Abstract:
Optical filaments are formed controllably in a gaseous medium such as air. A phase plate introducing a phase singularity is introduced into the path of the laser beam that forms the optical filaments in the medium. The phase plate is preferably a vortex phase plate having one or more singularities. The locations and characteristics of the phase singularities are selected to control the number and locations of the optical filaments.

Description:
FIELD OF THE INVENTION 
     The present invention is directed to the generation of optical filaments and more particularly to spatial control over the generation of optical filaments. 
     DESCRIPTION OF RELATED ART 
     An optical filament is a non-diffracting optical beam that can propagate over relatively long distances through a medium that possesses the appropriate nonlinear optical responses. When a beam of intense light passes through such a medium, the medium tries to focus the light. If the beam is focused to a sufficient degree, the intensity becomes extremely high, with the result that the medium starts to ionize. The resulting plasma tends to defocus the beam. A balance between the focusing and defocusing effects results in the optical filament. The threshold power for forming an optical filament is typically in the tens of megawatts. 
     Normal atmosphere contains such optical nonlinearities, as do many other substances. Optical filaments have applications such as laser-controlled discharges, long-range deposition of high laser intensities, and LIDAR monitoring. 
     The formation of optical filaments extending over several meters has been reported. However, to date, no reliable method has been developed or disclosed for controlling the formation of one or more optical filaments within a filament forming laser beam. Though the number of filaments could be somewhat controlled by the amount of energy in the beam, the transverse position(s) of filament(s) relative to the beam and the relative positions between multiple filaments could not be controlled. It was generally believed that intensity fluctuations across the beam seeded the formation of filaments in a random manner. 
     There is general speculation by several experimentalists that diffraction from hard edges in an optical system seeds filament formation. However, controllable filament generation on that basis has not been achieved. 
     In an entirely different field of endeavor, the use of phase plates for forming optical vortices is well understood. Such optical vortices have been formed using CW and low-power beams. However, the use of a phase plate for controlling ultrafast filamentation has not been recognized. 
     SUMMARY OF THE INVENTION 
     It will be readily apparent from the above that a need exists in the art for a way to control the formation of optical filaments. 
     It is therefore an object of the invention to control the formation of one or more optical filaments within the filament forming laser beam. 
     It is a further object of the invention to control the locations of the optical filaments. 
     It is a still further object of the invention to control, in a deterministic manner, the total number of optical filaments generated and their spatial positions of origin. 
     It is a still further object of the invention to do so without relying solely on the energy of the beam or on intensity fluctuations. 
     It is a still further object of the invention to provide energenically efficient generation of filaments. 
     It is a still further object of the invention to generate filaments that are robust to atmospheric turbulence. 
     To achieve the above and other objects, the present invention is based on the inventors&#39; discovery that filaments are formed from localized optical inhomogeneities, such as optical phase discontinuities and singularities, in the wave front. A phase plate can be generated to place optical phase singularities at specific locations in the beam. This allows the generation of specifically designed patterns of filaments in air or another gaseous medium within a beam. 
     The laser beam is an intense, pulsed laser beam having a high peak power, typically around five terawatts. The optical phase singularities permit vortex formation and thus a stable mode of propagation. 
     In the preferred embodiment, a phase plate for generating optical vortices is used to seed the formation of optical filaments at specific locations within an optical beam. The phase plate can be either reflective or trnasmissive and can be inserted in the beam before it is focused or compressed. The phase plate can be constructed by etching the pattern into glass, or any of the other standard methods of generating phase plates. The phase singularities are locations where the induced phase shift on the beam is undefined, and the induced phase shift varies from 0 to an integer multiple of 2π along a path around the singularity. It is possible to form an array of optical singularities on a phase plate. The induced phase singularities seed the formation of optical filaments in the designed pattern on the phase plate. 
     A phase plate can be generated to place optical phase singularities at specific locations in the beam. This allows the generation of specifically designed patterns of filaments within a beam. 
     The characteristics of the filaments can be controlled by controlling the singularity and the phase plate in general, e.g., by controlling the order of the singularity. The selection of the order of the singularity provides control over stability. A phase singularity in the middle of the filament increases the stability of the filament to phase changes in the air or other gaseous medium. Such phase changes can be caused, e.g., by air turbulence. Thus, the filament can be produced in a controlled manner in a plane perpendicular to the direction of propagation, as determined by the phase pattern. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A preferred embodiment will be disclosed in detail with reference to the drawings, in which: 
         FIG. 1  shows an experimental setup for creating filaments according to the preferred embodiment; 
         FIGS. 2–4  show the structure of individual filaments from a random distribution of phase singularities; 
         FIG. 5  shows an experimental setup used for verifying the presence of phase singularities in optical filaments in air; 
         FIGS. 6 and 7  show numerical simulations with and without a phase singularity, respectively; 
         FIG. 8  shows a comparison of experimental results with numerical simulations of diffraction patterns of a filament with a phase singularity; 
         FIGS. 9–13  show phase plates usable in the preferred embodiment; and 
         FIG. 14  shows a setup with a reflective phase plate. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     A preferred embodiment will now be set forth in detail with reference to the drawings. 
     The preferred embodiment uses a phase plate to impart a phase singularity. The phase plate can be a vortex plate, in which the phase delay increases in a circle around the singularity. 
       FIG. 1  shows a schematic diagram of an apparatus according to the preferred embodiment. In the apparatus  100 , a laser system  102  emits a laser beam L. The laser beam L passes through a phase plate  104 , which has a structure to be described below. The phase plate  104  imparts one or more phase singularities onto the laser beam L, which is then focused or compressed using focusing or compression optics  106 . The focused or compressed laser beam passes through a medium  108 , such as air, having the appropriate nonlinear properties. One or more optical filaments  110  form in the medium  108 . The optical filaments  112  form an effect such as a burn on a target  112 . 
       FIGS. 2–4  show the structure of the individual filaments from a random distribution of phase singularities. The structure shown in  FIGS. 2–4 , combined with the experimental and theoretical phase analysis, demonstrates that phase singularities seed the process of forming vortices that in turn support filaments. 
       FIG. 2  shows an 800 nm filament burn pattern on Plexiglas.  FIG. 3  shows electron microscope scans, which show that the damage is in an annular shape.  FIG. 4  shows burns in a “donut mode” that is consistent with phase singularities; possible equal-phase lines are superimposed on the image. 
     The results shown in  FIGS. 2–4  are shown to result from phase singularities for the following reasons. 
     The burn evidence points to phase singularities. Several burns from filaments show annular structure (400 nm filaments, burn on polycarbonate sheet (e.g., compact disk, or Macrolon™); 800 nm filaments, burns on plexiglass, polycarbonate sheet (e.g., compact disk, or Macrolon™) and tinted plexiglass; 1 ps 800 nm filaments, burns on polycarbonate sheet (e.g., compact disk, or Macrolon™) and plexiglass). Electron microscope images of the burns ( FIG. 3 ) verify that the annular structure is not an optical effect. 
     Such evidence has probably been missed in the past by other investigators for the following reasons. The burn process in most materials spreads or has too low a threshold to capture the structure of the filament. Plasma plumes off of metals or other materials diffuse so that filament structure cannot be observed. Volumetric damage in materials like glass is difficult to analyze. Diffraction experiments also verify the presence of a phase singularity. Such experiments have been performed for 400 nm and 800 μm filaments. 
       FIG. 5  shows an experimental setup  500  that was used for the diffraction experiments. An aperture  502  singles out one or more filaments or pre-filaments. A slit  504  is provided on a translation stage  506  for scanning across the filament. The central lobe of the diffraction pattern is shown on a screen  508 . 
     Calculations show that if filaments have phase singularities, the diffraction pattern should have two skewed, parallel horizontal lines at the central order, but should only have one if a singularity is not present. It is observed for 400 nm light, that the beam pattern has dark spots, which down the path of the beam, evolve into filaments. 
     Using the aperture to reduce the number of filaments, the slit was placed to select a filament upstream of where the filament was fully formed. The pre-formed filament was still intense enough to form a plasma plume off of the metal, but had not collapsed to the point to form a plasma plume when hitting paper. The pre-formed filament was not intense enough to get a burn. 
     The slit was scanned across the filament and the resulting diffraction patterns were photographed. 
       FIGS. 6 and 7  show numerical simulations with and without a phase singularity, respectively.  FIG. 8  compares the experimental results from the 400 nm experiments with the numerical simulations with a singularity and shows the match between the two. 
       FIG. 9  shows a phase plate  900  that can be used to seed optical filaments. The phase plate  900  shown is an n th  order singularity phase plate having a phase singularity  902 . The variation in phase around the singularity  902  is indicated in the drawing by lines  904  of equal phase. The singularity  902  seeds the formation of a filament  906 . The phase plate  900  is branch cut at phase φ=0 represented by an n*wavelength ledge  908  or a phase discontinuity. 
     The orders of the singularities can be selected to control filament properties such as size and inner null diameter. Thus, whether the phase plate has a single singularity or multiple singularities, the order or orders of the singularity or singularities can be selected to provide the appropriate control over the filament properties. 
       FIGS. 10 and 11  show phase plates  1000 ,  1100  for seeding two optical filaments  1002  or  1102 . The phase plate  1000  of  FIG. 10  has counter-rotating singularities  1004 ,  1006 . The phase plate  1100  of  FIG. 11  has parallel-rotating singularities  1104 ,  1106  of orders m and n. 
       FIG. 12  shows a generalized phase plate  1200  for seeding an arbitrary number of optical filaments  1202  by the use of singularities  1204 . The phase plate  1200  of  FIG. 12  is a generalization of those of  FIGS. 10 and 11 . Branch cuts  1206  can be placed in the phase plate to allow any combination or position of multiple singularities of arbitrary sign or order. Generally, only one or no branch cuts are required to extend to the perimeter of the phase plate, though more may be used to distribute the discontinuities. Regular arrays or arbitrary patterns of filaments may be seeded. 
       FIG. 13  shows a phase plate  1300  for producing a focused filament. By spiraling the phase n×wavelength phase discontinuity  1304  around the singularity  1306 , focus/defocus can be added to control the filament. By providing focus and additional control in the filament formation, the spiraling phase lines provide an additional degree of control. 
     The phase plates disclosed above are transmissive. However, as shown in  FIG. 14 , any of the above phase plates, or any other suitable phase plate, can be implemented as a reflective phase plate  1400 . The use of the laser system  102  has been disclosed above; therefore, that disclosure will not be repeated here. 
     While two preferred embodiments have been set forth above, those skilled in the art who have reviewed the present disclosure will readily appreciate that other embodiments can be realized within the scope of the invention. For example, a phase plate can impart a combination of singularities and discontinuities. Further, a phase singularity or discontinuity can be created in any suitable way, e.g., by varying the index of refraction of the material of the phase plate. Also, a plate can be used to impart other localized optical inhomogeneities. Moreover, numerical values and the like are illustrative rather than limiting. Therefore, the present invention should be construed as limited only by the appended claims.