Abstract

We present the light-propagation characteristics of OmniGuide fibers, which guide light by concentric multi-layer dielectric mirrors having the property of omnidirectional reflection. We show how the lowest-loss TE01 mode can propagate in a single-mode fashion through even large-core fibers, with other modes eliminated asymptotically by their higher losses and poor coupling, analogous to hollow metallic microwave waveguides. Dispersion, radiation leakage, material absorption, nonlinearities, bending, acircularity, and interface roughness are considered with the help of leaky modes and perturbation theory, and both numerical results and general scaling relations are presented. We show that cladding properties such as absorption and nonlinearity are suppressed by many orders of magnitude due to the strong confinement in a hollow core, and other imperfections are tolerable, promising that the properties of silica fibers may be surpassed even when nominally poor materials are employed.

© Optical Society of America

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References

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  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton, 1995).
  2. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S.-J. Russell, and P. J. Roberts, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
    [CrossRef] [PubMed]
  3. P. Yeh, A. Yariv, and E. Marom, "Theory of Bragg fiber," J. Opt. Soc. Am. 68, 1196-1201 (1978).
    [CrossRef]
  4. N. J. Doran and K. J. Bulow, "Cylindrical Bragg fibers: a design and feasibility study for optical communications," J. Lightwave Tech. 1, 588-590 (1983).
    [CrossRef]
  5. A. N. Lazarchik, "Bragg fiber lightguides," Radiotekhnika i electronika 1, 36-43 (1988).
  6. C. M. de Sterke and I. M. Bassett, "Differential losses in Bragg fibers," J. Appl. Phys. 76, 680-688 (1994).
    [CrossRef]
  7. 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]
  8. F. Brechet, P. Roy, J. Marcou, and D. Pagnoux, "Singlemode propagation into depressed-core-index photonic-bandgap fibre designed for zero-dispersion propagation at short wavelengths," Elec. Lett. 36, 514-515 (2000).
    [CrossRef]
  9. F. Brechet, P. Leproux, P. Roy, J. Marcou, and D. Pagnoux, "Analysis of bandpass filtering behavior of singlemode depressed-core-index photonic bandgap fibre," Elec. Lett. 36, 870-872 (2000).
    [CrossRef]
  10. M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, "An all-dielectric coaxial waveguide," Science 289, 415-419 (2000).
    [CrossRef] [PubMed]
  11. Y. Xu, R. K. Lee, and A. Yariv, "Asymptotic analysis of Bragg fibers," Opt. Lett. 25, 1756-1758 (2000).
    [CrossRef]
  12. T. Kawanishi and M. Izutsu, "Coaxial periodic optical waveguide," Opt. Express 7, 10-22 (2000), http://www.opticsexpress.org/oearchive/source/22933.htm.
    [CrossRef] [PubMed]
  13. Y. Xu and A. Yariv, "Asymptotic analysis of Bragg fibers and dielectric coaxial fibers," In Proc. SPIE, A. Dutta, A. A. S. Awwal, N. K. Dutta, and K. Okamoto, eds., 4532, 191-205 (2001).
    [CrossRef]
  14. 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]
  15. R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical Perspective (Academic Press, London, London, 1998).
  16. E. A. Marcatili and R. A. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers," Bell Syst. Tech. J. 43, 1783-1809 (1964).
  17. W. D. Warters, "WT4 millimeter waveguide system: introduction," Bell Syst. Tech. J. 56, 1825-1827 (1977), the introduction to a special issue with many useful articles.
  18. M. Miyagi, A. Hongo, and S. Kawakami, "Transmission characteristics of dielectric-coated metallic waveguides for infrared transmission: slab waveguide model," IEEE J. Quantum Elec. QE-19, 136-145 (1983).
    [CrossRef]
  19. M. Miyagi and S. Kawakami, "Design theory of dielectric-coated circular metallic waveguides for infrared transmission," J. Lightwave Tech. 2, 116-126 (1984).
    [CrossRef]
  20. J. A. Harrington, "A review of IR transmitting, hollow waveguides," Fiber Integr. Opt. 19, 211-227 (2000).
    [CrossRef]
  21. M. Ibanescu et al., to be published in 2002.
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  23. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).
  24. S. A. Jacobs et al., to be published in 2002.
  25. L. Gruner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, "Dispersion compensating fibers," Opt. Fiber Tech. 6, 164-180 (2000).
    [CrossRef]
  26. W. H. Weber, S. L. McCarthy, and G. W. Ford, "Perturbation theory applied to gain or loss in an optical waveguide," Appl. Opt. 13, 715-716 (1974).
    [CrossRef]
  27. A. Kumar, S. I. Hosain, and A. K. Ghatak, "Propagation characteristics of weakly guiding lossy fibers: an exact and perturbation analysis," Optica Acta 28, 559-566 (1981).
    [CrossRef]
  28. Z. Pantic and R. Mittra, "Quasi-TEM analysis of microwave transmission lines by the finite-element method," IEEE Trans. Microwave Theory Tech. MTT-34, 1096-1103 (1986).
    [CrossRef]
  29. S. X. She, "Propagation loss in metal-clad waveguides and weakly absorptive waveguides by a perturbation method," Opt. Lett. 15, 900-902 (1990).
    [CrossRef] [PubMed]
  30. V. L. Gupta and E. K. Sharma, "Metal-clad and absorptive multilayer waveguides: an accurate perturbation analysis," J. Opt. Soc. Am. A 9, 953-956 (1992).
    [CrossRef]
  31. C. Themistos, B. M. A. Rahman, A. Hadjicharalambous, and K. T. V. Grattan, "Loss/gain characterization of optical waveguides," J. Lightwave Tech. 13, 1760-1765 (1995).
    [CrossRef]
  32. D. Sarid and G. I. Stegeman, "Optimization of the effects of power dependent refractive indices in optical waveguides," J. Appl. Phys. 52, 5439-5441 (1981).
    [CrossRef]
  33. V. P. Tzolov, M. Fontaine, N. Godbout, and S. Lacroix, "Nonlinear self-phase-modulation effects: a vectorial first-order perturbation approach," Opt. Lett. 20, 456-458 (1995).
    [CrossRef] [PubMed]
  34. R. S. Grant, "Effective non-linear coefficients in optical waveguides," Optical and Quantum Elec. 28, 1161-1173 (1996).
    [CrossRef]
  35. B. Z. Katsenelenbaum, L. Mercader del Rio, M. Pereyaslavets, M. Sorolla Ayza, and M. Thumm, Theory of Nonuniform Waveguides: The Cross-Section Method (Inst. of Electrical Engineers, London, 1998).
    [CrossRef]
  36. L. Lewin, D. C. Chang, and F. Kuester, Electromagnetic Waves and Curved Structures (P. Peregrinus, England, 1977).
  37. M. Miyagi, K. Harada, and S. Kawakami, "Wave propagation and attenuation in the general class of circular hollow waveguides with uniform curvature," IEEE Trans. Microwave Theory Tech. MTT-32, 513-521 (1984).
    [CrossRef]
  38. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1998).
  39. M. Lohmeyer, N. Bahlmann, and P. Hertel, "Geometry tolerance estimation for rectangular dielectric waveguide devices by means of perturbation theory," Opt. Commun. 163, 86-94 (1999).
    [CrossRef]
  40. D. Q. Chowdhury and D. A. Nolan, "Perturbation model for computing optical fiber birefringence from a two-dimensional refractive-index profile," Opt. Lett. 20, 1973-1975 (1995).
    [CrossRef] [PubMed]
  41. D. Q. Chowdhury, "Comparison between optical fiber birefringence induced by stress anisotropy and geometric deformation," IEEE J. Selected Topics Quantum Elec. 6, 227-232 (2000).
    [CrossRef]
  42. V. P. Kalosha and A. P. Khapalyuk, "Mode birefringence in a single-mode elliptic optical fiber," Sov. J. Quantum Elec. 13, 109-111 (1983).
    [CrossRef]
  43. V. P. Kalosha and A. P. Khapalyuk, "Mode birefringence of a three-layer elliptic single-mode fiber waveguide," Sov. J. Quantum Elec. 14, 427-430 (1984).
    [CrossRef]
  44. M. Skorobogatiy et al., to be published in 2002.
  45. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  46. Characteristics of a single-mode optical fibre cable (Intl. Telecom. Union, 2000), No. G.652.
  47. A. W. Snyder, "Radiation losses due to variations of radius on dielectric or optical fibers," IEEE Trans. Microwave Theory Tech. MTT-18, 608-615 (1970).
    [CrossRef]
  48. S. G. Johnson et al., to be published in 2002.
  49. C. Cohen-Tannoudji, B. Din, and F. Laloe, Quantum Mechanics (Hermann, Paris, 1977), Vol. One, ch. 2; and Vol. Two, ch. 11 and 13.
  50. L. A. Yudin, S. P. Efimov, M. I. Kapchinsky, and I. L. Korenev, "Electrodynamics as a problem of eigenvalues," Phys. Plasmas 3, 42-58 (1996).
    [CrossRef]
  51. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt Saunders, Philadelphia, 1976).
  52. A. Messiah, Quantum Mechanics: Vol. II (Wiley, New York, 1976), ch. 17.
  53. G. H. Song and W. J. Tomlinson, "Fourier analysis and synthesis of adiabatic tapers in integrated optics," J. Opt. Soc. Am. A 9, 1289-1300 (1992).
    [CrossRef]

Other (53)

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

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S.-J. Russell, and P. J. Roberts, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

P. Yeh, A. Yariv, and E. Marom, "Theory of Bragg fiber," J. Opt. Soc. Am. 68, 1196-1201 (1978).
[CrossRef]

N. J. Doran and K. J. Bulow, "Cylindrical Bragg fibers: a design and feasibility study for optical communications," J. Lightwave Tech. 1, 588-590 (1983).
[CrossRef]

A. N. Lazarchik, "Bragg fiber lightguides," Radiotekhnika i electronika 1, 36-43 (1988).

C. M. de Sterke and I. M. Bassett, "Differential losses in Bragg fibers," J. Appl. Phys. 76, 680-688 (1994).
[CrossRef]

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]

F. Brechet, P. Roy, J. Marcou, and D. Pagnoux, "Singlemode propagation into depressed-core-index photonic-bandgap fibre designed for zero-dispersion propagation at short wavelengths," Elec. Lett. 36, 514-515 (2000).
[CrossRef]

F. Brechet, P. Leproux, P. Roy, J. Marcou, and D. Pagnoux, "Analysis of bandpass filtering behavior of singlemode depressed-core-index photonic bandgap fibre," Elec. Lett. 36, 870-872 (2000).
[CrossRef]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, "An all-dielectric coaxial waveguide," Science 289, 415-419 (2000).
[CrossRef] [PubMed]

Y. Xu, R. K. Lee, and A. Yariv, "Asymptotic analysis of Bragg fibers," Opt. Lett. 25, 1756-1758 (2000).
[CrossRef]

T. Kawanishi and M. Izutsu, "Coaxial periodic optical waveguide," Opt. Express 7, 10-22 (2000), http://www.opticsexpress.org/oearchive/source/22933.htm.
[CrossRef] [PubMed]

Y. Xu and A. Yariv, "Asymptotic analysis of Bragg fibers and dielectric coaxial fibers," In Proc. SPIE, A. Dutta, A. A. S. Awwal, N. K. Dutta, and K. Okamoto, eds., 4532, 191-205 (2001).
[CrossRef]

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]

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

E. A. Marcatili and R. A. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers," Bell Syst. Tech. J. 43, 1783-1809 (1964).

W. D. Warters, "WT4 millimeter waveguide system: introduction," Bell Syst. Tech. J. 56, 1825-1827 (1977), the introduction to a special issue with many useful articles.

M. Miyagi, A. Hongo, and S. Kawakami, "Transmission characteristics of dielectric-coated metallic waveguides for infrared transmission: slab waveguide model," IEEE J. Quantum Elec. QE-19, 136-145 (1983).
[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]

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

M. Ibanescu et al., to be published in 2002.

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

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

S. A. Jacobs et al., to be published in 2002.

L. Gruner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, "Dispersion compensating fibers," Opt. Fiber Tech. 6, 164-180 (2000).
[CrossRef]

W. H. Weber, S. L. McCarthy, and G. W. Ford, "Perturbation theory applied to gain or loss in an optical waveguide," Appl. Opt. 13, 715-716 (1974).
[CrossRef]

A. Kumar, S. I. Hosain, and A. K. Ghatak, "Propagation characteristics of weakly guiding lossy fibers: an exact and perturbation analysis," Optica Acta 28, 559-566 (1981).
[CrossRef]

Z. Pantic and R. Mittra, "Quasi-TEM analysis of microwave transmission lines by the finite-element method," IEEE Trans. Microwave Theory Tech. MTT-34, 1096-1103 (1986).
[CrossRef]

S. X. She, "Propagation loss in metal-clad waveguides and weakly absorptive waveguides by a perturbation method," Opt. Lett. 15, 900-902 (1990).
[CrossRef] [PubMed]

V. L. Gupta and E. K. Sharma, "Metal-clad and absorptive multilayer waveguides: an accurate perturbation analysis," J. Opt. Soc. Am. A 9, 953-956 (1992).
[CrossRef]

C. Themistos, B. M. A. Rahman, A. Hadjicharalambous, and K. T. V. Grattan, "Loss/gain characterization of optical waveguides," J. Lightwave Tech. 13, 1760-1765 (1995).
[CrossRef]

D. Sarid and G. I. Stegeman, "Optimization of the effects of power dependent refractive indices in optical waveguides," J. Appl. Phys. 52, 5439-5441 (1981).
[CrossRef]

V. P. Tzolov, M. Fontaine, N. Godbout, and S. Lacroix, "Nonlinear self-phase-modulation effects: a vectorial first-order perturbation approach," Opt. Lett. 20, 456-458 (1995).
[CrossRef] [PubMed]

R. S. Grant, "Effective non-linear coefficients in optical waveguides," Optical and Quantum Elec. 28, 1161-1173 (1996).
[CrossRef]

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

L. Lewin, D. C. Chang, and F. Kuester, Electromagnetic Waves and Curved Structures (P. Peregrinus, England, 1977).

M. Miyagi, K. Harada, and S. Kawakami, "Wave propagation and attenuation in the general class of circular hollow waveguides with uniform curvature," IEEE Trans. Microwave Theory Tech. MTT-32, 513-521 (1984).
[CrossRef]

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1998).

M. Lohmeyer, N. Bahlmann, and P. Hertel, "Geometry tolerance estimation for rectangular dielectric waveguide devices by means of perturbation theory," Opt. Commun. 163, 86-94 (1999).
[CrossRef]

D. Q. Chowdhury and D. A. Nolan, "Perturbation model for computing optical fiber birefringence from a two-dimensional refractive-index profile," Opt. Lett. 20, 1973-1975 (1995).
[CrossRef] [PubMed]

D. Q. Chowdhury, "Comparison between optical fiber birefringence induced by stress anisotropy and geometric deformation," IEEE J. Selected Topics Quantum Elec. 6, 227-232 (2000).
[CrossRef]

V. P. Kalosha and A. P. Khapalyuk, "Mode birefringence in a single-mode elliptic optical fiber," Sov. J. Quantum Elec. 13, 109-111 (1983).
[CrossRef]

V. P. Kalosha and A. P. Khapalyuk, "Mode birefringence of a three-layer elliptic single-mode fiber waveguide," Sov. J. Quantum Elec. 14, 427-430 (1984).
[CrossRef]

M. Skorobogatiy et al., to be published in 2002.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

Characteristics of a single-mode optical fibre cable (Intl. Telecom. Union, 2000), No. G.652.

A. W. Snyder, "Radiation losses due to variations of radius on dielectric or optical fibers," IEEE Trans. Microwave Theory Tech. MTT-18, 608-615 (1970).
[CrossRef]

S. G. Johnson et al., to be published in 2002.

C. Cohen-Tannoudji, B. Din, and F. Laloe, Quantum Mechanics (Hermann, Paris, 1977), Vol. One, ch. 2; and Vol. Two, ch. 11 and 13.

L. A. Yudin, S. P. Efimov, M. I. Kapchinsky, and I. L. Korenev, "Electrodynamics as a problem of eigenvalues," Phys. Plasmas 3, 42-58 (1996).
[CrossRef]

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

A. Messiah, Quantum Mechanics: Vol. II (Wiley, New York, 1976), ch. 17.

G. H. Song and W. J. Tomlinson, "Fourier analysis and synthesis of adiabatic tapers in integrated optics," J. Opt. Soc. Am. A 9, 1289-1300 (1992).
[CrossRef]

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Figures (16)

Fig. 1.
Fig. 1.

(a) Hollow dielectric waveguide of radius R. Light is confined in the hollow core by a multilayer dielectric mirror made of alternating layers with high (blue) and low (green) indices of refraction. (b) Hollow metallic waveguide of radius R. Light is confined in the hollow core by a metallic cylinder.

Fig. 2.
Fig. 2.

(Left) Projected band structure associated with the planar dielectric mirror. The blue regions correspond to (β, ω) pairs for which light can propagate within the mirror. White and gray regions correspond to situations where light cannot propagate within the mirror. The thick black line represents the light line (ω=). Shown in gray are the two omnidirectional frequency ranges of the mirror. (Right) Dispersion relations ω(β) of the lowest 7 modes supported by a hollow metallic waveguide of radius R=2a are plotted. TE/TM-polarized modes are shown in red/blue, and the modes have angular dependence eimφ . Note the degeneracy of the TE01 and the TM11 modes.

Fig. 3.
Fig. 3.

Guided modes supported by a hollow OmniGuide fiber of radius R=2a: red lines are for TE and HE modes, while blue is for TM and EH modes. In black is the light line (ω=), and the solid blue regions represent the continuum of modes that propagate within the multilayer cladding. Only the first three modes in each band gap are labeled.

Fig. 4.
Fig. 4.

An OmniGuide fiber with core radius R=30a, the parameters that we employ in the remainder of this paper. The omnidirectional mirror here comprises 17 layers, starting with a high-index layer, with indices 4.6/1.6 and thicknesses 0.22a/0.78a, respectively. (The omnidirectional mirror is surrounded by some coating for mechanical support; this layer is not shown to scale.) We choose a=0.434µm, so that the lowest dissipation losses occur roughly at λ=1.55µm.

Fig. 5.
Fig. 5.

Transverse electric-field distributions in the OmniGuide fiber of Fig. 4 for the TE01 mode (left) and the EH11 mode (right), which have β=0.27926 · 2π/a and β=0.27955·2π/a, respectively, at ω=0.28·2πc/a.

Fig. 6.
Fig. 6.

The (unnormalized) electric field Eφ for the TE01 mode in the OmniGuide fiber of Fig. 4. The lower plot displays the same field, but with the vertical scale exaggerated in order to show the field amplitude in the cladding. The field has a node near the core interface at R, and so the field amplitude in the cladding is determined by the slope at that point.

Fig. 7.
Fig. 7.

Radiation leakage through a finite number (17) of cladding layers in the OmniGuide fiber of Fig. 4. The lowest-loss mode is TE01 (solid blue) and the next-lowest is TE02 (red dots), while the linearly-polarized EH11 mode (black circles) typifies the higher losses for mixed-polarization modes due to the smaller TM band gap.

Fig. 8.
Fig. 8.

Group-velocity (chromatic) dispersion of the TE01 mode in both the OmniGuide fiber of Fig. 4 (solid blue) and a hollow metallic waveguide with the same core radius (green circles).

Fig. 9.
Fig. 9.

Absorption losses due to the cladding materials the OmniGuide fiber (with core radius 30a), as a fraction of the bulk cladding losses. The lowest-loss mode is TE01 (solid blue) and the next-lowest is TE02 (red dots), while the linearly-polarized EH11 mode (black circles) typifies the higher losses for mixed-polarization modes due to the smaller TM band gap.

Fig. 10.
Fig. 10.

The TE01 mode’s suppression factor for cladding nonlinearities in the OmniGuide fiber of Fig. 4, relative to nonlinearities that include the core.

Fig. 11.
Fig. 11.

Scaling of the cladding absorption and nonlinearity suppression factors for a core radius R varying from 7a to 30a (taking the minimum over the TE01 band at each radius). Hollow squares/circles show the computed values, and the solid lines display the values predicted by starting from the 30a value and applying the scaling laws.

Fig. 12.
Fig. 12.

Minimum bending radius R 0.1% to achieve 0.1% worst-case scattering losses for the TE01 mode in the OmniGuide fiber of Fig. 4. Conversely, the losses for a given bending radius Rb are 0.1% · (R 0.1%/Rb )2. The sharp peak (actually a divergence) in R 0.1% is due to the point of degeneracy between TE01 and EH11.

Fig. 13.
Fig. 13.

Scaling of the ellipticity-induced phase shift ℜ[Δ β ˜ (2)] and loss Δα(2) for the OmniGuide-fiber TE01 mode at λ=1.55µm as a function of the core radius R, varying from 20–80a. The abscissa is the expected scaling form of 1/R 2 and 1/R, respectively. The amount of ellipticity is δ=1% and the cladding has 17 layers.

Fig. 14.
Fig. 14.

The estimated radiative loss α+Δα(2) of the TE01 mode at λ=1.55µm for the OmniGuide fiber of Fig. 4 with an elliptical perturbation, plotted versus the number of cladding layers for three ellipticities: δ=0.5%,1%,2%. Red circles indictate the losses for the perturbed fibers, while solid blue lines above and below are the losses of the unperturbed HE21 and TE01 modes, respectively. As the number of layers increases, the losses become dominated by coupling to HE21, due to the weaker band gap for TM polarizations.

Fig. 15.
Fig. 15.

Enhanced loss of the TE01 mode at λ=1.55µm from randomly-varying ellipticity with rms δ0 =1%, as a function of the ellipticity correlation length Lc , due to coupling with the HE21 and EH21 modes. The inset shows the fractional scattered power in the parasitic HE21/EH21 modes as a function of Lc . If the correlation length exceeds ~1.6mm, the induced losses become smaller than 0.01 dB/km and the fractional parasitic power is less than 10-4.

Fig. 16.
Fig. 16.

Roughness radiation efficiency ρs , as defined by Eq. (24) for the TE01 mode of the OmniGuide fiber of Fig. 4, based on the | E |2 at the core/cladding interface (blue dots) or averaged over a 10nm interval (red circles). Approximate roughness losses are computed by multiplying ρs with a dimensionful quantity s that is dependent on the scatterer quantity; e.g. s=0.03 dB/km for one 10nm scatterer every 10µm2.

Tables (1)

Tables Icon

Table 1. Scaling relations with core radius R for TE01 in OmniGuide fibers.

Equations (50)

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

d hi d lo = n lo 2 1 n hi 2 1
normalized T E 0 cladding E 1 R 2 .
fraction of E 2 in cladding for TE 0 1 R 3 ,
mode separation Δ β 1 R 2 ;
TE 01 and EH 11 mode separation Δ β 1 R .
f m ( ω , β ˜ ) det [ M m ( ω , β ˜ ) ] ,
TE 0 radiation leakage α 1 R 3 ,
D ω 2 2 π c d 2 β d ω 2 ,
Δ ε = 2 n n 2 E 2 .
TE 0 cladding absorption 1 R 3 .
TE 0 cladding nonlinearity γ γ 0 1 R 5 .
n Δ A ̂ n = E x E y E z H z H y H z ω x cR b ( ε ε ε μ μ μ ) E x E y E z H z H y H z
n Δ A ̂ n = β n x R b ( E t * × H t + E t × H t * )
i R b ( E y * H z H y * E z ) .
n ; m Δ A ̂ n ; m = ( r integral ) · 0 2 π e i Δ m φ ( e i φ + e i φ ) d φ 4 π
= ( r integral ) · δ Δ m , ± 1 2 ,
minimum bend R b for 0.1 % losses , R 0.1 % R 2 .
Δ α n ( 2 ) n n n Δ A ̂ n 2 Δ β n n 2 ( α n α n ) ,
n ; m Δ A ̂ n ; m = E r E φ H r H φ ω c b η ( ε ± ε ± i ε ε μ ± i μ ± i μ μ ) E r E φ H r H φ δ m , m 2 , ,
TE 0 Δ A ̂ m = ± 2 δ R 2 .
[ Δ β ˜ ( 2 ) ] δ 2 R 2 .
Δ α ( 2 ) = 2 [ Δ β ˜ ( 2 ) ] δ 2 R .
P n z = α n P n + m M n m ( P m P n ) ,
P s = c 2 μ 0 ε 0 12 π ( ω c ) 4 p 2 = ω 4 12 π Δ ε E V s 2 ,
α = P s · 2 π R σ s P = ( ω 4 12 π Δ ε E 2 · 2 π R · 4 ) · σ s V s 2 ,
ρ s 2 ω 4 R 3 Δ ε E 2 ,
s σ s V s 2 a 5 · 10 ln 10 ,
κ te n ˜ lo n ˜ hi ,
κ tm n lo 2 n ˜ hi n hi 2 n ˜ lo > κ te .
fraction of E 2 in cladding for TE 0 f hi 2 ( 1 κ te 2 ) ( a R ) 3 .
TE 0 cladding absorption n ̅ f hi 2 ( 1 κ te 2 ) ( a R ) 3 .
TE 0 cladding nonlinearity γ γ 0 n ̅ f hi 4 ( 1 κ te 4 ) ( a R ) 5 .
Δ ω tm ω 0 = 4 π sin 1 ( n hi 2 n ˜ lo n lo 2 n ˜ hi n hi 2 n ˜ lo + n lo 2 n ˜ hi ) ,
ω 0 = n ˜ lo + n ˜ hi 4 n ˜ lo n ˜ hi · 2 π c a .
H z = i c ω μ t × E t ,
E z = i c ω ε t × H t
A ̂ ψ = i z B ̂ ψ ,
ψ ( E t ( z ) H t ( z ) ) ,
ψ ψ E t * · E t + H t * · H t ,
A ̂ ( ω ε c c ω t × 1 μ t × 0 0 ω μ c c ω t × 1 ε t × ) ,
B ̂ ( 0 z ̂ × z ̂ × 0 ) = ( 1 1 1 1 ) = B ̂ 1 .
e i ( β z ω t ) ψ .
A ̂ ψ = β B ̂ ψ .
ψ B ̂ ψ = z ̂ · E t * × H t + E t × H t * ,
Δ β n ( 1 ) = n Δ A ̂ n ,
Δ β n ( 2 ) = n n n Δ A ̂ n 2 Δ β n n ,
dc n dz = i β n c n + i n n Δ A ̂ n c n .
c n ( z ) 2 c n ( 0 ) 2 4 n Δ A ̂ n 2 Δ β n n 2 sin 2 ( Δ β n n z 2 ) .
dc n dz = i β n c n n n n d A ̂ dz n Δ β n n c n .
n Δ A ̂ n = E x E y E z ω c ( Δ ε Δ ε Δ ε ) E x E y E z + O ( Δ ε 2 ) .

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