OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 10, Iss. 23 — Nov. 18, 2002
  • pp: 1342–1346
« Show journal navigation

Elimination of polarization degeneracy in round waveguides

Ian M. Bassett and Alexander Argyros  »View Author Affiliations


Optics Express, Vol. 10, Issue 23, pp. 1342-1346 (2002)
http://dx.doi.org/10.1364/OE.10.001342


View Full Text Article

Acrobat PDF (329 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We show how to design a round optical fiber so that it is effectively single moded, with no polarization degeneracy. Such fibers would be free from the consequences of polarization degeneracy or near degeneracy – phenomena such as polarization fading in interferometry, and polarization mode dispersion – and so may offer an alternative to polarization maintaining fibers for the avoidance of these phenomena. The design presented builds on an earlier observation of polarization selective refection in Bragg fibers.

© 2002 Optical Society of America

We are used to polarization of light as it occurs in free plane waves – formed by a superposition of two orthogonal linear polarizations with any relative amplitude and phase, giving the familiar linear, circular and elliptical polarization states. Polarization of light guided in an ordinary single mode fiber is similar. It is perhaps easy to forget that polarization in this sense is not an inherent property of light. Just as the radiation field is modified in photonic crystal structures [1

1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059 (1987). [CrossRef] [PubMed]

,2

2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1987). [CrossRef] [PubMed]

] the accessible polarization states of the field in a waveguide may differ from those of free radiation. In a sense this is obvious – ordinary step index fibers have TE and TM modes without polarization degeneracy. This is easily overlooked as in ordinary single mode fiber these modes are unguided, and do not commonly intrude on observations, and in multimode fiber, in the ray optics regime, polarization reappears in its 2-fold form.

Fig.1. Schematic refractive index profiles of (a) a step index fiber, and (b) a Bragg fiber.

Bragg fibers of finite radius support no strictly bound modes, only leaky modes with varying loss. However, as a practical matter, a sufficiently low loss rate is as good as binding by radial evanescence. Whether a mode with a given loss coefficient (fractional loss per m) should be regarded as in practice guided or not, depends on the length of the fiber. Whether a fiber should be regarded as single moded or not, depends on its length and on the relative lossiness of the least lossy mode and all the other modes. For example, consider a fiber having three modes with fractional power losses of 10-6, 10-4 and 10-2 per m respectively, and with all other modes much lossier. For a fiber length of 1 m, all three modes are guided, at 100 m, the first two are guided and the third is not, while at 10 km, the fiber is effectively single moded.

Since all modes in a Bragg fiber are lossy, it is clear that single modedness depends on there being one mode which has a low enough loss, while all other modes are sufficiently lossy – it is the contrast which counts. Our design strategy makes use of the Brewster angle phenomenon to help to achieve such contrast.

Fig. 2. Schematic of the electric field in the hybrid, TE, and TM modes of a round waveguide.

Table 1a. Key modal properties of TE Bragg fiber A

table-icon
View This Table
| View All Tables

Table 1b. Key modal properties of TE Bragg fiber B

table-icon
View This Table
| View All Tables

The individual modes are characterized by two lengths, L1%, at which the transmitted power in that mode is reduced to 1%, and L.01%=2L1%, at which the power is reduced to 0.01%. We characterize each fiber as a whole by two lengths, Lmax = L1% for the best guided mode, and Lsm = L.01% for the second best guided mode. We consider the fiber to be usefully single moded for lengths between Lsm and Lmax. Thus fiber A is usefully single moded for lengths between about 400 μm and 26 m and fiber B is single moded for lengths between about 2 cm and 400 m. We take into account only the second best guided mode in calculating the onset of single modedness, as the remaining higher loss modes do not contribute significantly. Modes omitted from Tables 1 are lossier than those shown.

Consider a ray incident on a plane boundary between two transparent media. If the angle of incidence is at the Brewster angle, i.e. if it is such that the reflected ray is at right angles to the transmitted ray, the component of the incident light with polarization parallel to the plane of incidence, analogous to TM radiation, is not reflected. If in a planar multilayer stack with alternating indices n1, n2, the Brewster angle condition holds at one interface, it will hold at all interfaces. The condition that a TM wave be not reflected at the interfaces of a curved concentric stack approaches the Brewster condition for a plane stack at large radius. If θ i(i = 1, 2) is the angle of incidence in the layer with refractive index n i, the Brewster condition is θ 1+θ 2 = π/2. Snell’s law then gives n 1sinθ 1 = n 2sinθ 2 = n 2cosθ 1 and then from the geometry of Fig. 3, n12 β 2 = n22(n12 k 2β 2) or

βk=neff=n1n2n12+n22.
(1)
Fig. 3. Relationship between the propagation constant and the transverse wavenumber in a medium of refractive index n1, and illustration of the Brewster angle of incidence at a plane boundary.

For a given wavelength and a Bragg fiber with indices n1, n2 the neff of the best guided mode can be adjusted quite freely by varying the thickness of the layers (and so the Bragg condition) and the size of the core. For values of neff close to the Brewster condition (equation 1) Bragg reflection is undermined for TM modes, and for hybrid modes, which have a component of TM polarization. In the language of band gaps, the superposition of the Brewster and Bragg effects results in a polarization dependent band gap; a band gap for TE but not for TM polarization. The modes must satisfy a cavity resonance condition (a resonance with a width corresponding to the loss). A single TE mode can be isolated by reducing the core size so that all TE modes but one lie outside the range of n eff that corresponds to the Bragg condition. Increasing the core size allows other TE modes to be better guided, leading to an increase in the length required for single modedness. This is illustrated by comparison of fibers A and B, which differ only in the core size.

A constraint on the value of neff is that it must be lower than all the refractive indices that make up the fiber. This ensures that the fields are oscillatory (and not evanescent) in the core and the surrounding layers, which is necessary for Bragg reflection. Equation 1 ensures that neff is less than n1 and n2, so the remaining constraint is that it be less than the core index. For a depressed core of index nco the condition n1n2n12+n22<nco is equivalent to

n1<n2ncon22+nco2andn2<n1ncon12nco2,
(2)

which imposes the necessary condition

min(n1,n2)<2nco.
(3)

We present briefly, for an instructive contrast with the fibers of Table 1, another air core Bragg fiber [10

10. S. G. Johnson et al., “Low-loss asymptotically single-mode propagation in large-core Omniguide fibers,” Opt. Express 9, 748–779, (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-748. [CrossRef] [PubMed]

]. This fiber has extremely low structural loss for the best guided modes, but does not satisfy the Brewster condition, and has poor contrast of lossiness, with Lmax only about twice Lsm (Table 2). While nominally single moded for lengths greater than Lsm = 5330 km, non-structural losses would supervene at much shorter lengths. By our criteria, the fiber is effectively multimoded.

Table 2. Key modal properties of a Bragg fiber (defined in reference [10])

table-icon
View This Table
| View All Tables

Acknowledgements

The authors thank Martijn de Sterke, Maryanne Large, Martijn van Eijkelenborg, John Canning and Simon Fleming for helpful discussions, especially concerning the meaning of singlemodedness for waveguides with no bound modes.

References and Links

1.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059 (1987). [CrossRef] [PubMed]

2.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1987). [CrossRef] [PubMed]

3.

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

4.

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

5.

C. M. de Sterke, I. M. Bassett, and A. G. Street, “Differential losses in Bragg fibres,” J. Appl. Phys. 76, 680 (1994). [CrossRef]

6.

A. Ferrando and J. J. Miret, “Single-polarization single-mode intraband guidance in supersquare photonic crystals fibers,” Appl. Phys. Lett. 78, 3184–3186 (2001). [CrossRef]

7.

W. C. Chew, Waves and fields in inhomogeneous media, Chapter 3 (Van Nostrand Reinhold, New York, 1990).

8.

A. Argyros, I. M. Bassett, M. A. van Eijkelenborg, M. C.J. Large, J. Zagari, N. A. P. Nicorovici, R. C. McPhedran, and C. M. de Sterke, “Ring structures in microstructured polymer optical fibres,” Opt. Express 9, 813 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-813. [CrossRef] [PubMed]

9.

M. Born and E. Wolf, Principles of Optics, Chapter 1.6 (Pergamon Press, Oxford, 1980).

10.

S. G. Johnson et al., “Low-loss asymptotically single-mode propagation in large-core Omniguide fibers,” Opt. Express 9, 748–779, (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-748. [CrossRef] [PubMed]

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2400) Fiber optics and optical communications : Fiber properties
(060.2430) Fiber optics and optical communications : Fibers, single-mode
(260.5430) Physical optics : Polarization

ToC Category:
Research Papers

History
Original Manuscript: October 11, 2002
Revised Manuscript: November 5, 2002
Published: November 18, 2002

Citation
Ian Bassett and Alexander Argyros, "Elimination of polarization degeneracy in round waveguides," Opt. Express 10, 1342-1346 (2002)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-23-1342


Sort:  Journal  |  Reset  

References

  1. E. Yablonovitch, �??Inhibited spontaneous emission in solid-state physics and electronics,�?? Phys. Rev. Lett. 58, 2059 (1987). [CrossRef] [PubMed]
  2. S. John, �??Strong localization of photons in certain disordered dielectric superlattices,�?? Phys. Rev. Lett. 58, 2486 (1987). [CrossRef] [PubMed]
  3. P. Yeh, A. Yariv, and E. Marom, �??Theory of Bragg fiber,�?? J. Opt. Soc. Am. 68, 1196 (1978). [CrossRef]
  4. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).
  5. C. M. de Sterke, I. M. Bassett and A. G. Street, �??Differential losses in Bragg fibres,�?? J. Appl. Phys. 76, 680 (1994). [CrossRef]
  6. A. Ferrando and J. J. Miret, �??Single-polarization single-mode intraband guidance in supersquare photonic crystals fibers,�?? Appl. Phys. Lett. 78, 3184-3186 (2001). [CrossRef]
  7. W. C. Chew, Waves and fields in inhomogeneous media, Chapter 3 (Van Nostrand Reinhold, New York, 1990).
  8. A. Argyros, I. M. Bassett, M. A. van Eijkelenborg, M. C.J. Large, J. Zagari, N. A. P. Nicorovici, R. C. McPhedran and C. M. de Sterke, �??Ring structures in microstructured polymer optical fibres,�?? Opt. Express 9, 813 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-813">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-813</a>. [CrossRef] [PubMed]
  9. M. Born and E. Wolf, Principles of Optics, Chapter 1.6 (Pergamon Press, Oxford, 1980).
  10. S. G. Johnson et al., �??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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig.1. Fig. 2. Fig. 3.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited