6533b853fe1ef96bd12ad4d4
RESEARCH PRODUCT
A RADIATION CONDITION FOR UNIQUENESS IN A WAVE PROPAGATION PROBLEM FOR 2-D OPEN WAVEGUIDES
Rolando MagnaniniGiulio Ciraolosubject
Electromagnetic fieldAsymptotic analysisHelmholtz equationWave propagationGeneral Mathematicsmedia_common.quotation_subject78A40 35J05 78A50 35A05Mathematical analysisGeneral Engineeringelectromagnetic fields • wave propagation • Helmholtz equation • optical waveguides • uniqueness of solutions • radiation conditionInfinitylaw.inventionAmplitudeMathematics - Analysis of PDEslawFOS: Mathematicswave propagation; Helmholtz equation; optical waveguides; radiation condition; uniqueness theoremsUniquenessWaveguidemedia_commonMathematicsAnalysis of PDEs (math.AP)description
We study the uniqueness of solutions of Helmholtz equation for a problem that concerns wave propagation in waveguides. The classical radiation condition does not apply to our problem because the inhomogeneity of the index of refraction extends to infinity in one direction. Also, because of the presence of a waveguide, some waves propagate in one direction with different propagation constants and without decaying in amplitude. Our main result provides an explicit condition for uniqueness which takes into account the physically significant components, corresponding to guided and non-guided waves; this condition reduces to the classical Sommerfeld-Rellich condition in the relevant cases. Finally, we also show that our condition is satisfied by a solution, already present in literature, of the problem under consideration.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-01-01 |