Abstract:
A modified photonic crystal fiber yielding a higher peak power for a given maximum intensity. The multi-mode signal core has a depressed index of refraction that pushes the mode distribution to the core edges while a pattern of larger air holes is used to flatten the mode distribution. The core is further surrounded by tuned cladding elements defined by a pattern of smaller air holes that cause loss in all of the core modes except the fundamental while maintaining robust guiding of the fundamental mode.

Description:
STATEMENT OF GOVERNMENT INTEREST 
   The conditions under which this invention was made are such as to entitle the Government of the United States under paragraph I(a) of Executive Order 10096, as represented by the Secretary of the Air Force, to the entire right, title and interest therein, including foreign rights. 

   BACKGROUND OF THE INVENTION 
   Fiber lasers and amplifiers make use of a dielectric waveguide, the fiber, to constrain the degrees of freedom of the electromagnetic field while it is amplified by excited laser atoms within the core of the fiber. Given an amplifying waveguide, a fiber laser is formed by introducing it into a resonant cavity. One of the main advantages of fiber lasers is that if a single transverse waveguide mode is present in the fiber, then the output will have diffraction limited beam quality. Only one type of dielectric waveguide is considered here, a modified total internal reflection photonic crystal fiber (MTIR PCF), also known as solid-core photonic crystal fiber, microstructured fiber, or holey fiber. All fibers are assumed to be uniform along their length (axisymmetric) and, therefore, completely determined by the geometry of their cross-section. 
     FIG. 1  is a typical MTIR PCF with plots showing relevant parameters.  FIG. 1   a  is the cross-section of a standard photonic crystal fiber lattice with 10-micron spacing between lattice elements. It consists of an array of air-filled circular inclusions  12  in the fiber material  11  and a core  13  comprised of an area in the fiber material  11  in the center that is missing air holes. The inner cladding  11  is enclosed by an outer cladding  14 . The multimode central core  13  is appropriately doped with an active lasing ionic species designed for operation at a desired fundamental wavelength mode. The array can be described as a uniformly spaced lattice with one or more defects comprising the core and consisting of a missing or filled-in hole.  FIG. 1   b  is a plot of the calculated effective index vs. mode number of the lattice in  FIG. 1   a . The plot in  FIG. 1   c  shows the calculated fundamental (solid line) and higher order (dashed lines) core normalized modal intensity vs. the position within the core in units of lattice spacing (10 microns). The arrows between  FIGS. 1   b  and  1   c  show the effective index correspondence of the modes. 
   The guiding mechanism for a MTIR PCF can be thought of in the context of total internal reflection. Rays within the core that hit the air holes will be reflected due to the index difference on the boundary of the air hole. Maxwell&#39;s equations may be solved to determine the detailed characteristics of the guided mode. 
   In general, the modes of an MTIR-PCF may be described by an electromagnetic field distribution over the cross-section of the fiber and a propagation constant that determines the periodicity of the fields along the axis of the fiber at a given optical wavelength. In addition to the guided modes, there are also modes that are not localized to the core. In these modes, the field intensity is spread across the cladding and they are called cladding modes. Their properties will be determined by the geometry of the cladding, specifically, the index difference at the cladding boundary. Double-clad fibers have a region outside the cladding in order to confine pump light to the cladding. These fibers are also called cladding pumped fibers. Single-clad fibers have no special material outside the cladding except that which provides mechanical stability to the fiber. 
   The signal in the core of a single-mode fiber also experiences loss as a result of manufacturing irregularities and physical perturbations such as bending. The lost energy transfers to the cladding modes in this case. This can be viewed as a coupling process. The irregularities cause the core mode to couple to the cladding modes. Cladding modes may also be characterized by a field distribution and propagation constant. 
   The maximum power in a diffraction-limited beam from rare-earth doped fiber lasers is limited by the maximum electromagnetic intensity that can persist within the core without undesired effects and the maximum core area that can operate with a single propagating transverse mode. The intensity limit is fixed by the material properties. Therefore, any significant increase in power output must be achieved by increasing the core size and flattening the mode for a given maximum intensity level. As the core size of a modified total internal reflection photonic crystal fiber is increased, either the beam quality degrades due to the propagation of multiple transverse modes, or the fundamental mode losses become excessive as the waveguide is made weaker by decreasing the air hole size in order to eliminate the higher order modes. Standard single-mode fibers designed to operate at a wavelength of about 1 micron have a core diameter of approximately 7 microns. One successful strategy that has yielded a three-fold increase in core size is to use a fiber with a core supporting multiple modes, but then introducing mode-dependent losses so that the higher order modes experience more loss than the fundamental mode. In other words, the higher order modes experience a greater amount of coupling into the cladding modes. By the time the signal reaches the output of the fiber, only the fundamental mode is propagating in the fiber core. 
   In practice this mode discrimination is often accomplished in a step index fiber by coiling the fiber at an optimal radius. A coiled fiber exhibits substantially more loss in the higher order modes than the fundamental for a core sized up to approximately 25 microns (Koplow et. al., Optics Letters, 25, 442 (2000).) Above this diameter, however, the loss differential between the modes becomes so small that it does not sufficiently discriminate the fundamental mode from the higher order modes during amplification. (Liu et. al., SSDLTR 2004 paper, FIBER-5 (2004).) If larger area cores are sought, the tradeoff between fundamental mode loss and multi-mode operation is unavoidable if the cladding around the core is uniform, either in the sense of having a uniform index of refraction or having a uniform array of air holes in the case of the MTIR PCF. The uniformity of the cladding causes the cladding modes to couple uniformly to the fundamental mode and the undesired higher order guided modes leading to inefficient mode discrimination. 
   The maximum power in a diffraction-limited beam from rare-earth doped fiber lasers is currently limited by the maximum core area that can operate with a single propagating transverse mode and the maximum intensity permitted by material limitations. Increases in the core area is the subject of co-pending U.S. patent application Ser. No. 11/204,146 filed Aug. 15, 2005 and is hereby incorporated by reference. That application enabled large increases in the core area but with a relatively narrow profile of the fundamental mode intensity curve. 
   Further power increases will not only require a fiber with a larger core area as obtained with the tuned cladding fiber designed for a multimode central core, but also will need to flatten the intensity curve for a given maximum intensity level. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1   a  is a standard photonic crystal fiber lattice in cross-section. 
       FIG. 1   b  is a plot of calculated effective index vs. mode number for a standard photonic crystal fiber. 
       FIG. 1   c  is a plot of calculated fundamental and higher-order core normalized modal intensity vs. position in standard photonic crystal fiber in units of lattice spacing. 
       FIG. 2   a  is a tuned cladding fiber lattice in cross-section. 
       FIG. 2   b  is a plot of calculated effective index vs. mode number for a tuned cladding fiber. 
       FIG. 2   c  is a plot of calculated fundamental and higher-order core normalized modal intensity vs. position in the tuned cladding fiber in units of lattice spacing showing power coupling out of the undesired core modes. 
       FIG. 3  is a cross-section of tuned cladding photonic crystal fiber yielding a large flattened fundamental mode intensity curve showing the core area, inner cladding, an outer cladding. 
       FIG. 4  is a plot of the fundamental mode intensity (solid line) in arbitrary units of the LFMTCPCF vs. the distance in microns from the center of the core area overlaid with the corresponding mode intensity (dashed line) of the standard tuned cladding fiber of  FIG. 2   c.    
       FIG. 5  is a plot of the higher order mode loss vs. mode number for a standard photonic crystal fiber and for the LFMTCPCF for the particular set of parameters used in  FIG. 3 . 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENT 
   Computer simulations show that microstructures that guide a fundamental mode with an effective index matched to the effective index of the undesired higher-order modes will couple the power away from the undesired modes in the core. This is analogous to index matching at an optical boundary inhibiting reflection at that boundary. Different detailed microstructures may, therefore, be used for each of the different undesired modes in the core. 
   Increases in the core area are the subject of co-pending U.S. patent application Ser. No. 11/204,146 filed Aug. 15, 2005.  FIG. 2   a  is a cross-section of a tuned cladding fiber example from the &#39;146 application having an outer cladding layer  24  of uniform index of refraction n 3 . The inner cladding  21  is comprised of tuned cladding fiber material that has an average index of refraction of n 2 &lt;n 3  that is either homogeneous (glass of index n 1 ) or microstructured (glass tuned element areas  26  defined by missing or filled in air holes). In this tuned cladding fiber, the geometry of the material forming the inner cladding  21  is engineered to produce cladding modes that efficiently couple to the undesired guided modes but not to the fundamental mode. This is accomplished by calculated microstructure elements  26  (tuned elements) in the inner cladding  21 . The shapes  26  in  FIG. 2   a  are only examples, a general tuned element being comprised of any arrangement of missing or filled in air holes or the inclusion of air holes of arbitrary size. These tuned elements  26  are defined by air holes  22  in the glass  21 , similar to a photonic crystal fiber with a non-uniform but purposefully designed lattice of air holes. The multimode central core area  23  is doped with an active lasing ionic species designed for operation at a desired fundamental wavelength. It may be counter doped to maintain a constant glass index n 1 . The tuned elements  26  and the multimode central core area  23  are comprised of glass. 
   Single or multiple instances of each tuned element may be employed to provide a path, not unlike a transmission line, for the energy in the undesired core modes to be coupled all the way out to the outer cladding  24 . If the cladding modes are tuned in this manner, the overall average index of the inner cladding  21  can be lower, thus ensuring robust guiding and amplification through the gain medium  23  of the fundamental mode with low loss. This effect will only occur at specific wavelengths for which the fiber must be designed. Away from this wavelength, the inner cladding will no longer be tuned to the higher order modes of the core  23 . This is in contrast to the ability for conventional TIR PCF to exhibit endlessly single mode behavior over a wide wavelength range. 
     FIG. 2  shows a tuned cladding fiber designed for a multimode central core  23  size of 52 microns, an operating wavelength of 1064 nanometers, and a line width of &lt;100 MHz. The lattice pitch is 10 microns, and the diameter of the air holes is 3.2 microns with a hexagonally close packed spacing. The lattice of tuned elements that best coupled out the undesirable core modes in this example is shown in  FIG. 2   a .  FIG. 2   b  is a plot of the calculated effective index vs. mode number for the tuned cladding fiber of  FIG. 2   a .  FIG. 2   c  is a plot of the calculated fundamental (solid line) and higher-order (dashed lines) normalized modal intensity vs. the position in the tuned cladding fiber in units of lattice spacing (10 microns) showing power coupling out of the undesired core modes. The arrows show the effective index correspondence of the modes. Note the high but narrow peak intensity  25  curve achieved for the fundamental mode. For a given maximum intensity permitted by the fiber material characteristics, a higher peak power can be obtained by broadening the peak intensity curve. 
   One embodiment of the present invention is a method for designing large mode area photonic crystal fibers in which the mode is flattened in order to give a higher peak power for a given maximum intensity. This is accomplished by lowering the refractive index in the core (n core ) to slightly below that of silica n 1  and adjusting the size of selected air holes within the inner cladding. The lowered index of the core, n core , is still higher than the average index n 2  of the inner cladding. 
     FIG. 3  is an example of a large flattened mode tuned cladding photonic crystal fiber (LFMTCPCF)  31 . The outer cladding layer  36  has a uniform index of refraction n 3 . The inner cladding  37  is comprised of tuned cladding fiber material that has an average index of refraction of n 2 &lt;n 3  that is either homogeneous (glass of index n 1 ) or microstructured (glass tuned element areas defined by missing or filled in air holes of varying diameter). The geometry of the material forming the inner cladding  37  is engineered to produce cladding modes that efficiently couple to the undesired guided modes but not to the fundamental mode. This is accomplished by calculated microstructure elements, such as  40 ,  41 ,  42  (tuned elements) in the inner cladding  37 . These tuned elements  40 ,  41 ,  42  are defined by air holes in the glass  37 , similar to a photonic crystal fiber with a non-uniform but purposefully designed lattice of air holes The tuned elements  40 ,  41 ,  42  and the multimode central core area  32  are comprised of glass. In this example, the air hole diameters are 1, 3, or 8 microns in diameter  35 ,  34 , or  35 , respectively, and the hole spacing is 10 microns on center. The lowered core index flattens the core mode but concentrates the energy in the corners. The 3- and 8-micron air holes push in the corners yielding the desired even flattened mode. The 1-micron holes define tuned elements that dissipate the higher order modes of the core. 
   Single or multiple instances of each tuned element may be employed to provide a path, not unlike a transmission line, for the energy in the undesired core modes to be coupled all the way out to the outer cladding  36 . If the cladding modes are tuned in this manner, the overall average index of the inner cladding  37  can be lower, thus ensuring robust guiding and amplification through the gain medium  32  of the fundamental mode with low loss. This effect will only occur at specific wavelengths for which the fiber must be designed. Away from this wavelength, the inner cladding will no longer be tuned to the higher order modes of the core  32 . This is in contrast to the ability for conventional TIR PCF to exhibit endlessly single mode behavior over a wide wavelength range. 
   The multimode central core area  32  of  FIG. 3  is doped with an active lasing ionic species designed for operation at a desired fundamental wavelength. In this example, the doped core  32  parameters are: Δn=−8.0×10−4±1.0×10−5, absorption equals 320 decibels per meter times the ratio of the areas of the core and pump cladding at 975 nm, and the spatial extent of the core area is 50 microns. The effective diameter is 100 microns and the effective area is 7,800 square microns. These calculations were performed using the multi-pole method (White, el. al., J. Opt. Soc. Am. B19, 2322 (2002). 
     FIG. 4  is a plot of the fundamental mode intensity in arbitrary units vs. the distance in microns from the center of the core area. The dashed line  55  is the fundamental mode intensity for a standard tuned cladding fiber (see  FIG. 2   c ). The solid line  56  is the intensity of the fundamental mode for the LFMTCPCF of  FIG. 3  demonstrating the ability of producing a higher peak power for a given maximum intensity. 
   The core of this fiber is multi-mode. However, single mode operation can be obtained by low overlap of the mode profile with the gain provided by the active core region and high loss in the higher order modes. Low overlap is achieved by using a tuned cladding (as per application Ser. No. 11/204,146) and by depressing the index of the core thereby pushing the mode distribution to the core edges. The 1-micron holes in  FIG. 3  create the tuned elements. The 3-micron holes are the base lattice within which the 1 micron holes form the tuned elements. The 8 micron holes push the corners of the core inward leading to a more circular mode since these holes are further from the center of the core than the others forming the core boundaries. High loss is achieved by using a tuned inner cladding  37  that index matches the higher order modes thus allowing them to pass through the lattice into the outer cladding  36 . 
     FIG. 5  is a plot of the higher order mode loss vs. mode number for a standard photonic crystal fiber and for the large flattened mode tuned cladding photonic crystal fiber having the previously enumerated characteristics. The fundamental mode loss for the LFMTCPCF is 0.07 db/m demonstrating that the tuned elements cause very high loss in the undesirable higher order modes only and not in the fundamental mode. 
   The design analysis process for the LFMTCPCF is comprised of a sequence of steps. The geometry of the core is chosen first by determining how many missing air holes there will be. The next step is to increase the size of the air holes at the corners of the core region to create a more circular effective core area. Then specify the average index of the inner cladding in order to achieve the desired fundamental mode loss for the particular operating parameters of the laser such as the laser ion species, the pump power, the output power, and for an amplifier, the input power and gain. Next, calculate the effective indices and for all the guided modes in the core. There are several methods for calculating the effective indices of guided fiber modes including the beam propagation method, the plane wave expansion, and the multi-pole method. These methods have been implemented in commercially available software packages. For a regularly shaped core, circle or hexagon for example, there will be many degenerate modes. For example, the University of Sydney in Australia has a software program to calculate the modes of an arbitrary photonic crystal structure with circular air holes. The software is available from their website at: http/www.physics.usyd.edu.au/cudos/mofsoftware/index.html. 
   Next determine the core index difference Δn, i.e., the difference between the average inner cladding index and the core index. Depressing the index of the core slightly below that of glass n 1  pushes the mode distribution toward the core edges. Then calculate the mode shape (intensity distribution  56  of the fundamental mode,  FIG. 4   b ) for different values of the index difference Δn and choose the value that gives the desired flattened mode shape. Once this step is finished, the remaining process is the same as that for the tuned cladding fiber (application Ser. No. 11/204,146). 
   Specifically, for each undesired, higher order core-guided mode, specify a tuned element geometry whose fundamental mode effective index matches the effective index of that core-guided mode. Begin with a tuned element size approximately equal to the size of the local maxima in the intensity in that mode and calculate the effective index. If it is higher than the effective index of the specified core mode, then make the tuned element slightly smaller and if it is lower, make the tuned element slightly larger. Refine the tuned element geometry in this manner until the effective indices match to within the manufacturing tolerances for the fiber, usually on the order of 10 −4  in the index of refraction. Then check to see if any of the higher order modes of the tuned element accidentally match any of the higher order modes of the core. If this is the case, then these higher order modes do not need a separate tuned element with matching fundamental mode. Once all the required tuned elements are identified, place them within the cladding in multiple instances leading from the neighboring region of the core to the uniform cladding area. Then, calculate the effective index and power loss per unit length of each of the modes of the overall structure. The tuned elements will cause overall modes to propagate with a slightly different effective index then they would individually due to coupling between elements. At this point, slightly vary the size of each tuned element so that there are no higher order modes localized in the core and the fundamental core mode is the only localized mode or so the loss in the higher order modes is maximized relative to that of the fundamental mode. 
   The design may then be incorporated into a fiber pre-form and the fiber fabricated through the normal draw process. Once the fiber is drawn, it may be incorporated into a laser or amplifier in the standard fashion. The tuned cladding fiber may or may not be double clad, however, for large power handling capacity, it is anticipated that the fiber will normally be double clad.