Abstract:
A photonic crystal optical fiber made up of an array of conventional hollow core optical fibers is disclosed. The array of optical fibers omits at least one fiber to form a central hollow core. The fiber works on the principle of two-dimensional photonic crystals to confine the radiation in a guided wave within the central hollow core. The fiber has a true photonic bandgap in which radiation of a particular energy or wavelength is totally forbidden, thereby providing a very high reflection coefficient to radiation incident the walls of the central hollow core over a select range of angles. The central hollow core allows for radiation propagation with minimal absorption.

Description:
RELATED APPLICATION  
       [0001]    This application is a continuation of U.S. application Ser. No. 10/099,044 filed on Mar. 13, 2002, and incorporated herein by reference. 
     
    
     
       FIELD OF THE INVENTION  
         [0002]    The present invention relates to optical fibers, and in particular to a hollow core photonic bandgap optical fiber.  
         BACKGROUND OF THE INVENTION  
         [0003]    Optical fibers are long, thin waveguide strands. They are used in a variety of applications involving the reception, transmission and detection of radiation, ranging from optical telecommunications to scientific instrumentation to ornamental displays. Conventional optical fibers have a high-index core surrounded by a low-index cladding, a geometry that results in the total internal reflection of radiation entering the fiber over a select range of angles. Other forms of conventional optical fibers are referred to as “light tunnels” and use reflection from reflective walls rather than total internal reflection. Conventional optical fibers can have a variety of core geometries, including elliptical cores, double cores, polarization-maintaining cores, and hollow cores.  
           [0004]    Hollow core optical fibers are desirable where transmission losses need to be minimized, since in conventional optical fibers most of the radiation loss in an optical fiber occurs from absorption in the solid core. However, conventional optical fibers that depend on total internal reflection for waveguiding and confinement need to have a core with a higher dielectric constant than that of the cladding. Such a structure is at odds with an optical fiber having a hollow central core, since air has a dielectric constant lower than all known practical cladding materials. Thus, hollow core optical fibers generally require specialized design considerations.  
           [0005]    There are a number of different types of hollow core optical waveguides that operate on the either principle of total internal reflection or the principles of conventional reflection. For example, hollow optical waveguides through silicon wafers with highly reflective coatings on the side of the hollow core are disclosed in U.S. Pat. No. 6,090,636 to Geusic et al. An optical fiber interconnect through a silicon wafer with a hole filled with two different dielectric materials is disclosed in U.S. Pat. No. 6,150,188 to Geusic et al. A hollow optical fiber or hollow core waveguide consisting of a dielectric material coated with a highly reflective exterior coating is disclosed in U.S. Pat. No. 5,815,627 to Harrington, wherein the hollow core can contain one guided wave and the annular ring another guided wave. A hollow core optical waveguide having a highly reflective coating on the inside of a glass tube is disclosed in U.S. Pat. No. 6,141,476 to Matsuura.  
           [0006]    As mentioned above, a desirable property for an optical fiber is minimal transmission loss. Accordingly, there has been significant effort to form optical fibers from materials that have high transmission and high reflection. Some of this effort has been directed to forming optical fibers from quasi-two-dimensional photonic crystals. A photonic crystal is a substrate within which is formed an array of period structures through which radiation of a particular wavelength or energy is forbidden to propagate. The result is a material with a very high reflectivity. Two-dimensional photonic bandgap crystal structures have been reported not only at optical wavelengths but at acoustic wavelengths as well.  
           [0007]    It is well known in the semiconductor industry that a series of cylindrical holes judiciously formed in a solid semiconductor material can be used to form a quasi-two-dimensional photonic bandgap crystal. FIG. 1 is a plan view of a conventional two-dimensional photonic crystal formed from a substrate  110  patterned with an triangular array of cylindrical holes  120 .  
           [0008]    An example prior art quasi-two-dimensional photonic bandgap optical fiber  210  is illustrated in FIGS. 2A and 2B. The optical fiber  210  includes an array of holes  220  formed within a cylindrical substrate  226 . The fiber includes an outer cladding  228 . A solid core  232 , referred to as a “core defect,” is at the center of the substrate. Radiation  242  is reflected within the bandgap of the photonic crystal produced by the periodic array of holes surrounding the core and is confined to the core. The radiation travels down the length of the solid core by total internal reflection made possible by the low average index of refraction of the cladding as compared to that of solid core  232 . Though optical fiber  210  is photonic crystal based, it utilizes total internal reflection like a conventional optical fiber and is relatively lossy because the solid core absorbs radiation.  
           [0009]    Accordingly, what is needed is a photonic crystal optical fiber with a hollow core that allows for low-loss radiation propagation down the fiber by virtue of highly reflectivity walls as a result of the photonic bandgap of the crystal.  
         SUMMARY OF THE INVENTION  
         [0010]    A hollow core photonic crystal optical fiber formed from several smaller hollow core optical fibers layered around a hollow core is shown. The fiber works on the principle of quasi-two-dimensional photonic crystals to confine radiation in a guided wave. The fiber has a true photonic bandgap in which radiation of a particular frequency (or equivalently, energy or wavelength) is totally forbidden, thereby providing a very high reflection coefficient to radiation incident the walls of the hollow core.  
           [0011]    The present invention includes an array of hollow core optical fibers arranged longitudinally about an axis to define a central hollow core about the axis. The array is formed so as to act as a quasi-two-dimensional photonic crystal with a photonic bandgap that allows radiation of a select frequency range to propagate down the central hollow core.  
           [0012]    The present invention further includes a plurality of hollow core optical fibers arranged longitudinally in an array having a two-dimensional triangular lattice structure so as to form a quasi-two-dimensional photonic crystal having a photonic bandgap, and a central hollow core sized to accept radiation corresponding to the photonic bandgap. The hollow core optical fibers are, for example, conventional silica fibers.  
           [0013]    The present invention also includes a system that includes a hollow core photonic bandgap optical fiber having an input end and an output end. The photonic bandgap optical fiber is made up of an array of hollow core optical fibers arranged longitudinally to form a two-dimensional photonic crystal lattice having a photonic bandgap. The array of optical fibers has at least one omitted optical fiber so as to leave a longitudinal central aperture that forms the hollow core in the array. The hollow core in the array is capable of guiding light having a frequency within the photonic bandgap of the array. The system further includes a radiation source optically coupled to the input end, and a photodetector optically coupled to the output end.  
           [0014]    The present invention also includes a method of guiding radiation. The method includes forming a two-dimensional array of hollow core optical fibers to form a quasi-two-dimensional photonic crystal. The crystal has a photonic bandgap. In forming the array of fibers, at least one hollow core optical fiber is omitted. This creates a central hollow core in the array through which light of a select frequency that falls within the photonic bandgap is guided. The method further includes introducing radiation into the central hollow core having a frequency within the photonic bandgap.  
           [0015]    These and other embodiments, aspects, advantages and features of the present invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art by reference to the following description of the invention and referenced drawings or by practice of the invention. The aspects, advantages, and features of the invention are realized and attained by means of the instrumentalities, procedures, and combinations particularly pointed out in the appended claims.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0016]    [0016]FIG. 1 is a plan view of a conventional two-dimensional photonic crystal formed from a substrate and having triangular an array of cylindrical holes formed therein;  
         [0017]    [0017]FIG. 2A is a front-end view of a prior art photonic-crystal-based optical fiber having a plurality of holes surrounding a solid core;  
         [0018]    [0018]FIG. 2B is a cross-sectional view of the prior art optical fiber of FIG. 2A taken along the line  2 B- 2 B;  
         [0019]    [0019]FIG. 3A is a front-end view of an embodiment of the hollow core photonic bandgap optical fiber of the present invention;  
         [0020]    [0020]FIG. 3B is a close-up front end view of the optical fiber of FIG. 3A showing the individual conventional hollow core optical fibers making up the hollow core photonic bandgap optical fiber;  
         [0021]    [0021]FIG. 3C is a partial cross-sectional view of the optical fiber of FIG. 3A as taken along the line  3 C- 3 C;  
         [0022]    [0022]FIG. 4A is a plot of the optimal filling factor F OPT  versus the background dielectric constant ε B  for a triangular lattice structure;  
         [0023]    [0023]FIG. 4B is a plot of the width of the photonic bandgap as fraction of the center frequency of the bandgap versus the background dielectric constant ε B  for a triangular lattice structure;  
         [0024]    [0024]FIG. 5 is a face-on view of an alternate embodiment of the hollow core photonic bandgap optical fiber of the present invention that includes a cladding with a polygonal outer surface;  
         [0025]    [0025]FIG. 6A is a face-on view of an apparatus for forming the hollow core photonic bandgap optical fiber of the present invention, showing first spools of fiber used to form the first layer of fibers on a rod;  
         [0026]    [0026]FIG. 6B is a side view of the apparatus of FIG. 6A, showing second spools of fiber used to form the second fiber layer along with two of the heating units used to melt the fiber when it is pulled longitudinally off of the rod; and  
         [0027]    [0027]FIG. 7 is a side view of a system employing the hollow core photonic bandgap optical fiber of the present invention. 
     
    
       [0028]    In the Figures, the first digit of the reference number corresponds to the Figure number. Accordingly, like elements in different Figures have reference numbers that differ only in the first digit that identifies the Figure number.  
       DETAILED DESCRIPTION OF THE INVENTION  
       [0029]    In the following detailed description of the embodiments of the invention, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration specific embodiments in which the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention, and it is to be understood that other embodiments may be utilized and that changes may be made without departing from the scope of the present invention. The following detailed description is, therefore, not to be taken in a limiting sense, and the scope of the present invention is defined only by the appended claims.  
         [0030]    [0030]FIG. 3A is a full front-end view of an embodiment of a hollow core photonic bandgap optical fiber  310  of the present invention. Optical fiber  310  includes an array  314  of coventional hollow core optical fibers  320  each longitudinally arranged about a central axis A 1 . Optical fibers  320  each having an endface  322 , a hollow core  326  with a dielectric constant ε 0 =1, and an annular cladding  330  surrounding the hollow core and having a thickness T and a dielectric constant ε B &gt;1. Note that the dielectric constant of hollow core  326  is taken as the free-space dielectric constant ε 0 , which differs from that of air by only about six parts in ten-thousand. In an example embodiment, hollow core  326  is circular in cross-section and has a radius R 2 . For the sake of discussion, optical fibers  320  are presumed hereinafter to have a circular hollow core.  
         [0031]    [0031]FIG. 3B is a close-up front end view of optical fiber  310  of FIG. 3A. The total radius R 1  of each fiber  320  is given by R 1 =R 2 +T. The total diameter of each fiber is thus D 1 =2R 1 . The triangularly layered arrangement of fibers  320  omits at least one fiber from central axis A 1 , thereby leaving a longitudinal aperture or hollow core  340  centered on the central axis. Hollow core  340  is not exactly circular in cross-section, but has an effective circular cross-section  342  (dashed line). Also, hollow core  340  is also referred to hereinafter as a “central” hollow core to distinguish it from hollow cores  326  of the conventional optical fibers  320 . Here, the word “central” is not intended to limit the location of the hollow core to the exact center of array  314 .  
         [0032]    Where optical fibers  320  have a circular cross-section, their arrangement in in array  314  forms small gaps  350 . For fibers arranged in a triangular arrangement (FIG. 3B), the gaps occur by virtue of the cusps  354  formed by placing two fibers together, and then adding a third fiber to the first two fibers at the cusps.  
         [0033]    In an example embodiment, fiber array  314  constitutes a two-dimensional photonic crystal with a triangular lattice structure and a lattice constant a=2R 1 . The center wavelength and size of the bandgap of the photonic crystal depends on a number of factors, including the lattice constant a, and the difference (contrast) between dielectric constants ε 0  and ε B . It is convenient to define single parameter called the “filling factor,” which is the ratio of the volume of empty space in the crystal to the total volume of the crystal.  
         [0034]    [0034]FIG. 3C is a partial cross-sectional view of optical fiber  310  of FIG. 3A taken along the line  3 C- 3 C. FIG. 3C illustrates how radiation  367  is guided in central hollow core  340 . In example embodiments, central hollow core  340  has an effective diameter D ranging anywhere from 0.5 microns to 5 microns, depending on the wavelength of radiation  367  to be guided. As a general rule, the longest wavelength of radiation capable of being accepted by the central hollow core is about twice the central core diameter D. Thus, to form a hollow core photonic bandgap optical fiber capable of guiding infrared radiation of 1.5 microns for example, the diameter D of central hollow core  340  should be approximately 0.75 microns.  
         [0035]    Because the photonic crystal formed by fiber array  314  is two-dimensional, the associated bandgap is in the directions orthogonal to radiation propagation down hollow core  330 . For large incident angles θ (e.g., near degrees) measured relative to the central axis, the bandgap remains complete. For smaller angles, the bandgap width is reduced, and for increasingly large angles, the bandgap width is reduced and becomes incomplete. Thus, optical fiber  310  has a limited range of acceptance angles.  
         [0036]    [0036]FIGS. 4A and 4B are plots adapted from FIGS. 4 and 6 of the article by M. Plihal et al., entitled “Photonic band structure of two-dimensional systems: The triangular lattice,” Phys. Rev. B, 44 (16), 8565-8571, Oct. 15, 1991, which article is incorporated by reference herein. FIG. 4A plots a curve  410  of the optimal filling factor F OPT  as a function of background dielectric constant ε B  (also called the CcontrastC) for a two-dimensional triangular lattice structure of cylindrical holes, such as shown in FIG. 1. The optimal filling factor F OPT  is that which yields the widest bandgap for the lowest frequency. The results are applicable to the triangular lattice structure of fiber array  314  (FIG. 3B). In an example embodiment, optical fibers  320  (FIGS. 3A-3C) are made of silica, which has a dielectric constant ε B ˜4. From curve  410 , it is seen that the corresponding optimum filling factor F OPT  is about 0.55 or 55%.  
         [0037]    In an example embodiment, optical fibers  320  are selected and assembled to provide the optimum filling factor for optical fiber array  314 , as described below. FIG. 4B plots a curve  420  of the normalized width W=(ω G a)/(2πc) of the photonic bandgap (i.e., the width of the bandgap as a fraction of the center frequency ω G ) versus the background dielectric constant ε B . Here, c is the speed of light. It can be seen from curve  420  that for a background dielectric constant ε B =4, the normalized width W of the bandgap is 0.08, or 8% of the center frequency ω G .  
         [0038]    Note also that the normalized width W of the bandgap depends directly on the lattice constant a, which is given by a=2R 1 . Thus, the bandgap is determined by the radius R 1  of optical fibers  320  used to form the optical fiber array/photonic crystal  314 . Further, the frequency of radiation capable of being guided in hollow core  340  of optical fiber  310  is determined by diameter D of the central hollow core. Thus, the lattice constant a of optical fiber array  314  and the diameter D of central hollow core  340  formed therein are selected so that the frequency of radiation accepted by central hollow core  340  overlaps the photonic bandgap associated with the fiber array  314 .  
         [0039]    Designing Fiber for a Select Filling Factor  
         [0040]    The design of optical fiber array  314  as shown in FIGS. 3A-3C is now described. The design process includes selecting a desired filling factor F.  
         [0041]    To this end, first an imaginary triangle  364  of area A T  with vertices at the centers of three adjacent optical fibers  320  is formed (FIG. 3B).  
         [0042]    The area A T  of the imaginary triangle is given by:  
           A   T =½(2 R   1 )( R   1 )(3) 1/2 =1.73( R   1 ) 2    Equation 1  
         [0043]    The area A C  occupied by optical fibers  320  in area A T  (i.e., the total area A T  minus the area of gaps  350 ) is given by:  
           A   C =3(⅙)π( R   1 ) 2 =1.57( R   1 ) 2    Equation 2  
         [0044]    The area A A  of air due to hollow cores  326  of optical fibers  320  in area A T  is given by:  
           A   A =(π/2)( R   2 ) 2 =1.57( R   2 ) 2    Equation 3  
         [0045]    The filling factor F is then defined as:  
           F=A   A /A T =[1.57( R   2 ) 2 ]/[1.73( R   1 ) 2 ]0.91[( R   2 ) 2 /( R   1 ) 2 ]  Equation 4 
         [0046]    Equation 4 is used to choose the radii R 1  and R 2  to obtain a select filling factor F. For example, filling factor F may be selected to be the optimum filling factor F OPT . Using the example embodiment discussed above, F=F OPT =0.55, so that R 2 = 0 . 78 (R 1 ).  
         [0047]    It is worth noting that the area associated with gaps  350  is small (e.g., about 10%), whereas the filling factor F needed to create a significant bandgap is generally in excess of 50%. Accordingly, gaps  350  generally do not constitute a significant perturbation to the photonic crystal lattice.  
         [0048]    Other embodiments of hollow core photonic bandgap optical fiber similar to that of optical fiber  310  are possible with the present invention. For example, with reference to FIG. 5, there is shown a hollow core photonic bandgap optical fiber  510  made up of an array of optical fibers  520  each having an elliptical cross-section hollow core  526  surrounded by a cladding  528  having a outer surface  538  with a polygonal cross-section ( e.g., hexagonal, as shown). A polygonal hollow core  540  is centered on central axis A 1 . In an alternative embodiment to optical fiber  510 , hollow cores  526  each have a circular cross-section. This alternate embodiment can be considered a special case of the elliptical cross-section hollow core embodiment.  
         [0049]    The polygonal cross-sections can be selected so that the filling factor in cases where gaps  350  are determined to be undesirable. Also, polygonal cross-section fibers may in some instances prove easier to stack when forming the hollow core optical fiber array.  
         [0050]    Method of Fabrication  
         [0051]    A method of forming the hollow core photonic bandgap optical fiber of the present invention is now described. For the sake of illustration, the method is described in connection with forming optical fiber  310  as shown in FIGS. 3A-3C, though the method applies equally to other example embodiments.  
         [0052]    [0052]FIG. 6A shows front-end view of a fiber-forming apparatus  601  having a number (e.g., nine) of first spools  603  of conventional hollow core optical fiber  620 . Each optical fiber  620  has an endface  622 . First spools  603  are arranged radially outward from a central axis A 2  of a forming rod  615 . The forming rod has an outer surface  617 , an end  619  and a radius R R . In an example embodiment, radius R R =R 1 , or alternatively, R R ˜R 1 .  
         [0053]    [0053]FIG. 6B is a side view of apparatus  601  of FIG. 6A, showing a number of second spools  627  of optical fiber  620 . Second spools  627  are also arranged radially outward from rod central axis A 2  but are located closer to rod end  619  so that optical fiber can be arranged over the forming rod or over existing layers of optical fiber placed onto the forming rod. Apparatus  601  includes a number of heat sources  643  are provided adjacent axis A 2  in a position to provide heat to the optical fibers surrounding the forming rod.  
         [0054]    The technique of forming the hollow core photonic bandgap optical fiber of the present invention is similar to the method of forming a wound electrical cable. Thus, optical fibers  620  from first spools  603  are arranged so that a portion of each optical fiber lies along rod outer surface  617 . These fibers form a first optical fiber layer  653 . Next, more optical fibers  620  from second spools  627  are arranged so that a portion each fiber lies over the fibers in the first layer in cusps  654  formed by adjoining fibers (FIG. 3B). This forms a second optical fiber layer  657 .  
         [0055]    The process of layering opticcal fibers  620  from additional spools (not shown) is repeated until a desired number of layers is formed. Heat is then applied to the layered optical fibers via heat sources  643 . When heated to the point where the fibers begin to melt, the layers of optical fibers are pulled off of the forming rod along the direction of the rod axis A 2 . Optical fibers  620  unwind from the spools during the pulling (arrows  662 ), thereby forming a continuous optical fiber with a hollow core  640  centered on axis A 1  coaxial with forming rod axis A 2 .  
         [0056]    Optical system with hollow core photonic bandgap optical fiber  
         [0057]    With reference to FIG. 7, there is shown an optical system  705 . The system includes, in order along an axis A 3 , a radiation source  707 , a first optional optical coupler  709 , and a hollow core photonic bandgap optical fiber  710  according to the present invention. Optical fiber includes an input end  711 , an output end  713 , and a hollow core  760 . System  705  also includes a second optional optical coupler  727  adjacent output end  713 , and a photodetector  737 .  
         [0058]    Radiation source  707  is capable of outputting radiation  767  of a frequency within the photonic bandgap of optical fiber  710 . In one example embodiment, radiation source  707  is a laser, such as a laser diode. In another example embodiment, radiation source  707  is an incoherent radiation source, such as a light-emitting diode or a conventional lamp.  
         [0059]    First optical coupler  709  is an optical system designed to facilitate the coupling of radiation from radiation source  707  to hollow core  760  at input end  711  of optical fiber  710 . Likewise, second optical coupler  727  is an optical system designed to facilitate the coupling of radiation from hollow core  760  at output end  713  of optical fiber  710  to photodetector  737 . First and second optical couplers can include any number or type of optical components, such as lenses, prisms and gratings.  
         [0060]    In operation, radiation source  707  outputs a radiation signal  767  having a frequency or range of frequencies within the photonic bandgap of optical fiber  710 . Radiation source  707  may also output radiation at frequencies different than the photonic bandgap, but such radiation will not be guided as effectively, if at all, by optical fiber  710 . In this sense, optical fiber  710  acts as a radiation filter.  
         [0061]    Radiation signal  767  is coupled into hollow core  760  of optical fiber  710  over within a range of input angles by optical coupler  709 . The radiation signal is confined to the hollow core by virtue of the photonic bandgap of the surrounding hollow core fiber array and propagates down the optical fiber. At the output end, the radiation signal exits the hollow core and is collected by optical coupler  727 , which directs the radiation signal to photodetector  737 . The latter receives and detects the radiation signal and outputs a corresponding electrical signal  771 , such as a photocurrent, which is further processed by an electronic device  777  downstream of the photodetector. In an example embodiment, electronic device  777  is a transimpedance amplifier that converts a photocurrent signal to a voltage signal.  
         [0062]    Conclusion  
         [0063]    The present invention is a hollow core photonic bandgap optical fiber and method of forming same. The hollow core photonic bandgap optical fiber of the present invention utilizes the advantages of a quasi-two-dimensional bandgap structure to provide a high reflectivity over a select radiation frequency range, while also providing a hollow core that minimizes radiation loss due to absorption. The photonic bandgap is formed by combining conventional hollow core optical fibers in an array along an axis but not on the axis, leaving a hollow core centered on the axis. The diameter of the hollow core is sized to allow for the propagation of select radiation frequencies corresponding to the frequencies of the bandgap associated with the fiber array making up the hollow core photonic bandgap optical fiber.  
         [0064]    Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that any arrangement that is calculated to achieve the same purpose may be substituted for the specific embodiments shown. This application is intended to cover any adaptations or variations of the present invention. It is to be understood that the above description is intended to be illustrative, and not restrictive. Combinations of the above embodiments, and other embodiments will be apparent to those of skill in the art upon reviewing the above description. The scope of the invention includes any other applications in which the above structures and fabrication methods are used. The scope of the invention should be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.