Symmetry breaking in the transmittance of passive photonic systems

Breaking structural parity symmetry of passive photonic systems is not a sufficient condition to break parity symmetry of their transmittance. It is believed that transmittance should still have even parity as a result of reciprocity that cannot be violated in passive systems where dynamically modulated components, a static magnetic field or non-linearity are absent. Nevertheless, we will show that transmission parity symmetry is equivalent to reciprocity only for systems where there is only a unique channel for the outgoing light. Any passive photonic system, with broken structural parity symmetry, can also break transmission parity symmetry provided at least one additional channel exists for the outgoing light. Actually, the latter is the key underpinning mechanism responsible for the reported transmission asymmetry in a plethora of complex photonic structures which possess a cross-polarization transmission channel in addition to co-polarized transmission. However, we demonstrate here that also a simple passive grating structure that preserves polarization without any cross-polarization effects exhibits an onset of parity asymmetry in the transmittance at frequencies above the Bragg condition, where higher-order output diffraction channels emerge.