Abstract:
Increased yield of optical elements from cubic crystal rods, such as made of calcium fluoride, is made possible by orienting the optical elements for supporting the propagation of light along one of the &lt;1 1 {overscore (2)}&gt;, &lt;1 2 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axis, which extend perpendicular to a main &lt;1 1 1&gt; crystal axis. A cleave is taken through the crystal rod along a primary crystal plane {1 1 1} normal to the &lt;1 1 1&gt; main axis. One of the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axes is located by optical inspection and indicated on the crystal rod with an orientation label. Additional cuts are taken parallel to the {1 1 1} primary crystal plane to divide the crystal rod into disks each containing a portion of the orientation label. The disks can be cut again and sides formed perpendicular to the {1 1 1} primary crystal plane with regard to the orientation labels for forming optical elements, such as prisms, oriented for supporting the propagation of polarized light along one of the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, and &lt;{overscore (2)} 1 1 &gt; alternative crystal axes.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     1. Field of the Invention  
         [0002]     The invention relates to cubic crystalline optical elements, particularly calcium fluoride, in forms such as prisms for propagating highly collimated, linearly polarized light along predetermined crystal axes and to the manufacture and use of such cubic crystalline optical elements.  
         [0003]     2. Description of Related Art  
         [0004]     The short-wavelength high-photon-energy content of deep ultraviolet (UV) light (wavelengths between approximately 120 nanometers and 250 nanometers) significantly limits the number of materials capable of transmitting ultraviolet light and amplifies weaknesses in the limited number of materials that do transmit such ultraviolet light. Most ordinary optical materials are either insufficiently transmissive or subject to breakdown by absorption.  
         [0005]     Calcium fluoride (CaF 2 ) is among the optical materials capable of transmitting deep UV light. Despite calcium fluoride&#39;s highly symmetric cubic crystalline structure, calcium fluoride exhibits intrinsic birefringence at the short wavelengths. Different polarization components of the ultraviolet light experience different refractive indices depending upon both the direction of polarization and the direction of propagation of the light through the crystal material. A description of the nature of the intrinsic birefringence in calcium fluoride crystals is found in a paper by John Burnett, Zachary Levine, Eric Shirley, and John Bruning entitled “Symmetry of spatial-dispersion-induced birefringence and its implications for CaF 2  ultraviolet optics”, Society of Photo-Optical Instrumentation Engineers, J. Microlith., Microfab., Microsyst. p. 213-224, October 2002, which is hereby incorporated by reference.  
         [0006]     There are 14 crystal axes, which can be referenced according to Miller indicies, along which deep ultraviolet light can be propagated through calcium fluoride crystals without encountering intrinsic birefringence effects. These include propagations in both directions along the three cube axes (i.e., the family of &lt;1 0 0&gt; directions) and along the four cube body diagonals (i.e., the family of &lt;1 1 1&gt; directions, referred to herein as the &lt;1 1 1&gt; main axis). The &lt;1 1 1&gt; main axis is a normal to the natural {1 1 1} cleavage plane of calcium fluoride crystals, referred to herein as the {1 1 1} primary plane. The {1 1 1} primary plane is the plane along which the crystal tends to break first when struck. Optical elements made from calcium fluoride crystals are generally oriented for propagation of light along the &lt;1 1 1&gt; main axis, because the natural cleavage of calcium fluoride crystals presents planar surfaces normal to the crystal&#39;s &lt;1 1 1&gt; main axis.  
         [0007]     Prisms for use in the deep UV are frequently cut out of calcium fluoride crystals grown in rod form with either ordered or randomly oriented crystal axes. One end of the rods is cleaved along the {1 1 1} primary plane (normal to the &lt;1 1 1&gt; main axis) to provide a basis for prism orientation. The sides of the oriented rods are cut and polished to form slabs. A line of prisms are traced on the slab-, and the slab is further cleaved for orienting each of the prisms to support the propagation of light along the &lt;1 1 1&gt; main axis of the crystal.  
         [0008]     The crystal rods are expensive to manufacture, considerable waste is associated with the formation of the slabs, and a separate cleave is generally required for each prism. A higher yield from these rods would be desirable.  
       BRIEF SUMMARY OF THE INVENTION  
       [0009]     The invention contemplates the propagation of highly collimated, linearly polarized, deep UV light along cubic crystal axes that are oriented perpendicular to the &lt;1 1 1&gt; main axis along which light is usually propagated. The alternative axes, designated as &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt; and &lt;{overscore (2)} 1 1&gt; axes, occupy even 60° intervals about the &lt;1 1 1&gt; main axis. Although unpolarized light propagating along the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt; and &lt;{overscore (2)} 1 1&gt; alternative axes is subject to intrinsic birefringence effects, properly oriented polarized light propagating along the same alternative &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt; and &lt;{overscore (2)} 1 1&gt; axes experiences little polarization conversion (change) though a modest range of angular misalignments and crystal stress variations. The electric field vectors of the properly polarized light are oriented substantially perpendicular to the &lt;1 1 1&gt; main axis (i.e., aligned substantially perpendicular to the {1 1 1} primary plane).  
         [0010]     Increased yield from cubic crystal bodies is possible for optical element designs in which the direction of intended light propagation lies along one of the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt; and &lt;{overscore (2)} 1 1&gt; alternative axes. The cubic crystal bodies can be grown as usual with either ordered or randomly oriented crystal axes, and the crystal axes can be referenced as usual by first cleaving the crystal body along the {1 1 1} primary plane defined as normal to the &lt;1 1 1&gt; crystal axis. However, in accordance with the invention, inspection, such as by x-ray diffractometry, determines the orientation of an alternative crystal plane {1 1 {overscore (2)}}, {1 {overscore (2)} 1}, or {{overscore (2)} 1 1} defined as normal to one of the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, and &lt;{overscore (2)} 1 1&gt; alternative crystal axes.  
         [0011]     The crystal body is divided into a plurality of optical elements each having at least one surface substantially parallel to the {1 1 1} primary crystal plane and at least one surface substantially perpendicular to the primary crystal plane {1 1 1}. The at least one surface substantially perpendicular to the {1 1 1} primary crystal plane is oriented with respect to one of the {1 1 {overscore (2)}}, {1 {overscore (2)} 1}, or {{overscore (2)} 1 1} alternative crystal planes so that an intended direction of propagation of light refracted into each of the optical elements is along the one of the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, and &lt;{overscore (2)} 1 1&gt; alternative crystal axes.  
         [0012]     Preferably, a plurality of cuts substantially parallel to the {1 1 1} primary crystal plane along even increments of the crystal body length produce a plurality of commonly oriented slabs, preferably in the form of disks. Each of the disks has a top and bottom surface connected by a peripheral surface corresponding to a peripheral surface of the crystal body. The peripheral surfaces of the commonly oriented disks are finished to produce at least one optical surface in each of the disks oriented substantially perpendicular to the {1 1 1} primary crystal plane at a predetermined inclination to the one {1 1 {overscore (2)}}, {1 {overscore (2)} 1}, or { {overscore (2)} 1 1} alternative crystal plane. The at least one surface substantially perpendicular to the { 1 1 1} primary crystal plane is preferably inclined with respect to the {1 1 {overscore (2)}}, {1 {overscore (2)} 1}, or {{overscore (2)} 1 1} alternative crystal plane so that a highly-collimated beam of linearly-polarized light refracts into its intended direction of propagation of light through each of the optical elements along the one &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axis.  
         [0013]     For purposes of further increasing the yield from the crystal body, the new orientations enable the disks to be divided into a number of parts with each part fashioned into a separate optical element. The periphery of the crystal body is preferably marked to identity the orientation of the {1 1 {overscore (2)}}, {1 {overscore (2)} 1}, or {{overscore (2)} 1 1} alternative crystal plane. The markings allow the intended optical elements to be traced onto the individual disks oriented as desired to the one &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axis and for each of the disks to be cut into oriented parts for separating adjacent surfaces of the intended optical elements.  
         [0014]     The invention is particularly applicable to the manufacture of prisms. Two faces of the prisms can be formed from top and bottom surfaces of the disks cut substantially parallel to the {1 1 1} primary crystal plane, and side faces of the prisms can be formed in the peripheral surfaces of the disks substantially perpendicular to the {1 1 1} primary crystal plane. Each of the disks can be cut in planes substantially perpendicular to the {1 1 1} primary crystal plane for forming another crystal side face, particularly as an entrance face oriented for directing light along the alternative &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; crystal axis. 
     
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)  
       [0015]      FIG. 1  illustrates a seven step method, designated as steps A-G, for increasing the yield of a cubic crystal rod for forming a plurality of prisms.  
         [0016]      FIG. 2  is an enlargement of a disk from Step F of  FIG. 1  showing the traces of two prisms and three alternative crystal axes in the disk.  
         [0017]      FIG. 3  is a side view of one of the prisms arranged for refracting light along one of the alternative crystal axes.  
         [0018]      FIG. 4  is a perspective view of the prism of  FIG. 3  in wire outline form showing more of the prism surfaces.  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0019]     A sequence of processing steps laid out in  FIG. 1  exemplifies a method for increasing yield of optical elements from a cubic crystal material in accordance with the invention. Beginning with Step A, a crystal rod  10  made of calcium fluoride is grown either with randomly oriented crystal axes or with crystal axes having a preferred orientation imposed by seeding. Either way, the exact orientation of the crystal axes is not immediately apparent from the crystal rod.  
         [0020]     In Step B, the crystal rod  10  is cleaved near one end along the {1 1 1} plane normal to the &lt;1 1 1&gt; main axis. In such calcium fluoride crystals, this is the crystal plane along which the crystal most readily breaks and provides a convenient and accurate reference plane  14  for the crystal rod  10 . Although the {1 1 1} reference plane  14  identifies one of the crystal axes, i.e., the &lt;1 1 1&gt; main crystal axis, it is necessary to identify a second axis to fully orient the cubic crystal.  
         [0021]     Step C involves an inspection procedure for identifying a second crystal axis orthogonal to the &lt;1 1 1&gt; main axis. In particular, a Laue x-ray diffractometer is used to find one of the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axes. Two orientation labels  16  and  18  are applied to the periphery of the crystal rod  10  to identify the location of one of the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axes that extends perpendicular to the &lt;1 1 1&gt; main axis. The orientation labels  16  and  18  are preferably drawn on the crystal rod  10  as two diametrically opposed lines.  
         [0022]     Using the {1 1 1} reference plane  14  as a reference, parallel cuts  20  are made along the length of the rod  10  as shown in Step D, each at a predetermined thickness “T”. The parallel cuts  20  divide the crystal rod  10  into a plurality of slabs in the form of slightly eccentric disks  22  as shown in Step E. For example, the crystal rod  10  can be mounted in a sacrificial plastic holder and loaded into a saw, such as a  1 D or diamond saw, and accurately cut onto the plurality of eccentric disks  22 . The tops and bottoms of the eccentric disks  22  are then double-side lapped to create highly parallel ground surfaces  24  and  26  in much the same way as optical windows are formed. The top and bottom surfaces  24  and  26  of the disks  22  are ground parallel to the {1 1 1} reference plane  14  coincident with other of the set of parallel {1 1 1} planes. The &lt;1 1 1&gt; main axis extends normal to the cut parallel surfaces  24  and  26  of the disks  22 . The &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, and &lt;{overscore (2)} 1 1&gt; alternative crystal axes are known to be oriented perpendicular to the &lt;1 1 1&gt; main axis and parallel to the {1 1 1} planes that form the parallel surfaces  24  and  26  of the disks  22 . The orientation labels  16  and  18 , which are visible on each of the disks  22 , identify the orientation of the one &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axis around the &lt;1 1 1&gt; main axis in each of the disks  22 .  
         [0023]     Once both the &lt;1 1 1&gt; main axis and the one &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axis are known for each of the disks  22 , the orientation of the cubic crystal within each of the disks  22  is thoroughly known.  FIG. 2  shows an enlargement of the Step F in which the outline of two optical elements in the form of prisms  30  and  32  are drawn on each of the disks  22  in positions that are angularly oriented as desired to the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axes. Although the orientation labels  16  and  18  only identify one of the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axes by virtue of its direction across the surfaces  24  and  26  of the disks  22 , the other two of the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, and &lt;{overscore (2)} 1 1&gt; alternative crystal axes are also know by geometric reference. Accordingly, the prisms  30  and  32  can be oriented with respect to any one of the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axes.  
         [0024]     As laid out in  FIGS. 3 and 4  with respect to the prism  30 , each of the prisms  30  and  32  includes two end faces  36  and  38  that correspond to the parallel surfaces  24  and  26  of the disks  22  and that lie in the {1 1 1} crystal planes and three side faces  40 ,  42 , and  44  that extend perpendicular to both the parallel surfaces  24  and  26  of the disks  22  and the {1 1 1} crystal planes. The chosen direction for propagation of light through the prisms  30  and  32  along the &lt;1 1 {overscore (2)}&gt; alternative crystal axis is shown by the dashed lines  34 .  
         [0025]     Also in step F, the disks  22  are cut in half in a known orientation, such as along or referenced to one of the other &lt;1 {overscore (2)} 1&gt; or &lt;{overscore (2)} 1 1&gt; alternative crystal axes—the &lt;1 {overscore (2)} 1&gt; alternative axis being shown as an appropriate cut line in  FIG. 2 . Each of the half disks  50  and  52  are finished formed into the prisms  30  and  32 . For example, the half disks  50  and  52  can be loaded into a micro-grinding machine, such as grinding machines available from OptoTech Optical Machinery Inc, East Greenville, Pa. or LOH Optical Machinery, Inc., of Milwaukee/Germantown, Wis., and ground into their desired form as the prisms  30  and  32 . The result, which is a set of the prisms  30  and  32  finished from a plurality of the disks  22 , is shown as the final Step G.  
         [0026]     The new method shown in the Steps A-G makes more efficient use of the crystal material of the rod  10  and can be applied to extract similar efficiencies from other cubic crystal bodies and for making other optical elements oriented for propagating light along one of the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axes. The crystal bodies are cut into slabs having top and bottom surfaces from which two end faces of the optical elements are finished along the {1 1 1} reference planes immediately adjacent to one another. The slabs themselves can be cut apart for finishing adjacent side faces of the optical elements. Slabs (e.g., disks) having larger areas relative to the desired size of the finished optical elements can be cut into more than two parts for forming more than two optical elements from each of the slabs. Generally, the parts are cut into subparts for forming even numbers of optical elements from each of the slabs, each subsequent cut being a complete cut that divides the remainder by half.  
         [0027]     The side faces  40 ,  42 , and  44  of the prisms  30  are oriented during use as shown in  FIGS. 3 and 4  so that the side face  40  functions as an entrance surface, the side face  42  functions as an exit surface, and the side face  44  functions as a base. Normals  54  and  56  of the entrance and exit surfaces  40  and  42  are inclined to both the directions  60  and  62  of light propagation to and from the prism  30  and the &lt;1 1 {overscore (2)}&gt; alternative crystal axis along which the light is intended for propagation through the prism  30 . The inclination of the normal to the entrance surface  40  with respect to the direction  60  of light propagation to the entrance surface  40  through the angle “φ I ” avoids unwanted retroreflections of the light from the entrance surface  40 . The normals  54  and  56  are preferably inclined true length within the {1 1 1} plane (the plane of  FIG. 3 ) so that the entrance and exit surfaces  40  and  42  remain perpendicular to the {1 1 1} crystal plane. Thus, the angles “φ I ” of incidence and ”φ R ” of refraction also remain in the {1 1 1} crystal plane.  
         [0028]     Although the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, and &lt;{overscore (2)} 1 1&gt; alternative crystal axes exhibit an intrinsic birefringence, the effects of the birefringence can be avoided by limiting electric field fluctuations of light propagating along the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axes to within the {1 1 1} plane. In other words, the propagating light is linearly polarized and the direction of polarization is within the {1 1 1} plane. The polarization direction is also preferably within the plane of incidence at which the polarized light strikes the entrance surface  40 , and is therefore referenced as “P” polarized light. The normal to the entrance surface  40  is inclined to the one &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axis through the angle of refraction “φ R ” SO that upon refraction through the entrance surface  40 , the “P” polarized light propagates along the one &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axis.  
         [0029]     In practice, the light emitted by conventional lasers, including lasers operating in the deep UV, is not perfectly collimated, and is, therefore, more accurately referred to as “highly” collimated light. For example, emission angles of ±6 degrees are within the range of normal expectations for the highly collimated light, although higher or lower emission angle ranges are possible depending upon the choice of light source. The &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, and &lt;{overscore (2)} 1 1&gt; alternative crystal axes also define directions of propagation through the cubic crystal material that accommodate such variations in ray angle with minimum of polarization conversion of the light propagating through the prisms  30  from linearly polarized light to polarized light in a different form (e.g., elliptical or rotated). In other words, substantially linearly polarized light incident upon the prisms  30  exits the prisms  30  as substantially the same linearly polarized light despite small variations in ray angle.  
         [0030]     In addition to the intrinsic birefringence effects dealt with by orientations of both ray angle and polarization, such cubic crystal materials are also subject to stress birefringence that can affect the polarization of light propagated through the crystals. For example, two main sources of stress birefringence in calcium fluoride crystals are (a) birefringence created during the crystal growth process and modified during the cutting in polishing of the optical elements, and (b) birefringence created by heat gradients in the optics during their use. Among the possible directions of propagation through the cubic crystal material perpendicular to the &lt;1 1 1&gt; axis, the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, and &lt;{overscore (2)} 1 1&gt; alternative crystal axes are least sensitive to the birefringence effects of stress. In fact, the amount of stress-induced polarization conversion associated with propagations along the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, and &lt;{overscore (2)} 1 1&gt; alternative crystal axes is expected to be roughly comparable or even less than the amount of stress-induced polarization conversion associated with propagations along the &lt;1 1 1&gt; axis over a modest range of stress magnitudes (e.g., less than 100 kPa). For purposes of making the comparison, a fixed value of the stress magnitude is considered over a full range of orientations to identify the maximum polarization conversion associated with propagations along the &lt;1 1 1&gt; main crystal axis and the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, and &lt;{overscore (2)} 1 1&gt; alternative crystal axes.  
         [0031]     The invention is particularly applicable for use in line-narrowing modules for laser systems operating at wavelengths around 157 nm or 193 nm. Highly polarized light propagates through a series of prisms traveling in one direction through the prisms on a first pass and traveling in nearly the opposite direction through the prisms in a second pass to provide effective feedback for the lasers. For example, excimer lasers made by Lambda Physik of Göttingen, Germany and Cymer, Inc. of San Diego, Calif. produce linearly polarized light, regarded as “P” polarized within the plane of light ray travel. A series of prisms make in accordance with the invention can be used to convey the “P” polarized light within the laser cavity with a minimum of polarization conversion (e.g., “P” polarized converted into “S” polarized light) due to both intrinsic or stress-induced birefringence. Performance comparable to propagations along &lt;1 1 1&gt; crystal axes can be achieved in the new prism designs by propagating the “P” polarized light along one of the &lt;1 1 {overscore (2)}&gt;, &lt;1 {overscore (2)} 1&gt;, or &lt;{overscore (2)} 1 1&gt; alternative crystal axes, while increasing the number of such prisms that can be harvested from a crystal body.  
         [0032]     Although described with respect to particular embodiments, which are intended to be illustrative rather than limiting, it will be apparent that numerous variations and modification of these embodiments can be practiced within the scope of the appended claims.