Abstract:
An improved method and apparatus for passively conjugating the phases of a distorted wavefronts resulting from optical phase mismatch between elements of a fiber laser array are disclosed. A method for passively conjugating a distorted wavefront comprises the steps of: multiplexing a plurality of probe fibers and a bundle pump fiber in a fiber bundle array; passing the multiplexed output from the fiber bundle array through a collimating lens and into one portion of a non-linear medium; passing the output from a pump collection fiber through a focusing lens and into another portion of the non-linear medium so that the output from the pump collection fiber mixes with the multiplexed output from the fiber bundle; adjusting one or more degrees of freedom of one or more of the fiber bundle array, the collimating lens, the focusing lens, the non-linear medium, or the pump collection fiber to produce a standing wave in the non-linear medium.

Description:
Research leading to this invention was funded by the High Energy Laser Joint Technology Office under the Multidisciplinary Research Program “High Power Eye Safer Fiber Laser Arrays” at the United States Air Force Academy. It may be manufactured and used by or for the Government of the United States for all governmental purposes without the payment of any royalty. 
    
    
     BACKGROUND OF THE INVENTION 
     This disclosure relates to phase conjugation of distorted wavefronts. In particular, it relates to phase conjugation of distorted wavefronts that result from optical phase mismatch between elements of a fiber laser array. If the wavefronts of beams in a fiber laser array cannot be conjugated, the resulting distortion, sometimes referred to as “piston” error, prevents a uniform wavefront from being achieved at the output of the laser. This reduces power output from the laser, and may cause the laser to shut down. 
     Recent research has explored different ways to combine multiple fiber lasers or amplifiers to achieve power scaling while maintaining near diffraction limited performance. This research has taken several approaches. These approaches include both coherent and spectral combining. 
     Passive coherent phasing of laser arrays offers a simpler approach but has met with only limited success. Current passive coherently-combined fiber laser schemes are limited to a coherent brightness gain of approximately 8-12 for large arrays. Some further improvements such as an intensity dependent index (Kerr) nonlinearity have shown modest expected maximum improvement, with coherent brightness gain saturating at 10-14, depending on the strength of the nonlinearity. 
     This phenomenon has been confirmed theoretically and experimentally. Schemes employing stimulated Brillouin scattering phase conjugate mirrors have been proposed, however, they require a master oscillator as well as a Faraday rotator medium, which cause system engineering difficulties. 
     Thus, there remains a need for a method and apparatus that provide improved phase conjugation of distorted wavefronts to yield improved coherent brightness gains that facilitate utilization of such output in directed energy and similar applications. In particular, improvements in passive phase conjugation of distorted wavefronts are needed. 
     SUMMARY OF THE INVENTION 
     This disclosure represents a major improvement in the phase conjugation of distorted wavefronts that result from optical phase mismatch between elements of a fiber laser array. The disclosed methods and apparatuses provide a way to combine separate laser beams into a single phase locked beam. They also potentially enable power scaling of passively coherently combined directed energy weapons based on these arrays. 
     This disclosure overcomes a key technical obstacle of how to multiplex pump waves that are essential to the non-linear optical process and responsible for the wavefront correction together with the beams creating the wavefront. It does so through employment of a novel fused fiber bundle geometry. This improved method and apparatus will potentially result in significant savings in the cost and weight of currently proposed systems for military and other applications, and offer other improvements in key areas such as precision engagement. 
     This disclosure also provides a method and apparatus that compensate for phase differences in the signal of each element of an array of fiber-optic sources. This phase difference is sometimes also referred to as “piston” error. When the fiber elements of the array are spatially combined in a close-packed fiber bundle to fill an aperture, such piston error can result in a combined wavefront that is non-uniform. Such non-uniform wavefronts result in poor spatial coherence. However, if these wavefront are then conjugated, or reversed, the return signal in each fiber array element will be injected in phase at that location by the phase conjugation or reversal. As a result, the return signal in each fiber array element will be in phase at the opposite end of the fiber array elements where laser output occurs. 
     The disclosed methods and apparatuses accomplish this conjugation through a four-wave mixing in a suitable non-linear material or medium within which the combined output of the fiber bundle array is focused. The four-wave mixing process requires that two counter-propagating pump beams be focused into the non-linear medium so that their combined intensity is uniform in the region of overlap with the fiber bundle array output. 
     This mixing process can be accomplished by feeding a pump signal through a central element of the fiber bundle array. This central element or bundle pump fiber has a core that is smaller in diameter than the cores of the other fibers in the fiber bundle array. Uniformity in the overlap region in the non-linear medium is accomplished through the bundle pump fiber having a smaller diameter core than the cores of the other signal fibers in the fiber bundle array. The smaller core of the bundle pump fiber causes the pump beam to spread out more rapidly as it propagates and thereby encompass the combined beam emanating from the other fibers in the fiber bundle array. Another pump beam is delivered by another pump fiber that is identical to the central fiber of the bundle. This pump collection fiber outputs a counter-propagating beam to the non-linear medium. The disclosed method and configuration facilitate perfect or near-perfect mode-matching of the counter-propagating beams by enabling a counter propagating pump in each delivery fiber to be maximized, thereby leading to maximum four-wave mixing and thus greatly improved phase conjugation efficiency. 
     A method for passively conjugating a distorted wavefront comprises the steps of: multiplexing a plurality of probe fibers and a bundle pump fiber in a fiber bundle array; passing the multiplexed output from the fiber bundle array through a collimating lens and into one portion of a non-linear medium; passing the output from a pump collection fiber through a focusing lens and into another portion of the non-linear medium so that the output from the pump collection fiber mixes with the multiplexed output from the fiber bundle; adjusting one or more degrees of freedom of one or more of the fiber bundle array, the collimating lens, the focusing lens, the non-linear medium, or the pump collection fiber to produce a standing wave in the non-linear medium. 
     An apparatus for passively conjugating the phases of a fiber bundle array, comprises: a fiber bundle array that includes a plurality of probe fibers and a bundle pump fiber; a collimating lens disposed substantially adjacent to the fiber bundle array; a non-linear medium disposed adjacent to the collimating lens; a focusing lens disposed adjacent to the non-linear medium; and a pump collection fiber disposed substantially adjacent to the pump collection fiber, wherein one or more degrees of freedom of said fiber bundle array, said collimating lens, said focusing lens, and said pump collection fiber can be adjusted so that beams emitted from said probe fibers and said bundle pump fiber pass through said collimating lens and said non-linear medium and engage a beam emitted from said pump collection fiber to produce a standing wave in said non-linear medium. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a cross-sectional view of a fiber bundle array. 
         FIG. 2  is a side elevation of a fiber bundle phase conjugate mirror. 
         FIG. 3  is a cross-sectional view of another fiber bundle array. 
         FIG. 4  is a laser with a fiber bundle phase conjugate mirror. 
     
    
    
     DETAILED DESCRIPTION 
     According to a preferred embodiment, a pump fiber is disposed at the center of a fiber bundle array. Such fiber bundle arrays may be fabricated by introducing the fibers into a fused-silica capillary tube which is then drawn down in a tapering machine which is available commercially. The pump fiber core has a generally smaller aperture or tighter focal spot than the apertures of the other fibers in the bundle. The smaller core of the pump fiber makes the pump fiber beam expand more rapidly. 
     As shown in  FIG. 1 , the first element of the device is a fiber bundle array  100 . The fiber bundle array  100  consists of an array of close-packed fibers  101 . The largest fill factor in such an array may be obtained by using a triangular-shaped lattice array. As shown in  FIG. 1 , a generally triangular-shaped lattice geometry is used. Other suitable geometries for the fiber bundle array  100  include generally rectangular- or square-shaped arrays, shown in  FIG. 3 . However, persons skilled in the art will appreciate that other lattice geometries may be used for the fiber bundle array  100 . For example, the fiber bundle array  200  in  FIG. 3  may be configured of more close-packed fibers  201  that may overlap (not shown). 
     The fiber bundle array  100  includes a plurality of outer fibers  101 . The outer fibers  101  are referred to as probe fibers  101 . Each probe fiber  101  has a core  102  and a cladding layer  103 . A central pump fiber  105  is disposed at the center of the outer fibers  101  of the fiber bundle array  100 . This central pump fiber  105  is referred to as a bundle pump fiber  105 . The bundle pump fiber  105  has a core  106  and a cladding layer  107 . 
     The core  106  of the bundle pump fiber  105  is smaller in diameter than the diameter of the core  102  of each of the probe fibers  105  in the fiber bundle array  100 . The bundle pump fiber  105  guides a single transverse radiation mode at the operating wavelength. The smaller the core  106  of the bundle pump fiber  105  is made, the more uniform will be the pump field produced by the beam of the bundle pump fiber  105  within a non-linear medium. This is so because a smaller diameter pump beam expands more rapidly and thereby overlaps the beams of the probe fibers  101  of the fiber bundle array  100  in a non-linear medium. Increasing the numerical aperture of the core  106  of the bundle pump fiber  105  enables the use of a smaller size core  106  in the bundle pump fiber  105 . The diameter of the core  106  of the bundle pump fiber  105  will depend on the operating wavelength of the beams of the other probe fibers  101 . If the wavelengths of the beams of the probe fibers  101  are in the 1 micron range, the diameter of the core  106  of the bundle pump fiber  105  should be approximately 5 microns. 
     The diameter of the core  102  of each probe fiber  101  in the fiber bundle array  100  should be as large as possible while still maintaining single-transverse mode of operation. If the wavelengths of the beams of the probe fibers  101  are in the 1 micron range, the diameter of the core  102  of the probe fibers  101  should be in the 25 micron range. These dimensions generally scale linearly with wavelength. 
     As shown in  FIG. 3 , another configuration of fiber bundle array  300  includes a plurality of outer fibers  301 , referred to as probe fibers  301 . Each probe fiber  301  has a core  302  and a cladding layer  303 . A central pump fiber  305  is disposed at the center of the outer fibers  301  of the fiber bundle array  300 . The bundle pump fiber  305  has a core  306  and a cladding layer  307 . 
     As with the previous embodiment, the core  306  of the bundle pump fiber  305  is smaller in diameter than the diameter of the core  302  of each of the probe fibers  305  in the fiber bundle array  300 . The bundle pump fiber  305  guides a single transverse radiation mode at the operating wavelength. The smaller the core  306  of the bundle pump fiber  305  is made, the more uniform will be the pump field produced by the beam of the bundle pump fiber  305  within a non-linear medium. As with the previous embodiment, a smaller diameter pump beam expands more rapidly and thereby overlaps the beams of the probe fibers  301  of the fiber bundle array  300  in a non-linear medium. Increasing the numerical aperture of the core  306  of the bundle pump fiber  305  enables the use of a smaller size core  306  in the bundle pump fiber  305 . 
     As with the previous embodiment, the diameter of the core  306  of the bundle pump fiber  305  will depend on the operating wavelength of the beams of the other probe fibers  301 . If the wavelengths of the beams of the probe fibers  301  are in the 1 micron range, the diameter of the core  306  of the bundle pump fiber  305  should be approximately 5 microns. The diameter of the core  302  of each probe fiber  301  in the fiber bundle array  300  should be as large as possible while still maintaining single-transverse mode of operation. If the wavelengths of the beams of the probe fibers  301  are in the 1 micron range, the diameter of the core  302  of the probe fibers  301  should be in the 25 micron range. These dimensions generally scale linearly with wavelength. 
     A phase conjugation mirror or device  200  according to the present disclosure is shown in  FIG. 2 . This device  200  provides phase conjugation of the beams from the probe fibers  101  in the following manner. Beams output from each of the probe fibers  101  of the fiber bundle array  100  are multiplexed with the beam of the bundle pump fiber  105 . The smaller aperture core  106  of the bundle pump fiber  105  causes the beam of the bundle pump fiber  105  to expand faster than the beams of the probe fibers  101 . As a result, the beam of the bundle pump fiber  105  overlaps the beams of the probe fibers  101  in the non-linear medium  202 . 
     The optical output from the fiber bundle array  100  should then traverse a collimating lens  201 , a non-linear medium  202 , a focusing lens  203 , and a pump collection fiber  204 , as shown in  FIG. 2 . The focusing lens  203  is identical in configuration and composition as the collimating lens  201 . The pump collection fiber  204  is identical in configuration and composition to the bundle pump fiber  105 . The pump collection fiber  204  has a core  205  and a cladding layer  206 . The core  205  of the pump collection fiber  204  has the same diameter and index of refraction as the core  106  of the bundle pump fiber  105 . 
     The non-linear medium  202  is positioned so that it is centered on the waist of the beam of the bundle pump fiber  105 . The non-linear material  202  may comprise any suitable material for the operating wavelength of the beams of the fiber bundle array  100  and should possess a strong third-order non-linearity to promote the four-wave mixing process. Examples of suitable materials for the non-linear medium  202  include photorefractive crystals, gasses, liquids, and laser crystals doped with ionic species active at the operating wavelength. In one embodiment, the non-linear medium  202  may comprise a Ytterbium and Erbium co-doped glass material. 
     To maximize the phase conjugation and output of the fiber bundle array  100 , the fiber bundle  100 , collimating lens  201 , focusing lens  203 , non-linear medium  202 , and pump collection fiber  204  should be positioned so that the single-transverse mode output of the bundle pump fiber  105  is matched to the single-transverse mode output of the pump collection fiber  204 . As discussed in more detail hereinafter, this can be accomplished by adjusting the orientation and position of the fiber bundle array  100  and the pump collection fiber  204  in relation to the collimating lens  201 , the focusing lens  203 , and the non-linear medium  202  to produce a standing wave in the non-linear medium  202  and maximum power output from the fiber bundle array  100 . This also provides single mode fiber coupling. 
     By varying the adjustment and degrees of freedom of the fiber bundle array  100 , pump collection fiber  204 , collimating lens  201 , and focusing lens  203 , the distorted wavefront produced by the fiber bundle array  100  can be conjugated to a provide a unified wavefront wherein maximum power can be produced from the bundle array  100 . At least seven degrees of freedom are provided in the fiber bundle array  100 , pump collection fiber  204 , collimating lens  201 , focusing lens  203 , and non-linear medium  202 . The seven degrees of freedom include the distance between the collimating lens  201  and the focusing lens  203 , the distance between the end of the fiber bundle array  100  and the collimating lens  201 , the distance between the focusing lens  203  and the pump collection fiber  204 , the horizontal and vertical displacement from the center of the fiber bundle array  100  relative to the center of the collimating lens  201 , and the horizontal and vertical displacements of the pump collection fiber  204  from the center of the focusing lens  203 . The combined function of these degrees of freedom is to provide efficient coupling of radiation from the core  106  of the center fiber  105  of the fiber bundle array  100  to the core  205  of the pump collection fiber  204 , and from the core  205  of the pump collection fiber  204  to the core  106  of the center bundle pump fiber  105  of the fiber bundle array  100 . Persons skilled in the art will understand that these degrees of freedom may be aligned and locked at a factory so that no additional adjustment is necessary for a field application, as is common with commercial laser systems. Alternatively, a device could be assembled with zero degrees of freedom with sub-micron dimensional tolerances. In either case, the seven degrees of freedom provide a means to efficiently and effectively couple radiation from the center fiber  105  with radiation of the pump collection fiber  205 . 
     As adjustments to the various degrees of freedom are made, a power detector  401  measures the power output from the pump collection fiber  204 . The power detector  401  may be positioned at a distal end of the pump collection fiber  204 , as shown in  FIG. 4 , to measure the power transmitted through the pump collection fiber  204  and thereby determine when the maximum power level has been produced from the fiber bundle array  100 . These adjustments are typically made before the high-power laser is turned on. Only the FWM pump laser  402  is employed for this alignment. When the system reaches maximum power output, this point generally corresponds to the creation or presence of a standing wave in the non-linear medium  202 , and correspondingly to phase conjugation of the wave front produced by the radiation of the probe fibers  101  of the fiber bundle array  100 . 
     By providing phase conjugation of the beams of the fiber bundle array  100  in the back end of a laser cavity, it can be ensured that the energy output from the laser at the business end of the probe fibers  101  and the fiber bundle array  100  has the same wavefront. The fully phase-conjugated wavefront passes through pump couplers  406  and active fiber  407  to the beam combiner  404  for high power laser output  405  from the laser  400 . Such phase conjugation provides a high power laser output  405  from the beam combiner  404  at the front end of the laser  400 . This facilitates high energy applications at the output end of the laser  400 . 
     A main advantage and another novel feature of this disclosure and invention is the introduction of the four wave mixing pump beam via the central bundle pump fiber  105 ,  305  of the fiber bundle array  100 ,  300  and the use of a smaller core  106 ,  306  in the central bundle pump fiber  105 ,  305  to maximize pump uniformity and overlap in the non-linear medium  202 . One method of accomplishing this is for the laser source that supplies the four wave mixing pump beam to be coupled to a fiber-optic coupler so that the four wave mixing pump beam is split into two equal-intensity beams via the coupler. One of the beams propagates outward through the bundle pump fiber  105 ,  305 . The other beam propagates outward through the pump collection fiber  204 . The overall intensity of the pump beams can be adjusted to maximize the phase conjugation efficiency of the device. The signal within each probe fiber  101  is then coupled to the fiber laser array through splicing or other means. 
     As shown in  FIG. 4 , this can be accomplished by using a 50/50 fiber splitter  408 . In this embodiment, the fibers  409  traveling from the FWM pump laser  402  and the fibers  410  traveling from the power detector  401  pass closely together so that they are in fact fused together to form a 50/50 splitter  408 . Such 50/50 fiber splitters are a common commercial product. The use of the 50/50 splitter  408  enables half of the pump power from the FWM pump laser  402  to be sent in each direction through the non-linear medium  200 . Half of the pump power from the FWM pump laser  402  passes from the 50/50 splitter  408  and passes through the pump collection fiber  204  to the non-linear medium  200 , while the other half of the power from the FWM pump laser  402  passes from the 50/50 splitter  408  and passes through the bundle pump fiber  105  to the non-linear medium  200 . Persons skilled in the art will appreciate that there are other ways to split the four wave mixing pump beam and send it to the non-linear medium. 
     Alternative modes of practicing the inventions disclosed herein include the use of different non-linear materials, operation at wavelengths from the visible to the infra-red, use of different numbers of fibers in the fiber bundle array, corresponding to elements in the fiber laser array, the use of birefringent fibers in the array to enhance the four-wave mixing efficiency, use of an active nonlinear medium for example by pumping laser crystals in order to make use of non-linear gain saturation to obtain the required non-linearity. 
     Another embodiment can be obtained by splicing the non-linear material, if it is comprised of a suitable material, directly onto the fiber bundle array. In this case, all of the collimation and focusing optics for the pump beams are adjacent to the pump collection fiber. 
     The foregoing disclosure has been presented for purposes of illustration and description and is not intended to be exhaustive or to limit the invention to the various embodiments and forms disclosed herein. Persons skilled in the art will realize and appreciate that many modifications and variations are possible in light of the above teaching. The disclosed embodiments were chosen and described to best explain the principles of the invention and its practical application to thereby enable others skilled in the art to best use the invention in various embodiments and with various modifications suited to the particular use contemplated. The scope of the invention is to be defined by the following claims.