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Journal Articles SIAM Journal on Mathematical Analysis Year : 1990

Mathematical Analysis of the Guided Modes of an Optical Fiber

Abstract

A mathematical formulation for the guided modes of an optical fiber is derived from Maxwell's equations: this formulation leads to an eigenvalue problem for a family of self-adjoint noncompact operators. The main spectral properties of these operators are established. Then the min-max principle provides an expression of the nonlinear dispersion relation, which connects the propagation constants of guided modes to the frequency. Various existence results are finally proved and a complete description of the dispersion curves (monotonicity, asymptotic behavior, existence of cutoff values) is carried out.
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hal-01010733 , version 1 (20-06-2014)

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Alain Bamberger, Anne-Sophie Bonnet-Ben Dhia. Mathematical Analysis of the Guided Modes of an Optical Fiber. SIAM Journal on Mathematical Analysis, 1990, 21 (6), pp.1487-1510. ⟨10.1137/0521082⟩. ⟨hal-01010733⟩
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