Patent Publication Number: US-11648623-B2

Title: Systems and methods for processing transparent materials using adjustable laser beam focal lines

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of priority under 35 U.S.C. § 371 of International Application No. PCT/US2015/40259, filed on Jul. 14, 2015, which claims the benefit of priority under 35 U.S.C. § 119 of U.S. Provisional Application Ser. No. 62/024,122 filed on Jul. 14, 2014 the content of which is relied upon and incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     In recent years, precision micromachining and its improvement of process development to meet customer demand to reduce the size, weight and material cost of leading-edge devices has led to fast pace growth in high-tech industries in flat panel displays for touch screens, tablets, smartphones and TVs. Ultrafast industrial lasers are becoming important tools for applications requiring high precision micromachining. 
     There are various known ways to cut glasses. In conventional laser glass cutting processes, the separation of glass relies on laser scribing or perforation followed by separation with mechanical force or thermal stress-induced crack propagation. Nearly all current laser cutting techniques exhibit one or more shortcomings. For example, glass cutting by laser processes employing Gaussian laser beams require a large number of pulses to create the desired damage lines within the glass substrate due to the tight focus of the laser beam. Such laser cutting processes may be time consuming and therefore limit throughput. 
     SUMMARY 
     The embodiments disclosed herein relate to methods and systems that create small (few micron and smaller) “holes” in transparent materials (glass, sapphire, etc.) for the purpose of drilling, cutting, separating, perforating, or otherwise processing the materials. More particularly, an ultrashort (i.e., from 10 −10  to 10 −15  second) pulse laser beam (wavelengths such as 1064, 532, 355 or 266 nanometers) is focused to a line focus having an energy density above the threshold needed to create a defect in the region of focus at the surface of or within the transparent material. The length and diameter of the line focus is adjusted according to the type and thickness of the transparent material. By repeating the process, a series of laser-induced defects aligned along a predetermined path can be created. By spacing the laser-induced features sufficiently close together, a controlled region of mechanical weakness within the transparent material can be created and the transparent material can be precisely fractured or separated (immediately, or later with additional mechanical or thermal separation step) along the path defined by the series of laser-induced defects. In the case of high internal stress materials such as chemically strengthened glasses, the material may immediately fracture and separate along the path defined by the laser induced defects. In the case of low stress materials such as glasses made for TFT (thin film transistor) display applications, an additional separation step may be needed. Hence the ultrashort, line focus laser pulse(s) may be optionally followed by a carbon dioxide (CO 2 ) laser or other source of thermal stress to effect fully automated separation of a transparent material or part from a substrate, for example. 
     In one embodiment, a system for processing a transparent material includes a laser source operable to emit a pulsed laser beam, and an optical assembly disposed within an optical path of the pulsed laser beam. The optical assembly is configured to transform the pulsed laser beam into a laser beam focal line having an adjustable length and an adjustable diameter. At least a portion of the laser beam focal line is operable to be positioned within a bulk of the transparent material such that the laser beam focal line generates an induced multi-photon absorption within the transparent material. The induced multi-photon absorption produces a material modification within the transparent material along the laser beam focal line. 
     In another embodiment, a method of processing a transparent material includes focusing a pulsed laser beam to form a laser beam focal line along a beam propagation direction, wherein the laser beam focal line has a length and a diameter. The method further includes adjusting at least one of the length of the laser beam focal line and the diameter of the laser beam focal line, and directing the laser beam focal line into the transparent material such that at least a portion of the laser beam focal line is within a bulk of the material. The laser beam focal line generates an induced multi-photon absorption within the transparent material. The induced multi-photon absorption produces a material modification within the material along the laser beam focal line. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing will be apparent from the following more particular description of the example embodiments, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the representative embodiments. 
         FIG.  1    is a schematic illustration of a stack of three layers: a thin material A facing the laser energy, a modified interface, and a thick material B, the modified interface disrupting the laser energy form interacting with the portion of the stack on the side of the modified interface remote from the laser beam; 
         FIGS.  2 A and  2 B  are schematic illustrations of positioning of the laser beam focal line, i.e., laser processing of a material transparent to the laser wavelength due to the induced absorption along the focal line; 
         FIG.  3 A  is a schematic illustration of an optical assembly for laser processing; 
         FIGS.  3 B- 1 ,  3 B- 2 ,  3 B- 3 , and  3 B- 4    illustrate various possibilities for processing the substrate by forming the laser beam focal line at different positions within the transparent material relative to the substrate; 
         FIG.  4    is a schematic illustration of a second optical assembly for laser processing; 
         FIGS.  5 A and  5 B  are schematic illustrations of a third optical assembly for laser processing; 
         FIG.  6 A  is a schematic illustration of a fourth optical assembly for laser processing; 
         FIG.  6 B  is a schematic illustration of an axicon for laser processing; 
         FIG.  6 C  is a schematic illustration of a fifth optical assembly for laser processing; 
         FIG.  6 D  is a schematic illustration of a sixth optical assembly for laser processing; 
         FIG.  6 E  is a schematic illustration of a seventh optical assembly for laser processing; 
         FIG.  6 F  is a schematic illustration of a eighth optical assembly for laser processing; 
         FIG.  6 G  is a schematic illustration of a ninth optical assembly for laser processing; 
         FIG.  7    is a graph of laser emission as a function of time for a picosecond laser. Each emission is characterized by a pulse “burst” which may contain one or more sub-pulses. The frequency of the bursts is the repetition rate of the laser, typically about 100 kHz (10 μsec). The time between sub-pulses is much shorter, e.g., about 20 nanoseconds (nsec); 
         FIG.  8    is a comparison between a focused Gaussian beam and a Bessel beam incident upon a glass-air-glass composite structure; 
         FIG.  9    is a schematic illustration of stacking with transparent protective layers to cut multiple sheets while reducing abrasion or contamination; 
         FIG.  10    is a schematic illustration of an air gap and cutting of encapsulated devices; 
         FIG.  11    is a schematic illustration of cutting of interposers or windows with laser perforation then etch or laser perforation and CO 2  laser release; 
         FIG.  12    is a schematic illustration of cutting an article such as electrochromic glass coated with transparent conductive layers (e.g. indium tin oxide (ITO)); and 
         FIG.  13    is a schematic illustration of precision cutting of some layers in a stack while not damaging others. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments described herein relate to methods and systems for optically producing high precision cuts in or through transparent materials. Sub-surface damage from the cutting process may be limited to the order of 60 microns in depth or less, and the cuts may produce only low debris. Cutting of a transparent material with a laser in accordance with the present disclosure may also be referred to herein as drilling or laser drilling or laser processing. A material is substantially transparent to the laser wavelength when the absorption is less than about 10%, preferably less than about 1% per mm of material depth at this wavelength. 
     Generally, a laser beam is transformed to a laser beam focus line that is positioned within the bulk of a material, such as glass, to create damage lines within the material. The material may then be separated along these damage lines. The laser beam focus line may also be utilized to fabricate holes in a material, such as hole in an interposer of a semiconductor device assembly. Systems and methods for adjusting the length and the diameter of the laser line focus are described herein. The length and/or diameter of the laser line focus may be adjusted according to different types of materials as well as materials of different thicknesses. 
     In accordance with methods described below, in a single pass, a laser can be used to create highly controlled full line perforation through the material, with extremely little (&lt;75 μm, often &lt;50 μm) subsurface damage and debris generation. This is in contrast to the typical use of spot-focused laser to ablate material, where multiple passes are often necessary to completely perforate the glass thickness, large amounts of debris are formed from the ablation process, and more extensive sub-surface damage (&gt;100 μm) and edge chipping occur. 
     Thus, it is possible to create a microscopic (i.e., &lt;0.5 μm and &gt;100 nm in diameter) elongated “hole” (also called a perforation or a defect line) in transparent material using a single high energy burst pulse. According to the exemplary embodiments described herein a typical perforation will have a diameter of &gt;100 nm and less than 5 micrometer, for example 0.2 to 2 microns, 0.2 to 1 micron, or therebetween; and a length of 50 microns or greater (e.g., 0.1 mm to 100 mm, 150 microns to 2 mm, or 150 microns to 5 mm, or 150 microns to 10 mm). These perforations, defect regions, damage tracks, or defect lines are generally spaced from 1 to 25 microns apart, in some embodiments 1-15 microns apart (for example, 2-12 microns, 5-10 microns), but in some embodiments 15-25 microns apart. These individual perforations can be created at rates of several hundred kilohertz (several hundred thousand perforations per second, for example). Thus, with relative motion between the source and the material these perforations can be placed adjacent to one another (spatial separation varying from sub-micron to several microns as desired). This spatial separation is selected in order to facilitate cutting. In some embodiments, the defect line is a “through hole”, which is a hole or an open channel that extends from the top to the bottom of the transparent material. In some embodiments the defect line may not be a continuous channel, and may be blocked or partially blocked by portions or sections of solid material (e.g., glass). As defined herein, the internal diameter of the defect line is the internal diameter of the open channel or the air hole. For example, in the embodiments described herein the internal diameter of the defect line is &lt;500 nm, for example ≤400 nm, or ≤300 nm. The disrupted or modified area (e.g., compacted, melted, or otherwise changed) of the material surrounding the holes in the embodiments disclosed herein, preferably has diameter of &lt;50 μm (e.g., &lt;10 μm). 
     Micromachining and selective cutting of a stack of transparent materials is accomplished with precise control of the depth of cut through selection of an appropriate laser source and wavelength along with beam delivery optics, and the placement of a beam disruption element at the boundary of a desired layer. The beam disruption element may be a layer of material or an interface. The beam disruption element may be referred to herein as a laser beam disruption element, disruption element or the like. Embodiments of the beam disruption element may be referred to herein as a beam disruption layer, laser beam disruption layer, disruption layer, beam disruption interface, laser beam disruption interface, disruption interface, or the like. 
     The beam disruption element reflects, absorbs, scatters, defocuses or otherwise interferes with an incident laser beam to inhibit or prevent the laser beam from damaging or otherwise modifying underlying layers in the stack. In one embodiment, the beam disruption element underlies the layer of transparent material in which laser drilling will occur. As used herein, the beam disruption element underlies the transparent material when placement of the beam disruption element is such that the laser beam must pass through the transparent material before encountering the beam disruption element. The beam disruption element may underlie and be directly adjacent to the transparent layer in which laser drilling will occur. Stacked materials can be micromachined or cut with high selectivity by inserting a layer or modifying the interface such that a contrast of optical properties exists between different layers of the stack. By making the interface between materials in the stack more reflective, absorbing, and/or scattering at the laser wavelengths of interest, cutting can be confined to one portion or layer of the stack. 
     The wavelength of the laser is selected so that the material within the stack to be laser processed (drilled, cut, ablated, damaged or otherwise appreciably modified by the laser) is transparent to the laser wavelength. In one embodiment, the material to be processed by the laser is transparent to the laser wavelength if it absorbs less than 10% of the intensity of the laser wavelength per mm of thickness of the material. In another embodiment, the material to be processed by the laser is transparent to the laser wavelength if it absorbs less than 5% of the intensity of the laser wavelength per mm of thickness of the material. In still another, the material to be processed by the laser is transparent to the laser wavelength if it absorbs less than 2% of the intensity of the laser wavelength per mm of thickness of the material. In yet another embodiment, the material to be processed by the laser is transparent to the laser wavelength if it absorbs less than 1% of the intensity of the laser wavelength per mm of thickness of the material. 
     The selection of the laser source is further predicated on the ability to induce multi-photon absorption (MPA) in the transparent material. MPA is the simultaneous absorption of multiple photons of identical or different frequencies in order to excite a material from a lower energy state (usually the ground state) to a higher energy state (excited state). The excited state may be an excited electronic state or an ionized state. The energy difference between the higher and lower energy states of the material is equal to the sum of the energies of the two or more photons. MPA is a nonlinear process that is several orders of magnitude weaker than linear absorption. In the case of two-photon absorption, it differs from linear absorption in that the strength of absorption depends on the square of the light intensity, thus making it a nonlinear optical process. At ordinary light intensities, MPA is negligible. If the light intensity (energy density) is extremely high, such as in the region of focus of a laser source (particularly a pulsed laser source), MPA becomes appreciable and leads to measurable effects in the material within the region where the energy density of the light source is sufficiently high. Within the focal region, the energy density may be sufficiently high to result in ionization, breaking of molecular bonds, and vaporization of material. 
     At the atomic level, the ionization of individual atoms has discrete energy requirements. Several elements commonly used in glass (e.g., Si, Na, K) have relatively low ionization energies (˜5 eV). Without the phenomenon of MPA, a wavelength of about 248 nm would be required to create linear ionization at ˜5 eV. With MPA, ionization or excitation between states separated in energy by ˜5 eV can be accomplished with wavelengths longer than 248 nm. For example, photons with a wavelength of 532 nm have an energy of ˜2.33 eV, so two photons with wavelength 532 nm can induce a transition between states separated in energy by ˜4.66 eV in two-photon absorption (TPA), for example. 
     Thus, atoms and bonds can be selectively excited or ionized in the regions of a material where the energy density of the laser beam is sufficiently high to induce nonlinear TPA of a laser wavelength having half the required excitation energy, for example. MPA can result in a local reconfiguration and separation of the excited atoms or bonds from adjacent atoms or bonds. The resulting modification in the bonding or configuration can result in non-thermal ablation and removal of matter from the region of the material in which MPA occurs. This removal of matter creates a structural defect (e.g. a defect line or “perforation”) that mechanically weakens the material and renders it more susceptible to cracking or fracturing upon application of mechanical or thermal stress. By controlling the placement of perforations, a contour or path along which cracking occurs can be precisely defined and precise micromachining of the material can be accomplished. The contour defined by a series of perforations may be regarded as a fault line and corresponds to a region of structural weakness in the material. In one embodiment, micromachining includes separation of a part from the material processed by the laser, where the part has a precisely defined shape or perimeter determined by a closed contour of perforations formed through MPA effects induced by the laser. As used herein, the term closed contour refers to a perforation path formed by the laser line, where the path intersects with itself at some location. An internal contour is a path formed where the resulting shape is entirely surrounded by an outer portion of material. 
     Perforations can be accomplished with a single “burst” of high energy short duration pulses spaced close together in time. The laser pulse duration may be 10 −10  s or less, or 10 −11  s or less, or 10 −12  s or less, or 10 −13  s or less. These “bursts” may be repeated at high repetition rates (e.g. kHz or MHz). The perforations may be spaced apart and precisely positioned by controlling the velocity of a substrate or stack relative to the laser through control of the motion of the laser and/or the substrate or stack. 
     As an example, in a thin transparent substrate moving at 200 mm/sec exposed to a 100 kHz series of pulses, the individual pulses would be spaced 2 microns apart to create a series of perforations separated by 2 microns. This defect (perforation) spacing is sufficient close to allow for mechanical or thermal separation along the contour defined by the series of perforations. 
     Thermal Separation: 
     In some cases, a fault line created along a contour defined by a series of perforations or defect lines is not enough to separate the part spontaneously, and a secondary step may be necessary. If so desired, a second laser can be used to create thermal stress to separate it, for example. In the case of sapphire, separation can be achieved, after the creation of a fault line, by application of mechanical force or by using a thermal source (e.g., an infrared laser, for example a CO 2  laser or a CO laser) to create thermal stress and force a part to separate from a substrate. The optional thermal separation can be achieved, for example, with a defocused CO 2  laser continuous wave (cw) laser emitting at 10.6 μm and with power adjusted by controlling its duty cycle. Focus change (i.e., extent of defocusing up to and including focused spot size) is used to vary the induced thermal stress by varying the spot size. Defocused laser beams include those laser beams that produce a spot size larger than a minimum, diffraction-limited spot size on the order of the size of the laser wavelength. For example, spot sizes of about 7 mm, 2 mm and 20 mm can be used for CO 2  lasers, for example, whose emission wavelength is much smaller at 10.6 μm. Distance between adjacent defect lines  120  along the direction of the fault lines  110  can be, for example, greater than 0.5 μm and less than or equal to about 15 or 20 μm in some embodiments. Another option is to have the CO 2  laser only start the separation and then finish the separation manually, i.e. by applying mechanical force to separate the part along the laser-perforated contour. 
     Etching: 
     Acid etching can be used, for example, to separate a workpiece having a glass layer, for example. To enlarge the holes to a size useful for metal filling and electrical connections, parts can be acid etched. In one embodiment, for example, the acid used can be 10% HF/15% HNO 3  by volume. The parts can be etched for 53 minutes at a temperature of 24-25° C. to remove about 100 μm of material, for example. The parts can be immersed in this acid bath, and ultrasonic agitation at a combination of 40 kHz and 80 kHz frequencies can used to facilitate penetration of fluid and fluid exchange in the holes. In addition, manual agitation of the part within the ultrasonic field can be made to prevent standing wave patterns from the ultrasonic field from creating “hot spots” or cavitation related damage on the part. The acid composition and etch rate can be intentionally designed to slowly etch the part—a material removal rate of only 1.9 um/minute, for example. An etch rate of less than about 2 μm/minute, for example, allows acid to fully penetrate the narrow holes and agitation to exchange fresh fluid and remove dissolved material from the holes which are initially very narrow. 
     In the embodiment shown in  FIG.  1   , precise control of the depth of cut in a multilayer stack is achieved by inclusion of a beam disruption interface (labeled “modified interface”). The beam disruption interface prevents the laser radiation from interacting with portions of the multilayer stack beyond the position of the disruption interface. Although embodiments are shown and described herein as utilizing a multilayer stack, it should be understood that embodiments are not limited thereto. The laser cutting process using the laser beam line focus attributes described herein may be applied to a single layer of material, such as a glass substrate. 
     In one embodiment, the beam disruption element is positioned immediately below the layer of the stack in which modification via two-photon absorption will occur. Such a configuration is shown in  FIG.  1   , where the beam disruption element is a modified interface positioned immediately below material A and material A is the material in which formation of perforations through the two-photon absorption mechanism described herein will occur. As used herein, reference to a position below or lower than another position assumes that the top or uppermost position is the surface of the multilayer stack upon which the laser beam is first incident. In  FIG.  1   , for example, the surface of material A that is closest to the laser source is the top surface and placement of the beam disruption element below material A means that the laser beam traverses material A before interacting with the beam disruption element. 
     The disruption element has different optical properties than the material to be cut. For example, the beam disruption element may be a defocusing element, a scattering element, a translucent element, or a reflective element. A defocusing element is an interface or a layer comprising a material that prevents the laser light from forming the laser beam focal line on or below the defocusing element. The defocusing element may be comprised of a material or interface with refractive index inhomogeneities that scatter or perturb the wavefront of the optical beam. A translucent element is an interface or layer of material that allows light to pass through, but only after scattering or attenuating the laser beam to lower the energy density sufficiently to prevent formation of a laser beam focal line in portions of the stack on the side of the translucent element that are remote from the laser beam. In one embodiment, the translucent element effects scattering or deviating of at least 10% of the light rays of the laser beam. 
     More specifically, the reflectivity, absorptivity, defocusing, attenuation, and/or scattering of the disruption element can be employed to create a barrier or impediment to the laser radiation. The laser beam disruption element can be created by several means. If the optical properties of the overall stack system are not of a concern, then one or more thin films can be deposited as a beam disruption layer(s) between the desired two layers of the stack, where the one or more thin films absorb, scatter, defocus, attenuate, reflects, and/or dissipates more of the laser radiation than the layer immediately above it to protect layers below the thin film(s) from receiving excessive energy density from the laser source. If the optical properties of the entire stack system do matter, the beam disruption element can be implemented as a notch filter. This can be done by several methods:
         a) creating structures at the disruption layer or interface (e.g. via thin film growth, thin film patterning, or surface pattering) such that diffraction of incident laser radiation is at a particular wavelength or range of wavelengths occurs;   b) creating structures at the disruption layer or interface (e.g. via thin film growth, thin film patterning, or surface pattering) such that scattering of incident laser radiation occurs (e.g. a textured surface);   c) creating structures at the disruption layer or interface (e.g. via thin film growth, thin film patterning, or surface pattering) such that attenuated phase-shifting of laser radiation occurs; and   d) creating a distributed Bragg reflector via thin-film stack at the disruption layer or interface to reflect only laser radiation.       

     It is not necessary that the absorption, reflection scattering, attenuation, defocusing etc. of the laser beam by the disruption element be complete. The effect of the disruption element, when utilized, on the laser beam should be sufficient to reduce the energy density or intensity of the focused laser beam to a level below the threshold required for cutting, ablation, perforating etc. of the layers in the stack protected by (underlying) the disruption element. In one embodiment, the disruption element reduces the energy density or intensity of the focused laser beam to a level below the threshold needed to induce two-photon absorption. The disruption layer or disruption interface may be configured to absorb, reflect, or scatter the laser beam, where the absorption, reflection, or scattering are sufficient to reduce the energy density or intensity of the laser beam transmitted to the carrier (or other underlying layer) to a level below the level needed to induce nonlinear absorption in the carrier or underlying layer. 
     Turning to  FIGS.  2 A and  2 B , a method of laser drilling a material includes focusing a pulsed laser beam  2  into a laser beam focal line  2   b , viewed along the beam propagation direction. Laser beam focal line  2   b  is a region of high energy density. As shown in  FIG.  3   , laser  3  (not shown) emits laser beam  2 , which has a portion  2   a  incident to optical assembly  6 . The optical assembly  6  turns the incident laser beam into an extensive laser beam focal line  2   b  on the output side over a defined expansion range along the beam direction (length  1  of the focal line). 
     Embodiments of the present disclosure utilize non-diffracting beams (“NDB”) to form the laser beam focal line  2   b . Typically laser processing has used Gaussian laser beams. The tight focus of a laser beam with a Gaussian intensity profile has a Rayleigh range ZR given by: 
     
       
         
           
             
               
                 
                   
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     The Rayleigh range represents the distance over which the spot size w 0  of the beam will increase by √{square root over (2)} in a material of refractive index η 0  at wavelength η 0 . This limitation is imposed by diffraction. Note in Eq. (1) that the Rayleigh range is related directly to the spot size, thereby leading to the conclusion that a beam with a tight focus (i.e. small spot size) cannot have a long Rayleigh range. Such a beam will maintain this small spot size only for a very short distance. This also means that if such a beam is used to drill through a material by changing the depth of the focal region, the rapid expansion of the spot on either side of the focus will require a large region free of optical distortion that might limit the focus properties of the beam. Such a short Rayleigh range also requires multiple pulses to cut through a thick sample. 
     However, embodiments of the present disclosure utilize NDBs instead of the optical Gaussian beams discussed above. Non-diffracting beams may propagate for a considerable distance before diffraction effects inevitably limit the beam focus. Although an infinite NDB does not suffer from diffractive effects, a physically realizable NDB will have a limited physical extent. The central lobe of the beam can be quite small in radius and thus produce a high intensity beam. There are several types of NDBs including, but not limited to, Bessel beams, Airy beams, Weber beams and Mathieu beams whose field profiles are typically given by special functions which decay more slowly in the transverse direction than a Gaussian function. 
     It should be understood that, although NDBs described are described herein in the context of Bessel beams, embodiments are not limited thereto. The central spot size of a Bessel beam is given by: 
                     d   =     2   ⁢       2.405     λ   o           NA   ⁢   2   ⁢   n     o           ,           Eq   .           (   2   )                 
where NA is the numerical aperture given by the cone of plane waves making an angle of β with the optical axis (see  FIG.  6 B ). A key difference between Bessel beams and Gaussian beams is that Rayleigh range is given by:
 
                       Z   max     =          ⁢   Dd       4   ⁢   λ         ,           Eq   .           (   3   )                 
where D is the finite extent of the beam imposed by some aperture or optical element. It is therefore shown that the aperture size D may be used to increase the Rayleigh range beyond the limit imposed by the size of the central spot. A practical method for generating Bessel beams is to pass a Gaussian beam through an axicon or an optical element with a radially linear phase element as shown in  FIG.  6 B .
 
     In general, the optical method of forming the line focus (i.e., the laser beam focal line) can take multiple forms, such as, without limitation, using donut shaped laser beams and spherical lenses, axicon lenses, diffractive elements, or other methods to form the linear region of high intensity. The type of laser (picosecond, femtosecond, and the like) and wavelength (IR, visible, UV, and the like) may also be varied, as long as sufficient optical intensities are reached to create breakdown of the substrate material. 
     The laser power and lens focal length (which determines the line focus length and hence power density) are parameters that ensure full penetration of the substrate for cutting and drilling, while either purposefully generating cracks between the perforations (damage tracks) in the case of cutting, or possibly trying to suppress micro-cracking in the case of drilling. Accordingly, the dimensions of the line focus formed in the substrate should be precisely controlled. 
     Embodiments of the present disclosure are directed to systems and methods for adjusting both the diameter and the length of the line focus, enabling, with a single laser machine, the cutting of thin and thick materials, as well as the machining of materials that crack easily versus materials that have very high optical thresholds for material modification. This allows a single system to be rapidly adapted for cutting and drilling different substrates, thereby increasing manufacturing efficiency and improving capital utilization. 
     Referring once again to  FIGS.  2 A and  2 B , layer  1  is the layer of a multilayer stack in which internal modifications by laser processing and two-photon absorption is to occur. Layer  1  is a component of a larger workpiece, which typically includes a substrate or carrier upon which a multilayer stack is formed. Layer  1  is the layer within the multilayer stack in which holes, cuts, or other features are to be formed through two-photon absorption assisted ablation or modification as described herein. The layer  1  is positioned in the beam path to at least partially overlap the laser beam focal line  2   b  of laser beam  2 . Reference  1   a  designates the surface of the layer  1  facing (closest or proximate to) the optical assembly  6  or the laser, respectively, reference  1   b  designates the reverse surface of layer  1  (the surface remote, or further away from, optical assembly  6  or the laser). The thickness of the layer  1  (measured perpendicularly to the planes  1   a  and  1   b , i.e., to the substrate plane) is labeled with d. 
     As  FIG.  2 A  depicts, layer  1  is aligned perpendicular to the longitudinal beam axis and thus behind the same focal line  2   b  produced by the optical assembly  6  (the substrate is perpendicular to the plane of the drawing). Viewed along the beam direction, the layer  1  is positioned relative to the focal line  2   b  in such a way that the focal line  2   b  (viewed in the direction of the beam) starts before the surface  1   a  of the layer  1  and stops before the surface  1   b  of the layer  1 , i.e. focal line  2   b  terminates within the layer  1  and does not extend beyond surface  1   b . In the overlapping area of the laser beam focal line  2   b  with layer  1 , i.e. in the portion of layer  1  overlapped by focal line  2   b , the extensive laser beam focal line  2   b  generates nonlinear absorption in layer  1 . (Assuming suitable laser intensity along the laser beam focal line  2   b , which intensity is ensured by adequate focusing of laser beam  2  on a section of length  1  (i.e. a line focus of length  1 ), which defines an extensive section  2   c  (aligned along the longitudinal beam direction) along which an induced nonlinear absorption is generated in the layer  1 .) The induced nonlinear absorption results in formation of a defect line or crack in layer  1  along section  2   c . The defect or crack formation is not only local, but rather may extend over the entire length of the extensive section  2   c  of the induced absorption. The length of section  2   c  (which corresponds to the length of the overlapping of laser beam focal line  2   b  with layer  1 ) is labeled with reference L. The average diameter or extent of the section of the induced absorption  2   c  (or the sections in the material of layer  1  undergoing the defect line or crack formation) is labeled with reference D. This average extent D may correspond to the average diameter δ of the laser beam focal line  2   b , that is, an average spot diameter in a range of between about 0.1 μm and about 5 μm. 
     As  FIG.  2 A  shows, the layer  1  (which is transparent to the wavelength λ of laser beam  2 ) is locally heated due to the induced absorption along the focal line  2   b . The induced absorption arises from the nonlinear effects associated with the high intensity (energy density) of the laser beam within focal line  2   b .  FIG.  2 B  illustrates that the heated layer  1  will eventually expand so that a corresponding induced tension leads to micro-crack formation, with the tension being the highest at surface  1   a.    
     Representative optical assemblies  6 , which can be applied to generate the focal line  2   b , as well as a representative optical setup, in which these optical assemblies can be applied, are described below. All assemblies or setups are based on the description above so that identical references are used for identical components or features or those which are equal in their function. Therefore only the differences are described below. 
     To insure high quality (regarding breaking strength, geometric precision, roughness and avoidance of re-machining requirements) of the surface of separation after cracking along the contour defined by the series of perforations, the individual focal lines used to form the perforations that define the contour of cracking should be generated using the optical assembly described below (hereinafter, the optical assembly is alternatively also referred to as laser optics). The roughness of the separated surface is determined primarily by the spot size or the spot diameter of the focal line. A roughness of a surface can be characterized, for example, by an Ra surface roughness statistic (roughness arithmetic average of absolute values of the heights of the sampled surface). In order to achieve a small spot size of, for example, 0.5 μm to 2 μm in case of a given wavelength λ of laser  3  (interaction with the material of layer  1 ), certain requirements must usually be imposed on the numerical aperture of laser assembly  6 . 
     In order to achieve the required numerical aperture, the optics must, on the one hand, dispose of the required opening for a given focal length, according to the known Abbé formulae (N.A.=n sin (theta), n: refractive index of the material to be processed, theta: half the aperture angle; and theta=arctan (D/2f); D: aperture, f: focal length). On the other hand, the laser beam must illuminate the optics up to the required aperture, which is typically achieved by means of beam widening using widening telescopes between the laser and focusing optics. 
     The spot size should not vary too strongly for the purpose of a uniform interaction along the focal line. This can, for example, be ensured (see the embodiment below) by illuminating the focusing optics only in a small, circular area so that the beam opening and thus the percentage of the numerical aperture only varies slightly. 
       FIG.  3 A  depicts one method of generating a line focus. According to  FIG.  3 A  (section perpendicular to the substrate plane at the level of the central beam in the laser beam bundle of laser radiation  2 ; here, too, laser beam  2  is perpendicularly incident to the layer  1 , i.e. incidence angle β is 0° so that the focal line  2   b  or the extensive section of the induced absorption  2   c  is parallel to the substrate normal), the laser radiation  2   a  emitted by laser  3  is first directed onto a circular aperture  8  which is completely opaque to the laser radiation used. Aperture  8  is oriented perpendicular to the longitudinal beam axis and is centered on the central beam of the depicted beam bundle  2   a . The diameter of aperture  8  is selected in such a way that the beam bundles near the center of beam bundle  2   a  or the central beam (here labeled with  2   a Z) hit the aperture and are completely blocked by it. Only the beams in the outer perimeter range of beam bundle  2   a  (marginal rays, here labeled with  2   a R) are not blocked due to the reduced aperture size compared to the beam diameter, but pass aperture  8  laterally and hit the marginal areas of the focusing optic elements of the optical assembly  6 , which, in this embodiment, is designed as a spherically cut, bi-convex lens  7 . 
     Lens  7  is centered on the central beam and is designed as a non-corrected, bi-convex focusing lens in the form of a common, spherically cut lens. The spherical aberration of such a lens may be advantageous. As an alternative, aspheres or multi-lens systems deviating from ideally corrected systems, which do not form an ideal focal point but a distinct, elongated focal line of a defined length, can also be used (i.e., lenses or systems which do not have a single focal point). The zones of the lens thus focus along a focal line  2   b , subject to the distance from the lens center. The diameter of aperture  8  across the beam direction is approximately 90% of the diameter of the beam bundle (defined by the distance required for the intensity of the beam to decrease to 1/e of the peak intensity) and approximately 75% of the diameter of the lens of the optical assembly  6 . The focal line  2   b  of a non-aberration-corrected spherical lens  7  generated by blocking out the beam bundles in the center is thus used.  FIG.  3 A  shows the section in one plane through the central beam, the complete three-dimensional bundle can be seen when the depicted beams are rotated around the focal line  2   b.    
     One potential disadvantage of this type of focal line is that the conditions (spot size, laser intensity) may vary along the focal line (and thus along the desired depth in the material) and therefore the desired type of interaction (no melting, induced absorption, thermal-plastic deformation up to crack formation) may possibly occur only in selected portions of the focal line. This means in turn that possibly only a part of the incident laser light is absorbed by the material to be processed in the desired way. In this way, the efficiency of the process (required average laser power for the desired separation speed) may be impaired, and the laser light may also be transmitted into undesired regions (parts or layers adherent to the substrate or the substrate holding fixture) and interact with them in an undesirable way (e.g. heating, diffusion, absorption, unwanted modification). 
       FIG.  3 B- 1 - 4    show (not only for the optical assembly in  FIG.  3 A , but also for any other applicable optical assembly  6 ) that the position of laser beam focal line  2   b  can be controlled by suitably positioning and/or aligning the optical assembly  6  relative to layer  1  as well as by suitably selecting the parameters of the optical assembly  6 : As  FIG.  3 B -illustrates, the length  1  of the focal line  2   b  can be adjusted in such a way that it exceeds the layer thickness d (here by factor  2 ). If layer  1  is placed (viewed in longitudinal beam direction) centrally to focal line  2   b , an extensive section of induced absorption  2   c  is generated over the entire substrate thickness. 
     In the case shown in  FIG.  3 B- 2   , a focal line  2   b  of length  1  is generated which corresponds more or less to the layer thickness d. Since layer  1  is positioned relative to line  2   b  in such a way that line  2   b  starts at a point outside the material to be processed, the length L of the section of extensive induced absorption  2   c  (which extends here from the substrate surface to a defined substrate depth, but not to the reverse surface  1   b ) is smaller than the length  1  of focal line  2   b .  FIG.  3 B- 3    shows the case in which the layer  1  (viewed along the beam direction) is positioned above the starting point of focal line  2   b  so that, as in  FIG.  3 B- 2   , the length  1  of line  2   b  is greater than the length L of the section of induced absorption  2   c  in layer  1 . The focal line thus starts within the layer  1  and extends beyond the reverse surface  1   b .  FIG.  3 B- 4    shows the case in which the focal line length  1  is smaller than the layer thickness d so that—in the case of a central positioning of the substrate relative to the focal line viewed in the direction of incidence—the focal line starts near the surface  1   a  within the layer  1  and ends near the surface  1   b  within the layer  1  (e.g. 1=0.75·d). The laser beam focal line  2   b  can have a length  1  in a range of between about 0.1 mm and about 100 mm or in a range of between about 0.1 mm and about 10 mm, for example. Various embodiments can be configured to have length  1  of about 0.1 mm, 0.2 mm, 0.3 mm, 0.4 mm, 0.5 mm, 0.7 mm, 1 mm, 2 mm, 3 mm or 5 mm, for example. 
     It is particularly advantageous to position the focal line  2   b  in such a way that at least one of surfaces  1   a ,  1   b  is covered by the focal line, so that the section of induced nonlinear absorption  2   c  starts at least on one surface of the layer or material to be processed. In this way it is possible to achieve virtually ideal cuts while avoiding ablation, feathering and particulate generation at the surface. 
       FIG.  4    depicts another applicable optical assembly  6 . The basic construction follows the one described in  FIG.  3 A  so that only the differences are described below. The depicted optical assembly is based the use of optics with a non-spherical free surface in order to generate the focal line  2   b , which is shaped in such a way that a focal line of defined length  1  is formed. For this purpose, aspheres can be used as optic elements of the optical assembly  6 . In  FIG.  4   , for example, a so-called conical prism, also often referred to as axicon, is used. An axicon is a conically cut lens which forms a spot source on a line along the optical axis (or transforms a laser beam into a ring). The layout of such an axicon is principally known to those of skill in the art; the cone angle in the example is 10°. The apex of the axicon labeled here with reference  9  is directed towards the incidence direction and centered on the beam center. Since the focal line  2   b  produced by the axicon  9  starts within its interior, layer  1  (here aligned perpendicularly to the main beam axis) can be positioned in the beam path directly behind axicon  9 . As  FIG.  4    shows, it is also possible to shift layer  1  along the beam direction due to the optical characteristics of the axicon while remaining within the range of focal line  2   b . The section of extensive induced absorption  2   c  in the material of layer  1  therefore extends over the entire depth d. 
     However, the depicted layout is subject to the following restrictions: Since the region of focal line  2   b  formed by axicon  9  begins within the axicon  9 , a significant part of the laser energy is not focused into the section of induced absorption  2   c  of focal line  2   b , which is located within the material, in the situation where there is a separation between axicon  9  and the material to be processed. Furthermore, length  1  of focal line  2   b  is related to the beam diameter through the refractive indices and cone angles of axicon  9 . This is why, in the case of relatively thin materials (several millimeters), the total focal line is much longer than the thickness of the material to be processed, having the effect that much of the laser energy is not focused into the material. 
     For this reason, it may be desirable to use an optical assembly  6  that includes both an axicon and a focusing lens.  FIG.  5 A  depicts such an optical assembly  6  in which a first optical element (viewed along the beam direction) with a non-spherical free surface designed to form an extensive laser beam focal line  2   b  is positioned in the beam path of laser  3 . In the case shown in  FIG.  5 A , this first optical element is an axicon  10  with a cone angle of 5°, which is positioned perpendicularly to the beam direction and centered on laser beam. The apex of the axicon is oriented towards the beam direction. A second, focusing optical element, here the plano-convex lens  11  (the curvature of which is oriented towards the axicon), is positioned in the beam direction at a distance z 1  from the axicon  10 . The distance z 1 , in this case approximately 300 mm, is selected in such a way that the laser radiation formed by axicon  10  is circularly incident on the outer radial portion of lens  11 . Lens  11  focuses the circular radiation on the output side at a distance z 2 , in this case approximately 20 mm from lens  11 , on a focal line  2   b  of a defined length, in this case 1.5 mm. The effective focal length of lens  11  is 25 mm in this embodiment. The circular transformation of the laser beam by axicon  10  is labeled with the reference SR. 
       FIG.  5 B  depicts the formation of the focal line  2   b  or the induced absorption  2   c  in the material of layer  1  according to  FIG.  5 A  in detail. The optical characteristics of both elements  10 ,  11  as well as the positioning of them is selected in such a way that the length  1  of the focal line  2   b  in beam direction is exactly identical with the thickness d of layer  1 . Consequently, an exact positioning of layer  1  along the beam direction should be provided to position the focal line  2   b  exactly between the two surfaces  1   a  and  1   b  of layer  1 , as shown in  FIG.  5 B . 
     It is therefore advantageous if the focal line is formed at a certain distance from the laser optics, and if the greater part of the laser radiation is focused up to a desired end of the focal line. As described, this can be achieved by illuminating a primarily focusing element  11  (lens) only circularly (annularly) over a particular outer radial region, which, on the one hand, serves to realize the required numerical aperture and thus the required spot size, and, on the other hand, however, the circle of diffusion diminishes in intensity after the required focal line  2   b  over a very short distance in the center of the spot, as a basically circular spot is formed. In this way, the crack formation is stopped within a short distance in the required substrate depth. A combination of axicon  10  and focusing lens  11  meets this requirement. The axicon acts in two different ways: due to the axicon  10 , a usually round laser spot is sent to the focusing lens  11  in the form of a ring, and the asphericity of axicon  10  has the effect that a focal line is formed beyond the focal plane of the lens instead of a focal point in the focal plane. The length  1  of focal line  2   b  can be adjusted via the beam diameter on the axicon. The numerical aperture along the focal line, on the other hand, can be adjusted via the distance z 1  axicon-lens and via the cone angle of the axicon. In this way, the entire laser energy can be concentrated in the focal line. 
     If the crack formation is intended to continue to the back side of the layer or material to be processed, the circular (annular) illumination still has the advantage that (1) the laser power is used optimally in the sense that most of the laser light remains concentrated in the required length of the focal line, and (2) it is possible to achieve a uniform spot size along the focal line—and thus a uniform separation process along the perforations produced by the focal lines—due to the circularly illuminated zone in conjunction with the desired aberration set by means of the other optical functions. 
     Instead of the plano-convex lens depicted in  FIG.  5 A , it is also possible to use a focusing meniscus lens or another higher corrected focusing lens (asphere, multi-lens system). 
     In order to generate very short focal lines  2   b  using the combination of an axicon and a lens depicted in  FIG.  5 A , a very small beam diameter of the laser beam incident on the axicon may be needed. This has the practical disadvantage that the centering of the beam onto the apex of the axicon must be very precise and that the result is very sensitive to directional variations of the laser (beam drift stability). Furthermore, a tightly collimated laser beam is very divergent, i.e. due to the light deflection the beam bundle becomes blurred over short distances. 
     As shown in  FIG.  6 A , both effects can be avoided by including another lens, a collimating lens  12  in the optical assembly  6 . The additional collimating lens  12  serves to adjust the circular illumination of focusing lens  11  very tightly. The focal length f′ of collimating lens  12  is selected in such a way that the desired circle diameter dr results from distance z 1   a  from the axicon to the collimating lens  12 , which is equal to f′. The desired width br of the ring can be adjusted via the distance z 1   b  (collimating lens  12  to focusing lens  11 ). As a matter of pure geometry, the small width of the circular illumination leads to a short focal line. A minimum can be achieved at distance f′. 
     The optical assembly  6  depicted in  FIG.  6 A  is thus based on the one depicted in  FIG.  5 A  so that only the differences are described below. The collimating lens  12 , here also designed as a plano-convex lens (with its curvature towards the beam direction) is additionally placed centrally in the beam path between axicon  10  (with its apex towards the beam direction), on the one side, and the plano-convex lens  11 , on the other side. The distance of collimating lens  12  from axicon  10  is referred to as z 1   a , the distance of focusing lens  11  from collimating lens  12  as z 1   b , and the distance of the focal line  2   b  from the focusing lens  11  as z 2  (always viewed in beam direction). As shown in  FIG.  6 A , the circular radiation SR formed by axicon  10 , which is incident divergently and under the circle diameter dr on the collimating lens  12 , is adjusted to the required circle width br along the distance z 1   b  for an at least approximately constant circle diameter dr at the focusing lens  11 . In the case shown, a very short focal line  2   b  is intended to be generated so that the circle width br of approx. 4 mm at collimating lens  12  is reduced to approx. 0.5 mm at lens  11  due to the focusing properties of collimating lens  12  (circle diameter dr is 22 mm in the example). 
     In the depicted example it is possible to achieve a length of the focal line  1  of less than 0.5 mm using a typical laser beam diameter of 2 mm, a focusing lens  11  with a focal length f=25 mm, a collimating lens with a focal length f′=150 mm, and choosing distances Z 1   a =Z 1   b =140 mm and Z 2 =15 mm. 
     With reference to  FIG.  6 B , properties of a NDB formed by an axicon  10  will now be described.  FIG.  6 B  schematically depicts a Gaussian laser beam  2  impinging a flat entrance surface of a transmissive axicon  10 . The emergent surface of the axicon  10  deflects the laser beam  2  as shown. The typical energy profile in a plane located at a distance z from the tip of the axicon is given by:
 
 I ( r,z )= Io ( Rz ) Rz 2π k (sin(β)/cos 2(β)) Jo   2 ( kr  sin(β))  Eq. (4.1),
 
 Rz=z *tan(β)  Eq. (4.2).
 
     Here, β is the ray angle created by the axicon  10 , which is a function of the angle of the axicon cone provided by the angled emergent surface and the refractive index of the axicon  10 . Io(Rz) is the irradiance profile of the laser beam  2  illuminating the axicon  10 , which is assumed to be a Gaussian profile, and k is the wavevector k=2π/λ, and Jo denotes a first-order Bessel function. 
     To make the strongest damage tracks, or holes, in the hardest of materials, the diameter of the lone focus should be as small as possible. Based on the formulas above, the full width half maximum (“FWHM”) of the irradiance profile in any plane at some distance z from the apex of the axicon  10  is given by:
 
FWHM=2.52λ/(2π sin(β))  Eq. (4.3).
 
     As can be seen from Eq. (4.3), the diameter of the line focus is related to a single geometric system parameter, the aperture angle β as shown in  FIG.  6 B . 
     From Eq. 4.1, at the center of the line focus, the peak power is given by:
 
 I _peak( z )= Io ( Rz ) Rz 2π k (sin(β)/cos 2(β))  Eq. (4.4).
 
As can be seen in Eq. (4.4), the peak power is a function of the pupil irradiance profile Io(Rz), as well as a function of the aperture angle β.
 
     If we examine where the on-axis intensity decays to approximately one half of its maximum intensity, then the length (or extent along the optical axis) of the line focus can be approximated by:
 
 L˜ 0.8* Rz /sin(β)  Eq. (4.5)
 
Thus the length of the focused line is a function of both the input beam size (Rz) and the aperture angle β.
 
     In a laser cutting machine, the material to be cut may vary in thickness. As an example, such a laser machine may be used to cut glass with thicknesses varying from 0.1 to 2.0 mm. Accordingly, to ensure that it is possible to drill and cut thick material (i.e., glass), the useful portion of the line focus should be set at, for example, at least 2.0 mm by, for instance, spreading the pupil irradiance profile into a larger area. However, by doing so, the peak power density within the line focus will decrease because the maximum value of Io(Rz) decreases. To keep the peak power density greater than the material modification energy density threshold, the aperture angle β should be increased, which means that the FWHM of the line focus will decrease. 
     Therefore, in a system with a fixed choice of optics, the parameters should be adjustable for the most difficult cases. When cutting thinner substrates (e.g. 100 μm thick display glass), much of the laser energy may be wasted if a long line focus is set to allow cutting of thick materials (e.g. stacks of ion exchanged glass). Similarly, if the optics are set to produce a very short and small diameter line focus (high energy density) to cut very thin and hard materials (e.g. sapphire), the optical system may no longer work well for thicker materials (e.g., thick soda lime glass or ion-exchangeable glass substrates). 
     For at least these reasons, it may be desirable for making the irradiance profile Io(Rz) and/or the aperture angle β adjustable. It is desirable to have both parameters adjustable to apply the following strategy: for each glass thickness and material:
         adjust the input irradiance profile to achieve the desired line focus length; and   adjust the aperture angle to set the FWHM (or diameter) of the laser beam at the line focus, keeping the energy density optimal for modification of the given material.       

     It may be desirable to set the FWHM (or diameter) of the line focus  2   b  to be as narrow as possible, which allows the lowest laser power to be used to create the damage tracks within the material and hence provide the most process margin. However, in some cases, it may be desirable to have a larger diameter line focus, which reduces the amount of micro-cracking around the damage tracks. For example, larger diameter spots are helpful in drilling of holes that are subsequently acid-etched, where micro-cracks are not desired as they may create etch asymmetries. The upper limitation on the diameter of the line focus is that, given a maximum laser pulse energy available for a laser source, sufficient energy density must still be reached to allow modification of the material and creation of a damage track. 
     For the length of the line focus  2   b , it is desirable to make it at least equal to but preferentially greater than the thickness of the material, accounting for the fact that per Snell&#39;s law of refraction, the refractive index of the material (e.g. for glass n˜1.5) increases the effective length of the line focus  2   b  within the material itself. Longer focal lines give larger focus tolerance, and also allow various substrate thicknesses to be accommodated. The upper limitation upon the focal line length is again that, given a maximum laser pulse energy available for a laser source, sufficient energy density must still be reached to allow modification of the material and creation of a damage track throughout the thickness of the substrate. 
       FIGS.  6 C and  6 E- 6 G  depict non-limiting optical systems that allow for the adjustment of the length and the FWHM (i.e., the diameter) of the laser beam focal line  2   b  (i.e., line focus).  FIG.  6 C  depicts a system for cutting a material (not shown) using a laser beam focal line  2   b . The system comprises a laser source  3  (not shown) and an optical assembly  6 ′ configured to transform a Gaussian profile laser beam  2  into a Bessel profile laser beam having a focal line  2   b . The optical assembly  6 ′ is disposed within an optical path  1  of the laser beam  2 , and comprises a transparent (i.e. acting as a refractive element) axicon  10 , a first lens element  5  having a first focal length F 1 , and a second lens element  11  (i.e., a focusing lens element) having a second focal length F 2 . 
     The transparent axicon  10  forms a line focus  2   b ′ that is imaged by the first lens element  5  and the second lens element  11 , which act as a telescope that relays and magnifies the line focus  2   b ′ formed by the axicon  10  into the line focus  2   b  that is applied to the material. The magnification of the telescope defined by the first lens element  5  and the second lens element  11  is given by M=F 2 /F 1 , which may be varied by changing one or both of the two lens elements to achieve a different magnification M. The length of the line focus  2   b  gets scaled with the square of the magnification, while the diameter of the line focus in a given z-plane is scaled linearly with magnification. 
     Changing the focal length of the first and/or second lens  5 ,  11  may not be optimal in some applications as both line focus length and width scale together. Assuming that M is the magnification provided by the first and second focal lengths:
 
FWHM 1 =FWHM 0   *M   Eq. (5.1);
 
Length 1 =Length 0   *M   2   Eq. (5.2).
 
     Here FWHM 0  denotes the full-width at half maximum diameter of the line focus formed immediately after the axicon  10 , and FWHM 1  denotes the full-width at half maximum diameter of the line focus formed after the second lens element  11 . Similarly LENGTH 0  denotes the length, or spatial extent along the optical axis, of the line focus formed immediately after the axicon  10 , and LENGTH 1  denotes the length of the line focus formed after the second lens element  11 . If it is assumed that the resulting line focus  2   b  takes the form of a cylinder of length and diameter dimensions Length 1 ×FWHM 1 , then the power (or energy) density inside the cylinder will scale as 1/volume of that object, where volume=(pi/4)*diameter 2 *length. This means the power density will scale as:
 
PowerDensity 1 =PowerDensity 0   /M   4   Eq. (5.3).
 
     Thus, the diameter of the line focus increases linearly with the magnification of the telescope provided by the first and second lenses  5 ,  11 , the length of the line focus  2   b  increases as the square of the magnification, and the power or energy density scales at one over the 4 th  power of the magnification. This means that as shorter focal length lenses are used for F 2 , the diameter of the focus drops, the length gets much shorter, and the power density increases rapidly. 
     In some embodiments, an axicon  10  with an adjustable angle is provided as a third degree of freedom to achieve a system that is capable of adjusting both the length and diameter of the line focus  2   b . Suppose that the angle of the original axicon  10  discussed above is multiplied by a factor A. Then, assuming small angles (i.e., (sin(α)≈α), the following is true:
 
FWHM 2 =FWHM 1   /A   Eq. (6.1); and
 
Length 2 =Length 1   /A   Eq. (6.2).
 
Here, if an amplification A creates a larger axicon angle, then the FWHM (i.e., the diameter) of the line focus  2   b  gets smaller and the length of the line focus  2   b  gets smaller as well. Generally, to achieve the desired FWHM and length of the line focus  2   b  for a given system, it is possible to calculate A and M such that:
 
 M/A =FWHM 2 /FWHM 0   Eq. 6.3; and
 
 M   2   /A =Length 2 /Length 0   Eq. (6.4).
 
     Accordingly, the optical elements of the first lens element  5 , the second lens element  11 , and the axicon  10  may be exchanged to achieve the desired diameter and length for the line focus  2   b . In some embodiments, these optical elements are physically removed from the optical assembly  6 ′ and replaced by others having the desired optical properties. However, this may require realignment of the optical assembly  6 ′ when switching to another configuration. In some embodiments, a plurality of optical elements is provided on a rotary wheel (similar to a filter wheel) or a slider to selectively choose the desired optical element that is in the beam path. For example, if the axicon is chosen as the removable/adjustable element, multiple axicons may be fabricated on a single substrate. Referring now to  FIG.  6 D , an axicon assembly  600  comprising a plurality of individual axicons  10 A- 10 D having different angles in a single substrate is schematically illustrated. Any number of axicons may be provided. A desired individual axicon  10 A- 10 D may be translated into an optical path of the laser beam  2  either manually or by motorized control. 
     As an example and not a limitation, diamond turning may be used to form the plurality of individual axicons  10 A- 10 D in a transmissive material. Diamond turning allows very high precision (˜1 μm) features to be fabricated, in particular of the optical surfaces with respect to the outside features of a physical part that are referenced mechanically for alignment. The substrate may have a rectangular shape, and thus can be translated laterally to select a different axicon. For the wavelengths used in these laser cutting systems (commonly 1064 nm), ZnSe is an appropriate transmissive optical material which is compatible with diamond turning. Also, since diamond turning has an extremely high degree of precision to place objects relative to one other, the substrate could include mechanical repositioning features such as grooves or conical holes. It should be understood that similar lens element assemblies may be fabricated and utilized to select the various first and lens elements having different focal lengths (i.e., a first lens assembly and/or a second lens assembly). 
     In some embodiments, the input laser beam  2  is magnified by a factor N in the optical path prior to the axicon  10 , as shown in the optical assembly  6 ″ illustrated in  FIG.  6 E . The optical assembly  6 ″ illustrated in  FIG.  6 E  comprises an axicon  10 , a first lens element  5 , and a second lens element  11 , similar to the embodiment depicted in  FIG.  6 C . In the example optical assembly  6 ″ illustrated in  FIG.  6 E , a telescope assembly comprising a third lens element  13  having a third focal length and a fourth lens element  15  having a fourth focal length is provided. As indicated above with respect to  FIG.  6 C , the focal lengths of the third lens element  13  and the fourth lens element  15  are adjustable, such as by exchanging lens elements. 
     By magnifying the laser beam  2 , per Eqs. (4.3) and (4.5), the only parameter that is affected is the length of the line focus  2   b —the diameter remains unchanged. The telescope positioned prior to the axicon  10 , therefore, allows changes of only the length of the line focus  2   b  while leaving the diameter unchanged. 
     Interchanging optical elements, such as the first through fourth lenses, may not be desirable for a laser cutting system that operates in an industrial environment. In some embodiments, the third and fourth lens elements  13 ,  15  providing the magnification factor N and/or the first and second lens elements  5 ,  11  may instead be configured as one or more variable zoom assemblies. Such variable zoom assemblies may allow for continuous adjustment of the laser beam focal line length, as opposed to discrete steps available by interchanging axicons or lens elements. Such variable zoom assemblies may be actuated either manually or by motorization, where the latter allows programmatic adjustment of the system, which may be compatible with manufacturing requirements. 
     Another optical assembly  4  for separating a material using a laser beam line focus  2   b  is schematically depicted in  FIG.  6 F . Generally, the example optical assembly  4  utilizes a reflective axicon  19  and a ring-shaped reflection assembly  18  with an angled reflective surface having the same angle as the reflective axicon  19 . A first lens element  17  converges (or, diverges) the laser beam  2  prior to the reflective axicon  19 . The reflective axicon  19  and the ring-shaped reflection assembly  18  create a ring of collimated light. A second lens element  11  focuses the circular radiation SR to generate the laser beam line focus  2   b . The radius of the circular radiation h may be continuously varied by translating the reflective axicon  19  with respect to the ring-shaped reflection assembly  18  (or vice versa) as indicated by arrow A. Because the focal length of the second lens element  11  focuses the rays at approximately a distance F 2  from the second lens element  11 , this change in ring radius will in turn change the final aperture angle β, yielding a change in the length of the laser beam line focus  2   b , per Eq. (4.5). Larger rain radii h, created by moving the reflective axicon  19  to the right, will yield smaller focal line lengths. However, the diameter of the laser beam focal line  2   b  will also change, per Eq. (4.3). Larger ring radii h will yield smaller focal line diameters. 
       FIG.  6 G  schematically illustrates another optical assembly  4 ′ for creating a continuously adjustable collimated ring of light SR. The example optical assembly  4 ′ comprises a first lens element  17  prior to a first transmissive axicon  20 , a second transmissive axicon  21 , and a second lens element  11  prior to the second transmissive axicon  21 . The first lens element  17  creates a small convergence (or divergence in some embodiments) of the laser beam  2  which creates a spherical aberration in the system to make a line focus. 
     The laser beam  2  exits the first transmissive axicon  20  at its angled emergence surface. The second transmissive axicon  21  receives the laser beam at its angled entrance surface and creates a ring of collimated light SR. The angle of deflection of the first transmissive axicon  20  is substantially equal to the angle of deflection of the second transmissive axicon  21 . A second lens element  11  then focuses the light to generate the laser beam line focus  2   b . Adjusting the ring radii h may be achieved by varying the adjustable distance D between the first and second transmissive axicons  20 ,  21 . This movement adjusts the length and diameter of the laser beam line focus  2   b.    
     Note that, as shown in  FIG.  7   , the typical operation of such a picosecond laser creates a “burst”  710  of pulses  720 . Each “burst”  710  may contain multiple pulses  720  (such as two pulses, three pulses as shown in  FIG.  7   , four pulses, five pulses, 10 pulses, 15 pulses, 20 pulses, 25 pulses or more) of very short duration (˜10 psec). Each pulse  720  (also referred to as a sub-pulse herein) is separated in time by a duration in a range of between about 1 nsec and about 50 nsec, for example, 10 to 30 nsec, such as approximately 20 nsec (50 MHz), with the time often governed by the laser cavity design. The time between each “burst”  710  will be much longer, often about 10 μsec, for a laser repetition rate of about 100 kHz. In some embodiments the burst repetition frequency is in a range of between about 1 kHz and about 200 kHz. The exact timings, pulse durations, and repetition rates can vary depending on the laser design, but short pulses (i.e., less than about 15 psec) of high intensity have been shown to work well with this technique. (Bursting or producing pulse bursts is a type of laser operation where the emission of pulses is not in a uniform and steady stream but rather in tight clusters of pulses.) 
     The average laser power per burst measured at the material can be greater than 40 microJoules per mm thickness of material, for example between 40 microJoules/mm and 2500 microJoules/mm, or between 500 and 2250 microJoules/mm. For example, for 0.1 mm-0.2 mm thick Corning Eagle XG® glass one may use 200 μJ pulse bursts, which gives an exemplary range of 1000-2000 μJ/mm. For example, for 0.5-0.7 mm thick Corning Eagle XG® glass, one may use 400-700 μJ pulse bursts to perforate glass, which corresponds to an exemplary example, for the purpose of perforating some alkaline earth boro-aluminosilicate glass compositions a picosecond pulsed laser (e.g., a 1064 nm, or 532 nm picosecond pulsed laser) which produces bursts of multiple pulses in combination with line-focus beam forming optics may be used to create lines of damage (defect lines) in the glass composition. In one embodiment, a glass composition with up to 0.7 mm thickness was positioned so that it was within the region of the focal line produced by the optics. With a focal line about 1 mm in length, and a 1064 nm picosecond laser that produces output power of about 24 W or more at a burst repetition rate of 200 kHz (about 120 microJoules/burst) measured at the glass, the optical intensities in the focal line region are high enough to create non-linear absorption in the glass. The pulsed laser beam can have an average laser burst energy measured, at the material, greater than 40 microJoules per mm thickness of material. The average laser burst energy used can be as high as 2500 μJ per mm thickness of transparent material, for example 40-2500 μJ/mm, with 500-2250 μJ/mm being preferable, and 550 to 2100 μJ/mm being even more preferable because the energy density is strong enough to make a thorough damage track through the glass, while minimizing the extent of micro cracking orthogonal to the perforated line or cut edge. In some exemplary embodiments the laser burst energy is 40-1000 μJ/mm. This “average pulse burst laser energy” per mm can also be referred to as an average, per-burst, linear energy density, or an average energy per laser pulse burst per mm thickness of material. A region of damaged, vaporized, or otherwise modified material within the glass composition was created that approximately followed the linear region of high optical intensity created by the laser beam focal line. 
       FIG.  8    shows the contrast between a focused Gaussian beam and a Bessel beam incident upon a glass-air-glass composite structure. A focused Gaussian beam will diverge upon entering the first glass layer and will not drill to large depths, or if self-focusing occurs as the glass is drilled, the beam will emerge from the first glass layer and diffract, and will not drill into the second glass layer. In contrast, a Bessel beam will drill (and more specifically damage, perforate, or cut) both glass layers over the full extent of the line focus. An example of a glass-air-glass composite structure cut with a Bessel beam is shown in the inset photograph in  FIG.  8   , which shows a side view of the exposed cut edges. The top and bottom glass pieces are 0.4 mm thick 2320, CT101. The exemplary air gap between two layers of glass is about 400 μm. The cut was made with a single pass of the laser at 200 mm/sec, so that the two pieces of glass were cut simultaneously, even though they were separated by &gt;400 μm. 
     In some of the embodiments described herein, the air gap is between 50 μm and 5 mm, for example is between 50 μm and 2 mm, or between 200 μm and 2 mm. 
     Exemplary disruption layers include polyethylene plastic sheeting (e.g., Visqueen). Transparent layers, as shown in  FIG.  9   , include transparent vinyl (e.g., Penstick). Note that unlike with other focused laser methods, to get the effect of a blocking or stop layer, the exact focus does not need to be precisely controlled, nor does the material of the disruption layer need to be particularly durable or expensive. In many applications, one just needs a layer that interferes with the laser light slightly to disrupt the laser light and prevent line focus from occurring. The fact that Visqueen prevents cutting with the picosecond laser and line focus is a perfect example—other focused picosecond laser beams will most certainly drill right through the Visqueen, and one wishing to avoid drilling right through such a material with other laser methods one would have to very precisely set the laser focus to not be near the Visqueen. 
       FIG.  10    shows stacking with transparent protective layers to cut multiple sheets while reducing abrasion or contamination. Simultaneously cutting a stack of display glass sheets is very advantageous. A transparent polymer such as vinyl can be placed between the glass sheets. The transparent polymer layers serve as protective layers serve to reduce damage to the glass surfaces which are in close contact with one another. These layers would allow the cutting process to work, but would protect the glass sheets from scratching one another, and would furthermore prevent any cutting debris (albeit it is small with this process) from contaminating the glass surfaces. The protective layers can also be comprised of evaporated dielectric layers deposited on the substrates or glass sheets. 
       FIG.  11    shows air gap and cutting of encapsulated devices. This line focus process can simultaneously cut through stacked glass sheets, even if a significant macroscopic air gap is present. This is not possible with other laser methods, as illustrated in  FIG.  8   . Many devices require glass encapsulation, such as OLEDs (organic light emitting diode). Being able to cut through the two glass layers simultaneously is very advantageous for a reliable and efficient device segmentation process. Segmented means one component can be separated from a larger sheet of material that may contain a plurality of other components. Other components that can be segmented, cut out, or produced by the methods described herein are, for example, OLED (organic light emitting diode) components, DLP (digital light processor) components, an LCD (liquid crystal display) cells, semiconductor device substrates. 
       FIG.  12    shows cutting an article such as electrochromic glass coated with transparent conductive layers (e.g. ITO). Cutting glass that already has transparent conducting layers such as indium tin oxide (ITO) is of high value for electrochromic glass applications and also touch panel devices. This laser process can cut through such layers with minimal damage to the transparent conductive layer and very little debris generation. The extremely small size of the perforated holes (&lt;5 um) means that very little of the ITO will be affected by the cutting process, whereas other cutting methods are going to generate far more surface damage and debris. 
       FIG.  13    shows precision cutting of some layers in a stack while not damaging others, as also shown in  FIG.  1   , extending the concept to multiple layers (i.e., more than two layers). In the embodiment of  FIG.  13   , the disruption element is a defocusing layer. 
     Other Examples 
     In general, the higher the available laser power, the faster the material can be cut with the above process. Processes disclosed herein can cut glass at a cutting speed of 0.25 m/sec, or faster. A cut speed (or cutting speed) is the rate the laser beam moves relative to the surface of the transparent material (e.g., glass) while creating multiple holes or modified regions.) High cut speeds, such as, for example 400 mm/sec, 500 mm/sec, 750 mm/sec, 1 m/sec, 1.2 m/sec, 1.5 m/sec, or 2 m/sec, or even 3.4 m/sec, 5 m/sec, 5 m/sec, 7 m/sec, or 10 m/sec are often desired in order to minimize capital investment for manufacturing, and to optimize equipment utilization rate. The laser power is equal to the burst energy multiplied by the burst repetition frequency (rate) of the laser. In general, to cut such glass materials at high cutting speeds, the damage tracks are typically spaced apart by 1-25 microns, in some embodiments the spacing is preferably 3 microns or larger—for example 3-12 microns, or for example 5-10 microns, or 10-20 microns. 
     For example, to achieve a linear cutting speed of 300 mm/sec, 3 micron hole pitch corresponds to a pulse burst laser with at least 100 kHz burst repetition rate. For a 600 mm/sec cutting speed, a 3 micron pitch corresponds to a burst-pulsed laser with at least 200 kHz burst repetition rate. A pulse burst laser that produces at least 40 μJ/burst at 200 kHz, and cuts at a 600 mm/s cutting speed needs to have laser power of at least 8 Watts. Higher cut speeds therefore require even higher laser powers. 
     For example a 0.4 m/sec cut speed at 3 μm pitch and 40 μJ/burst would require at least a 5 Watt laser, a 0.5 m/sec cut speed at 3 μm pitch and 40 μJ/burst would require at least a 6 Watt laser. Thus, preferably the laser power of the pulse burst ps laser is 6 watts or higher, more preferably at least 8 Watts or higher, and even more preferably at least 10 W or higher. For example in order to achieve a 0.4 m/sec cut speed at 4 μm pitch (defect lines pacing, or between damage tracks spacing) and 100 μJ/burst one would require at least a 10 Watt laser, and to achieve a 0.5 m/sec cut speed at 4 μm pitch and 100 μJ/burst one would require at least a 12 Watt laser. For example, to achieve a cut speed of 1 m/sec at 3 μm pitch and 40 μJ/burst one would require at least a 13 Watt laser. Also for example 1 m/sec cut speed at 4 μm pitch and 400 μJ/burst would require at least a 100 Watt laser. The optimal pitch between damage tracks and the exact burst energy is material dependent, and can be determined empirically. However, it should be noted that raising the laser pulse energy or making the damage tracks at a closer pitch are not conditions that always make the substrate material separate better or with improved edge quality. Too dense a pitch (for example &lt;0.1 micron, in some exemplary embodiments &lt;1 μm, or in some embodiments &lt;2 μm) between damage tracks can sometimes inhibit the formation of nearby subsequent damage tracks, and often can inhibit the separation of the material around the perforated contour, and may also result in increased unwanted micro cracking within the glass. Too long a pitch (&gt;50 μm, and in some glasses &gt;25 μm) may result in “uncontrolled microcracking”—i.e., where instead of propagating from hole to hole the microcracks propagate along a different path, and cause the glass to crack in a different (undesirable) direction. This may ultimately lower the strength of the separated glass part, since the residual microcracks will acts as flaws which weaken the glass. Too high a burst energy (e.g., &gt;2500 μJ/burst, and in some embodiments &gt;500 μJ/burst) used to form each damage track can cause “healing” or re-melting of already formed microcracks of adjacent damage tracks, which will inhibit separation of the glass. Accordingly, it is preferred that burst energy be &lt;2500 μJ/burst, for example, ≤500 μJ/burst. Also, using a burst energy that is too high can cause formation of microcracks that are extremely large and create flaws which reduce the edge strength of the parts after separation. Too low a burst energy (&lt;40 μJ/burst) may result in no appreciable damage track formed within the glass, and hence very high separation strength or complete inability to separate along the perforated contour. 
     Typical exemplary cutting rates (speeds) enabled by this process are, for example, 0.25 m/sec and higher. In some embodiments the cutting rates are at least 300 mm/sec. In some embodiments described herein the cutting rates are at least 400 mm/sec, for example 500 mm/sec to 2000 mm/sec, or higher. In some embodiments the picosecond (ps) laser utilizes pulse bursts to produce defect lines with periodicity between 0.5 microns and 13 microns, e.g. 0.5 and 3 microns. In some embodiments the pulsed laser has laser power of 10 W-100 W and the material and/or the laser beam are translated relative to one another at a rate of at least 0.25 m/sec, for example at the rate of 0.25 to 0.35 m/sec, or 0.4 m/sec to 5 m/sec. Preferably, each pulse burst of the pulsed laser beam has an average laser energy measured at the workpiece greater than 40 microJoules per burst mm thickness of workpiece. Preferably, each pulse burst of the pulsed laser beam has an average laser energy measured at the workpiece greater of less than 2500 microJoules per burst per mm thickness of workpiece, and preferably lass than about 2000 microJoules per burst per mm, and in some embodiments less than 1500 microJoules per burst per mm thickness of workpiece, for example not more than 500 microJoules per burst per mm thickness of workpiece. 
     It has been discovered that much higher (5 to 10 times higher) volumetric pulse energy density (μj/μm 3 ) is required for perforating alkaline earth boro-aluminosilicate glasses with low or no alkali containing glasses as compared to that for glasses such as Corning Gorilla®. This can be achieved, for example, by utilizing pulse burst lasers, preferably with at least 2 pulses per burst and providing volumetric energy densities within the alkaline earth boro-aluminosilicate glasses (with low or no alkali) of about 0.05 μJ/μm 3  or higher, e.g., at least 0.1 μJ/μm 3 , for example 0.1-0.5 μJ/μm 3 . 
     Accordingly, it is preferable that the laser produces pulse bursts with at least 2 pulses per burst. For example, in some embodiments the pulsed laser has laser power of 10 W-150 W (e.g., 10-100 W) and produces pulse bursts with at least 2 pulses per burst (e.g., 2-25 pulses per burst). In some embodiments the pulsed laser has the power of 25 W-60 W, and produces pulse bursts with at least 2-25 pulses per burst, and periodicity or distance between the adjacent defect lines produced by the laser bursts is 2-10 microns. In some embodiments the pulsed laser has laser power of 10 W-100 W, produces pulse bursts with at least 2 pulses per burst, and the workpiece and the laser beam are translated relative to one another at a rate of at least 0.25 m/sec. In some embodiments the workpiece and/or the laser beam are translated relative to one another at a rate of at least 0.4 m/sec. 
     For example, for cutting 0.7 mm thick non-ion exchanged Corning code 2319 or code 2320 Gorilla glass, it is observed that pitches of 3-7 microns can work well, with pulse burst energies of about 150-250 μJ/burst, and burst pulse numbers that range from 2-15, and preferably with pitches of 3-5 microns and burst pulse numbers (number of pulses per burst) of 2-5. 
     At 1 m/sec cut speeds, the cutting of Eagle XG® glass typically requires utilization of laser powers of 15-84 Watts, with 30-45 Watts often being sufficient. In general, across a variety of glass and other transparent materials, applicants discovered that laser powers between 10 and 100 W are preferred to achieve cutting speeds from 0.2-1 m/sec, with laser powers of 25-60 Watts being sufficient (and optimum) for many glasses. For cutting speeds of 0.4 m to 5 m/sec, laser powers should preferably be 10 W-150 W, with burst energy of 40-750 μJ/burst, 2-25 bursts per pulse (depending on the material that is cut), and hole separation (or pitch) of 3 to 15 μm, or 3-10 μm. The use of picosecond pulse burst lasers would be preferable for these cutting speeds because they generate high power and the required number of pulses per burst. Thus, according to some exemplary embodiments, the pulsed laser produces 10-100 W of power, for example 25 W to 60 Watts, and produces pulse bursts at least 2-25 pulses per burst and the distance between the defect lines is 2-15 microns; and the laser beam and/or workpiece are translated relative to one another at a rate of at least 0.25 m/sec, in some embodiments at least 0.4 m/sec, for example 0.5 m/sec to 5 m/sec, or faster. 
     It should now be understood that embodiments described herein provide for systems and methods for separating substrates, such as glass substrates, by application of a laser beam focal line. The systems described herein allow for fast adjustment of a length and/or diameter of the laser beam focal line to account for different types of material as well as different thicknesses of material. 
     While exemplary embodiments have been described herein, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope encompassed by the appended claims.