The coupling strength between two parity-time (PT) symmetric resonators determines whether the PT phase is broken or not. Here we investigate the scenario that two optical waveguides are spatially curved so that they switch periodically between unbroken and broken PT phases. We show that the existence of locally broken PT phase does not necessarily render a broken phase to waves propagating inside. Criteria are proposed to characterize the collective dynamics of wave near the Brillouin zone (BZ) edge, toward the cases of a totally broken phase, a partially broken phase, or a totally unbroken phase. We also discuss the characteristics of two special kinds of exceptional points (EPs) at the BZ edge, and show that their field patterns are displaced by half a period with each other. Full-wave numerical simulation proves our analysis. Potential applications especially these associated with EPs are discussed. This study helps us to understand how the locally PT-symmetric related eigenstate influences the globally collective dynamics of wave in spatially periodic configuration.

We develop a coupled-mode theory on the optical transmission in parity-time ( PT) symmetric coaxial metamaterials. Modeled by coupled lossy Lorentzian oscillators, the theory provides a good fit to numerical full-wave simulation. In the scenario of unidirectional coupling, two polarization-sensitive anomalies are obtained: an amplified transmission and an ultra-narrow one analogous to bound states in continuum. We argue that these phenomena are associated with either a unidirectional-field-transfer process or an indirect unidirectional-field-trapping resonance. The broadening effect is shown to determine the magnitude and polarization of the transmission. Our theory and analysis provide a deep understanding on the importance of PT symmetry and dark helical modes and would contribute to applications such as light storage, field amplification, and even lasing.

We study the propagation of optical beams in two-dimensional Moiré lattices, and demonstrate position-dependent beam dynamics when a quasi-Bragg condition is satisfied. We show that when the optical beam is incident to a peak of the lattice envelop, an optical Zitterbewegung is obtained. If the optical beam is incident to a node of the envelop, a field localization effect takes place. The localized beam oscillates with a much larger spatial period than that of the optical Zitterbewegung. Variation of the oscillation period versus the split in periods is discussed. The position-dependent beam dynamics are explained by the excitation of proper bandedge eigenmodes of the Moiré lattice, and can be engineered via tuning the periods of the two superimposed Bragg lattices.

We investigate the excitation and propagation of surface plasmon polaritons (SPPs) at a geometrically flat metal-dielectric interface with a parity-time (PT) symmetric modulation on the permittivity ϵ(x) of the dielectric medium. We show that two striking effects can be simultaneously achieved thanks to the nonreciprocal nature of the Bloch modes in the system. First, SPPs can be unidirectionally excited when light is normally incident on the interface. Secondly, the backscattering of SPPs into the far field is suppressed, producing a radiative-loss-free effect on the unidirectional SPPs. As a result, the lifetime and propagation distance of SPPs can be significantly improved. These results show that PT symmetry can be employed as a new approach to designing transformative nanoscale optical devices, such as low-loss plasmonic routers and isolators for efficient optical computation, communication, and information processing.

Coaxial optical subwavelength elements support helical modes Lm with different topological indexes m. Here we propose to couple the two bright L±1 modes with the dark one L0 via a parity-time (PT) symmetric perturbation. We show that the cascading coupled configuration is similar to a three-level atomic system, and supports a special hybridized mode Lc via a classic analog of coherent-population-trapping effect. Resonant frequency of Lc is independent of the PT-symmetric perturbation. Populations in L±1 can be manipulated by tuning the PT-symmetric perturbation, and no population is trapped in L0. Since the L±1 modes are associated with optical waves of opposite circular polarizations, the polarization of transmitted wave is independent of the polarization of incidence but solely determined by the PT-symmetric perturbation. Such an effect can be utilized to manipulate the polarization state of light. Numerical simulation in a well-designed coaxial metamaterial verifies our analysis.

We review some of the statistical properties of polarization-related speckle phenomena, with an introduction of a less known concept of polarization speckles and their spatial degree of polarization. As a useful means to characterize two-point vector field correlations, we review the generalized Stokes parameters proposed by Korotkova and Wolf, and introduce its time-domain representation to describe the space-time evolution of the correlation between random electric vector fields at two different space-time points. This time-domain generalized Stokes vector, with components similar to those of the beam coherence polarization matrix proposed by Gori, is shown to obey the wave equation in exact analogy to a coherence function of scalar fields. Because of this wave nature, the time-domain generalized Stokes vector is referred to as generalized Stokes vector wave in this paper.

By controlling the irradiance of an extended quasimonochromatic, spatially incoherent source, an optical field is generated that exhibits spatial coherence with phase singularities, called coherence vortices. A simple optical geometry for direct visualization of coherence vortices is proposed, and the local properties and the spatial evolution of coherence vortex are experimentally investigated. To our knowledge, this is the first direct and quantitative experimental measurement of a generic coherence vortex.