Abstract
A finite element method is presented to find the propagation characteristics of an optical fiber with arbitrary cross section. This method uses a non-local boundary operator to reduce the infinite problem (open waveguide) to a bounded one. Evanescent energy in circular and square fibers of the same core area are computed and compared to show that square fibers can be effectively used in single molecule detection.
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References
W. Love, L. Button and R. Slovacek, Optical characteristics of fiberoptics evanescent wave sensor, in: Biosensors with Fiber Optics, eds. D.L. Wise and L.B. Wingard, Jr. (The Humana Press, 1991).
X. Fang and W. Tan, Imaging single fluorescent molecules at the interface of an optical fiber probe by evanescent wave excitation, Anal. Chem. 71 (1999) 3101-3105.
A.W. Snyder and J.D. Love, Optical Waveguide Theory (Chapman-Hall, London, 1983).
R.E. Collin, Field Theory of Guided Wave, 2nd ed. (IEEE Press, 1991).
J.E. Goell, A circular-harmonic computer analysis of rectangular dielectric waveguides, The Bell System Technical Journal (1969) 2133-2160.
E.A.J. Marcatili, Dielectric rectangular waveguide and directional coupler for integrated optics, The Bell System Technical Journal (1969) 2071-2102.
T. Tamir (ed.), Guided-wave Optoelectronics, 2nd ed. (Springer-Verlag, Berlin, 1990).
G. Bao and T. Van, Modeling of evanescent energy in optical fibers, J. Comput. Phys. (to appear).
D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, New York, 1974).
M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1972).
A.W. Snyder, Excitation and scattering of modes on a dielectric or optical fiber, IEEE Trans. Microwave Theory and Techniques 17 (1969) 1138-1144.
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Bao, G., Fang, X., Tan, W. et al. Evanescent energy in square and circular fibers. Journal of Mathematical Chemistry 27, 251–265 (2000). https://doi.org/10.1023/A:1018889304472
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DOI: https://doi.org/10.1023/A:1018889304472