Photon transport in binary photonic lattices
We present a review on the mathematical methods used to theoretically study classical propagation and quantum transport in arrays of coupled photonic waveguides. We focus on analysing two types of binary photonic lattices where selfenergies or couplings are alternated. For didactic reasons, we split...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2013 |
| País: | México |
| Recursos: | Instituto Nacional de Astrofísica, Óptica y Electrónica |
| Repositorio: | Repositorio Institucional del INAOE |
| Idioma: | inglés |
| OAI Identifier: | oai:inaoe.repositorioinstitucional.mx:1009/2195 |
| Acesso em linha: | http://inaoe.repositorioinstitucional.mx/jspui/handle/1009/2195 |
| Access Level: | acceso abierto |
| Palavra-chave: | info:eu-repo/classification/Inspec/Mathematical methods info:eu-repo/classification/Inspec/Electromagnetic field info:eu-repo/classification/Inspec/Binary lattices info:eu-repo/classification/Inspec/Photon transport info:eu-repo/classification/cti/1 info:eu-repo/classification/cti/22 info:eu-repo/classification/cti/2209 |
| Resumo: | We present a review on the mathematical methods used to theoretically study classical propagation and quantum transport in arrays of coupled photonic waveguides. We focus on analysing two types of binary photonic lattices where selfenergies or couplings are alternated. For didactic reasons, we split the analysis in classical propagation and quantum transport but all methods can be implemented, mutatis mutandis, in any given case. On the classical side, we use coupled mode theory and present an operator approach to Floquet-Bloch theory in order to study the propagation of a classical electromagnetic field in two particular infinite binary lattices. On the quantum side, we study the transport of photons in equivalent finite and infinite binary lattices by couple mode theory and linear algebra methods involving orthogonal polynomials. Curiously the dynamics of finite size binary lattices can be expressed as roots and functions of Fibonacci polynomials. |
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