A lattice of optical ring resonators can exhibit a topological insulator phase, with the direction of rotation in the resonators playing the role of spin. This occurs when the inter-resonator coupling is sufficiently large, and the synthetic magnetic vector potential set up by the couplers is zero. Using the transfer matrix method, we derive the band structure, phase diagram, and the projected band diagram showing the existence of spin-polarized edge states. When PT (parity/time-reversal) symmetric gain and loss are introduced, the system functions as an optical diode which does not require optical nonlinearities.

http://arxiv.org/abs/1212.5034
Optics (physics.optics); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

We analyze the optical properties of one-dimensional (1D) PT-symmetric structures of arbitrary complexity. These structures violate normal unitarity (photon flux conservation) but are shown to satisfy generalized unitarity relations, which relate the elements of the scattering matrix and lead to a conservation relation in terms of the transmittance and (left and right) reflectances. One implication of this relation is that there exist anisotropic transmission resonances in PT-symmetric systems, frequencies at which there is unit transmission and zero reflection, but only for waves incident from a single side. The spatial profile of these transmission resonances is symmetric, and they can occur even at PT-symmetry breaking points. The general conservation relations can be utilized as an experimental signature of the presence of PT-symmetry and of PT-symmetry breaking transitions. The uniqueness of PT-symmetry breaking transitions of the scattering matrix is briefly discussed by comparing to the corresponding non-Hermitian Hamiltonians.

http://arxiv.org/abs/1112.5167
Optics (physics.optics)

Using a scattering matrix formalism, we derive the general scattering properties of optical structures that are symmetric under a combination of parity and time-reversal (PT). We demonstrate the existence of a transition beween PT-symmetric scattering eigenstates, which are norm-preserving, and symmetry-broken pairs of eigenstates exhibiting net amplification and loss. The system proposed by Longhi, which can act simultaneously as a laser and coherent perfect absorber, occurs at discrete points in the broken symmetry phase, when a pole and zero of the S-matrix coincide.

http://arxiv.org/abs/1008.5156
Optics (physics.optics); Quantum Physics (quant-ph)