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BOUND STATES IN WEAKLY DEFORMED WAVEGUIDES: NUMERICAL VERSUS ANALYTICAL RESULTS

Part of: General mathematical topics and methods in quantum theory Spectral theory and eigenvalue problems Partial differential equations, boundary value problems

Published online by Cambridge University Press:  03 October 2017

PAOLO AMORE Open the ORCID record for PAOLO AMORE [Opens in a new window] ,
JOHN P. BOYD Open the ORCID record for JOHN P. BOYD [Opens in a new window] ,
FRANCISCO M. FERNÁNDEZ Open the ORCID record for FRANCISCO M. FERNÁNDEZ [Opens in a new window] ,
MARTIN JACOBO  and
PETR ZHEVANDROV Open the ORCID record for PETR ZHEVANDROV [Opens in a new window]
PAOLO AMORE*
Affiliation:
Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima, Mexico email paolo.amore@gmail.com
JOHN P. BOYD
Affiliation:
Department of Atmospheric, Oceanic & Space Science, University of Michigan, 2455 Hayward Avenue, Ann Arbor, MI 48109, USA email jpboyd@umich.edu
FRANCISCO M. FERNÁNDEZ
Affiliation:
INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd. 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata, Argentina email fernande@quimica.unlp.edu.ar
MARTIN JACOBO
Affiliation:
Facultad de Ciencias, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima, Mexico
PETR ZHEVANDROV
Affiliation:
Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Ciudad Universitaria, 58030 Morelia, Michoacán, Mexico email pzhevand@gmail.com
*
✉ paolo.amore@gmail.com
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Abstract

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We study bound states in weakly deformed and heterogeneous waveguides, and compare analytical predictions using a recently developed perturbative method with precise numerical results for three different configurations: a homogeneous asymmetric waveguide, a heterogenous asymmetric waveguide and a homogeneous broken strip. We have found excellent agreement between the analytical and numerical results in all the examples; this provides a numerical verification of the analytical approach.

Keywords

trapped modesbound statesdeformed waveguide

MSC classification

Primary: 81Q15: Perturbation theories for operators and differential equations
Secondary: 35P15: Estimation of eigenvalues, upper and lower bounds 65N25: Eigenvalue problems

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 2 , October 2017 , pp. 200 - 214
Copyright
© 2017 Australian Mathematical Society 

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