Graphene Electrodynamics in the presence of the Extrinsic Spin Hall Effect

We extend the electrodynamics of two dimensional electron gases to account for the extrinsic spin Hall effect (SHE). The theory is applied to doped graphene decorated with a random distribution of absorbates that induce spin-orbit coupling (SOC) by proximity. The formalism extends previous semiclassical treatments of the SHE to the non-local dynamical regime. Within a particle-number conserving approximation, we compute the conductivity, dielectric function, and spin Hall angle in the small frequency and wave vector limit. The spin Hall angle is found to decrease with frequency and wave number, but it remains comparable to its zero-frequency value around the frequency corresponding to the Drude peak. The plasmon dispersion and linewidth are also obtained. The extrinsic SHE affects the plasmon dispersion in the long wavelength limit, but not at large values of the wave number. This result suggests an explanation for the rather similar plasmonic response measured in exfoliated graphene, which does not exhibit the SHE, and graphene grown by chemical vapor deposition, for which a large SHE has been recently reported. Our theory also lays the foundation for future experimental searches of SOC effects in the electrodynamic response of two-dimensional electron gases with SOC disorder.Comment: 12 pages, 4 figure

Quantitative test of general theories of the intrinsic laser linewidth

We perform a first-principles calculation of the quantum-limited laser linewidth, testing the predictions of recently developed theories of the laser linewidth based on fluctuations about the known steady-state laser solutions against traditional forms of the Schawlow-Townes linewidth. The numerical study is based on finite-difference time-domain simulations of the semiclassical Maxwell-Bloch lasing equations, augmented with Langevin force terms, and thus includes the effects of dispersion, losses due to the open boundary of the laser cavity, and non-linear coupling between the amplitude and phase fluctuations ($\alpha$ factor). We find quantitative agreement between the numerical results and the predictions of the noisy steady-state ab initio laser theory (N-SALT), both in the variation of the linewidth with output power, as well as the emergence of side-peaks due to relaxation oscillations.Comment: 24 pages, 10 figure

Exceptional points in topological edge spectrum of PT symmetric domain walls

We demonstrate that the non-Hermitian parity-time (PT) symmetric interfaces formed between amplifying and lossy crystals support dissipationless edge states. These PT edge states exhibit gapless spectra in the complex band structure interconnecting complex-valued bulk bands as long as exceptional points (EPs) of edge states exist. As a result, regimes exist where the edge states can spectrally overlap with the bulk continuum without hybridization, and leakage into the bulk states is suppressed due to the PT symmetry. Two exemplary PT symmetric systems, based on valley and quantum hall topological phases, are investigated, and the connection with the corresponding Hermitian systems is established. We find that the edge states smoothly transit to the valley edge states found in Hermitian systems if the magnitude of gain/loss vanishes. The topological nature of the PT edge states can be established within the non-Hermitian Haldane model, where the topological invariance is found to be unaffected by gain or loss. Nonreciprocal PT edge states are discovered at the interfaces between PT-Haldane phases, indicating the interplay between the gain/loss and the magnetic flux. The proposed systems are experimentally feasible to realize in photonics. This has been verified by our rigorous full-wave simulations of edge states in PT-symmetric silicon-based photonic graphene.Comment: 24 pages, 9 figures, 2 table

Breaking of PT-symmetry in bounded and unbounded scattering systems

PT-symmetric scattering systems with balanced gain and loss can undergo a symmetry-breaking transition in which the eigenvalues of the non-unitary scattering matrix change their phase shifts from real to complex values. We relate the PT-symmetry breaking points of such an unbounded scattering system to those of underlying bounded systems. In particular, we show how the PT-thresholds in the scattering matrix of the unbounded system translate into analogous transitions in the Robin boundary conditions of the corresponding bounded systems. Based on this relation, we argue and then confirm that the PT-transitions in the scattering matrix are, under very general conditions, entirely insensitive to a variable coupling strength between the bounded region and the unbounded asymptotic region, a result that can be tested experimentally and visualized using the concept of Smith charts.Comment: 9 pages, 6 figures (final version, including newly added connection to the concept of "Smith charts"

Nonlinear topological photonics

Rapidly growing demands for fast information processing have launched a race for creating compact and highly efficient optical devices that can reliably transmit signals without losses. Recently discovered topological phases of light provide a novel ground for photonic devices robust against scattering losses and disorder. Combining these topological photonic structures with nonlinear effects will unlock advanced functionalities such as nonreciprocity and active tunability. Here we introduce the emerging field of nonlinear topological photonics and highlight recent developments in bridging the physics of topological phases with nonlinear optics. This includes a design of novel photonic platforms which combine topological phases of light with appreciable nonlinear response, self-interaction effects leading to edge solitons in topological photonic lattices, nonlinear topological circuits, active photonic structures exhibiting lasing from topologically-protected modes, and harmonic generation from edge states in topological arrays and metasurfaces. We also chart future research directions discussing device applications such as mode stabilization in lasers, parametric amplifiers protected against feedback, and ultrafast optical switches employing topological waveguides.Comment: 21 pages, 12 figure