OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Vol. 19, Iss. 12 — Dec. 2, 2002
  • pp: 2867–2875

Analysis of general geometric scaling perturbations in a transmitting waveguide: fundamental connection between polarization-mode dispersion and group-velocity dispersion

Maksim Skorobogatiy, Mihai Ibanescu, Steven G. Johnson, Ori Weisberg, Torkel D. Engeness, Marin Soljačić, Steven A. Jacobs, and Yoel Fink  »View Author Affiliations


JOSA B, Vol. 19, Issue 12, pp. 2867-2875 (2002)
http://dx.doi.org/10.1364/JOSAB.19.002867


View Full Text Article

Acrobat PDF (425 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We develop a novel perturbation theory formulation to evaluate polarization-mode dispersion (PMD) for a general class of scaling perturbations of a waveguide profile based on generalized Hermitian Hamiltonian formulation of Maxwell’s equations. Such perturbations include elipticity and uniform scaling of a fiber cross section, as well as changes in the horizontal or vertical sizes of a planar waveguide. Our theory is valid even for discontinuous high-index contrast variations of the refractive index across a waveguide cross section. We establish that, if at some frequencies a particular mode behaves like pure TE or TM polarized mode (polarization is judged by the relative amounts of the electric and magnetic longitudinal energies in the waveguide cross section), then at such frequencies for fibers under elliptical deformation its PMD as defined by an intermode dispersion parameter τ becomes proportional to group-velocity dispersion D such that τ=λδ|D|, where δ is a measure of the fiber elipticity and λ is a wavelength of operation. As an example, we investigate a relation between PMD and group-velocity dispersion of a multiple-core step-index fiber as a function of the core–clad index contrast. We establish that in this case the positions of the maximum PMD and maximum absolute value of group-velocity dispersion are strongly correlated, with the ratio of PMD to group-velocity dispersion being proportional to the core–clad dielectric contrast.

© 2002 Optical Society of America

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2310) Fiber optics and optical communications : Fiber optics
(060.2400) Fiber optics and optical communications : Fiber properties

Citation
Maksim Skorobogatiy, Mihai Ibanescu, Steven G. Johnson, Ori Weisberg, Torkel D. Engeness, Marin Soljačić, Steven A. Jacobs, and Yoel Fink, "Analysis of general geometric scaling perturbations in a transmitting waveguide: fundamental connection between polarization-mode dispersion and group-velocity dispersion," J. Opt. Soc. Am. B 19, 2867-2875 (2002)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-19-12-2867


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. S. J. Savori, “Pulse propagation in fibers with polarization-mode dispersion,” J. Lightwave Technol. 19, 350–357 (2001).
  2. A. W. Synder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  3. C. Vassallo, Optical Waveguide Concepts (Elsevier, Amsterdam, 1991).
  4. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1998), p. 357.
  5. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  6. 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).
  7. D. Chowdhury, “Comparison between optical fiber birefringence induced by stress anisotropy and geometric deformation,” IEEE J. Sel. Top. Quantum Electron. 6, 227–232 (2000).
  8. V. P. Kalosha and A. P. Khapalyuk, “Mode birefringence in a single-mode elliptic optical fiber,” Sov. J. Quantum Electron. 13, 109–111 (1983).
  9. V. P. Kalosha and A. P. Khapalyuk, “Mode birefringence of a three-layer elliptic single-mode fiber waveguide,” Sov. J. Quantum Electron. 14, 427–430 (1984).
  10. 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), http://www.opticsexpress.org.
  11. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (June 2002).
  12. S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. D. Engeness, M. Soljačić, 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), http://www.opticsexpress.org.
  13. Note, multiplying from the left by B⁁−1 on both sides of Eq. (8) and, thus, trying to make it look as a standard eigenvalue problem is erroneous as, in general, a resulting matrix on the right would not be Hermitian.
  14. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Non-Relativistic Theory) (Butterworth-Heinemann, Stoneham, Mass., 2000), p. 140.
  15. F. Curti, B. Daino, G. De Marchis, and F. Matera, “Statistical treatment of the evolution if the principal states of polarization in single-mode fibers,” J. Lightwave Technol. 8, 1162–1166 (1990).
  16. 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).
  17. G. B. Arfken and H. J. Webber, Mathematical Methods for Physicists (Academic, New York, 1995).

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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited