Abstract

The rigorous electromagnetic analysis of the coupling between two nonparallel optical-fiber waveguides is developed for the first time. Green's theorem, involving the dyadic Green's function of the fiber guiding the incident mode, is used to formulate the electric-field integral equation inside the second fiber. By applying the entire-domain Galerkin technique and by utilizing the generalized addition theorem for cylindrical waves for nonparallel axis translation, which is derived by the authors, this equation is analytically transformed into a system of coupled integral equations for the spectral weights of the field on the basis of TE and TM cylindrical vector wave functions. The Neumann-series iterative procedure is adopted to solve this system and obtain analytical expressions for the field scattering coefficients, which are sufficiently accurate for weakly coupled fibers.

© 2006 IEEE

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IEEE Photon. Technol. Lett. (1)

T. A. Birks, J. C. Knight, T. E. Dimmick, "High-resolution measurement of the fiber diameter variations using whispering gallery modes and no optical alignment," IEEE Photon. Technol. Lett. 12, 182-183 (2000).

IEEE Trans. Microw. Theory Tech. (1)

M. A. McHenry, D. C. Chang, "Coupled-mode theory of two nonparallel dielectric waveguides," IEEE Trans. Microw. Theory Tech. MTT-32, 1469-1475 (1984).

Int. J. Infr. Millim. Waves (1)

N. K. Uzunoglu, P. A. Mandis, "Analysis of the coupling of two non-parallel dielectric rod waveguides," Int. J. Infr. Millim. Waves 8, 535-547 (1987).

Int. J. Infrared Millim. Waves (1)

C. N. Capsalis, N. K. Uzunoglu, "Coupled wave propagation in closely spaced dielectric rod waveguides," Int. J. Infrared Millim. Waves 7, 813-831 (1986).

J. Lightw. Technol. (1)

A. W. Snyder, A. Ankiewicz, "Optical fiber couplers—Optimum solution for unequal cores," J. Lightw. Technol. 6, 463-474 (1988).

J. Opt. Soc. Amer. (3)

P. D. McIntyre, A. W. Snyder, "Power transfer between nonparallel and tapered optical fibers," J. Opt. Soc. Amer. 64, 285-288 (1974).

A. L. Jones, "Coupling of optical fibers and scattering in fibers," J. Opt. Soc. Amer. 55, 261-271 (1965).

W. Wijngaard, "Guided normal modes of two parallel circular dielectric rods," J. Opt. Soc. Amer. 63, 944-950 (1973).

J. Opt. Soc. Amer. A, Opt. Image Sci. (5)

I. D. Chremmos, N. K. Uzunoglu, "Integral equation analysis of scattering by a spherical microparticle coupled to a subwavelength-diameter wire waveguide," J. Opt. Soc. Amer. A, Opt. Image Sci. 23, 461-467 (2006).

J. A. Lock, "Scattering of a diagonally incident focused Gaussian beam by an infinitely long homogeneous circular cylinder," J. Opt. Soc. Amer. A, Opt. Image Sci. 14, 640-652 (1997).

J. P. Barton, "Internal and near-surface electromagnetic fields for an infinite cylinder illuminated by an arbitrary focused beam," J. Opt. Soc. Amer. A, Opt. Image Sci. 16, 160-166 (1999).

N. K. Uzunoglu, "Scattering from inhomogeneities inside a fiber waveguide," J. Opt. Soc. Amer. A, Opt. Image Sci. 71, 259-273 (1981).

I. D. Chremmos, N. K. Uzunoglu, "Transformation of radially traveling cylindrical waves between two skew cylindrical coordinate systems," J. Opt. Soc. Amer. A, Opt. Image Sci. 23, 1884-1888 (2006).

Nano Lett. (1)

C. J. Barrelet, A. B. Greytak, C. M. Lieber, "Nanowire photonic circuit elements," Nano Lett. 4, 1981-1985 (2004).

Nature (1)

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).

Opt. Express (1)

Physica (1)

R. Vanclooster, P. Phariseau, "The coupling of two parallel dielectric fibers: Basic equations," Physica 47, 485-500 (1970).

Science (1)

M. Law, D. J. Sirbuly, J. C. Johnson, J. Goldberger, R. J. Saykally, P. Yang, "Nanoribbon waveguides for subwavelength photonics integration," Science 305, 1269-1273 (2004).

Other (5)

R. Courant, D. Hilbert, Methods of Mathematical Physics (Wiley, 1989).

C. T. Tai, Dyadic Green Functions in Electromagnetic Theory (IEEE Press, 1994).

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, 1972).

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, 1960).

R. F. Harrington, Field Computation by Moment Methods (Macmillan, 1983).

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