Abstract:
An optical system for shaping an incoming beam having a divergence with an angular distribution at least in a first direction comprises at least one angle selective optical element ( 26,28 ) for clipping the angular distribution in the at least first direction. The approach according to the present invention bases on using an angle-selective device ( 25,32 ) operated by the principle of total internal reflection to reduce divergence of the incoming beam, in contrast to a spatially-selective device as for example a field-stop or slit. The method according to the present invention has the advantage that no physical sharp edges have to be exposed at high energy densities. Thus, thermal impact and demands on the optical elements to withstand a high power laser beam are significantly reduced.

Description:
CROSS REFERENCE TO RELATED APPLICATION  
       [0001]     The present application claims priority of U.S. provisional patent application No. 60/753,829 filed on Dec. 23, 2005. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     The present invention generally relates to the field of shaping light beams, in particular laser light beams. More specifically, the present invention relates to an optical system, an optical unit and to a method for shaping an incoming beam, in particular laser beam. Such an optical system, an optical unit and a method as mentioned before are in particular useful for producing a thin laser beam for material processing, for example for a directional crystallization of amorphous silicon films. Furthermore, the optical system, optical unit and the method according to the invention can be used in a solid state ring laser, for example.  
         [0003]     Common lasers produce light beams which, on a macroscopic scale, appear to be exactly parallel with sharp edges when seen in cross-section of the beam. However, on a microscopic scale, there is an inherent divergence in the laser beam, i.e. the beam may be considered as a bundle of rays wherein the rays have slightly different propagation directions with respect to one another. The angle distribution of the laser beam intensity, thus, exhibits a profile which has a maximum in the main direction of propagation of the laser beam (angle 0°) and has a slope to both sides of the maximum (angle≠0°). Due to the natural divergence or angular spread of the laser beam, the edges of the laser beam are not exactly sharp but somewhat smeared out.  
         [0004]     For many optical applications, in particular laser applications like annealing of semiconductors, a very low divergence of a beam is required.  
         [0005]     Usually a field-stop is used to limit the field of view of an optical system (see for example Handbook of Optics, OSA, Eds. W. G. Driscoll and W. Vaughan, McGraw Hill, 1978, p. 2-52, W. J. Smith, Modern Optical Engineering, 3rd Ed., McGraw Hill, 2000, Ch. 6, p. 141-143). This approach is based on a spatial filtering, i.e. a diaphragm or a slit is used to reduce the size of the object which the system will image.  
         [0006]     Specifically, U.S. Pat. No. 5,721,416 discloses an optical device for generating a sharp illuminating line on an illuminating plane from a high-power laser beam. This known device is based on spatial filtering. The sharp illuminating line includes long and short axes. The optical device comprises an anamorphic setup of imaging and homogenizing optical systems for the separate imaging and homogenizing of the laser beam in the direction of the long and short axes. For imaging and homogenizing the laser beam in the direction of the short axes, a slit is illuminated homogenously and the slit is imaged on the illumination plane by reducing optics. Thus, this known optical system also uses a slit for shaping the laser beam.  
         [0007]     Despite the fact that an optical system using such a field-stop works quite well, the use of a slit or field-stop implies several drawbacks. One of the drawbacks arises when such a system is used in applications requiring a high energy density of the beam. Due to the high energy density of the beam, the body of the field-stop heats up to very high temperatures leading to deformations of the field-stop or slit. The result is that the beam shaping becomes inaccurate. Further, in order to produce very sharp edges of the light beam, the field-stop or slit must be manufactured with high precision machined sharp edges in order to be able to shape the incoming beam as desired.  
         [0008]     U.S. Pat. No. 4,060,308 discloses an angle selective coupler for coupling optical energy into and/or out of optical fibers. The coupler consists of a section of the optical fiber modified in such a way as to allow optical excitation of a plurality of higher order modes of optical transmission, each mode being defined by a given angle of propagation relative to the fiber axis. In one embodiment the coupling section comprises a single strand of glass fiber waveguide which is tapered along its length. The existence of the tapered section allows coupling of radiation from an external source into a given propagation angle in the fiber. This document does not deal with the technical problem of producing a laser beam having sharp edges.  
         [0009]     Due to the afore-mentioned drawbacks of the known optical systems and methods, there is still a need for an optical system and a method for shaping an incoming beam which does not rely on a spatial filtering.  
       SUMMARY OF THE INVENTION  
       [0010]     An object of the present invention is therefore to provide an optical system for shaping an incoming beam having a divergence with an angular distribution, wherein the physical effect the optical system uses deviates from that known from the prior art.  
         [0011]     It is a further object of the present invention to provide an optical system for shaping an incoming beam having a divergence with an angular distribution which is capable of shaping the incoming beam with high power and/or high energy densities.  
         [0012]     It is another object of the present invention to provide an optical system for shaping an incoming beam having a divergence, wherein the thermal impact is reduced significantly as compared to solutions known from the prior art.  
         [0013]     It is a further object of the present invention to provide an optical system being capable of reducing an illumination line with a width and a length on a surface which has sharp edges.  
         [0014]     It is still another object of the present invention to provide an optical system being capable of producing an illumination line with a width and a length on a surface which has a high aspect ratio with a length exceeding the width by several hundreds fold and has sharp edges.  
         [0015]     It is still a further object of the present invention to provide an optical system for producing a thin laser beam for material processing, in particular for use in a laser annealing apparatus for annealing a substrate.  
         [0016]     It is a further object of the present invention to provide an optical system for reducing an thin laser beam for material processing, in particular for use in a laser annealing and scanning apparatus for annealing a substrate, wherein the laser beam is scanned with respect to the surface of the substrate.  
         [0017]     It is a further object of the present invention to provide a method for shaping an incoming beam having a divergence with an angular distribution, wherein the physical effect used deviates from that known from the prior art.  
         [0018]     It is a further object of the present invention to provide a method for shaping an incoming beam having a divergence with an angular distribution and having high power and/or high energy densities.  
         [0019]     It is a further object of the present invention to provide a method for shaping an incoming beam having a divergence, wherein the thermal impact is reduced significantly as compared to solutions known from the prior art.  
         [0020]     It is a further object of the present invention to provide a method being capable of producing an illumination line with a width and length on a surface, wherein the illumination line has sharp edges.  
         [0021]     It is still another object of the present invention to provide a method being capable of producing an illumination line with a width and a length on a surface, wherein the illumination line has a high aspect ratio with a length exceeding the width by several hundreds fold and wherein the illumination line has sharp edges.  
         [0022]     According to an aspect of the invention, an optical system for shaping an incoming beam having a divergence with an angular distribution at least in a first direction is provided, wherein the optical system comprises at least one angle selective optical element for clipping the angular distribution in the at least first direction.  
         [0023]     According to another aspect of the invention, a beam shaping optical unit for shaping an intensity profile of an incident beam and forming an intensity profile of an exit beam is provided, wherein the incident beam has at least at one side a first intensity gradient due to a divergence of the incident beam at least in a first dimension, the beam shaping optical unit shaping the exit beam such that the exit beam has a second intensity gradient at the at least one side, wherein the second gradient is larger than the first gradient, the beam shaping optical unit forming the intensity profile of the exit beam by at least one total internal reflection.  
         [0024]     According to still another aspect of the invention, a method for shaping an incoming beam having a divergence with an angular distribution in a first direction is provided, comprising clipping the angular distribution in the first direction.  
         [0025]     The approach according to the present invention bases on using an angle-selective device to reduce divergence of the incoming beam, in contrast to a spatially-selective device as for example a field-stop or slit. The method according to the present invention has the advantage that no physical sharp edges have to be exposed at high energy densities. Thus, demands on the optical elements to withstand a high power laser beam are significantly reduced.  
         [0026]     In preferred embodiments, the system and the method of the present invention are based on the angle-selective properties of total internal reflection (TIR), i.e. the beam propagates in a material with a higher refraction index to an interface with the material having a lower index and will be reflected at the interface, if the incidence angle exceeds a certain critical angle called the total internal reflection angle. Those rays of the beam which propagate at an angle of≠0° with respect to the main direction of propagation of the beam will be at least partially transmitted through that interface, and are, thus, clipped or, in other words, cut off.  
         [0027]     In the case where it is intended to generate a beam with trapezoidal or rectangular cross-section, the present invention allows to reduce divergence in e.g. one certain direction (substitution of a slit formed e.g. by a field-stop as for example known from U.S. Pat. No. 5,721,416) and does not affect the divergence in, for example, the orthogonal direction. The combination of two such devices for two (for example orthogonal) dimensions provides independent adjustment of divergence for both (i.e. orthogonal) cross-sectional dimensions of the beam.  
         [0028]     Further features and advantages will become apparent from the following description and the accompanying drawings.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0029]     Exemplary embodiments are shown in the drawings and will be explained hereafter in more detail with reference to the drawings. In the drawings:  
         [0030]      FIG. 1  shows an optical system for shaping an incoming beam having a divergence according to a preferred general embodiment, illustrating the principles of the present invention;  
         [0031]      FIG. 2  shows another embodiment of an optical system for shaping an incoming beam;  
         [0032]      FIG. 3  shows a graph illustrating the effect of a high refractive coating on a total internal reflection (TIR) surface;  
         [0033]      FIG. 4  shows another preferred embodiment of an optical system for shaping an incoming beam;  
         [0034]      FIG. 5  shows another preferred embodiment of an optical system for shaping an incoming beam;  
         [0035]      FIG. 6  shows another preferred embodiment of an optical system for shaping an incoming beam;  
         [0036]      FIG. 7  shows another preferred embodiment of an optical system for shaping an incoming beam;  
         [0037]      FIG. 8  shows another preferred embodiment of an optical system for shaping an incoming beam;  
         [0038]      FIG. 9  shows another preferred embodiment of an optical system for shaping an incoming beam;  
         [0039]      FIG. 10  shows another preferred embodiment of an optical system for shaping an incoming beam;  
         [0040]      FIG. 11  shows another preferred embodiment of an optical system for shaping an incoming beam, wherein the system in  FIG. 11  is a stacked arrangement of the optical system in  FIG. 10 ;  
         [0041]      FIG. 12  shows a modification of the optical system in  FIG. 11  used as a ring laser;  
         [0042]      FIG. 13  shows a 3D-plot of the reflectance as a function of wavelength and incidence angle of a TIR interface;  
         [0043]      FIG. 14  shows an optical system for shaping an incoming beam wherein requirements for the correction of dispersion effects have been met;  
         [0044]      FIG. 15  is a scheme of a TIR interface exhibiting the effects of orthogonal divergence effects on beam shaping; and  
         [0045]      FIG. 16  shows another scheme for explaining the effects of orthogonal divergence on beam shaping. 
     
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS  
       [0046]      FIG. 1  generally shows an optical system or optical unit  10  for shaping an incoming beam  12 .  
         [0047]     The principles of the present invention explained with respect to the embodiment of  FIG. 1  are also valid for all other embodiments described herein.  
         [0048]     The incoming beam  12  propagates in direction of an arrow  14 . The beam  12  is depicted in  FIG. 1  by two lines  16  and  18  extending parallel to the main direction of propagation (arrow  14 ) of the incoming beam  12 , and by two margin lines  20  and  22  which are not parallel to the direction of propagation (arrow  14 ) but slightly diverge with respect thereto. Thus, the incoming beam  12  has a divergence in a first direction x which lies in the plane of the drawing of  FIG. 1 . Due to the divergence, the incoming beam  12  exhibits an angular intensity distribution as shown by a graph  24  where the intensity I is plotted versus the angle α which is assumed to be zero in the direction of propagation (arrow  14 ). As graph  24  shows, the maximum intensity is at angle α=0, while the intensity has a slope to angles α≠0, i.e. has a finite gradient. As a result, the incoming beam  12  does not have sharp edges in the direction x, but the edges are somewhat smeared out.  
         [0049]     Line  20  forms an edge of the incoming beam  12  on one side, and line  22  forms the opposite edge on the opposite side of the incoming beam  12  in the first direction x. The direction x may be, for example, the width dimension of the incoming beam  12 .  
         [0050]     What is desired is that the incoming beam  12  be shaped such that the parallel lines  16  and  18  form the two sharp edges of the beam  12  in the first direction or dimension x. In order to shape the incoming beam  12  in this way, the optical system or unit  10  is provided.  
         [0051]     The optical system  10  comprises at least one angle-selective optical element, with the embodiment showing two, angle-selective optical elements  26  and  28 . The angle-selective optical elements  26  and  28  are angle-selectively reflecting elements, in particular prisms  30  and  32 . Prism  30  comprises three surfaces  34 ,  36  and  38 , wherein the surfaces  34  and  36  on the one hand and the surfaces  34  and  38  on the other hand intersect at an angle of 45°. Thus, prism  30  is a right angle prism, wherein surfaces  36  and  38  form the katheti and surface  34  forms the hypotenuse.  
         [0052]     It is to be understood that prisms  30  and/or  32  can be replaced by any other suited optical element, for example a rod, a plate, a cuboid, a polygon shaped optical element, a trapezoid, a parallelogram, etc.  
         [0053]     Surface  36  is the entrance surface of the prism  30 , and surface  38  forms the exit surface.  
         [0054]     Likewise, the prism  32  comprises three surfaces  40 ,  42  and  44 , wherein the surfaces  40  and  42  on the one hand and  42  and  44  on the other hand intersect at an angle of 45°. Surface  40  of the prism  32  forms an entrance surface, and surface  44  an exit surface of the prism  32 .  
         [0055]     The prisms  30  and  32  are, for example, made of a medium having a refractive index which is larger than 1. The prisms  30  and  32  may be made from any suited material, in particular silica, calcium fluoride and the like, which is transmissive with respect to the wavelength of the beam  12 .  
         [0056]     In particular, the surfaces  34  and  42  of the prisms  30  and  32  form interfaces to the ambient environment  46 , which is, for example, air, which has a refractive index which is lower than the refractive index of the medium of the prisms  30  and  32 .  
         [0057]     The incoming beam  12 , which preferably has been collimated before, first enters the prism  30  through the entrance surface  36 , preferable at right angles in order to avoid a beam deflection. The prism  30  is positioned and designed such that the incoming beam  12  is incident on the surface  34  at an incidence angle which is close to the angle of total internal reflection (TIR) at the surface  34 . Those rays of the incoming beam  12  which are incident on the surface  34  at an angle which is larger than the TIR angle will be reflected at the surface  34  as it is the case for the rays illustrated by the lines  16  and  18  and  22  of the incoming beam  12 . The reflected rays are labeled with  16   a ,  18   a ,  22   a.    
         [0058]     Those rays of the incoming beam  12  which are incident on the surface  34  at an angle which is lower than the TIR angle, will be (at least partially) transmitted through the surface  34 . This is the case for the ray illustrated by the line  20  of the incoming beam  12 , i.e. the divergent rays on one side of the incoming beam  12  will be clipped or cut off by the first prism  30 . The transmitted ray is labeled with  20   a.    
         [0059]     It is to be noted that the rays of the incoming beam  12  illustrated by the divergent line  22 , are also incident on the surface  34  at an angle larger than the TIR angle, and, thus, will be reflected at the surface  34 . Thus, the prism  30  clips the angular distribution of the incoming beam  12  in the direction or dimension x only on one side (line  20 ), while the other side (line  22 ) is not cut off by the prism  30 .  
         [0060]     The second prism  32  is effective in shaping the other side of the angular distribution in the first direction or dimension x. As can be seen in  FIG. 1 , after having been reflected at the surface  34 , the ray according to line  22 ,  22   a  will be incident on the surface  42  of the prism  32  at an angle which is lower than the TIR angle at the surface  42  and, thus, is (at least partially) transmitted through surface  42  (illustrated by line  22   b ). Thus, the divergent part of the other edge of the incoming beam  12  is cut off by the prism  32 . The result is an exit beam  48  where the angular distribution is clipped on both sides in the first direction or dimension x. A graph  50  shows the angular intensity distribution of the exit beam  48 . As can be seen, the gradient of the angular distribution is larger than the gradient of the angular distribution of the incoming beam  12 .  
         [0061]     It is to be understood that surface  34  and/or  42  can have a plane shape, but also a sphere, a cylinder, an asphere or other shapes.  
         [0062]     The incidence angle of the incoming beam  20  on the surface  34  and on the surface  42  can be adjusted by actuators  52  and  54  for rotational control of the prisms  30  and  32  according to double arrows  56  and  58 . The control of the rotational angle of the prisms  30  and  32  can be used to determine how much of the angular distribution or spectrum of the beam  12  is cut off by the prisms  30  and  32 . Rotational control of both prisms  30  and  32  allows to reduce the divergence of the incoming beam  12  to any desired value. An angular intensity distribution according to a dashed line  60  in graph  50  exhibiting a divergence profile of the exit beam  48  with still a smaller divergence is obtained if both prisms  30  and  32  are rotated such that the incidence angles on the surfaces  34  and  42  are slightly higher.  
         [0063]     The transmitted, i.e. the clipped portions (lines  20   a ,  22   b ) can be caught by detectors  55 ,  56  for a feed-back control of actuators  52  and  54  in order to adjust the rotational position of prisms  30  and/or  32  in order to obtain the desired beam shape, wherein the control of the beam shape can be made for both sides of the beam  12  independent from one another, if desired.  
         [0064]     This kind of rotational control can be applied to any of the preferred embodiments presented below just as well, and to those skilled in the art it will be obvious that there are other methods of controlling the incidence angle on the TIR surfaces  34  and  42  (for example changing the orientation of a mirror which reflects the beam into the prism  30  or  32 ) which can be combined with any of the embodiments described here.  
         [0065]     Further the entrance surfaces  36  and  40  as well as the exit surfaces  38  and  44  of the prisms  30  and  32 , which preferably are orthogonal to the respective beam position, may be coated with an anti-reflective (AR) coating to reduce optical losses in the system  10 .  
         [0066]     To increase the gradient of the angular distribution, the angle filtering using TIR can be enhanced by coating the surfaces  34  and  42  with an appropriate high reflective (HR) coating.  
         [0067]     While  FIG. 1  has bees described with respect to the clipping or cutting off of an angular distribution in a first direction or dimension x,  FIG. 2  shows an optical system  10 ′ for shaping the incoming beam  12  which has a divergence with an angular distribution in a second direction or dimension y, which is orthogonal to the first direction or dimension x. The second dimension y defines a length of the incoming beam  12 , which may be hundred times larger than the width of the incoming beam  12  in the dimension x. For example, the incoming beam  12  may have an extension in the direction x which is less than about 15 μm, while the incoming beam  12  has an extension in the second direction, which is at least about 300 mm.  
         [0068]     The optical system  10 ′ again comprises two prisms  30 ′ and  32 ′ which are arranged such that the TIR surfaces  34 ′ and  42 ′ are orthogonal to the TIR surfaces  34  and  42  of the prisms  30  and  32 . The clipping or cutting off effect of the prisms  30 ′ and  32 ′ is based on the same principle as the clipping or cutting off effect of the prisms  30  and  32  so that reference is made to the description above.  
         [0069]     The optical system  10 ′ may be arranged in series with the optical system  10 , so that the exit beam  48  forms the incoming beam  12  with respect to the optical system  10 ′.  
         [0070]     The graph  24 ′ shows the angular intensity distribution of the incoming beam  12  in the second direction or dimension y, and the graph  50 ′ shows the clipped angular intensity distribution of the exit beam  48 ′ exhibiting sharp edges of the exit beam  48 ′ on both sides in the direction y.  
         [0071]     After having passed the optical system  10  and the optical system  10 ′, the beam  12  has been shaped in both directions or dimensions x and y, in each case on both sides thereof.  
         [0072]      FIG. 3  shows the effect of an HR coating on a TIR surface like the surfaces  34  and  42  or  34 ′ and  42 ′.  FIG. 3  shows a graph where the reflectance (in %) is plotted versus the incidence angle (in degrees) for an HR coated fused silica interface. The reflectance is 100% from a critical angle of TIR of about 42.6224° and drops to 30% in a range of about 0.0005°. Thus, an appropriate HR coating enhances the angle filtering effect of TIR.  
         [0073]      FIG. 4  shows another embodiment of an optical system  60  for shaping the intensity profile of an incoming beam  62  which is based on the same principle of angle filtering like the embodiments in  FIGS. 1 and 2 . The difference between the optical system  60  and the optical systems  10  and  10 ′ is that the direction of propagation of an exit beam  64  is parallel to the direction of propagation of the incoming beam  62 . This is achieved by the fact that two right-angled prisms  66  and  68  are arranged with respect to the incoming beam  62  such that a hypotenuse  70  of the prism  66  forms the entrance surface, and a first kathetus  72  forms the TIR surface of the prism  66  for clipping the angular intensity distribution on one side of the incoming beam  62 , and a hypotenuse  74  forms the entrance surface of the second prism  68  and a first kathetus  76  forms the TIR surface of the prism  68 . The hypotenuses  70  and  74  of the prisms  66  and  68  not only form the respective entrance surface of the prisms  66  and  68 , but also the respective exit surface of the prisms  66  and  68 , thus resulting in the exit beam  64  having a direction of propagation which is parallel to the direction of propagation of the incoming beam  62 .  
         [0074]     A graph  78  shows the angular intensity distribution of the incoming beam  62 , and a graph  80  shows the angular intensity distribution of the exit beam  64  which exhibits sharp edges on both sides in one dimension, which is the plane of drawing in  FIG. 4 .  
         [0075]      FIG. 5  shows another embodiment of an optical system  90  for shaping an incoming beam  92  which also uses an angle-selective optical element, in particular angle-selectively reflecting element  94  for clipping an angular distribution  96  of the incoming beam  92  by using TIR. The optical element  94  is a highly planar parallel plate or rod  98  comprising an optical medium having a refractive index which is higher than a refractive index of an environmental medium  100 , which, for example, is air. The medium of the optical element  98  may again comprise any suited material which is transmissive to the wavelength of the incoming beam  92 .  
         [0076]     The optical element  98  has two TIR surfaces  102  and  104  which may be coated with an HR coating. The optical element  98  clips the angular distribution  96  of the incoming beam  92  on one side, namely on the side illustrated by a line  106 , while the angular distribution is not clipped on the other side which is illustrated by a line  108 . Each time the incoming beam  92  strikes the surface  102  or the surface  104 , those rays of the incoming beam  92  which have a divergence such that they are incident on the surfaces  104  and  102  at an angle lower than the critical angle of TIR will at least partially be transmitted through the surfaces  102  and  104  and can be absorbed by a beam dump, for example a water-cooled beam dump  101 . An exit beam  112  emerges from an exit surface  110  of the optical element  98  having an angular intensity distribution  114  exhibiting a sharp edge on one side of the exit beam  112 .  
         [0077]     This embodiment uses multiple TIR for shaping the beam  92  (here four fold TIR).  
         [0078]      FIG. 6  shows a modification of the optical system  90  in form of an optical system  90 ′ which, in addition to the optical element  98  comprises a further optical element  118  in form of a planoparallel plate arranged in series with the optical element  98  and rotated by 90° with respect to the latter. While the optical element  98  clips the angular distribution  96  on one side of the incoming beam  92 , the optical element  118  clips the angular distribution on the other, i.e. opposite side of the beam  92 , or more exactly of the exit beam  112  so that an intensity distribution  120  is produced as shown in  FIG. 6  where the final exit beam  112 ′ has sharp edges on both sides thereof.  
         [0079]     It is to be understood that the optical element  98  and/or the optical element  118  shown in  FIGS. 5 and 6  can be provided with a rotational control similar to the embodiments shown in  FIGS. 1 and 2  for adjusting the profile shape of the exit beam  112  and/or  112 ′.  
         [0080]     Further, surfaces  102 ,  104  as well as the corresponding TIR surfaces of the optical elements  118  may be coated with an HR coating, and the entrance and exit surfaces  109  and  110  of the optical element  98  as well as the corresponding entrance and exit surfaces of the optical element  118  can be coated with an HR coating.  
         [0081]      FIG. 7  shows another embodiment of an optical system  130  for shaping an incoming beam  132  having a divergence with an angular distribution at least in a first direction. A graph  134  shows the angular intensity distribution of the incoming beam  132 .  
         [0082]     The optical system  130  comprises four angle-selective optical elements, in particular angle-selectively reflecting elements, in the present case four right-angled prisms  136 ,  138 ,  140 ,  142 .  
         [0083]     Prisms  136  and  138  are arranged in similar fashion like the prisms  30  and  32  of the optical system  10  in  FIG. 1 . The hypotenuses of the prisms  136  and  138  are arranged as TIR surfaces.  
         [0084]     In the direction of propagation of the incoming beam  132 , the prism  140  is arranged behind the prism  138 , and the prism  140  is followed by the prism  142  from which the beam  132  is again directed into the prism  136 .  
         [0085]     The incoming beam  132  first enters an entrance surface  144  of the prism  136  in a marginal region of the surface  144 . Departing from the TIR surface  146  of the prism  136 , the beam  132  follows a path through the four prisms  136  through  142  according to the arrows depicted in  FIG. 7 . As shown in  FIG. 7 , the beam  132  passes each prism three times, until an exit beam  148  emerges from prism  142  in a direction parallel to the direction of propagation of incoming beam  132 . In order to couple out the exit beam  148  from the optical system  130 , the prisms  136  and  138  are spaced apart from each other by a distance sufficient for the exit beam  148  to pass between both prisms  136  and  138 .  
         [0086]     The optical system  130  uses multiple TIR for enhancing the effects of clipping or cutting off the angular distribution in a direction or dimension x. In particular, the optical system  130  clips or cuts off the angular distribution in the direction or dimension x on both sides  150  and  152 , as shown by a graph  154 .  
         [0087]     It is to be understood that the TIR surfaces of the prisms  136  through  142  may be coated with an HR coating, while the entrance and exit surfaces of the prisms  136  through  142  may be coated with an anti-reflective coating in order to avoid losses in the optical system  130 .  
         [0088]      FIG. 8  shows an optical system  130 ′ which is slightly modified with respect to the optical system  130  in that the two prisms  140  and  142  are replaced by one retro-reflector prism  156  thus reducing the number of entrance and exit surfaces and, thus, reducing losses in the optical system  130 ′.  
         [0089]      FIG. 9  shows another embodiment of an optical system  130 ″ which is a further modification of the optical system  130  or  130 ′ in  FIG. 7  or  8 . In case of the optical system  130 ″, the two prisms  140  and  142  of the optical system  130  or the retro-reflective prism  156  of the optical system  130 ′ have been replaced by two mirrors  158 ,  160 . It is to be noted that the mirrors  158  and  160  do not contribute to the beam shaping as such, because there is no angular filtering by the mirrors  158  and  160 . The mirrors  158  and  160  only work as folding mirrors.  
         [0090]      FIG. 10  shows another embodiment of an optical system or unit  190  for shaping an incoming beam  192 .  
         [0091]     The optical system  190  again uses TIR for angular filtering an angular distribution  194  of the incoming beam  192  in one direction, e.g. the x-direction or the y-direction of the beam  192 .  
         [0092]     The optical system  190  comprises a first optical element  196 , having two parallel TIR surfaces  198  and  200  which clip the angular distribution  194  of the incoming beam  192  on one side as shown by a graph  202  showing the angular distribution of an exit beam  204 .  
         [0093]     The optical element  196  is formed as a rectangular plate having two further surfaces  206  and  208  parallel to each other for folding the beam  192  passing through the optical element  196 . The beam path of the beam  192  in the optical element  196  is illustrated by small arrows. The exit beam  204  emerges through an exit surface  210  of the optical element  196 . The optical element  196  is effective in clipping the angular distribution of the incoming beam  192  on one side only. In order to also clip the angular distribution on the opposite side, a second optical element  212  is provided having two TIR surfaces  214  and  216  for clipping the angular distribution on the opposite side of the beam  192 . The optical element  212  is arranged in series with the optical element  196 , wherein the exit beam  204  is the incoming beam with respect to the optical element  212 .  
         [0094]     A final exit beam  218  exhibits an angular distribution as shown by a graph  220 .  
         [0095]     The optical element  212  may be designed identical to the optical element  196 , wherein the optical element  212  is rotated in the plane of the drawing by an angle of 90° with respect to the optical element  196 .  
         [0096]      FIG. 11  shows another embodiment of an optical system  230  which uses a plurality of the optical elements  196  and  214  of the optical system  190  in order to further enhance the gradient of the angular distribution of the exit beam compared with an incoming beam  192 . The incoming beam  192  passes the optical elements  196 ,  212 ,  232 ,  234  and exits from the latter as exit beam  236 .  
         [0097]     According to  FIG. 10 , the beam  192  passes each of the optical elements  196  through  234  several times, thus further enhancing the gradient of the intensity distribution of the exit beam  236  by multiple TIR. Further, the optical system  230  allows the exit beam  236  to not only propagate in the same direction as the incoming beam  192 , but also without directional offset.  
         [0098]      FIG. 12  shows an optical system  230 ′ using the optical system  230  in  FIG. 11  but having an active medium  238  arranged between the optical elements  196 ,  212 ,  232  and  234 . In this way, the optical system  230 ′ can be used as ring laser producing a laser beam having a reduced divergence in one direction. A partial reflector  240  can be used as an output coupler. Using a three-dimensional arrangement, a divergence in both orthogonal directions (x and y) can be reduced.  
         [0099]     It is to be understood that each of the embodiments described above can be combined with one another into orthogonal planes for reducing a divergence of an incoming beam in both directions of the beam (x and y), in particular of an incoming beam having any rectangular profile.  
         [0100]     As already mentioned, all embodiments described above can comprise HR coatings to enhance the gradient of the slopes of the angular distribution and AR coatings to reduce optical losses in the system  
         [0101]     Further, as already described with respect to  FIG. 1  (detectors  55 ,  56 , actuators  52 ,  54 ) each of the above-described embodiments can be equipped with an active stabilization technique for an automatic adjustment of the angular distribution of the TIR active optical elements like prisms or plates etc. as described above. For example, a part of the incoming beam transmitted at a TIR surface, can be received by a light sensitive device (detectors  55 ,  56  for example) like a photo diode, a one- or two-dimensional photo diode array or CCD-camera. The information from this device can be used as a feed-back signal for some active mechanical elements like piezo or step motors, for example the actuators  52  and  54  in  FIG. 1  to adjust the slope of the angular distribution.  
         [0102]     The optical systems described above are preferably used in annealing apparatuses or other material processing apparatus and techniques, e.g. for directional crystallization of amorphous silicon films, where the illumination line shaped according to the principles of the present invention is scanned over a substrate to be processed.  
         [0103]     In the following, measures for the correction of dispersion and orthogonal divergence effects are described with respect to  FIGS. 13 through 16 .  
         [0104]     If the beam to be formed is not monochromatic, dispersion in the bulk material of the optical elements (for example prisms  30  and  32  of the optical system  10  in  FIG. 1 ) and in the coatings if provided have to be taken into account.  
         [0105]      FIG. 13  shows a typical dispersion of a coated TIR interface (for example TIR surface  34  in  FIG. 1 ).  
         [0106]     The angular dependency of reflectivity is essentially the same for different wavelengths, but the reflectivity curve is shifted to slightly different angles because of the dispersion of the optical material.  
         [0107]     The critical angle α TIR  for total internal reflection is given by 
 
sin α TIR (λ)=1 /n (λ) 
 
 wherein n(λ) is the refractive index at the respective wavelength, and the critical angle (and the reflectivity curve) in general shifts to smaller angles at shorter wavelengths, as can be seen in  FIG. 13 . 
 
         [0108]     If no correction means are present, this dispersion effect heavily limits the angular resolution of a divergence reduction element (for example prism  30  or  32  in  FIG. 1 ) as described in the above embodiments for non-monochromatic radiation. However, correction is possible by using dispersing prisms before and after the beam passes through the actual divergence reduction elements, for example through the prism  30  and  32  or the rods or plates  98  in  FIG. 5 . The incidence angles on the correction prism (and on the entrance surface of the actual divergence reduction element) have to be chosen such that beams with different wavelengths travel along the same direction again after the last correction prism, but are incident on the TIR surface at the respective TIR angle for the respective wavelength.  
         [0109]     There is a wide choice of combinations of incidence angles to achieve dispersion correction. However, it should be noted that the dispersive action of the refraction at the entrance surface of the divergence reduction element itself is never sufficient to achieve the above object. The reason is that dispersive effects are stronger for larger incidence angles, and for a single refraction at an angle which is smaller than the critical angle for TIR, the dispersive effect of a single refraction is not sufficient. Therefore, a dispersive element for the divergence reduction element is necessary. Likewise, the refraction at the exit surface of the divergence reduction element is not dispersive enough to compensate, and another dispersive element is required.  
         [0110]     For two elements  246 ,  248  reducing divergence on both sides of the angular spectrum, a total of four correction prisms  150 ,  152 ,  154 ,  156  can be used, as shown in  FIG. 14 .  
         [0111]     For the correction of dispersion effects, dispersive elements other than prisms like reflection or transmission gratings, etc. can be used as well.  
         [0112]     The correction of dispersion effects for polychromatic radiation has been described before. Such a correction is necessary because the critical angle for total internal reflection depends on the refractive index and thus on the wavelength of the radiation.  
         [0113]     But even for strictly monochromatic radiation, the divergence reduction as set forth above only works well if the angular spectrum of the incoming beam is very narrow in the direction perpendicular to the plane of incidence. Otherwise, the inclination angle β of the TIR interface surface and the pointing angle γ in the orthogonal direction together determine the incidence angle α on the TIR interface surface, which is larger than the angle β (see  FIG. 15 ). The angles are related by 
 
sin 2 α=sin 2 γ+sin 2 β cos 2 γ. 
 
         [0114]     The afore-mentioned angles are illustrated in  FIG. 15  where the rectangle illustrates the TIR surface.  
         [0115]     This means that the incidence angle α depends on the orthogonal angle γ, and a different inclination angle β would be required for each orthogonal angle to cover a certain orthogonal divergence range. The situation is similar to the effects of dispersion for polychromatic radiation, and, thus, the same correction mechanism as for dispersion effects can be used for the correction of orthogonal divergence effects. This can be seen with reference to  FIG. 16  as follows:  
         [0116]     Considering the refraction at a single surface using the nomenclature as above, seen in the projection in the plane of inclination β, the projected angle of refraction β′, in this projection, depends on the orthogonal incidence angle γ and it can be shown that the law of refraction can be rewritten in a modified form (for projected angles and depending on the orthogonal angle γ):  
         sin   ⁢           ⁢       β   ′     ⁡     (   γ   )         =       sin   ⁢           ⁢   β       n   ⁡     (   γ   )             
 
 wherein the effective index n(γ) depends on the orthogonal angle γ as follows:  
         n   ⁡     (   γ   )       =       n     cos   ⁢           ⁢   γ       ·         1   -         sin   2     ⁢   γ       n   2           .           
 
         [0117]     Using this modified law of refraction, beams for any orthogonal angles γ can be traced in the projection as usual and the only difference is in the refractive index n, which now depends on the orthogonal incidence angle γ and potentially also on the wavelength λ. In either case, compensation is possible as described above for correcting dispersion effects (see  FIG. 14 ), and any refractive dispersion-corrected device will also be corrected for orthogonal divergence.