Photon transport in binary photonic lattices
arXiv:1301.1376 · doi:10.1088/0031-8949/87/03/038116
Abstract
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 self-energies 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.
13 pages, 4 figures
References in corpus (12)
- f-Oscillators and Nonlinear Coherent States
- Photonic realization of the quantum Rabi model
- Discrete gap solitons in modulated waveguide arrays
- Photonic analogue of Zitterbewegung in binary waveguide arrays
- Classical analogue of displaced Fock states and quantum correlations in Glauber-Fock photonic lattices
- On the effective Dirac dynamics of ultracold atoms in bichromatic optical lattices
- Jaynes Cummings Photonic Superlattices
- Filtering Number States of the Vibrational Motion of an Ion
- Quantum simulator for the Schwinger effect with atoms in bi-chromatic optical lattices
- Exact dynamics of finite Glauber-Fock photonic lattices
- Quantum computation by quantum-like systems
- Soliton switching and Bloch-wave filtering in periodic photonic lattices