Spectral symmetry of Fano resonances in a waveguide coupled to a microcavity

We investigate the parity of transmission spectra in a photonic crystal (PhC) waveguide with a side-coupled cavity and a partially blocking element. We demonstrate, by means of numerical calculations, that by varying the cavity-block distance the spectra vary from being asymmetric with blue parity, to being symmetric (Lorentzian), to being asymmetric with red parity. For cavity-block distances larger than five PhC lattice constants, we show that the transmission spectrum is accurately described as the transmission spectrum of a Fabry-Perot etalon with a single propagating Bloch mode, and that the parity of the transmission spectrum correlates with the Fabry-Perot roundtrip phase.