Abstract:
Single transverse mode fiber amplifier and laser operation is obtained with a multi-mode signal core surrounded by cladding containing irregular microstructuring that causes loss in all of the core modes except the fundamental while maintaining robust guiding of the fundamental mode resulting in higher fiber laser power capacity.

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. The cross section of a MTIR PCF is shown in  FIG. 2   a . It consists of an array of air-filled circular inclusions  22  in the fiber material  21  and a core  23  comprised of an area in the fiber material  21  in the center that is missing air holes. 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. 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. As the core size 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 this introduces 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. Further power increases will require a fiber with a larger core area that can still discriminate between the fundamental mode and the undesired higher order guided modes. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is the cross-section of a generalized tuned cladding photonic crystal fiber. 
       FIG. 2   a  is a standard photonic crystal fiber lattice in cross-section. 
       FIG. 2   b  is a plot of calculated effective index vs. mode number for a standard photonic crystal fiber. 
       FIG. 2   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. 3   a  is a tuned cladding fiber lattice in cross-section. 
       FIG. 3   b  is a plot of calculated effective index vs. mode number for a tuned cladding fiber. 
       FIG. 3   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. 
   

   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 as depicted in  FIG. 1 . 
     FIG. 1  is a cross-section of a tuned cladding fiber  11  having an outer cladding layer  12  of uniform index of refraction n 3 . The inner cladding  13  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  15  defined by missing or filled in air holes). In this new tuned cladding fiber, the geometry of the material forming the inner cladding  13  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  15  (tuned elements) in the inner cladding  13 . The shapes  15  in  FIG. 1  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  15  are defined by air holes in the glass  13 , similar to a photonic crystal fiber with a non-uniform but purposefully designed lattice of air holes. The multimode central core area  14  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  15  and the multimode central core area  14  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  12 . If the cladding modes are tuned in this manner, the overall average index of the inner cladding  13  can be lower, thus ensuring robust guiding and amplification through the gain medium  14  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  14 . This is in contrast to the ability for conventional TIR PCF to exhibit endlessly single mode behavior over a wide wavelength range. 
   The design analysis process for this type of fiber is comprised of a sequence of steps. First, choose a core size and geometry for the central core. 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 (see White, el. al., J. Opt. Soc. Am. B19, 2322 (2002).) 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. 
   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  14  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. 
     FIG. 2  is a typical MTIR PCF with plots showing relevant parameters for comparison purposes.  FIG. 2   a  is the cross-section of a standard photonic crystal fiber lattice with 10 micron spacing between lattice elements.  FIG. 2   b  is a plot of the calculated effective index vs. mode number of the lattice in  FIG. 2   a . The plot in  FIG. 2   c  shows the calculated fundamental (solid line) and higher order (dashed lines) core normalized modal intensity vs. the position of the lattice element in units of lattice spacing (10 microns). The arrows between  FIGS. 2   b  and  2   c  show the effective index correspondence of the modes. 
     FIG. 3  is a tuned cladding fiber designed for a multimode central core  34  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. 3   a .  FIG. 3   b  is a plot of the calculated effective index vs. mode number for the tuned cladding fiber of  FIG. 3   a .  FIG. 3   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 again show the effective index correspondence of the modes. 
   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, as shown in  FIG. 1 .