Abstract:
A fiber-based device and associated method effectively convert a laser beam with an initial intensity distribution of Gaussian shape into a beam with another intensity distribution, which might typically be uniform or ring-shaped although other configurations are possible. The device comprises a single mode fiber with a core in which the beam is guided and a cladding surrounding the core. A component inline with the fiber couples a portion of the guided beam from the core into the cladding for propagation through the cladding toward an output end of the fiber. Interaction between core and cladding propagation modes produces the other intensity distribution at a predetermined distance from the output end of the fiber.

Description:
FIELD OF THE INVENTION 
       [0001]    The invention relates generally to shaping of laser beams, and more specifically, to conversion of a laser beam with a Gaussian intensity distribution effectively into a beam with another intensity distribution. Substantially uniform and ring-shaped intensity distributions are of primary interest but other distributions can be achieved with the invention. 
       DESCRIPTION OF THE PRIOR ART 
       [0002]    The Gaussian-shaped laser beam typically produced by a laser is satisfactory for applications that involve cutting or marking. However, other applications such as laser lithography or medical treatment require a beam with a substantially uniform intensity profile often referred to as a “top-hat” profile. It is known to use diffractive optical components to bend a Gaussian-shaped distribution of rays to approximate a beam of uniform intensity [1]. (References to technical publications are identified with numbers in square brackets and are detailed below after the description of preferred embodiments.) Another approach is to use a laser beam homogenizer that breaks a Gaussian input beam into many beamlets using a lens array and then uses a lens to superimpose them on an output plane [2]. A major shortcoming of both approaches is the need to use bulk optical components that require precise fabrication and alignment. Moreover, reflection at operative surfaces of the optical components can be expected to introduce power losses unless anti-reflective coatings adapted to accommodate high laser power are used. 
         [0003]    With rapid progress in high-power fiber laser technology, it would be desirable to provide a fiber-based solution for transforming a Gaussian intensity profile into a top-hat profile. In that regard, it is noted that Matsuura et al. [3]reported use of a 0.7 mm diameter silver-halide fiber tip attached to a hollow waveguide to homogenize a CO 2  laser beam and reduce waveguide bending losses. Beam uniformity was not, however, detailed. Hayes et al. [4] recently reported a square core jacketed air-clad fiber designed to deliver Q-switched Nd:YAG radiation from highly multimode sources. A top-hat intensity profile was achieved at the near-field of its approximately 400 μm square core but far-field beam homogeneity was not reported. A shortcoming associated with such approaches is that specialty fibers or fiber tips are required. Additionally, these approaches are incompatible with use of single mode fibers, and do not lend themselves to production of other useful intensity distributions, such as ring-shaped distributions. 
       SUMMARY OF THE INVENTION 
       [0004]    In one aspect, the invention provides a method of applying a laser beam to an object in which the laser beam has an initial intensity distribution of Gaussian shape and a final intensity distribution of predetermined shape at a surface of the object. The method involves guiding the laser beam along a single mode fiber from an input end of the fiber toward an output end of the fiber, the fiber comprising a core in which the laser beam is guided and a cladding that surrounds the core. A portion of the guided beam is coupled from the core into the cladding for propagation along the cladding toward the output end of the fiber. This is preferably achieved with a long-period grating (“LPG”) installed inline with the fiber, which may typically be adapted to couple the single transmission mode of the core to a lower order cladding mode. The surface of the object is placed at a position spaced from the output end of the fiber where interaction between core and cladding propagation modes produces the final intensity distribution. Although a single LPG can be used for such purposes, multiple components may be used to couple the single mode of the core to varying degrees into different cladding modes, allowing greater freedom in shaping the laser beam. As will be demonstrated below, it is possible to produce useful approximations of a uniform intensity distribution, a ring-shaped distribution and others. 
         [0005]    In another aspect, the invention provides a device for shaping a laser beam that has an intensity distribution of Gaussian shape. The device comprises a single mode fiber with an input end for receiving the laser beam, an output end for discharging the beam from the fiber, a core in which the received laser beam is guided from the input end toward the output end, and a cladding that surrounds the core. The device further comprises means inline with the fiber for imparting a predetermined intensity distribution to the discharged beam at a predetermined distance from the output end of the fiber. Such means couple a portion of the guided beam from the core into the cladding for propagation through the cladding toward the output end of the fiber such that interaction between core and cladding propagation modes produces the predetermined intensity distribution. 
         [0006]    The invention relies on interaction between core and cladding propagation modes to effectively shape a laser beam. In that regard, it is well-known that an LPG can couple light from the guided core mode into forward-propagating cladding modes if the phase matching condition, expressed by equation (1) below, is satisfied [5]: 
         [0000]      β 01 −β 0m =2π/Λ  (1) 
         [0000]    where, β 01  and β 0m  are the propagation constants of the core mode LP 01  and the m-radial cladding mode LP 0m  respectively, and A is the LPG period. If the LPG is formed perpendicular to the fiber axis, only radially symmetric cladding modes are excited. As regards low-order radial modes, the effective mode indices are sufficiently different that the phase matching condition constrains the core mode to be coupled to only one selected LP 0m  mode. This coupling can be made very efficient, and a conversion efficiency of over 99% at the resonant wavelength can be easily achieved using an LPG 2 to 4 cm long [5]. In practice, an insertion loss of only 0.1 dB was necessitated. 
         [0007]    Coupling the core mode LP 01  into a low-order cladding mode LP 0m  effectively enlarges the beam size since a Gaussian distribution is converted into a series of larger concentric rings with m nodes. The lower-order LP 0m  modes can propagate a long distance with negligible modal distortion or coupling into higher order LP 1m  modes, as has been demonstrated [6]. If only part of the core mode is coupled into a cladding mode, the two modes will interfere. Because of their different propagation constants, the interference pattern will vary as the modes propagate along the fiber and through free space at the end of the fiber. Since destructive interference can lead to reduced field intensity at the centre of the beam and enhanced field intensity in the first or second ring of the cladding mode, it is possible to achieve an approximation to a beam of uniform intensity. 
         [0008]    The complex amplitudes of the core and cladding modes at the end of the LPG can be calculated using coupled mode analysis [7]. The total field at the end of the fiber is then 
         [0000]        E ( r )= Aψ   01 ( r )+ Bψ   0m ( r )Exp[ iΔφ   m ]  (2) 
         [0000]      where 
         [0000]      Δφ m =Δφ m +(β 0m −β 01 ) L   f   (3) 
         [0000]    A 2  and B 2  are the relative powers in the core and cladding modes, respectively, and are related by the equation A 2 +B 2 =1. ψ 01  and ψ 0m  are the mode amplitudes for the core and the cladding modes, respectively. L f  is the distance from the end of the LPG to the end of the fiber, and L f  and other geometric parameters may be better understood with reference to  FIG. 1 . Δφ m  is the phase difference between the two modes at the end of the LPG calculated according to coupled mode analysis. This phase difference depends mainly on the grating parameters and β 01  and β 0m . The propagation inside the remaining part of the fiber causes only an extra phase shift, as shown in equation (3). The field distribution at an observation plane spaced a distance D from the output end of the fiber is calculated using the expression for Fresnel propagation in cylindrical coordinates: 
         [0000]    
       
         
           
             
               
                 
                   
                     
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         [0000]    where, ρ is the radius of the field amplitude at the output end of the fiber, and R is the outer cladding radius. Equations (2) through (4) demonstrate that there are several factors affecting laser beam shaping using an LPG: the field distribution of the cladding mode, the amount of light coupled from the core to the cladding, the phase difference between the core and cladding, and the distance from the fiber end to the observation plane or the surface of an object to be irradiated. 
         [0009]    Various aspects of the invention will be apparent from the foregoing summary of the invention and from a description below of preferred embodiments, and will be more specifically defined in the appended claims. 
     
    
     
       DESCRIPTION OF THE DRAWINGS 
         [0010]    The invention will be better understood with reference to drawings in which: 
           [0011]      FIG. 1  schematically illustrates an experimental device for implementing the invention; 
           [0012]      FIG. 2  is the transmission spectrum of an LPG comprised by the device; 
           [0013]      FIG. 3  ( a ) is a plot of field intensity relative to x and y axes at a distance of 7 mm from the output end of the device; and, 
           [0014]      FIG. 3  ( b ) is a plot of field intensity comparable to that of  FIG. 3  with the LPG in effect removed from the device by appropriate tuning of the wavelength of the source laser beam; 
           [0015]      FIG. 4  is a graph showing simulated intensity profiles of the laser beam discharged from the device at discrete distances from the output end of the device; 
           [0016]      FIG. 5  is a graph showing qualitatively the intensity profile of the laser beam at a distance of 6 mm from the output end of the fiber; 
           [0017]      FIG. 6  is a graph showing how the discharged laser beam diverges as a function of distance from the output end of the device; and, 
           [0018]      FIG. 7  is a graph showing the intensity profile of another device embodying the invention. 
       
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0019]    Reference is made to  FIG. 1 , which schematically illustrates a prototype fiber-based device  10  that effectively converts a Gaussian shaped beam into a beam of substantially uniform intensity. The device  10  comprises a single mode fiber  12  with a core  14 , a cladding  16  surrounding the core  14 , an input end  18 , and an output end  20 . The input end  18  receives a laser beam from a tunable laser (not shown) operating in the near infrared range, which beam has a typical Gaussian intensity profile  21 . The laser beam is guided within the core  14  toward the output end  20  of the fiber  12 . The device  10  also comprises an LPG  22  inscribed inline with the core  14  of the fiber  12  upstream of the output end  20  of the fiber  12 , which LPG  22  couples a portion of the light guided in the core  14  into the cladding  16  for forward propagation toward the output end  20 . In this embodiment, the core mode is coupled to the LP 03  cladding mode. The LPG  22  has a length designated L G  and is spaced a distance designated L f  upstream from the output end  20  of the fiber  12 . An object  24  to be irradiated is positioned with a surface  26  of the object  24  at a distance D from the output end  20  of the fiber  12 . As explained more fully below, the distance D is selected such that the beam has a substantially uniform intensity profile  27  at the surface  26  of the object  24 . 
         [0020]    The LPG  22  was formed in a hydrogen-loaded Corning™ SMF28 fiber by irradiating the core with 248 nm KrF excimer laser light though an amplitude mask, which induces a periodic refractive index modulation along the fiber axis. The length L G  of the LPG  22  is approximately 40 mm, and the distance L f  from the end of the LPG  22  to the output end  20  of the fiber is approximately 8 mm. It has a period of 620 μm, which ensures phase matching between the fundamental core mode and the LP 03  cladding mode within the tuning range of the laser. The transmission spectrum of the LPG  22 , shown in  FIG. 2 , is centered about a wavelength of 1574 nm. It displays a peak coupling efficiency of 99.5% and a full-width-at-half-maximum bandwidth of 10.8 nm. Since the bandwidth of the LPG  22  is much broader than that of the relatively narrow-band output of the tunable laser, the amount of light coupled to the selected cladding mode can be controlled by tuning the laser wavelength across the loss peak of the LPG  22  or even its side lobes. 
         [0021]    Laser beam intensity profiles for the device  10  were measured using a laser beam profiler (Photon Inc. Model Beam Scan 1180) for line scanning with a 1 μm slit and by an infrared camera with a spatial resolution of 20 μm in a horizontal direction and 18 μm in a vertical direction (Hamamatsu Electronics, Model C2741) for 2D measurements. 
         [0022]      FIG. 3   a  displays a 2D beam profile measured at a wavelength of 1584.7 nm, which corresponds to about a 10% coupling of light from the core mode to the LP 03  cladding mode. Along the x-axis, the intensity variation is less than 5% of the average intensity within a diameter of about 400 μm. Two local maximum intensity spots were observed in the top and bottom of the second ring in  FIG. 3(   a ) but may not be apparent from the drawings attached to this specification. These appear attributable to coupling of a small amount of light into the higher order LP 11  mode, and it is believed that the fringes of the LPG  22  may not have been oriented completely perpendicular to the fiber axis during fabrication. Nevertheless, the intensity variation along the y-axis is still less than about 10% of its average intensity within a diameter of about 400 μm. In contrast,  FIG. 3(   b ) displays the Gaussian distribution characteristic of the source laser. This was obtained by setting the wavelength of the source laser to a value distant from the transmission peak at 1574 nm where no significant amount of light is coupled from the core mode to any cladding mode.  FIGS. 3(   a ) and  3 ( b ) clearly demonstrate the beam homogenizing effect of the device  10 . 
         [0023]    The significance of spacing the object  24  at a distance D from the output end  20  of the fiber  12  will be more apparent from  FIG. 4 , the results of a simulation producing intensity profiles as a function of distance D, which varies from 3 mm to 10 mm. The simulation considered 10% power coupled from the core mode to the LP 03  mode at a wavelength of 1585 nm in the near infrared region of the spectrum. The phase difference Δφ m  was fixed with cladding mode leading core mode by 1.87π. As the beam propagates away from the output end  20  of the fiber  12 , the beam profile shows an increasing dip in the center since the core mode diverges faster than the cladding mode. Any such profile can be adopted as the final intensity distribution of the beam at the surface  26  of the object  24  by appropriate selection of the distance D. In this embodiment, destructive interference at the center results in a substantially uniform intensity profile at about 7 mm from the output end  20  of the fiber  12 , which can be used to set a working distance for practical applications requiring a substantially uniform intensity distribution. 
         [0024]      FIG. 5  shows the profile of the beam at a distance of 6 mm from the output end  20  of the fiber  12 . The drawing is not to scale but shows qualitatively the general shape of the simulated profile and, for comparison, the shape of a corresponding ideal uniform intensity profile, shown in phantom outline. The simulated profile has a large central region  28  in which the intensity at any given point varies by no more than 10% from the average intensity value in that region, and a peripheral region  30  in which the intensity drops rapidly toward zero. The net result is a reasonable approximation of a uniform intensity beam. 
         [0025]    The divergence of the beam output by the device  10  is shown in  FIG. 6 . The divergence was determined using the beam width at 50% of its maximum intensity, measured by a beam profiler at a distance varying from 6 mm to 14 mm from the end of the fiber  12 . Least-square fitting of the data gives a half divergence angle of 1.27°, which is a significant reduction from the 8° divergence angle characteristic of the core mode. 
         [0026]    Unlike certain beam shaping devices identified above, the fiber-based device  10  has no interface involving bulk optical components and no need for alignment of such components, and negligible losses are consequently expected. Experimentally, an insertion loss of only about 0.1 dB was measured. Although this embodiment was made for operation in the near infrared range, the principles demonstrated here would also apply to laser beam shaping at other wavelengths. 
         [0027]    Another embodiment of the invention, an experimental prototype with the same basic configuration and physical parameters shown in  FIG. 1 , will be described. An LPG with a loss peak at 660 nm and a period of 480 μm was fabricated using a single mode fiber SMF630A from Prime Optic Fiber Corp. and irradiating the core of the fiber through an appropriate mask with 248 nm light. The length L G  of the LPG was 33 mm, and the distance L f  between the LPG and the end of the fiber was set to 6 mm. A Gaussian laser beam of wavelength 660 nm in the visible spectrum was applied to the input end of the fiber, and  FIG. 7  is a corresponding plot of field intensity at a distance D of 10.5 mm from the output end of the device, derived from a charge coupled device (“CCD”) camera. The intensity values on the vertical axis of the graph are in arbitrary units, and the values on the horizontal axis are in pixels. The radial profile presented in  FIG. 7  corresponds substantially to a ring-shape, the ring-shape being more evident in the insert  32  in  FIG. 7 , a two dimensional image taken with the CCD camera. 
         [0028]    It will be appreciated that particular embodiments of the invention have been described and that modifications may be made therein without necessarily departing from the scope of the appended claims. 
       REFERENCES 
       [0000]    
       
         [1] J. A. Hoffnagle and C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. 39, pp 5488-5499, 2000. 
         [2] D. M. Brown, F. M. Dickey and L. W. Weichman, “Multi-aperture beam integration systems”, p 273 in “Laser Beam Shaping”, by F. M. Dickey and S. C. Holswade, Marcel Dekker, New York, 2000. 
         [3] Y. Matsuura, M. Miyagi, A. German, L. Nagli and A. Katzir, “Silver-halide fiber tip as a beam homogenizer for infrared hollow waveguides”, Optics Letters, Vol. 22, No. 17, pp 1308-1310, September 1997. 
         [4] J. R. Hayes, J. C. Flanagan, T. M. Monro, D. J. Richardson, P. Grunewald and R. Allott, “Square core jacketed air-clad fibre”, Optics Express, Vol. 14, No. 22, pp 10345-10350, October 2006. 
         [5] A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, J. E. Sipe and T. E. Ergodan, “Long-period fibre gratings as band-rejection filters”, Journal of Lightwave Technology, Vol. 14, p 58, 1996. 
         [6] S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light propagation with ultralarge modal areas in optical fibres”, Optics Letters, Vol. 31, No. 12, pp 1797-1799, June, 2006. 
         [7] H. Stoll, A. Yariv, “Coupled modes analysis of dielectric waveguides,” Optics Communications, Vol. 8, No. 1, pp 5-8, 1973.