUMMARY 
     In accordance with embodiments of the present invention, laser systems having shapeable output beams are utilized to optimize and simplify materials-processing tasks such as cutting and welding of metallic materials. For example, in accordance with embodiments of the invention, the output beam shape of the laser system is altered (e.g., from a Gaussian-like, focused spot beam to a larger-area annular beam) as the thickness of a part and/or the angle of the part presented to the laser beam vary. In other exemplary embodiments, the output beam of the laser system is altered during a welding process (e.g., a spot weld, butt weld, or lap weld) to form large-area welds without any (or with minimal) relative motion between the laser beam and the workpiece(s) being processed. 
     Embodiments of the invention also provide systems and techniques for altering and optimizing the polarization and/or other characteristics (e.g., BPP, shape) of a beam during processing, and maintaining the optimal characteristics of the beam throughout processing—e.g., even as the beam path varies or the nature or thickness of the material changes. 
     Embodiments of the invention may alter the polarization of the beam as the thickness of the workpiece changes and/or for workpieces of different thicknesses. For example, the circularity (i.e., the degree of change from linear to elliptical to circular, where any number of ellipses of varying dimensions and curvatures are possible between fully linear and fully circular) of the polarization of the beam may be altered to make the beam more circular (e.g., linear to elliptical, less circular ellipse to more circular ellipse, elliptical to circular, etc.) as the thickness of the workpiece increases. (In various embodiments, the circularity of the polarization is inversely related to the eccentricity of the elliptical polarization, where an eccentricity of 0 represents circular polarization and an eccentricity of 1 represents linear polarization.) In various embodiments, the polarization state of the beam is altered at least in part via use of a Babinet-Soleil compensator, which enables continuously variable polarization of any degree of eccentricity. Embodiments of the invention may also vary the polarization of the beam from linear to radial in order to, e.g., enable focusing of the beam to a smaller spot size. 
     Embodiments of the present invention are typically utilized to process a workpiece such that the surface of the workpiece is physically altered and/or such that a feature is formed on or within the surface, in contrast with optical techniques that merely probe a surface with light (e.g., reflectivity measurements). Exemplary processes in accordance with embodiments of the invention include cutting, welding, drilling, and soldering. Various embodiments of the invention also process workpieces at one or more spots or along a one-dimensional processing path, rather than flooding all or substantially all of the workpiece surface with radiation from the laser beam. 
     Embodiments of the present invention use optical elements capable of laser beam shaping to achieve desired spatial beam profiles that modify beam quality (particularly BPP) and/or the shape of the beam. More specifically, changing the optical geometry of optical elements by moving or displacing their position transverse or longitudinal to the optical axis of the laser beam may be utilized to vary shape and/or BPP. In embodiments of the invention, optical elements are located in the beam path with switchable states, producing different beam deflections or diffractions, depending on their position. The use of optical elements in accordance with embodiments of the present invention enables variation of shape and/or BPP regardless the shape, quality, wavelength, bandwidth, and number of beams corresponding to the input laser beam(s). The output beam with controllably variable shape and/or BPP may be utilized to process a workpiece in such applications as welding, cutting, drilling, etc. As utilized herein, changing the “shape” of a laser beam refers to altering the shape and geometric extent of the beam (e.g., at a point at which the beam intersects a surface). Changes in shape may be accompanied by changes in beam size, angular intensity distribution of the beam, and BPP, but mere changes in beam BPP are not necessarily sufficient to change laser beam shape and vice versa (for example, see  FIG. 21 , which depicts two beams having different shapes but the same BPP). 
     One advantage of variable shape and/or BPP is improved laser application performance for different types of processing techniques or different types of materials being processed. Embodiments of the invention may also utilize various techniques for varying BPP and/or shape of laser beams 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 Jun. 23, 2015, U.S. patent application Ser. No. 14/852,939, filed Sep. 14, 2015, U.S. patent application Ser. No. 15/188,076, filed Jun. 21, 2016, and U.S. patent application Ser. No. 15/479,745, filed Apr. 5, 2017, the disclosure of each of which is incorporated in its entirety herein by reference. In addition, differing beam intensity distribution that is induced by optical elements (refractive optics) modifies beam quality and, therefore, BPP. By using translation (e.g., motorized translation) of the optical elements that have different effective optical geometries in the beam path, real-time dynamic changes of shape and/or BPP may be realized. 
     Laser beam shaping is the process of redistributing the intensity (irradiance) and phase of the beam. The intensity distribution defines the beam profile, such as Gaussian, Bessel, annular, multimode, rectangular, top-hat, elliptical or circular, and different intensity profiles may be critical and necessary for specific laser materials processing techniques. (As utilized herein, an “annular” beam is ring-shaped, i.e., having less or substantially no beam intensity in a center portion that is surrounded by a region of higher beam intensity, but not necessarily circular; that is, “annular” beams may be oval-shaped or otherwise quasi-annular.) In embodiments of this invention, the optical element is located in the delivery system that delivers the laser beam to the workpiece and focuses the laser. The delivery system may be configured and/or packaged as, for example, at least a portion of a cutting head or a welding head. Embodiments of the invention vary the beam quality in order to enable a controllably variable shape and/or BPP at the work station (and/or at the workpiece disposed thereon). The variable shape and/or BPP module may include one or more optical elements, a motorized translating stage, a collimating lens, and a focusing lens. Embodiments of the invention may feature any one or more of multiple types of refractive optics for the optical elements are used to vary shape and/or BPP. 
     Embodiments of the invention vary beam quality by dynamically changing the position of one or more optical elements in the optical path of the laser beam. In one embodiment, the beam profile is tailored by adjusting the beam pointing position on the optical element. The optical elements may have different geometries dependent on a desired beam profile and, therefore, BPP. One optical element in accordance with embodiments of the invention has a planar surface and a flat-top (i.e., truncated) cone shaped surface. Another optical element in accordance with embodiments of the invention has a planar surface and a flat-top spherical shaped surface. Yet another optical element in accordance with embodiments of the invention is a meniscus lens. The diverging light rays from the beam delivery fiber are directed towards the optical element(s) to redistribute beam intensity within the optical elements. Other optical elements in accordance with embodiments of the invention include paired positive and negative axicon lenses. In other embodiments, optical elements include twinned, complementary phase-plate lenses, one of which has a partially convex surface and one of which has a complementarily partially concavely curved surface. The edges of the optical elements may be rounded off in order to suppress diffraction effects. The advantages of dynamic variation of BPP with the automated movement of optical elements may be applied to, for example, laser-cutting applications on round-cut or square-cut corners where BPP changes during free-form cutting are required. Such advantages may also be applied to laser-drilling applications that may utilize the ability to vary both BPP and focal length. Automated closed-loop motor control of optical elements in accordance with embodiments of the invention produces reliable and repeatable performance and enables precise control of optics position, thereby providing accurate BPP variation. 
     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. In addition, references to “lasers,” “laser emitters,” or “beam emitters” herein include not only single-diode lasers, but also diode bars, laser arrays, diode bar arrays, and single or arrays of vertical cavity surface-emitting lasers (VCSELs). 
     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, shape, and/or polarization control. 
     In an aspect, embodiments of the invention feature a method of processing a workpiece. A processing path is defined by causing relative motion between a laser output beam and the surface of the workpiece. The thickness of the workpiece along a direction parallel to the laser output beam varies along the processing path. The laser output beam physically alters the surface of the workpiece along at least a portion of the processing path. During the relative motion between the laser output beam and the surface of the workpiece, the shape of the laser output beam is altered based at least in part on the thickness of the workpiece. 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. The shape of the laser output beam may be varied between a focused spot and an annulus as the thickness of the workpiece increases. The shape of the laser output beam may be varied between a focused spot and a diffuse spot (e.g., a spot having a diameter larger than the diameter of the focused spot) as the thickness of the workpiece increases. A diameter and/or BPP of the laser output beam may be increased as the thickness of the workpiece increases. An angle between the laser output beam and the surface of the workpiece may be altered (e.g., via tilting the incoming laser output beam, tilting the workpiece, and/or via angled topology on the surface of the workpiece) to thereby vary the thickness of the workpiece along the direction parallel to the laser output beam. The thickness of the workpiece along the direction parallel to the laser output beam may vary due at least in part to a change in an angle between the laser output beam and the surface of the workpiece (e.g., via tilting the incoming laser output beam, tilting the workpiece, and/or via angled topology on the surface of the workpiece). The shape of the laser output beam may be altered while maintaining an angle between the laser output beam and the surface of the workpiece substantially constant (e.g., the laser output beam may not be tilted with respect to the surface of the workpiece, or the topology of the surface of the workpiece may present a substantially constant angle to the incoming laser output beam). The thickness of the workpiece may be measured during the relative motion between the laser output beam and the surface of the workpiece. The shape of the laser output beam may be altered based on a composition of the workpiece. The laser output beam may be composed of multiple wavelengths. 
     In another aspect, embodiments of the invention feature a system for processing a workpiece. The system includes, consists essentially of, or consists of a beam emitter for emission of a laser output beam, a positioning device for varying a position of the laser output beam with respect to the workpiece, means for altering a shape of the laser output beam, and a controller, coupled to the positioning device and the shape-altering means, for (i) operating the beam emitter cause the laser output beam to traverse a path across at least a portion of the workpiece to physically alter a surface thereof and (ii) altering the shape of the laser output beam based at least in part on a thickness of the workpiece along the path. 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. The beam emitter may include, consist essentially of, consist of, be disposed within, or be coupled to (e.g., via an optical fiber) a processing head from which the laser output beam is emitted. The shape-altering means may include, consist essentially of, or consist of (i) one or more optical elements within the processing head and (ii) a second controller for altering a position of at least one of the optical elements within the processing head. The second controller may be discrete and separate from the controller, or the controller and the second controller may be parts of a single control system. The controller may be configured to vary an output power of the beam emitter along the path. The controller may be configured to vary the shape of the laser output beam based on a composition of the workpiece. The system may include a database containing a plurality of records each relating a laser output beam shape to workpiece parameters. The workpiece parameters may include, consist essentially of, or consist of workpiece thickness and/or workpiece composition. The beam emitter may include, consist essentially of, or consist of a beam source emitting a plurality of discrete input beams, focusing optics for focusing the plurality of input beams onto a dispersive element, a dispersive element for receiving and dispersing the received focused beams, and a partially reflective output coupler positioned to receive the dispersed beams, transmit a portion of the dispersed beams therethrough as the laser output beam, and reflect a second portion of the dispersed beams back toward the dispersive element. The laser output beam may be composed of multiple wavelengths. 
     In yet another aspect, embodiments of the invention feature a method of joining first and second workpieces at a processing point. The first and second workpieces overlap and/or are in proximity to each other at the processing point. A laser output beam is focused and/or disposed proximate the processing point to melt a portion of at least one of the first or second workpieces, thereby joining the first and second workpieces together. During the joining, the shape of the laser output beam is varied without causing relative motion between the laser output beam and the first and second workpieces. 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. The shape of the laser output beam may be varied between a focused spot and an annulus. The shape of the laser output beam may be varied between a focused spot and a diffuse spot (e.g., a spot having a diameter larger than the diameter of the focused spot). The laser output beam may be composed of multiple wavelengths. 
     In another aspect, embodiments of the invention feature a method of joining, using a laser output beam focusable to a minimum spot size, first and second workpieces with a weld having a spatial extent larger than the minimum spot size. The laser output beam is focused and/or disposed on the first and/or second workpieces to cause at least partial melting thereof and/or at least partial melting of a bonding agent (e.g., a brazing material, a solder material, or a flux material) disposed on or between the first and second workpieces. Without causing relative motion between the laser output beam and the first and second workpieces, a shape of the laser output beam is varied to increase a size of the weld or joint. 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. The shape of the laser output beam may be varied between a focused spot and an annulus. The shape of the laser output beam may be varied between a focused spot and a diffuse spot (e.g., a spot having a diameter larger than the diameter of the focused spot). The laser output beam may be composed of multiple wavelengths. 
     In an aspect, embodiments of the invention feature a system for processing a workpiece. The system includes, consists essentially of, or consists of a beam emitter, a positioning device for varying a position of a beam of the beam emitter with respect to the workpiece, a variable polarizer for varying a polarization of the beam, a beam shaper for varying a shape of the beam, and a controller, coupled to the positioning device, the polarizer, and the beam shaper, for operating the beam emitter cause the beam to traverse a path across at least a portion of the workpiece for processing thereof, and to vary the polarization and/or shape of the beam along the path based at least in part on one or more properties of the workpiece. 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. The controller may be configured to maintain a linear polarization of the beam having a polarization direction approximately parallel to the path as the beam traverses the path. The controller may be configured to vary an eccentricity of the polarization of the beam based at least in part on a thickness of the workpiece. The controller may be configured to vary the polarization of the beam between a linear polarization state and a radial polarization state. The variable polarizer may include, consist essentially of, or consist of a wave plate. The variable polarizer may include, consist essentially of, or consist of a wave plate and a rotation element, the rotation element being operated by the controller. The wave plate may include, consist essentially of, or consist of a half-wave plate and/or a quarter-wave plate. The beam may be linearly polarized. The controller may operate the rotation element to maintain a polarization direction parallel to the path. The variable polarizer may include, consist essentially of, or consist of a compensator plate, a fixed birefringent wedge disposed over the compensator plate, and a movable birefringent wedge disposed over the fixed birefringent wedge. The variable polarizer may include, consist essentially of, or consist of a compensator plate, a fixed birefringent wedge disposed over the compensator plate, a movable birefringent wedge disposed over the fixed birefringent wedge, and a translation element, the translation element being operated by the controller. The variable polarizer may include, consist essentially of, or consist of a radial polarization converter. 
     The system may include a memory, accessible to the controller, for storing data corresponding to the path, and a database for storing polarization data for a plurality of materials. The controller may be configured to query the database to obtain the polarization data for a material of the workpiece and to vary the polarization of the beam based at least in part on the polarization data. The path may include at least one directional change. The workpiece may have at least two portions having different thicknesses. The workpiece may have at least two portions that include, consist essentially of, or consist of different materials. The beam emitter may include, consist essentially of, or consist of a beam source emitting a plurality of discrete input beams, focusing optics for focusing the plurality of input beams onto a dispersive element, a dispersive element for receiving and dispersing the received focused beams, and a partially reflective output coupler positioned to receive the dispersed beams, transmit a portion of the dispersed beams therethrough as the beam of the beam emitter, and reflect a second portion of the dispersed beams back toward the dispersive element. The beam (e.g., the output processing beam) of the beam emitter may be composed of multiple wavelengths. 
     The beam shaper may include, consist essentially of, or consist of a collimating lens for collimating a beam received from the beam emitter, a focusing lens for receiving the collimated beam and focusing the beam toward the workpiece, disposed between the beam source and the collimating lens, an optical element for receiving the beam and altering the shape thereof, and a lens manipulation system for changing a position of the optical element within a path of the beam. The controller may be configured to control the lens manipulation system to vary the shape of the beam. The optical element may include, consist essentially of, or consist of a lens having (i) a first surface having the shape of a truncated cone, and (ii) opposite the first surface, a second surface that is substantially planar. The optical element may include, consist essentially of, or consist of a lens having (i) a first surface having the shape of a truncated sphere, and (ii) opposite the first surface, a second surface that is substantially planar. The optical element may include, consist essentially of, or consist of a meniscus lens. The lens manipulation system may be configured to position the optical element transversely off-center within the path of the beam. The system may include a second optical element disposed between the focusing lens and the workpiece. The lens manipulation system may be configured to change a position of the second optical element within the path of the beam. The second optical element may include, consist essentially of, or consist of a lens having (i) a first surface having the shape of a truncated cone, and (ii) opposite the first surface, a second surface that is substantially planar. The second optical element may include, consist essentially of, or consist of a lens having (i) a first surface having the shape of a truncated sphere, and (ii) opposite the first surface, a second surface that is substantially planar. The second optical element may include, consist essentially of, or consist of a meniscus lens. 
     The beam shaper may include, consist essentially of, or consist of a collimating lens for collimating a beam received from the beam emitter, a focusing lens for receiving the collimated beam and focusing the beam toward the workpiece, disposed between the beam source and the collimating lens, first and second optical elements for receiving the beam and altering the shape thereof, and a lens manipulation system for changing (i) a position of the first optical element within a path of the beam, (ii) a position of the second optical element within the path of the beam, and/or (iii) a distance between the first and second optical elements. The controller may be configured to control the lens manipulation system to vary the shape of the beam. The first optical element may include, consist essentially of, or consist of a double-concave axicon lens. The second optical element may include, consist essentially of, or consist of a double-convex axicon lens. The lens manipulation system may be configured to change the distance between the first and second optical elements within the range of approximately 0 mm to approximately 20 mm. The first optical element may include, consist essentially of, or consist of a lens having (i) a first surface that is substantially planar, and (ii) opposite the first surface, a second surface having (a) a first portion that is convexly curved and (b) a second portion that is substantially planar. The second optical element may include, consist essentially of, or consist of a lens having (i) a first surface that is substantially planar, and (ii) opposite the first surface, a second surface having (a) a first portion that is concavely curved and (b) a second portion that is substantially planar. The lens manipulation system may be configured to position the first optical element and/or the second optical element transversely off-center within the path of the beam. 
     In an aspect, embodiments of the invention relate to a system for processing a workpiece. In various embodiments, the system comprises a beam emitter, a positioning device for varying a position of a beam of the beam emitter with respect to the workpiece, a variable polarizer for varying a polarization of the beam, and a controller, coupled to the positioning device and the polarizer, for operating the beam emitter cause the beam to traverse a path across at least a portion of the workpiece for processing thereof and to maintain a consistent polarization of the beam with respect to the workpiece along the path. 
     In various embodiments, the variable polarizer comprises a wave plate and a rotation element, the rotation element being operated by the controller. For example, the wave plate may be one or more half-wave plates, one or more quarter-wave plates, or some combination thereof. The beam may, for example, be linearly polarized, with the controller operating the rotation element to maintain a polarization direction parallel to the path. 
     In some embodiments, the system further comprises a memory, accessible to the controller, for storing data corresponding to the path, and a database for storing polarization data for a plurality of materials. The controller is configured to query the database to obtain the polarization data for a material of the workpiece, and the polarization data determines the consistent polarization of the beam. The path may include at least one directional change. 
     The beam emitter may emit a plurality of beams. The beam emitter may be at least one laser and/or at least one polarized fiber. 
     In another aspect, the invention pertains to a method of processing a workpiece. In various embodiments, the method comprises the steps of operating a beam emitter to direct a beam traversing a path along the workpiece to process the workpiece, where the beam has an output polarization; and altering the output polarization along at least a portion of the path so as to maintain a consistent polarization of the beam with respect to the workpiece throughout processing thereof. 
     The step of processing the workpiece may comprise one or more of cutting, welding, soldering, drilling, or etching the workpiece. The step of altering may comprise directing the beam through a wave plate and varying a rotation angle of the wave plate with respect to the beam. For example, the wave plate may be one or more half-wave plates and/or one or more quarter-wave plates. The beam may, for example, be linearly polarized, and the altering step maintains a polarization direction of the beam parallel to the path. 
     In some embodiments, the method further comprises the steps of storing data corresponding to the path, storing polarization data for a plurality of materials, and querying the database to obtain the polarization data for a material of the workpiece, the polarization data determining the consistent polarization of the beam. The path may include at least one directional change. 
     In an aspect, embodiments of the invention feature a laser delivery system for receiving and altering a spatial power distribution of a radiation beam from a beam source and focusing the radiation with the altered spatial power distribution onto a workpiece. The laser system includes or consists essentially of a collimating lens for collimating the radiation beam, a focusing lens for receiving the collimated beam and focusing the beam toward the workpiece, an optical element for receiving the radiation beam and altering the spatial power distribution thereof, a lens manipulation system for changing a position of the optical element within a path of the radiation beam, and a controller for controlling the lens manipulation system to achieve a target altered spatial power distribution on the workpiece. The optical element may be disposed between the beam source and the collimating lens (i.e., optically downstream of the beam source and optically upstream of the collimating lens). 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. The optical element may include, consist essentially of, or consist of a lens having (i) a first surface having the shape of a truncated cone, and (ii) opposite the first surface, a second surface that is substantially planar. The first surface may face the beam source. The first surface may face away from the beam source. The optical element may include, consist essentially of, or consist of a lens having (i) a first surface having the shape of a truncated sphere, and (ii) opposite the first surface, a second surface that is substantially planar. The first surface may face the beam source. The first surface may face away from the beam source. The optical element may include, consist essentially of, or consist of a meniscus lens. The meniscus lens may be a positive meniscus lens. The meniscus lens may be a negative meniscus lens. The optical element may include, consist essentially of, or consist of fused silica and/or zinc sulfide. The lens manipulation system may be configured to position the optical element transversely off-center within the path of the radiation beam. 
     The laser delivery system may include a second optical element disposed in the path of the radiation beam. The second optical element may be disposed between the focusing lens and the workpiece (i.e., disposed optically downstream of the focusing lens and disposed optically upstream of the workpiece). The lens manipulation system may be configured to change a position of the second optical element within the path of the radiation beam. The second optical element may include, consist essentially of, or consist of a lens having (i) a first surface having the shape of a truncated cone, and (ii) opposite the first surface, a second surface that is substantially planar. The first surface may face the beam source. The first surface may face away from the beam source. The second optical element may include, consist essentially of, or consist of a lens having (i) a first surface having the shape of a truncated sphere, and (ii) opposite the first surface, a second surface that is substantially planar. The first surface may face the beam source. The first surface may face away from the beam source. The second optical element may include, consist essentially of, or consist of a meniscus lens. The meniscus lens may be a positive meniscus lens. The meniscus lens may be a negative meniscus lens. The second optical element may include, consist essentially of, or consist of fused silica and/or zinc sulfide. 
     The beam source may include or consist essentially of a beam emitter emitting a plurality of discrete beams, focusing optics for focusing the plurality of beams onto a dispersive element, a dispersive element for receiving and dispersing the received focused beams, and a partially reflective output coupler positioned to receive the dispersed beams, transmit a portion of the dispersed beams therethrough as the radiation beam, and reflect a second portion of the dispersed beams back toward the dispersive element. The radiation beam may be composed of multiple wavelengths of radiation. The focusing optics may include or consist essentially of one or more cylindrical lenses, one or more spherical lenses, one or more spherical mirrors, and/or one or more cylindrical mirrors. The dispersive element may include or consist essentially of a diffraction grating (e.g., a transmissive diffraction grating or a reflective diffraction grating). 
     In another aspect, embodiments of the invention feature a laser delivery system for receiving and altering a spatial power distribution of a radiation beam from a beam source and focusing the radiation with the altered spatial power distribution onto a workpiece. The laser delivery system includes or consists essentially of a collimating lens for collimating the radiation beam, a focusing lens for receiving the collimated beam and focusing the beam toward the workpiece, first and second optical elements for receiving the radiation beam and altering the spatial power distribution thereof, a lens manipulation system for changing (i) a position of the first optical element within a path of the radiation beam, (ii) a position of the second optical element within the path of the radiation beam, and/or (iii) a distance between the first and second optical elements, and a controller for controlling the lens manipulation system to achieve a target altered spatial power distribution on the workpiece. The first and/or second optical element may be disposed between the beam source and the collimating lens (i.e., disposed optically downstream of the beam source and optically upstream of the collimating lens). 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. The first optical element may include, consist essentially of, or consist of a double-concave axicon lens. The second optical element may include, consist essentially of, or consist of a double-convex axicon lens. The first optical element may be disposed optically upstream of the second optical element. The first optical element may be disposed optically downstream of the second optical element. The lens manipulation system may be configured to change the distance between the first and second optical elements within the range of approximately 0 mm to approximately 50 mm, within the range of approximately 0 mm to approximately 20 mm, within the range of approximately 2 mm to approximately 50 mm, or with the range of approximately 2 mm to approximately 20 mm. The first optical element may include, consist essentially of, or consist of a lens having (i) a first surface that is substantially planar, and (ii) opposite the first surface, a second surface having (a) a first portion that is convexly curved and (b) a second portion that is substantially planar. The second optical element may include, consist essentially of, or consist of a lens having (i) a first surface that is substantially planar, and (ii) opposite the first surface, a second surface having (a) a first portion that is concavely curved and (b) a second portion that is substantially planar. The first optical element may be disposed optically upstream of the second optical element. The first optical element may be disposed optically downstream of the second optical element. The second surface of the first optical element may face the second surface of the second optical element. The first surface of the first optical element may face the first surface of the second optical element. The first surface of the first optical element may face the second surface of the second optical element. The second surface of the first optical element may face the first surface of the first optical element. The lens manipulation system may be configured to position the first optical element and/or the second optical element transversely off-center within the path of the radiation beam. The first optical element may include, consist essentially of, or consist of fused silica and/or zinc sulfide. The second optical element may include, consist essentially of, or consist of fused silica and/or zinc sulfide. 
     The beam source may include or consist essentially of a beam emitter emitting a plurality of discrete beams, focusing optics for focusing the plurality of beams onto a dispersive element, a dispersive element for receiving and dispersing the received focused beams, and a partially reflective output coupler positioned to receive the dispersed beams, transmit a portion of the dispersed beams therethrough as the radiation beam, and reflect a second portion of the dispersed beams back toward the dispersive element. The radiation beam may be composed of multiple wavelengths of radiation. The focusing optics may include or consist essentially of one or more cylindrical lenses, one or more spherical lenses, one or more spherical mirrors, and/or one or more cylindrical mirrors. The dispersive element may include or consist essentially of a diffraction grating (e.g., a transmissive diffraction grating or a reflective diffraction grating). 
     In yet another aspect, embodiments of the invention feature a laser delivery system for receiving and altering a spatial power distribution of a radiation beam from a beam source and focusing the radiation with the altered spatial power distribution onto a workpiece. The laser delivery system includes or consists essentially of one or more divergence-increasing optical elements for increasing a divergence of the radiation beam, a focusing lens for receiving the radiation beam and focusing the beam toward the workpiece, at least one optical element for receiving the radiation beam and altering the spatial power distribution thereof, a lens manipulation system for changing a position of the at least one optical element within a path of the radiation beam, and a controller for controlling the lens manipulation system to achieve a target altered spatial power distribution on the workpiece. 
     Embodiments of the invention may include one or more of the following in any of a variety of combinations. The focusing lens may be disposed optically downstream of the one or more divergence-increasing optical elements. The at least one optical element may be disposed optically upstream of the focusing lens. The one or more divergence-increasing optical elements may include, consist essentially of, or consist of a triple collimator. The triple collimator may include, consist essentially of, or consist of (i) a first plano-concave lens, (ii) a second meniscus lens, and (iii) a third plano-convex lens. The first plano-concave lens may be disposed optically upstream of the second meniscus lens. The second meniscus lens may be disposed optically upstream of the third plano-convex lens. The at least one optical element may be disposed optically downstream of the first plano-concave lens. The at least one optical element may be disposed optically upstream of the second meniscus lens and/or the third plano-convex lens. The at least one optical element may include, consist essentially of, or consist of a lens having (i) a first surface having the shape of a truncated cone, and (ii) opposite the first surface, a second surface that is substantially planar. The at least one optical element may include, consist essentially of, or consist of a lens having (i) a first surface having the shape of a truncated sphere, and (ii) opposite the first surface, a second surface that is substantially planar. The at least one optical element may include, consist essentially of, or consist of a meniscus lens (e.g., a positive meniscus lens or a negative meniscus lens). The lens manipulation system may be configured to position at least one said optical element transversely off-center within the path of the radiation beam. 
     The at least one optical element may include, consist essentially of, or consist of a first optical element and a second optical element. The first optical element and the second optical element may be separated by a gap therebetween. The lens manipulation system may be configured to change (i) a position of the first optical element within a path of the radiation beam, (ii) a position of the second optical element within the path of the radiation beam, and/or (iii) a distance between the first and second optical elements. The first optical element may include, consist essentially of, or consist of a double-concave axicon lens. The second optical element may include, consist essentially of, or consist of a double-convex axicon lens. The first optical element may be disposed optically upstream of the second optical element. The first optical element may be disposed optically downstream of the second optical element. The lens manipulation system may be configured to change the distance between the first and second optical elements within the range of approximately 0 mm to approximately 50 mm, within the range of approximately 0 mm to approximately 20 mm, within the range of approximately 2 mm to approximately 50 mm, or with the range of approximately 2 mm to approximately 20 mm. The first optical element may include, consist essentially of, or consist of a lens having (i) a first surface that is substantially planar, and (ii) opposite the first surface, a second surface having (a) a first portion that is convexly curved and (b) a second portion that is substantially planar. The second optical element may include, consist essentially of, or consist of a lens having (i) a first surface that is substantially planar, and (ii) opposite the first surface, a second surface having (a) a first portion that is concavely curved and (b) a second portion that is substantially planar. The first optical element may be disposed optically upstream of the second optical element. The first optical element may be disposed optically downstream of the second optical element. The second surface of the first optical element may face the second surface of the second optical element. The first surface of the first optical element may face the first surface of the second optical element. The first surface of the first optical element may face the second surface of the second optical element. The second surface of the first optical element may face the first surface of the first optical element. The lens manipulation system may be configured to position the first optical element and/or the second optical element transversely off-center within the path of the radiation beam. The first optical element may include, consist essentially of, or consist of fused silica and/or zinc sulfide. The second optical element may include, consist essentially of, or consist of fused silica and/or zinc sulfide. 
     The beam source may include or consist essentially of a beam emitter emitting a plurality of discrete beams, focusing optics for focusing the plurality of beams onto a dispersive element, a dispersive element for receiving and dispersing the received focused beams, and a partially reflective output coupler positioned to receive the dispersed beams, transmit a portion of the dispersed beams therethrough as the radiation beam, and reflect a second portion of the dispersed beams back toward the dispersive element. The radiation beam may be composed of multiple wavelengths of radiation. The focusing optics may include or consist essentially of one or more cylindrical lenses, one or more spherical lenses, one or more spherical mirrors, and/or one or more cylindrical mirrors. The dispersive element may include or consist essentially of a diffraction grating (e.g., a transmissive diffraction grating or a reflective diffraction 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  illustrates a conventional method of cutting a curve out of material with the polarization of the cutting beam being fixed; 
         FIG. 2A  illustrates an exemplary adjustment of polarization according to the cutting path in the material in accordance with various embodiments of the invention; 
         FIG. 2B  illustrates an exemplary adjustment of polarization according to the thickness of the material in accordance with various embodiments of the invention; 
         FIG. 2C  illustrates an exemplary adjustment of polarization from linear polarization to radial polarization in accordance with various embodiments of the invention; 
         FIGS. 3A-3G  illustrate exemplary systems for varying beam polarization based at least in part on processing direction or material thickness in accordance with various embodiments of the invention; 
         FIG. 4A  illustrates a method for cutting or welding a material using an automatically adjusting polarization beam in accordance with various embodiments of the invention; 
         FIGS. 4B-4D  are graphs of cutting speed as a function of workpiece thickness, comparing laser beams with controlled polarization in accordance with various embodiments of the invention with conventional unpolarized beams; 
         FIG. 5  is a schematic diagram of a laser beam delivery system in accordance with various embodiments of the invention; 
         FIG. 6  is a schematic diagram of a flat-top cone optical element in accordance with various embodiments of the invention; 
         FIG. 7A  is a graph of BPP variation as a function of the distance of a fused silica flat-top cone optical element from a beam source in accordance with various embodiments of the invention; 
         FIG. 7B  is a graph of BPP variation as a function of the distance of a zinc sulfide flat-top cone optical element from a beam source in accordance with various embodiments of the invention; 
         FIG. 8A  is a schematic diagram of a laser delivery system having an off-center optical element in accordance with various embodiments of the invention; 
         FIGS. 8B-8D  depict beam profiles as a function of off-center distance produced by the laser delivery system of  FIG. 8A ; 
         FIG. 8E  is a graph of irradiance as a function of position for the two-peak beam profile depicted in  FIG. 4D ; 
         FIG. 9  is a schematic diagram of a flat-top spherical optical element in accordance with various embodiments of the invention; 
         FIG. 10A  is a graph of BPP variation as a function of the distance of a fused silica flat-top spherical optical element from a beam source in accordance with various embodiments of the invention; 
         FIG. 10B  is a graph of BPP variation as a function of the distance of a zinc sulfide flat-top spherical optical element from a beam source in accordance with various embodiments of the invention; 
         FIGS. 11A-11C  depict beam profiles as a function of off-center distance produced by a laser delivery system incorporating the optical element of  FIG. 9  in accordance with various embodiments of the invention; 
         FIG. 11D  is a graph of irradiance as a function of position for the two-peak beam profile depicted in  FIG. 11C ; 
         FIG. 12A  is a schematic diagram of a portion of a laser delivery system having two axicon-lens optical elements in accordance with various embodiments of the invention; 
         FIGS. 12B and 12C  depict geometric design parameters of axicon lenses in accordance with various embodiments of the invention; 
         FIG. 13  is a graph of the BPP variation as a function of gap distance between positive and negative axicon lenses in accordance with various embodiments of the invention; 
         FIG. 14  depicts beam profiles at different gap distances between positive and negative axicon lenses in accordance with various embodiments of the invention; 
         FIG. 15  depicts beam profiles at different gap distances between positive and negative axicon lenses that are transversely off-centered in the beam path in accordance with various embodiments of the invention; 
         FIG. 16A  is a schematic diagram of a portion of a laser delivery system having twin phase plate lenses in accordance with various embodiments of the invention; 
         FIGS. 16B and 16C  depict geometric design parameters of phase plate lenses in accordance with various embodiments of the invention; 
         FIG. 16D  is a graph of BPP as a function of the inner diameter of twin phase plates in accordance with various embodiments of the invention; 
         FIG. 16E  is a graph of optimized inner diameter of twin phase plates as a function of separation from an input fiber end cap in accordance with various embodiments of the invention; 
         FIG. 16F  is a graph of the BPP variation as a function of gap distance between twin phase plate lenses in accordance with various embodiments of the invention; 
         FIG. 16G  depicts beam profiles at different gap distances between twin phase plate lenses in accordance with various embodiments of the invention; 
         FIG. 17A  is a schematic diagram of a meniscus lens optical element in accordance with various embodiments of the invention; 
         FIG. 17B  is a graph of BPP variation as a function of the distance of a fused silica meniscus lens optical element from a beam source in accordance with various embodiments of the invention; 
         FIG. 18A  is a schematic diagram of a partial laser beam delivery system incorporating a triplet collimator for increased beam divergence in accordance with various embodiments of the invention; 
         FIG. 18B  is a graph of BPP variation as a function of the distance of a flat-top spherical optical element from a beam source in the laser delivery system of  FIG. 18A  in accordance with various embodiments of the invention; 
         FIG. 18C  is a graph of BPP variation as a function of the distance of a meniscus lens optical element from a beam source in the laser delivery system of  FIG. 18A  in accordance with various embodiments of the invention; 
         FIG. 18D  is a schematic diagram of a partial laser beam delivery system incorporating a triplet collimator for increased beam divergence and twin phase plate optical elements in accordance with various embodiments of the invention; 
         FIG. 18E  is a graph of the BPP variation as a function of gap distance between the twin phase plate lenses in the laser beam delivery system of  FIG. 18D  in accordance with various embodiments of the invention; 
         FIG. 19  is a schematic diagram of a wavelength beam combining laser system that may be utilized to supply the input beam for laser beam delivery systems in accordance with various embodiments of the invention; 
         FIG. 20  is a schematic diagram of a laser system in accordance with various embodiments of the invention; 
         FIG. 21  is a series of images depicting example beam shapes utilized in accordance with various embodiments of the invention; 
         FIGS. 22A and 22B  are schematic diagrams of workpieces being processed with laser beams having different shapes in accordance with various embodiments of the invention; and 
         FIGS. 23A-23D  are a series of schematic diagrams of a welding process utilizing a laser beam having multiple different beam shapes in accordance with various embodiments of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     Aspects and embodiments relate generally to the field of adjusting polarization and/or shape of a laser beam used in manufacturing, so as to produce better manufacturing results including less dross and clean cuts and welds. In various embodiments, therefore, the present invention relates to optimizing the polarization and/or shape of a laser beam with respect to a material undergoing processing. More particularly, systems and methods for adjusting polarization may involve varying the orientation of a wave plate through which the beam passes in order to selectively vary the polarization thereof, e.g., based on the geometry, material and thickness of the material undergoing processing and the instantaneous orientation of the beam with respect thereto. The approaches and embodiments described herein may apply to single- and dual-beam output systems that use polarization-maintaining optical fibers to deliver the output beams from the laser system to a laser head. In some instances, these laser systems may be wavelength beam-combining systems, which produce a multi-wavelength output beam. 
     Thus, embodiments of the present invention establish an optimal polarization direction for a given material and maintain this direction with respect to the processing direction as processing proceeds. This is in contrast to the behavior of prior-art systems, as exemplified in  FIG. 1 , that do not alter the polarization direction. In  FIG. 1 , a sheet  100  of material is processed by a linearly polarized beam that follows a desired cutting path  102 , which may be curved. The linear polarization, indicated at  104 , maintains a fixed orientation regardless of the varying orientation of the beam relative to the material  100 . In many systems, the optimal beam polarization is parallel to the direction of processing. In  FIG. 1 , this occurs only once, and in fact, at most locations, the polarization is disadvantageously perpendicular to the processing direction. This may retard the processing, produce dross, create an imperfect cut, etc. 
     One optimal behavior for the exemplary system is illustrated  FIG. 2A : the polarization orientation  204  of the processing beam remains parallel to the processing direction throughout the processing path  102 . Another optimal behavior for the exemplary system is illustrated in  FIG. 2B : the polarization state  210  of the processing beam changes from linear polarization to elliptical polarization to circular polarization as the thickness of the material  100  increases. In yet another embodiment, illustrated in  FIG. 2C , the polarization state  210  of the processing beam changes from linear polarization to radial polarization along the processing path  102 . While the processing paths in  FIGS. 2B and 2C  are substantially linear, in embodiments of the invention processing paths may include one or more directional changes, as shown in  FIG. 2B . In general, processing paths may be curvilinear or linear, and “linear” processing paths may feature one or more directional changes, i.e., linear processing paths may be composed of two or more substantially straight segments that are not necessarily parallel to each other. 
     A representative system for accomplishing polarization variations in accordance with embodiments of the present invention is shown in  FIGS. 3A-3C . With reference to  FIG. 3A , the system  300  includes a laser (or other beam emitter, such as a polarized fiber)  305  and a controller  310 . The controller  310  controls the operation of the laser  305  (i.e., it actives the laser  305  and controls beam parameters, such as intensity, as appropriate during processing). The controller also operates a conventional positioning system  315  and a polarization controller  320 . The positioning system  315  may be any controllable optical, mechanical or opto-mechanical system for directing the beam through a processing path along a two- or three-dimensional workpiece. During processing, the controller  310  may operate the positioning system  315  and the laser  305  so that the laser beam traverses a processing path along the workpiece. The processing path may be provided by a user and stored in an onboard or remote memory  325 , which may also store parameters relating to the type of processing (cutting, welding, etc.) and the beam parameters necessary to carry out that processing. In this regard, a local or remote database  330  may maintain a library of materials and thicknesses that the system  300  will process, and upon user selection of material parameters (type of material, thickness, etc.), the controller  310  queries the database  330  to obtain the corresponding parameter values. The stored values may include a polarization orientation and/or state suitable to the material. 
     As is well understood in the plotting and scanning art, the requisite relative motion between the beam and the workpiece may be produced by optical deflection of the beam using a movable mirror, physical movement of the laser using a gantry, lead-screw or other arrangement, and/or a mechanical arrangement for moving the workpiece rather than (or in addition to) the beam. The controller  310  may, in some embodiments, receive feedback regarding the position and/or processing efficacy of the beam relative to the workpiece from a feedback unit  335 , which will be connected to suitable monitoring sensors. In response to signals from the feedback unit  335 , the controller  310  alters the path, composition and/or polarization of the beam. 
     In one embodiment shown in  FIGS. 3B and 3C , polarization adjustment is accomplished within a laser head component  350 , which is usually the last opto-mechanical portion of a laser system emitting a beam used in manufacturing. The laser head  350  includes a collimating lens  355 , an adjusting/rotating wave plate  360 , and a focusing lens  365  to direct beam  370  onto the surface of the workpiece. The wave plate  360  may be a quarter-wave plate, a half-wave plate, or other wave plate for rotating the polarization of the beam  370 . With reference to  FIGS. 3A-3C , a conventional electro-mechanical rotating device  375  rotates the wave plate  360  under the control of the controller  310  as the beam moves through the processing path  102 , thus enforcing a consistent polarization direction of the beam  370  relative to the path  102 . In other configurations, multiple wave plates may be employed and separately rotated by individual rotating devices  375 . The use of multiple wave plates may improve response time. The polarization of the beam  370  is shown at a first orientation  380   a  prior to encountering the wave plate  360  and at a second orientation  380   b  after passing through the wave plate  360 . 
     In one embodiment shown in  FIGS. 3D and 3E , polarization adjustment is also accomplished within a laser head component  350 . The laser head  350  includes collimating lens  355  and focusing lens  365  to direct beam  370  onto the surface of the workpiece, just as the laser head  350  depicted in  FIG. 3B . In the embodiment of  FIG. 3D , the laser head  350  includes a Babinet-Soleil compensator  385  between the collimating lens  355  and the focusing lens  365 . As known in the art, Babinet-Soleil compensator  385  is a continuously variable optical retarder capable of altering the polarization of light traveling therethrough from linear to circular and any elliptical polarization state therebetween. In various embodiments, the Babinet-Soleil compensator  385  includes, consists essentially of, or consists of a compensator plate  386 , a fixed birefringent wedge  387 , and a movable birefringent wedge  388 . The long axis of the compensator plate  386  is typically perpendicular to the long axes of the wedges  387 ,  388 . Movement of the wedge  388  relative to the plate  386  and the wedge  377  alters the polarization state of the beam  370  to any elliptical state between linear and circular. With reference to  FIGS. 3A, 3D, and 3E , a conventional electro-mechanical translation device  389  translates the movable wedge  388  of the Babinet-Soleil compensator  385  under the control of the controller  310  as the beam moves through the processing path  102  (e.g., as the thickness of the workpiece changes), thereby changing the polarization state as a function of the thickness of the workpiece along the path  102 . For example, the circularity (i.e., the transition from linear to elliptical or circular) of the polarization state of the beam  370  may be increased as the thickness of the workpiece increases. The polarization of the beam  370  is shown at a first state  390   a  prior to encountering the Babinet-Soleil compensator  385  and at a second state  390   b  after passing through the Babinet-Soleil compensator  385 . 
     In another embodiment shown in  FIGS. 3F and 3G , polarization adjustment is also accomplished within a laser head component  350 . The laser head  350  includes collimating lens  355  and focusing lens  365  to direct beam  370  onto the surface of the workpiece, just as the laser head  350  depicted in  FIGS. 3B and 3D . In the embodiment of  FIG. 3F , the laser head  350  includes a radial polarization converter  391  between the collimating lens  355  and the focusing lens  365 . As known in the art, a radial polarization converter  391  may include, consist essentially of, or consist of a glass wave plate that converts linear polarization to radial polarization or azimuthal polarization. For example, the radial polarization converter  391  may be a half-wave plate with a continuously varying slow axis direction or a space variant quarter-wave plate possessing radial symmetry. The radial polarization converter  391  may include, consist essentially of, or consist of a glass plate having thereon a nanostructured grating, e.g., the S-waveplate Radial Polarization Converter available from UAB Altechna of Vilnius, Lithuania, or one of the Radial Polarization Converters available from Edmund Optics Inc. of Barrington, N.J. In other embodiments, the radial polarization converter  391  may include, consist essentially of, or consist of a liquid crystal in which the liquid crystal molecules are specifically aligned to produce the desired radial or azimuthal polarization, e.g., the Arcopix Radial Polarization converter available from Arcopix of Neuchatel, Switzerland. Movement of the radial polarization converter  391  within the path of beam  370  alters the polarization state of the beam  370  from linear to radial or azimuthal or vice versa. In various embodiments, beam  370  that is radially polarized is focusable to a smaller spot size than beam  370  having a linear polarization. With reference to  FIGS. 3A, 3F, and 3G , a conventional electro-mechanical translation device  389  translates radial polarization converter  391  under the control of the controller  310  as the beam moves through the processing path  102 , thereby changing the polarization state along the path  102 . The polarization of the beam  370  is shown at a first state  392   a  prior to encountering the radial polarization converter  391  (i.e., linear polarization) and at a second state  392   b  after passing through the radial polarization converter  391  (i.e., radial polarization). 
       FIG. 4A  illustrates a representative method  400  of operating the system  300  to perform a cutting operation. In a first step  410 , the user preprograms the desired path into the system  300  using any suitable input device or by means of file transfer. In step  420 , the controller  310  analyzes the curves, features (e.g., thickness), and cutting direction of the path, queries the database  330  as necessary, determines how fast the cut can be made, and determines the optimal polarization direction and/or state of the laser beam relative to the cutting direction. In operation, indicated at step  430 , the controller  330  operates the laser  305  and subsystems  315 ,  320  to cut along the preprogrammed path, maintaining the proper polarization. If the composition and/or thickness of the material being processed changes, the location and nature of the change may be programmed, and the controller  310  can adjust the laser beam parameters (including polarization and/or beam shape) accordingly. It should be noted that the optimal cutting, welding or manufacturing solution may not necessarily be the cleanest cut or weld, because additional steps in the process (e.g., de-burring, grinding, and/or polishing) may be needed regardless. Thus overall optimization may be based on the desired output, and the present methods and systems are configured to produce those desired results whatever they may be. As noted earlier, cutting is only one example of laser processing that may benefit from the approach of embodiments of the present invention. 
     The controller  310  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 above. 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. 
     Although the methods described herein for improving processing work well for linearly polarized beams (delivered via a free-space laser or polarization-maintaining fiber), the techniques also work with elliptically polarized beams (dominated by one polarization) as well. For example, a beam from a standard multimode fiber would be likely elliptically polarized and could benefit from the approaches described herein. 
     Embodiments of the invention may be advantageously utilized for more efficient cutting of various materials, e.g., metallic materials.  FIG. 4B  is a graph of achievable cutting speed as a function of workpiece thickness for a workpiece composed of  304  stainless steel under a flow of nitrogen gas. Four different laser systems were utilized for the cutting. First, a laser system in accordance with embodiments of the invention operating at 1 kW of power and utilizing a 58 μm polarization-maintaining optical output fiber to produce a linearly polarized laser output beam was utilized to cut the workpiece in directions parallel and perpendicular to the polarization direction. Trend line  440  depicts the cutting speed achievable for the beam polarized parallel to the cutting direction, and trend line  445  depicts the cutting speed achievable for the beam polarized perpendicular to the cutting direction. As shown, the parallel polarized beam is capable of cutting speeds vastly higher than the perpendicular polarized beam, particularly for thinner workpieces. Trend lines  450  and  455  depict the data for two different commercially available 1 kW laser systems having unpolarized output beams (i.e., utilizing output fiber optic cables that are not polarization-maintaining fibers). As shown, the unpolarized beam is capable of faster cutting compared with the perpendicular polarized beam of trend line  445  but is slower compared to the parallel polarized beam of trend line  440 . Trend line  460  depicts data for a 2 kW laser having a 100 μm output fiber but that also produces an unpolarized beam. As would be expected, this more powerful laser system is capable of faster cutting speeds than the lower-power laser systems, although that advantage diminishes and even disappears for thinner workpieces, which the parallel polarized beam of trend line  440  cuts at higher speed despite operating at lower power and with a smaller output fiber. 
       FIG. 4C  is a graph of achievable cutting speed as a function of workpiece thickness for a workpiece composed of 3003 aluminum under a flow of nitrogen gas. The laser systems utilized are the same as those described above for  FIG. 4B . As shown, the parallel polarized beam represented by trend line  440  exhibits the best cutting performance, and the performance of the parallel polarized beam is even superior to that of the 2 kW, 100 μm unpolarized beam of trend line  460 , particularly for thinner workpiece thicknesses. As in  FIG. 4B , the perpendicular polarized beam of trend line  445  depicts the worst performance, emphasizing an advantageous effect of embodiments of the invention in which polarization direction is maintained parallel to the cutting direction. 
       FIG. 4D  is a graph of achievable cutting speed as a function of workpiece thickness for a workpiece composed of brass under a flow of nitrogen gas. The laser systems utilized are the same as those described above for  FIG. 4B . As shown, the parallel polarized beam represented by trend line  440  exhibits fast cutting performance, particularly for thinner workpiece thicknesses. The parallel polarized beam represented by trend line  440  also exhibits much faster cutting speed than the comparable 1 kW unpolarized beam represented by trend line  450 . As in  FIGS. 4B and 4C , the perpendicular polarized beam of trend line  445  depicts the worst performance, and in fact was incapable of appreciable cutting speeds for the workpiece having a thickness of 3 mm. 
     Embodiments of the present invention combine or replace polarization adjustments of a beam in response to workpiece material and/or physical properties with techniques for shaping the beam and/or adjusting the BPP of the beam.  FIG. 5  depicts a schematic diagram of a laser beam delivery system  500  incorporating beam-manipulating optical elements in accordance with embodiments of the present invention. In various embodiments, the laser beam delivery system  500  may be disposed within, for example, a laser-based cutting head or welding head (e.g. cutting head  350 ) and may be combined with various components therein (e.g., optical elements, controllers, etc.) utilized to adjust the polarization of the output beam. The beam delivery system  500  may feature a beam delivery fiber, terminating in a fiber end cap  505 , that is connected to remaining portions of the laser-generating system (for example, a WBC laser system, not shown in  FIG. 5 ), a collimating lens  510 , a focusing lens  515 , and an optical element  520  that is positioned between the end cap  505  and the collimating lens  510 . In various embodiments of the invention featuring combined functionality for beam shaping and polarization adjustment, elements such as collimating lens  510  and focusing lens  515  may be shared between those functionalities, i.e., the laser beam delivery system in various embodiments may have various optical elements that facilitate both beam shaping and polarization adjustment. In various embodiments, the optical element  520  is disposed close to the fiber end cap  505  to minimize the size of the beam striking the optical element  520 . Refraction of a smaller beam may be performed with optics having smaller geometric dimensions of the optics and may vary the output profile with more sensitivity.  FIG. 5  also depicts an optional second optical element  525  disposed between the focusing lens  515  and a workpiece  530 . The workpiece  530  may include or consist essentially of, for example, one or more parts (e.g., metallic parts) to be welded, drilled, and/or cut by the beam focused by focusing lens  515 . In various embodiments, the first optical element  520  is disposed between the focusing lens  515  and the workpiece  530  and the second optical element  525  is omitted. Optical elements  520 ,  525  may each include or consist essentially of, for example, a phase plate. 
     The positions of first optical element  520  and/or second optical element  525  may be translated within the beam profile via use of a lens manipulation system that may include or consist essentially of, for example, one or more mechanized or motorized translation stages  535  capable of motion along two or three axes. The lens manipulation system may be responsive to a controller  540 . The controller  540  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, thickness of the workpiece, etc.) and configured to position optical element  520  and/or optical element  525  to cause the manipulated beam  545  to strike the workpiece  530  with the target radiation power distribution or beam quality. The controller  540  may be programmed to achieve the desired power distribution and/or output BPP and/or beam quality via a particular optical element positioning as detailed herein. The controller  540  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  80 x 86  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. 
       FIG. 6  is a schematic diagram of an optical element  600  having the shape of a truncated cone (flat-top cone shape or tapered cylinder shape) in accordance with embodiments of the invention. For example, optical element  600  may be utilized as optical element  520  and/or optical element  525  in delivery system  500 . The parameters D, d, θ, and H are geometrical design parameters for outside diameter, inside diameter (which may correspond to the beam size of the beam when it strikes the optical element), slope angle which defines the maximum sagitta (or “sag,” h) and the separation of outer ring of the beam from the spot center of the beam, and the thickness of the optical element  600 , respectively. Ray tracing of geometric optics may be used to design optical elements in accordance with embodiments of the present invention based on the conservation of energy, the constancy of optical path length and Snell&#39;s law. The lens design and its surface profiles may, for example, transform the beam profile from a Gaussian into a Bessel laser beam with a desired intensity distribution. 
     Table 1 provides exemplary design values for exemplary optical elements  600  including, consisting essentially of, or consisting of two different materials, fused silica and zinc sulfide (e.g., ZnS MultiSpectral, available from II-VI Inc. of Saxonburg, Pa.). 
     
       
         
           
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 Optical Element Material 
                 Fused Silica 
                 Zinc Sulfide 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 D (mm) 
                 25 
                 25 
               
               
                 d (mm) 
                 8 
                 8 
               
               
                 H (mm) 
                 2 
                 0.85 
               
               
                 h (μm) 
                 50 
                 17 
               
               
                 Θ (mrad) 
                 5.9 
                 2 
               
               
                   
               
            
           
         
       
     
       FIGS. 7A and 7B  are graphs of BPP at different distances from the fiber end cap  505  to the exemplary fused silica ( FIG. 7A ) and zinc sulfide ( FIG. 7B ) optical elements  600  having the design parameters provided in Table 1. In the plots, the initial position of the optical element  600  is assumed to be 25 mm from the end cap  505 . As shown, in both cases, the BPP of the beam may be increased from about 4 to about 12 via displacement of the optical element  600  by approximately 30 mm. The slope of this change in BPP as a function of displacement may be altered via changes in the numerical aperture of the fiber output at the end cap  505 . The beam profiles at a 50 mm distance of the optical element  600  to the fiber end cap  505  are also shown in  FIGS. 7A and 7B . 
     A tailored beam profile that has two peaks in one axis may be obtained by positioning the optical element  600  (or other optical elements detailed herein) transversely off-center in the beam path (i.e., partially introducing it into the input laser beam) as shown in  FIG. 8A . Depending on the degree of introduction, the beam profile of the output laser beam may be optimally adapted to a variety of laser applications. In  FIGS. 8B-8D , the beam profiles at different off-centered distances (0 mm, 2 mm, and 4 mm) for optical element  600  at a 40 mm distance to the end cap  505  are shown.  FIG. 8E  is a graph of irradiance as a function of position for the beam profile depicted in  FIG. 8D , clearly showing the two-peak nature of the beam profile. In various embodiments, the variation of BPP at different off-centered positions of the optical element  600  is approximately zero, even while the irradiance as a function of position across the beam profile changes. 
     Optical elements in accordance with embodiments of the invention may also have a truncated spherical (i.e., flat-top spherical) configuration and may be used to also produce a Bessel beam profile. The geometric design for optical elements  900  in accordance with such embodiments is depicted schematically in  FIG. 9 . Optical element  900  may be utilized as optical element  520  and/or optical element  525  in delivery system  500 . The design parameters are the same as those detailed above for the flat-top cone optical element  600  except for the curvature radius R, which also defines the maximum sag (h) and the separation of the resulting annular beam ring from the beam spot center. 
     Table 2 provides exemplary design values for exemplary optical elements  900  including, consisting essentially of, or consisting of two different materials, fused silica and zinc sulfide. 
     
       
         
           
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Optical Element Material 
                 Fused Silica  
                 Zinc Sulfide 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 D (mm) 
                 25 
                 25 
               
               
                 d (mm) 
                 8 
                 8 
               
               
                 H (mm) 
                 2 
                 0.85 
               
               
                 h (μm) 
                 58 
                 23 
               
               
                 R (mm) 
                 1200 
                 3000 
               
               
                   
               
            
           
         
       
     
       FIGS. 10A and 10B  are graphs of BPP at different distances from the fiber end cap  505  to the exemplary fused silica ( FIG. 10A ) and zinc sulfide ( FIG. 10B ) optical elements  900  having the design parameters provided in Table 2. In the plots, the initial position of the optical element  900  is assumed to be 25 mm from the end cap  505 . As shown, in both cases, the BPP of the beam may be increased from about 4 to about 12 via displacement of the optical element  900  by approximately 30 mm (e.g., approximately 28 mm-approximately 32 mm). The slope of this change in BPP as a function of displacement may be altered via changes in the numerical aperture of the fiber output at the end cap  505 . The beam profiles at a 50 mm distance of the optical elements  900  to the fiber end cap  505  are also shown in  FIGS. 10A and 10B , as are graphs of their irradiance as a function of position for the 50 mm spacing between optical element  900  and end cap  505 . 
     In  FIGS. 11A-11C , the beam profiles at different off-centered distances (0 mm, 2 mm, and 4 mm) for optical element  900  (i.e., as shown for optical element  600  in  FIG. 6A ) at a 40 mm distance to the end cap  505  are shown.  FIG. 11D  is a graph of irradiance as a function of position for the beam profile depicted in  FIG. 11C , clearly showing the two-peak nature of the intensity of the beam profile. In various embodiments, the variation of BPP at different off-centered positions of the optical element  900  is approximately zero, even while the irradiance as a function of position across the beam profile changes. 
     Embodiments of the invention utilize optical elements to produce annular beam shapes. Embodiments of the invention feature one or more optical elements that include, consist essentially of, or consist of axicon lenses. As known in the art, axicon lenses are lenses having at least one conical surface, and such lenses may be utilized to image a point source into a line segment along the optical axis. The conical surface of revolution is capable of blending light from a point source, which is located on the axis of revolution, by reflection or refraction, or both. Embodiments of the invention utilize a combination of a double-positive (i.e., double convex) axicon lens  1200  and a double-negative (i.e., double concave) axicon lens  1210  between the fiber end cap  505  and the collimating lens  510  as shown in  FIG. 12A , and the beam size at the workpiece may be varied utilizing this lensing system. As shown, lenses  1200 ,  1210  are separated in the beam path by a gap distance  1220 . θ 1  and θ 2  are the slope variables of the conic surfaces that define the maximum sags (h 1  and h 2 ) and the separation of the annular beam ring from the beam spot center as schematically drawn in  FIGS. 12B and 12C . In various embodiments of the invention, the conical surfaces of one or both of lenses  1200 ,  1210  have smooth edges and radii of curvature less than approximately 5 μm. 
       FIG. 13  is a graph depicting control over the BPP of the laser delivery system as a function of the gap distance  1220  between the two axicon lenses  1200 ,  1210 . As shown in  FIG. 13 , an approximate 7 mm variation in the gap distance  1220  results in a BPP increase from 4 to 12, demonstrating the wide range of BPP control enabled by such embodiments of the present invention. The beam profiles as a function of gap distance  1220  between the lenses  1200 ,  1210  are shown in  FIG. 14 , where the gap distances are listed in millimeters. As shown, adjustment of the gap distance  1220  may transform a beam profile having a single peak to one having two, three, or more peaks.  FIG. 15  depicts similar beam profiles for the case in which the two axicon lenses  1200 ,  1210  are transversely off-center by 4 mm in the beam path and separated by the listed gap distances  1220  (gap distances are listed in millimeters). 
     Embodiments of the invention feature one or more optical elements that include, consist essentially of, or consist of phase plates having one planar surface and an opposing surface at least a portion of which is convexly or concavely curved.  FIG. 16A  depicts a partial beam delivery system featuring two such plates  1600 ,  1610  separated by a gap Z. As shown, plate  1600  is separated from fiber end cap  505  by a distance S.  FIGS. 16B and 16C  depict plates  1600 ,  1610  in more detail. As shown, plates  1600 ,  1610  have an outer diameter D, and the convex/concave portions of their surfaces have an inner diameter d that defines the maximum sag h (in conjunction with R, detailed below). The thicknesses of the plates at their outer perimeters (i.e., the thicknesses between planar portions of their opposing surfaces) are represented by H, and the radii of curvature of the convex/concave portions are represented by R. As depicted in  FIGS. 16B and 16C , the plates  1600 ,  1610  have approximately the same H, D, d, and R, although various embodiments of the invention feature twin plates (i.e., one having a partial concave surface and one having a partial convex surface) that differ in one or more of those parameters. 
     Table 3 provides exemplary design values for exemplary optical elements  1600 ,  1610  including, consisting essentially of, or consisting of two different materials, fused silica and zinc sulfide. 
     
       
         
           
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 Optical Element Material 
                 Fused Silica 
                 Zinc Sulfide 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 D (mm) 
                 25 
                 25 
               
               
                 d (mm) 
                 5 
                 5 
               
               
                 H (mm) 
                 2 
                 1 
               
               
                 h (μm) 
                 25 
                 9.3 
               
               
                 R (mm) 
                 500 
                 1350 
               
               
                   
               
            
           
         
       
     
       FIGS. 16D and 16E  depict that, in accordance with embodiments of the invention, the inner diameter d of plates  1600 ,  1610  may be optimized to maximize the output BPP of the laser delivery system as a function of the distance S from the fiber end cap  505 .  FIG. 16D  is a graph of BPP as a function of inner diameter d for plates  1600 ,  1610  having a distance S of 40 mm, a gap distance Z of 10 mm, and a radius of curvature R of 500. As shown, the resulting BPP is maximized at an inner diameter d of approximately 5 mm; this BPP is substantially independent of changes in the gap distance Z and the radius of curvature R.  FIG. 16E  is a graph of the optimized inner diameter d (i.e., the inner diameter d that maximizes the output BPP) as a function of the distance S between the end cap  505  and the plate  1600 . As shown, an optimized inner diameter d may be selected that maximizes BPP of the output beam as a function of the distance S. 
       FIG. 16F  is a graph of BPP at different gap distances Z between plates  1600 ,  1610  having the design parameters provided in Table  3  (with the design parameters of Table 3, both the fused silica and zinc sulfide plates  1600 ,  1610  provide the same results). In the plot, the distance S to the end cap  505  is assumed to be 40 mm. As shown, the BPP of the beam may be increased from about 4 to about 12 via alteration of the gap Z between plates  1600 ,  1610  by approximately 9 mm. Various beam profiles of the output beam as a function of the gap Z (in mm) are illustrated in  FIG. 16G , as are graphs of their irradiance as a function of position. As shown, as the beam BPP increases, the beam shape proceeds from having a single peak to having a broader, multi-peak irradiance profile. 
     Optical elements in accordance with embodiments of the invention may also include, consist essentially of, or consist of meniscus lenses. The geometric design for optical elements  1700  in accordance with such embodiments is depicted schematically in  FIG. 17A ; as shown, in various embodiments, one surface of optical element  1700  is convexly curved over substantially the entire surface, while the opposing surface is concavely curved over a portion of the surface, defining an inner diameter d. Optical element  1700  may be utilized as optical element  520  and/or optical element  525  in delivery system  500 . As shown, optical element  1700  may have an outer diameter D, inner diameter d, thickness H, maximum sag h 1  of the convexly curved surface, and maximum sag h 2  of the partially concavely curved surface. The radius of curvature R, which may be approximately the same for both surfaces of optical element  1700 , defines the maximum sags h 1  and h 2 , as well as the separation of the resulting annular beam ring from the beam spot center. 
     Table 4 provides exemplary design values for exemplary optical elements  1700  including, consisting essentially of, or consisting of two different materials, fused silica and zinc sulfide. 
     
       
         
           
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 Optical Element Material 
                 Fused Silica 
                 Zinc Sulfide 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 D (mm) 
                 25 
                 25 
               
               
                 d (mm) 
                 8 
                 8 
               
               
                 H (mm) 
                 3 
                 1.8 
               
               
                 h1 (μm) 
                 87 
                 31 
               
               
                 h2 (μm) 
                 9 
                 3.2 
               
               
                 R (mm) 
                 900 
                 2500 
               
               
                   
               
            
           
         
       
     
       FIG. 17B  is a graph of BPP at different distances from the fiber end cap  505  to the exemplary fused silica optical element  1700  having the design parameters provided in Table 4. In the plot, the initial position of the optical element  1700  is assumed to be 25 mm from the end cap  505 . As shown, the BPP of the beam may be increased from about 4 to about 12 via displacement of the optical element  1700  by approximately 24 mm. The beam profile at a 46 mm distance of the optical element  1700  to the fiber end cap  505  is also shown in  FIG. 17B , as is a graph of the irradiance as a function of position for the 46 mm spacing between optical element  1700  and end cap  505 . 
     Laser beam delivery systems in accordance with embodiments of the present invention may also utilize various lens arrangements to form larger, more diverged input beams for BPP variation as a function of optical element movement.  FIG. 18A  depicts portions of a laser delivery system  1800  that incorporates a movable optical element  1805  for BPP variation and a triplet collimator for increasing divergence of the laser beam. As shown, the triplet collimator increases the divergence of the beam from an angle α to an angle β. In various embodiments, the ratio of β to α is between approximately 2 and approximately 1.5, e.g., approximately 1.74. As described in more detail below, this increased divergence enables greater control over BPP with less movement of the optical element  1805 . In various embodiments, the optical element  1805  includes, consists essentially of, or consists of any one or more of optical element  600 , optical element  900 , optical element  1700 , phase plates  1600 / 1610 , or axicon lenses  1200 ,  1210 . 
     Triplet collimators for increasing beam divergence in accordance with embodiments of the invention may be composed of various combinations of lenses.  FIG. 18A  depicts one such embodiment that includes a plano-concave lens  1810 , a meniscus lens  1815  (e.g., a positive meniscus lens), and a plano-convex lens  1820 . In various embodiments of the invention, the optical element  1805  is disposed in the beam path between plano-concave lens  1810  and meniscus lens  1815 . In other embodiments, the optical element  1805  may be disposed in the beam path between meniscus lens  1815  and plano-convex lens  1820  or even optically downstream of plano-convex lens  1820 . 
       FIG. 18B  is a graph of BPP at different distances from the fiber end cap  505  to the exemplary fused silica optical element  600  having the design parameters provided in Table 1 when utilized in laser beam delivery system  1800  in conjunction with a triplet collimator for increased beam divergence. In the plot, the initial position of the optical element  600  is assumed to be 25 mm from the end cap  505 . As shown, the BPP of the beam may be increased from about 4 to about 12 via displacement of the optical element  600  by only approximately 16 mm, or about a factor of 2 less displacement (i.e., greater control) when compared to the beam delivery system lacking the triplet collimator of  FIG. 18A  (see  FIG. 7A ). The beam profile at a 21 mm distance of the optical element  600  to the fiber end cap  505  is also shown in  FIG. 18B . 
       FIG. 18C  is a graph of BPP at different distances from the fiber end cap  505  to the exemplary fused silica optical element  1700  having the design parameters provided in Table  4  when utilized in laser beam delivery system  1800  in conjunction with a triplet collimator for increased beam divergence. In the plot, the initial position of the optical element  1700  is assumed to be 25 mm from the end cap  505 . As shown, the BPP of the beam may be increased from about 4 to about 12 via displacement of the optical element  600  by only approximately 12 mm, or about a factor of 2 less displacement (i.e., greater control) when compared to the beam delivery system lacking the triplet collimator of  FIG. 18A  (see  FIG. 17B ). The beam profile at a 17.5 mm distance of the optical element  1700  to the fiber end cap  505  is also shown in  FIG. 18C . 
       FIG. 18D  is a schematic of partial laser beam delivery system  1800  incorporating the twin phase plate optical elements  1600 ,  1610  described above separated within the beam path by a gap distance Z.  FIG. 18E  is a graph of BPP for different gap spacings Z of the exemplary fused silica optical elements  1600 ,  1610  having the design parameters provided in Table 3 when utilized in laser beam delivery system  1800  in conjunction with a triplet collimator for increased beam divergence. In the plot, the position of the optical element  1600  is assumed to be 25 mm from the end cap  505 . As shown, the BPP of the beam may be increased from about 4 to about 12 via increasing the gap distance Z between the optical elements  1600 ,  1610  by only approximately 3 mm, or about a factor of 3 less displacement (i.e., greater control) when compared to the beam delivery system lacking the triplet collimator of  FIG. 18A  (see  FIG. 16F ). The beam profile at a 3 mm gap distance between optical elements  1600 ,  1610  is also shown in  FIG. 18C . 
     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, beam shape, and/or polarization as detailed herein.  FIG. 19  depicts an exemplary WBC laser system  1900  that utilizes one or more lasers  1905 . In the example of  FIG. 19 , laser  1905  features a diode bar having four beam emitters emitting beams  1910  (see magnified input view  1915 ), 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  1915 , each beam  1910  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  1920  may be used to collimate each beam  1910  along the fast dimension. Transform optic(s)  1925 , which may include or consist essentially of one or more cylindrical or spherical lenses and/or mirrors, are used to combine each beam  1910  along a WBC direction  1930 . The transform optics  1925  then overlap the combined beam onto a dispersive element  1935  (which may include or consist essentially 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  1940 . The output coupler  1940  then transmits the combined beams  1945  as shown on the output front view  1950 . The output coupler  1940  is typically partially reflective and acts as a common front facet for all the laser elements in this external cavity system  1900 . 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  1945  is a thus a multiple-wavelength beam (combining the wavelengths of the individual beams  1910 ), and may be utilized as the input beam in laser beam delivery systems detailed herein and/or may be coupled into an optical fiber. 
       FIG. 20  depicts a laser system  2000  having a variable-shape output beam utilized in accordance with various embodiments of the present invention. As shown, the laser system  2000  may include a laser source  2010  (e.g., a WBC laser system  1900  forming an output beam composed of multiple wavelengths) coupled to an optical fiber  2020 . At the distal end of the optical fiber  2020  is a processing head or laser beam delivery system  2030 . Processing head  2030  may include, consist essentially of, or consist of, for example, all or some of the components of laser beam delivery system  500  described above. For example, processing head  2030  may incorporate and/or be responsive to a controller (e.g., controller  540 ) that controls the output beam shape at a focal point  2040  at or proximate the surface of a workpiece. In various embodiments, as detailed herein, processing head  2030  may include or consist essentially of various optical elements shaped and/or movable relative to each other in order to form an output laser beam having a variable output beam shape.  FIG. 21  depicts a series of different output beam shapes formable by the laser system  2000  in accordance with embodiments of the present invention. As shown, the output beam shapes range from highly focused spot beams to diffuse, defocused larger spots to annular beams, depending on the control voltage applied within the processing head  2030  (e.g., via the controller to control the position of one or more optical elements therewithin). As also shown in  FIG. 21 , the BPP of the beam may also change as the beam shape changes. 
     In various embodiments, the laser system  2000  includes a controller (e.g., controller  540 , as mentioned above) and/or a positioning system (e.g., positioning system  315 ). The controller controls the operation of the laser system (i.e., it actives the laser and controls beam parameters, such as intensity and/or output beam shape, as appropriate during processing). The controller also may operate the positioning system. The positioning system may be any controllable optical, mechanical or opto-mechanical system for directing the beam through a processing path along a two- or three-dimensional workpiece. During processing, the controller may operate the positioning system and the laser system  2000  so that the laser beam traverses a processing path along the workpiece and/or so that the laser output beam is positioned at a particular point on the workpiece to be processed (e.g., a position for a weld). The processing path and/or one or more processing points may be provided by a user and stored in an onboard or remote memory, which may also store parameters relating to the type of processing (cutting, welding, etc.) and the beam parameters (e.g., output beam shape) necessary to carry out that processing. In this regard, a local or remote database may maintain a library of materials and thicknesses that the laser system will process, and upon user selection of material parameters (type of material, thickness, etc.), the controller may query the database to obtain the corresponding parameter values. 
     As is well understood in the plotting and scanning art, any requisite relative motion between the output beam and the workpiece may be produced by optical deflection of the beam using a movable mirror, physical movement of the laser using a gantry, lead-screw or other arrangement, and/or a mechanical arrangement for moving the workpiece rather than (or in addition to) the beam. The controller may, in some embodiments, receive feedback regarding the beam position and/or processing efficacy of the beam relative to the workpiece from a feedback unit, which will be connected to suitable monitoring sensors. In response to signals from the feedback unit, the controller alters the path, position, BPP, and/or shape of the beam. 
     In addition, the laser system may incorporate one or more systems for detecting the thickness of the workpiece and/or heights of features thereon. For example, the laser system may incorporate systems (or components thereof) for interferometric depth measurement of the workpiece, as detailed in U.S. patent application Ser. No. 14/676,070, filed on Apr. 1, 2015, the entire disclosure of which is incorporated by reference herein. Such depth or thickness information may be utilized by the controller to control the output beam shape to optimize the processing (e.g., cutting or welding) of the workpiece, e.g., in accordance with records in the database corresponding to the type of material being processed. 
       FIGS. 22A and 22B  depict exemplary cutting scenarios in accordance with embodiments of the invention. In various embodiments of the invention, the laser system  2000  is utilized to make cuts of differing depths and/or different sizes in a workpiece  2200  and/or to make a consistently sized cut within a workpiece  2200  having a variable thickness. As shown, the output beam shape may have a highly focused spot for shallow cuts and be gradually or substantially abruptly varied to have a defocused spot and/or annular shape (and/or spot with two or more distinct peaks in intensity) for deeper cuts necessitated by thicker regions on the workpiece  2200  and/or changes in the angle between the processing head  2030  and the workpiece  2200 . For example, as shown in  FIG. 22A , the output beam may strike the workpiece  2200  at an angle substantially perpendicular to the surface of the workpiece  2200 , and the output beam may have the shape of a highly focused spot in order to make a relatively shallow cut through all or a portion of the thickness of workpiece  2200 . As also shown in  FIG. 22A , the shape of the beam may be altered to a defocused spot or an annular shape to make a larger-width cut into the workpiece  2200  and/or when the angle between the output beam and the surface of the workpiece  2200  is altered (e.g., decreased) such that the distance through the workpiece  2200  along the output beam direction is increased. 
     In various embodiments, as shown in  FIG. 22B , the angle of the processing head  2030  (and thus the output beam) may be kept constant (e.g., substantially vertical) as the topology, thickness, and/or surface angle of the workpiece  2200  varies during relative motion between the beam and the workpiece  2200 , and the controller controls the beam shape according to the effective thickness of the workpiece  2200  (i.e., the depth of the cut required to cut through or to a specified distance within the workpiece  2200 ) presented to the processing head  2030  at various processing points or over the processing path. For example, the thickness of workpiece  2200  presented to processing head  2030  on the left side of  FIG. 22B  is larger than that on the right side of  FIG. 22B  due to, e.g., the topology of the surface, and the beam shape is adjusted accordingly. Such arrangements obviate the need for the processing head  2030  and/or the output beam to be repositioned to present a consistent angle between the beam and the workpiece surface. Thus, complex robotics and/or other equipment for the angular repositioning of the processing head, and the cost and complexity concomitant therewith, may be avoided. 
     In various embodiments of the invention, the laser system is utilized to weld one or more workpieces while minimizing or substantially eliminating the need to scan the output beam over the surface of the workpiece(s).  FIGS. 23A-23D  depict an exemplary welding sequence in accordance with embodiments of the invention. As shown, an output beam shape  2300  is varied during a spot weld from a larger-area annular shape ( FIG. 23A ) to a smaller annulus ( FIG. 23B ) to a large focused spot ( FIG. 23C ) to a smaller-area focused spot ( FIG. 23D ) in order to weld together two workpieces  2310 ,  2320  without the need for relative motion between the output beam and the workpieces. In this manner, a uniform weld larger than the spot size  2300  in  FIG. 23D  (and/or at least as large as the outer boundary of the spot size  2300  in  FIG. 23A ) is formed between the two workpieces  2310 ,  2320  without the beam being scanned along the surface thereof. In various embodiments, the controller may vary the output power and/or BPP of the beam during the welding process in addition to varying the shape of the output beam. For example, the output power of a highly focused beam shape may be reduced to substantially match the output power of a more defocused and/or annular beam to facilitate the formation of spatially uniform welds. In this manner, large uniform single welds may be produced on a workpiece merely by altering the beam shape (and, in some embodiments, the beam power), obviating the need to form multiple smaller spot welds over the same area (as well as the need to move the workpiece relative to the beam for each weld). Although  FIGS. 23A-23D  depict an exemplary spot welding process, embodiments of the invention include other processing techniques and types of welds, e.g., lap welds and spot welds. In addition, the various welding steps using different beam shapes depicted in  FIGS. 23A-23D  may be performed in any order in accordance with embodiments of the invention. While  FIGS. 23A-23D  depict a series of four different beam shapes utilized for a weld, embodiments of the invention may utilize two, three, or more than four different beam shapes when welding a workpiece. 
     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.