  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.
