Abstract

We present a method for dispersion-tailoring of OmniGuide and other photonic band-gap guided fibers based on weak interactions (“anticrossings”) between the core-guided mode and a mode localized in an intentionally introduced defect of the crystal. Because the core mode can be guided in air and the defect mode in a much higher-index material, we are able to obtain dispersion parameters in excess of 500,000 ps/nm-km. Furthermore, because the dispersion is controlled entirely by geometric parameters and not by material dispersion, it is easily tunable by structural choices and fiber-drawing speed. So, for example, we demonstrate how the large dispersion can be made to coincide with a dispersion slope that matches commercial silica fibers to better than 1%, promising efficient compensation. Other parameters are shown to yield dispersion-free transmission in a hollow OmniGuide fiber that also maintains low losses and negligible nonlinearities, with a nondegenerate TE01 mode immune to polarization-mode dispersion (PMD). We present theoretical calculations for a chalcogenide-based material system that has recently been experimentally drawn.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, J. D. Joannopoulos, and Y. Fink, �??Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,�?? Opt. Express 9, 748�??779 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-748">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-748</a>
    [CrossRef] [PubMed]
  2. P. Yeh, A. Yariv, and E. Marom, �??Theory of Bragg fiber,�?? J. Opt. Soc. Am. 68, 1196�??1201 (1978).
    [CrossRef]
  3. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, �??A dielectric omnidirectional reflector,�?? Science 282, 1679�??1682 (1998).
    [CrossRef] [PubMed]
  4. J. A. Harrington, �??A review of IR transmitting, hollow waveguides,�?? Fiber Integr. Opt. 19, 211�??227 (2000).
    [CrossRef]
  5. A. Ferrando, E. Silvestre, P. Andrés, J. J. Miret and M. V. Andrés �??Designing the properties of dispersion-flattened photonic crystal fibers,�?? Opt. Express 9, 687�??697 (2001), <a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687</a>
    [CrossRef] [PubMed]
  6. J. Marcou, F. Brechet, and P. Roy, �??Design of weakly guiding Bragg fibres for chromatic dispersion shifting towards short wavelengths,�?? J. Opt. A: Pure Appl. Opt. 3, S144�??S153 (2001).
    [CrossRef]
  7. G. Ouyang, Y. Xu, and A. Yariv, �??Theoretical study on dispersion compensation in air-core Bragg fibers,�?? Opt. Express 10, 899�??908 (2002), <a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-899">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-899</a>
    [CrossRef] [PubMed]
  8. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, �??Extremely large group-velocity dispersion of line-defect waveguides in photonic crystals,�?? Phys. Rev. Lett. 87, 253902 (2001).
    [CrossRef] [PubMed]
  9. T. A. Birks, D. Mogilevstev, J. Knight, and P. S. Russell, �??Dispersion compensation using single-material fibers,�?? IEEE Phot. Techn. Lett. 11, 674�??676 (1999).
    [CrossRef]
  10. S. O. Konorov, A. B. Fedotov, O. A. Kolevatova, E. A. Serebryannikov, D. A. Sidorov-Biryukov, J. M. Mikhailova, A. N. Naumov, V. I. Beloglazov, N. B. Skibina, L. A. Melnikov, A. V. Shcherbakov and A. M. Zheltikov �??Waveguide modes and dispersion properties of hollow-core photonic-crystal and aperiodic-cladding fibers,�?? Laser Physics 13, 148�??160 (2003)
  11. Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, �??Guiding optical light in air using an all-dielectric structure,�?? J. Lightwave Tech. 17, 2039�??2041 (1999).
    [CrossRef]
  12. S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, �??External reflection from omnidirectional dielectric mirror fibers,�?? Science 296, 510�??513 (2002).
    [CrossRef] [PubMed]
  13. B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, �??Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,�?? Nature 420, 650�??653 (2002).
    [CrossRef] [PubMed]
  14. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).
  15. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  16. R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical Perspective (Academic, London, 1998).
  17. L. G. Cohen, C. Lin, and W. G. French, �??Tailoring zero chromatic dispersion into the 1.5-1.6 mu-m low-loss spectral region of single mode fibers,�?? Electron. Lett. 15, 334�??335 (1979).
    [CrossRef]
  18. C. Lin, H. Kogelnik, and L. G. Cohen, �??Optical-pulse equalization of low-dispersion transmission in single-mode fibers in the 1.3-1.7-mu-m spectral region,�?? Opt. Lett. 5, 476�??478 (1980).
    [CrossRef] [PubMed]
  19. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).
  20. S. G. Johnson and J. D. Joannopoulos, �??Block-iterative frequency-domain methods for Maxwell�??s equations in a planewave basis,�?? Opt. Express 8, 173�??190 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173</a>
    [CrossRef] [PubMed]
  21. M. Skorobogatiy, M. Ibanescu, S. G. Johnson, O.Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, and Y. Fink, �??Analysis of general geometric scaling perturbations in a transmitting waveguide. The fundamental connection between polarization mode dispersion and group-velocity dispersion,�?? J. Opt. Soc. B 19, 2867�??2875 (2002).
    [CrossRef]
  22. S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O.Weisberg, J. D. Joannopoulos, and Y. Fink, �??Perturbation theory for Maxwell�??s equations with shifting material boundaries,�?? Phys. Rev. E 65, 066611 (2002).
    [CrossRef]
  23. M. Skorobogatiy, S. A. Jacobs, S. G. Johnson, and Y. Fink, �??Geometric variations in high indexcontrast waveguides, coupled mode theory in curvilinear coordinates,�?? Opt. Express 10, 1227�??1243 (2002),<a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1227"> http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-21-1227</a>
    [CrossRef] [PubMed]
  24. M. Miyagi and S. Kawakami, �??Design theory of dielectric-coated circular metallic waveguides for infrared transmission,�?? J. Lightwave Tech. 2, 116�??126 (1984).
    [CrossRef]
  25. D. Gloge, �??Weakly guiding fibers,�?? Appl. Opt. 10, 2252-2258 (1971).
    [CrossRef] [PubMed]
  26. M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, �??Analysis of mode structure in OmniGuide fibers,�?? Phys. Rev. E 67, 046608, (2003). 27. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt Saunders, Philadelphia, 1976).
    [CrossRef]
  27. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt Saunders, Philadelphia, 1976).
  28. H. Haus and W.-P. Huang, �??Coupled-mode theory,�?? Proc. IEEE 79, 1505�??1518 (1991).
    [CrossRef]
  29. W.-P. Huang, �??Coupled-mode theory for optical waveguides: an overview,�?? JOSA A 11, 963�??983 (1994).
    [CrossRef]
  30. R. Kashyap, Fiber Bragg Gratings (Academic, San Diego, Calif., 1999).
  31. K. Thyagarajan, R. K. Varshney, P. Palai, A. K. Ghatak, and I. C. Goyal, �??A novel design of a dispersion compensating Fiber,�?? IEEE Phot. Techn. Lett. 8, 1510�??1512 (1996).
    [CrossRef]
  32. D. Moss, L. Lunardi, M. Lamont, G. Randall, and P. Colbourne, �??Tunable dispersion compensation at 10 Gb/s and 40 Gb/s using multicavity all-pass etalons,�?? in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2003), Vol. 1, paper TuD1.
  33. L. M. Lundardi, D.J. Moss, S. Chandrasekhar, L.L. Buhl, M. Lamont, S. McLaughlin, G. Randall, P. Colbourne, S. Kiran, and C.A. Hulse, �??Tunable dispersion compensation at 40 Gb/s using a multicavity etalon all-pass filter with NRZ, RZ and CS-RZ modulation,�?? J. Lightwave Tech. 20, 2136�??2144 (2002).
    [CrossRef]
  34. J. L. Auguste, R. Jindal, J. M. Blondy, M. Clapeau, J. Marcou, B. Dussardier, G. Monnom, D. B. Ostrowsky, B. P. Pal, and K. Thyagarajan, �??-1800ps/(nm-km) chromatic dispersion at 1.55 mm in dual concentric core fibre,�?? El. Lett. 36, 1689�??1691 (2000).
    [CrossRef]
  35. T. Kato, Y. Koyano, and M. Nishimura, �??Temperature dependence of chromatic dispersion in various types of optical fiber,�?? Opt. Lett. 25, 1156�??1158 (2000).
    [CrossRef]
  36. J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Lu, and C. Xu, �??Adiabatic coupling in tapered air-silica microstructured optical fiber,�?? IEEE Phot. Tech. Lett. 13, 52�??54 (2001).
    [CrossRef]
  37. B. Z. Katsenelenbaum, L. Mercader del Río, M. Pereyaslavets, M. Sorolla Ayza, and M. Thumm, Theory of Nonuniform Waveguides: The Cross-Section Method (Inst. of Electrical Engineers, London, 1998).
    [CrossRef]
  38. M. Skorobogatiy, C. Anastassiou, O.Weisberg, T. D. Engeness, S. G. Johnson, S. A. Jacobs, and Y. Fink, submitted to J. Lightwave Technol.
  39. T. Kanamori, Y. Terunuma, S. Takahashi, and T. Miyashita, �??Chalcogenide glass-fibers for mid-infrared transmission,�?? J. Lightwave Technol. 2, 607�??613 (1984).
    [CrossRef]

Electr. Lett.

J. L. Auguste, R. Jindal, J. M. Blondy, M. Clapeau, J. Marcou, B. Dussardier, G. Monnom, D. B. Ostrowsky, B. P. Pal, and K. Thyagarajan, �??-1800ps/(nm-km) chromatic dispersion at 1.55 mm in dual concentric core fibre,�?? El. Lett. 36, 1689�??1691 (2000).
[CrossRef]

Electron. Lett.

L. G. Cohen, C. Lin, and W. G. French, �??Tailoring zero chromatic dispersion into the 1.5-1.6 mu-m low-loss spectral region of single mode fibers,�?? Electron. Lett. 15, 334�??335 (1979).
[CrossRef]

Fiber Integr. Opt.

J. A. Harrington, �??A review of IR transmitting, hollow waveguides,�?? Fiber Integr. Opt. 19, 211�??227 (2000).
[CrossRef]

IEEE Phot. Tech. Lett.

J. K. Chandalia, B. J. Eggleton, R. S. Windeler, S. G. Kosinski, X. Lu, and C. Xu, �??Adiabatic coupling in tapered air-silica microstructured optical fiber,�?? IEEE Phot. Tech. Lett. 13, 52�??54 (2001).
[CrossRef]

IEEE Phot. Techn. Lett.

K. Thyagarajan, R. K. Varshney, P. Palai, A. K. Ghatak, and I. C. Goyal, �??A novel design of a dispersion compensating Fiber,�?? IEEE Phot. Techn. Lett. 8, 1510�??1512 (1996).
[CrossRef]

T. A. Birks, D. Mogilevstev, J. Knight, and P. S. Russell, �??Dispersion compensation using single-material fibers,�?? IEEE Phot. Techn. Lett. 11, 674�??676 (1999).
[CrossRef]

J. Lightwave Tech.

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, �??Guiding optical light in air using an all-dielectric structure,�?? J. Lightwave Tech. 17, 2039�??2041 (1999).
[CrossRef]

M. Miyagi and S. Kawakami, �??Design theory of dielectric-coated circular metallic waveguides for infrared transmission,�?? J. Lightwave Tech. 2, 116�??126 (1984).
[CrossRef]

L. M. Lundardi, D.J. Moss, S. Chandrasekhar, L.L. Buhl, M. Lamont, S. McLaughlin, G. Randall, P. Colbourne, S. Kiran, and C.A. Hulse, �??Tunable dispersion compensation at 40 Gb/s using a multicavity etalon all-pass filter with NRZ, RZ and CS-RZ modulation,�?? J. Lightwave Tech. 20, 2136�??2144 (2002).
[CrossRef]

J. Lightwave Technol.

T. Kanamori, Y. Terunuma, S. Takahashi, and T. Miyashita, �??Chalcogenide glass-fibers for mid-infrared transmission,�?? J. Lightwave Technol. 2, 607�??613 (1984).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

J. Marcou, F. Brechet, and P. Roy, �??Design of weakly guiding Bragg fibres for chromatic dispersion shifting towards short wavelengths,�?? J. Opt. A: Pure Appl. Opt. 3, S144�??S153 (2001).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. B

M. Skorobogatiy, M. Ibanescu, S. G. Johnson, O.Weisberg, T. D. Engeness, M. Soljacic, S. A. Jacobs, and Y. Fink, �??Analysis of general geometric scaling perturbations in a transmitting waveguide. The fundamental connection between polarization mode dispersion and group-velocity dispersion,�?? J. Opt. Soc. B 19, 2867�??2875 (2002).
[CrossRef]

JOSA A

W.-P. Huang, �??Coupled-mode theory for optical waveguides: an overview,�?? JOSA A 11, 963�??983 (1994).
[CrossRef]

Laser Physics

S. O. Konorov, A. B. Fedotov, O. A. Kolevatova, E. A. Serebryannikov, D. A. Sidorov-Biryukov, J. M. Mikhailova, A. N. Naumov, V. I. Beloglazov, N. B. Skibina, L. A. Melnikov, A. V. Shcherbakov and A. M. Zheltikov �??Waveguide modes and dispersion properties of hollow-core photonic-crystal and aperiodic-cladding fibers,�?? Laser Physics 13, 148�??160 (2003)

Nature

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, �??Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,�?? Nature 420, 650�??653 (2002).
[CrossRef] [PubMed]

Opt. Express

G. Ouyang, Y. Xu, and A. Yariv, �??Theoretical study on dispersion compensation in air-core Bragg fibers,�?? Opt. Express 10, 899�??908 (2002), <a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-899">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-899</a>
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

T. Kato, Y. Koyano, and M. Nishimura, �??Temperature dependence of chromatic dispersion in various types of optical fiber,�?? Opt. Lett. 25, 1156�??1158 (2000).
[CrossRef]

C. Lin, H. Kogelnik, and L. G. Cohen, �??Optical-pulse equalization of low-dispersion transmission in single-mode fibers in the 1.3-1.7-mu-m spectral region,�?? Opt. Lett. 5, 476�??478 (1980).
[CrossRef] [PubMed]

Phys. Rev.

M. Ibanescu, S. G. Johnson, M. Soljacic, J. D. Joannopoulos, Y. Fink, O. Weisberg, T. D. Engeness, S. A. Jacobs, and M. Skorobogatiy, �??Analysis of mode structure in OmniGuide fibers,�?? Phys. Rev. E 67, 046608, (2003). 27. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt Saunders, Philadelphia, 1976).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O.Weisberg, J. D. Joannopoulos, and Y. Fink, �??Perturbation theory for Maxwell�??s equations with shifting material boundaries,�?? Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Phys. Rev. Lett.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, �??Extremely large group-velocity dispersion of line-defect waveguides in photonic crystals,�?? Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Science

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, �??External reflection from omnidirectional dielectric mirror fibers,�?? Science 296, 510�??513 (2002).
[CrossRef] [PubMed]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, �??A dielectric omnidirectional reflector,�?? Science 282, 1679�??1682 (1998).
[CrossRef] [PubMed]

Other

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical Perspective (Academic, London, 1998).

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt Saunders, Philadelphia, 1976).

H. Haus and W.-P. Huang, �??Coupled-mode theory,�?? Proc. IEEE 79, 1505�??1518 (1991).
[CrossRef]

D. Gloge, �??Weakly guiding fibers,�?? Appl. Opt. 10, 2252-2258 (1971).
[CrossRef] [PubMed]

R. Kashyap, Fiber Bragg Gratings (Academic, San Diego, Calif., 1999).

D. Moss, L. Lunardi, M. Lamont, G. Randall, and P. Colbourne, �??Tunable dispersion compensation at 10 Gb/s and 40 Gb/s using multicavity all-pass etalons,�?? in Optical Fiber Communication Conference (Optical Society of America, Washington, D.C., 2003), Vol. 1, paper TuD1.

B. Z. Katsenelenbaum, L. Mercader del Río, M. Pereyaslavets, M. Sorolla Ayza, and M. Thumm, Theory of Nonuniform Waveguides: The Cross-Section Method (Inst. of Electrical Engineers, London, 1998).
[CrossRef]

M. Skorobogatiy, C. Anastassiou, O.Weisberg, T. D. Engeness, S. G. Johnson, S. A. Jacobs, and Y. Fink, submitted to J. Lightwave Technol.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1.
Fig. 1.

(a) Defect-free OmniGuide fiber and (b) OmniGuide dispersion-compensating fiber. (Not to scale.) The defect-free (“long-haul”) fiber consists of an air core (R=15.35 µm) surrounded by consecutive layers of refractive index=1.5 (blue) and refractive index=2.8 (red) materials. In this fiber, all the high-index layers have the same thickness (0.153 µm) and all the low-index layers have the same thickness (0.358 µm). The outermost region is a thick layer that provides structural stability. The actual number of layers used is larger than in this figure; in order to minimize radiation losses one would use 20 layers or more. The OmniGuide dispersion-compensating fiber is a modified structure that includes a defect, i.e. the thickness of one of the dielectric layers has been altered.

Fig. 2.
Fig. 2.

Nomenclature: “Layer 1” denotes the material layer closest to the air core, the next-closest material layer is “layer 2,” etc. “Core” means the air core inside the dielectric mirror and “cladding” means all layers outside the core. This figure is not drawn to scale and includes a reduced number of layers.

Fig. 3.
Fig. 3.

(a) Band gaps and light line for OmniGuide long-haul fiber and (b) dispersion relations for the lowest-order modes.

Fig. 4.
Fig. 4.

Fraction of energy in the TE01 mode that is not confined in the core. The entire line shows the degree of confinement across the TE band gap, while the solid part of the curve indicate the part that is within the TM band gap (1430–1830nm) as well as the TE gap.

Fig. 5.
Fig. 5.

Dispersion parameter for the TE01 mode in the OmniGuide long-haul fiber, where the solid part of the curve indicates the range that is within the TM band gap. Within the TM band gap the dispersion parameter D ranges from 7.5 to 11.4 ps/nm-km.

Fig. 6.
Fig. 6.

Schematic representation of the effect of interaction between defect and core modes. Panel (a) shows the dispersion relations for the two modes without interaction and panel (b) shows how modal interaction changes the dispersion relations.

Fig. 7.
Fig. 7.

Schematic representation of the effect of varying strengths of modal interaction. The modal interaction is weaker in panel (a) than in panel (b), resulting in a sharper “kink” in (a) and therefore a larger value of the dispersion parameter over a more narrow wavelength range.

Fig. 8.
Fig. 8.

Schematic representation of the interaction between a defect mode and multiple core modes. Panel (a) shows the defect mode (blue) and the core modes (red) separately, while panel (b) shows the resulting modal structure when the modes interact.

Fig. 9.
Fig. 9.

Dispersion relation (a) and dispersion curve (b) for four different locations of the defect. Both curves show that the transition from core-confined mode to the defect mode takes place more rapidly when the defect is located far from the core which results in a large negative dispersion parameter over a narrower band. The point ofminimumdispersion parameter is indicated with a dot on the dispersion relations.

Fig. 10.
Fig. 10.

Dispersion curve for two slightly different sizes of the defect. The defect for the red curve is 1.5% larger than the defect for the blue curve.

Fig. 11.
Fig. 11.

Dispersion curve for two different core sizes, the large core (red) having a core radius of 14.8 µm and the small core (blue) having a radius of 2.98 µm.

Fig. 12.
Fig. 12.

Panel (a) shows the energy density of the operating mode as a function of distance from core center at two different wavelengths. The solid (blue) line represents the energy distribution at 1.55 µm, which is in the center of the operating band and the dotted (red) line represents a wavelength on the other side of the anticrossing. The vertical black line represents the core radius. Panel (b) shows the dispersion curve with dots signaling the two wavelengths for which the energy distributions can be found in panel 9a).

Fig. 13.
Fig. 13.

Dispersion curves for OmniGuide zero dispersion fiber. Panel (a) shows the dispersion of the zero dispersion fiber together with the OmniGuide long haul fiber over a broad wavelength range. Panel (b) zooms in on the dispersion properties for the zero dispersion fiber over a 20 nm band.

Fig. 14.
Fig. 14.

Schematic representation of the interaction between multiple defect modes and multiple core-confined modes.Panel (a) shows three defect modes (blue) and the coreconfined modes (red) separately, while panel (b) shows the resulting modal structure when the modes interact.

Fig. 15.
Fig. 15.

Dispersion curve for the OmniGuide multiple zero dispersion fiber.

Tables (1)

Tables Icon

Table 1. The dispersion increase at an anticrossing is roughly proportional to the amplitude of the exponential field tails as a function of defect location, causing the product of the two to be roughly constant (with some oscillation).

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

D = 2 π c λ 2 · d 2 β d ω 2 ,
L d · D d + L t · D t = 0
L d · δ D d δ λ + L t · δ D t δ λ = 0
R = 1 D · δ D δ λ
F ( r ) e i ( β z ω t + m ϕ ) ,
H z = AJ + BY
E z = CJ + DY
d hi d lo = n lo 2 1 n hi 2 1
A = 1 2 Dd λ = 1 2 λ ( 1 ν g ) d λ = Δ ( 1 ν g ) = 1 ν g , 1 1 ν g , 2
Δ ω ~ ψ 1 H ̂ ψ 2
B 2 · D · L < 2 · 10 5

Metrics