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] 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 >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] 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] 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] 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] 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] 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.