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We analyze chiral topological edge modes in a non-Hermitian variant of the 2D Dirac equation. Such modes appear at interfaces between media with different "masses" and/or signs of the "non-Hermitian charge". The existence of these edge modes is intimately related to exceptional points of the bulk Hamiltonians, i.e., degeneracies in the bulk spectra of the media. We find that the topological edge modes can be divided into three families ("Hermitian-like", "non-Hermitian", and "mixed"), these are characterized by two winding numbers, describing two distinct kinds of half-integer charges carried by the exceptional points. We show that all the above types of topological edge modes can be realized in honeycomb lattices of ring resonators with asymmetric or gain/loss couplings., Comment: 6 pages, 3 figures, and Supplementary Materials, to appear in Phys. Rev. Lett

In the time-reversed counterpart to laser emission, incident coherent optical fields are perfectly absorbed within a resonator that contains a loss medium instead of a gain medium. The incident fields and frequency must coincide with those of the corresponding laser with gain. We demonstrated this effect for two counterpropagating incident fields in a silicon cavity, showing that scattering [corrected] can be modulated [corrected] by two orders of magnitude, the maximum predicted by theory for our experimental setup. In addition, we showed that absorption can be reduced substantially by varying the relative phase of the incident fields. The device, termed a "coherent perfect absorber," functions as an absorptive interferometer, with potential practical applications in integrated optics.

We demonstrate terahertz (THz) frequency laser emission around 3.2 THz from localized modes in one-dimensional disordered grating systems. The disordered structures are patterned on top of the double-metal waveguide of a THz quantum cascade laser. Multiple emission peaks are observed within a frequency range corresponding to the bandgap of a periodic counterpart with no disorder, indicating the presence of mode localization aided by Bragg scattering. Simulations and experimental measurements provide strong evidence for the spatial localization of the THz laser modes. National Research Foundation (NRF) Published version Ministry of Education—Singapore (MOE) (MOE 2016-T2-1-128); Agency for Science, Technology and Research (A*STAR) (1426500050); National Research Foundation Singapore (NRF) (NRF-CRP18-2017-02); Engineering and Physical Sciences Research Council (EPSRC) (EP/P021859/1); Royal Society and Wolfson Foundation.

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., 12 pages, 4 figures

We study the topological properties of 3D Floquet bandstructures, which are defined using unitary evolution matrices rather than Hamiltonians. Previously, 2D bandstructures of this sort have been shown to exhibit anomalous topological behaviors, such as topologically-nontrivial zero-Chern-number phases. We show that the bandstructure of a 3D network model can exhibit Weyl phases, which feature "Fermi arc" surface states like those found in Weyl semimetals. Tuning the network's coupling parameters can induce transitions between Weyl phases and various topologically distinct gapped phases. We identify a connection between the topology of the gapped phases and the topology of Weyl point trajectories in k-space. The model is feasible to realize in custom electromagnetic networks, where the Weyl point trajectories can be probed by scattering parameter measurements., 11 pages, 7 figures

Non-Hermitian systems host unconventional physical effects that be used to design new optical devices. We study a non-Hermitian system consisting of 1D planar optical waveguides with suitable amount of simultaneous gain and loss. The parameter space contains an exceptional point, which can be accessed by varying the transverse gain and loss profile. When light propagates through the waveguide structure, the output mode is independent of the choice of input mode. This “asymmetric mode conversion” phenomenon can be explained by the swapping of mode identities in the vicinity of the exceptional point, together with the failure of adiabatic evolution in non-Hermitian systems. NRF (Natl Research Foundation, S’pore) Published version

We propose a technique to realize a tachyonic band structure in a coherent network, such as an array of coupled ring resonators. This is achieved by adding "PT symmetric" spatially-balanced gain and loss to each node of the network. In a square-lattice network, the quasi-energy bandstructure exhibits a tachyonic dispersion relation, centered at either the center or corner of the Brillouin zone. There is one tachyonic hyperboloid in each gap, unlike in PT-symmetric tight-binding honeycomb lattices where the hyperboloids occur in pairs. The dispersion relation can be probed by measuring the peaks in transmission across a finite network as the gain/loss parameter is varied., 6 pages, 5 figures

Topological photonic states, inspired by robust chiral edge states in topological insulators, have recently been demonstrated in a few photonic systems, including an array of coupled on-chip ring resonators at communication wavelengths. However, the intrinsic difference between electrons and photons determines that the ‘topological protection’ in time-reversal-invariant photonic systems does not share the same robustness as its counterpart in electronic topological insulators. Here in a designer surface plasmon platform consisting of tunable metallic sub-wavelength structures, we construct photonic topological edge states and probe their robustness against a variety of defect classes, including some common time-reversal-invariant photonic defects that can break the topological protection, but do not exist in electronic topological insulators. This is also an experimental realization of anomalous Floquet topological edge states, whose topological phase cannot be predicted by the usual Chern number topological invariants., Nanyang Technological University (NAP Start-up Grant, Singapore Ministry of Education, Grant No. MOE2015-T2-1-070), Nanyang Technological University (NAP Start-up Grant, Singapore Ministry of Education, Grant No. MOE2011-T3-1-005), Singapore. National Research Foundation (Grant No. NRFF2012-02), United States. Army Research Office. Institute for Soldier Nanotechnologies (contract number W911NF-13-D-0001), National Science Foundation (U.S.) (NSF MRSEC Program, Award No. DMR-1419807), United States. Dept. of Energy (MIT S3TEC EFRC, DOE Grant No. DE-SC0001299), National Natural Science Foundation (China) (Grant No. 61322501), National Natural Science Foundation (China) (NNSFC Grant no. 61574127), National Natural Science Foundation (China) (NNSFC Grant no. 61275183), China. Ministry of Education (National Top-Notch Young Professionals Program), National Council for Educational Technology (NCET-12-0489 ), Financial Resources Federal Credit Union (FRFCU-2014XZZX003-24)

We propose a scheme to directionally couple light into graphene plasmons by placing a graphene sheet on a magneto-optical substrate. When a magnetic field is applied parallel to the surface, the graphene plasmon dispersion relation becomes asymmetric in the forward and backward directions. It is possible to achieve unidirectional excitation of graphene plasmons with normally incident illumination by applying a grating to the substrate. The directionality can be actively controlled by electrically gating the graphene, or by varying the magnetic bias. This scheme may have applications in graphene-based opto-electronics and sensing. NRF (Natl Research Foundation, S’pore) MOE (Min. of Education, S’pore) Published version

A generalization of the Aubry-André-Harper (AAH) model is developed, containing a tunable phase shift between on-site and off-diagonal modulations. A localization transition can be induced by varying just this phase, keeping all other model parameters constant. The complete localization phase diagram is obtained. Unlike the original AAH model, the generalized model can exhibit a transition between topologically trivial band structures and topologically nontrivial band structures containing protected boundary states. These boundary states can be pumped across the system by adiabatic variations in the phase shift parameter. The model can also be used to demonstrate the phenomenon of adiabatic pumping breakdown due to localization. Published version

We present a multimode laser-linewidth theory for arbitrary cavity structures and geometries that contains nearly all previously known effects and also finds new nonlinear and multimode corrections, e.g. a bad-cavity correction to the Henry $\alpha$ factor and a multimode Schawlow--Townes relation (each linewidth is proportional to a sum of inverse powers of all lasing modes). Our theory produces a quantitatively accurate formula for the linewidth, with no free parameters, including the full spatial degrees of freedom of the system. Starting with the Maxwell--Bloch equations, we handle quantum and thermal noise by introducing random currents whose correlations are given by the fluctuation--dissipation theorem. We derive coupled-mode equations for the lasing-mode amplitudes and obtain a formula for the linewidths in terms of simple integrals over the steady-state lasing modes., Comment: 24 pages, 7 figures

We present a multimode laser-linewidth formula that generalizes previous theories, including corrections for cavity losses, nonlinear gain and dispersion, but is derived in a more general setting and is therefore applicable to complex wavelength-scale lasers.

Coherent illumination and wave-front shaping can be used to make a weakly absorbing cavity perfectly absorbing and to enhance strongly the absorption of a multiple scattering medium.

Direct FDTD simulations of the Maxwell-Bloch equations coupled to Langevin noise equations are shown to quantitatively agree with a recent analytic linewidth formula and predicted scaling relations.

We present a mechanism by which a metamaterial surface, or metasurface, can act as an ideal phase-controlled rotatable linear polarizer. Using coupled-mode theory and the idea of coherent perfect absorption into auxiliary polarization channels, we show how the losses and near-field couplings on the metasurface can be balanced so that, with equal-power linearly polarized beams incident on each side, varying the relative phase rotates the polarization angles of the output beams while maintaining zero ellipticity. The system can be described by a non-Hermitian effective Hamiltonian which is parity-time (PT) symmetric, although there is no actual gain present; perfect polarization conversion occurs at the eigenfrequencies of this Hamiltonian, and the polarization rotating behavior occurs at the critical point of its PT-breaking transition. Published version

We present an erratum regarding the number of space group in our paper.

Weyl points have recently been predicted and experimentally observed in double-gyroid photonic crystals, as well as in other complex photonic structures such as stacked hexagonal-lattice slabs and helical waveguide arrays. In all above structures, the Weyl points are located between high frequency bands, and are difficult to probe experimentally. In this work, we show that a photonic crystal with a simple tetrahedral structure can host frequency-isolated Weyl points between the second and third bands. The minimal number of two Weyl points emerges from a threefold quadratic degeneracy at the Brillouin zone corner when time-reversal symmetry is broken. We verify theoretically that the Weyl points carry opposite topological charges, and are associated with Fermi arc-like surface states. This photonic crystal can be realized using ferromagnetic rods in the microwave frequency regime, providing a simple platform for studying the physics of Weyl points.

We report on the measurement of topological invariants in an electromagnetic topological insulator analog formed by a microwave network, consisting of the winding numbers of scattering matrix eigenvalues. The experiment can be regarded as a variant of a topological pump, with non-zero winding implying the existence of topological edge states. In microwave networks, unlike most other systems exhibiting topological insulator physics, the winding can be directly observed. The effects of loss on the experimental results, and on the topological edge states, is discussed., 10 pages, 10 figures

A recently proposed class of photonic topological insulators is shown to map onto Chalker-Coddington-type networks, which were originally formulated to study disordered quantum Hall systems. Such network models are equivalent to the Floquet states of periodically driven lattices. We show that they can exhibit topologically protected edge states even if all bands have zero Chern number, which is a characteristic property of Floquet band structures. These edge states can be counted by an adiabatic pumping invariant based on the winding number of the coefficient of reflection from one edge of the network. Published version

Perfect absorption of radiation in a graphene sheet may play a pivotal role in the realization of technologically relevant optoelectronic devices. In particular, perfect absorption of radiation in the terahertz (THz) spectral range would tremendously boost the utility of graphene in this difficult range of photon energies, which still lacks cheap and robust devices operating at room temperature. In this work we show that unpatterned graphene flakes deposited on appropriate substrates can display gate-tunable coherent perfect absorption (CPA) in the THz spectral range. We present theoretical estimates for the CPA operating frequency as a function of doping, which take into account the presence of common sources of disorder in graphene samples., To appear in 2D Materials

A recent S-matrix-based theory of the quantum-limited linewidth, which is applicable to general lasers, including spatially nonuniform laser cavities operating above threshold, is analyzed in various limits. For broadband gain, a simple interpretation of the Petermann and bad-cavity factors is presented in terms of geometric relations between the zeros and poles of the S matrix. When there is substantial dispersion, on the frequency scale of the cavity lifetime, the theory yields a generalization of the bad-cavity factor, which was previously derived for spatially uniform one-dimensional lasers. This effect can lead to sub–Schawlow-Townes linewidths in lasers with very narrow gain widths. We derive a formula for the linewidth in terms of the lasing mode functions, which has accuracy comparable to the previous formula involving the residue of the lasing pole. These results for the quantum-limited linewidth are valid even in the regime of strong line pulling and spatial hole burning, where the linewidth cannot be factorized into independent Petermann and bad-cavity factors. Published version

We derive and test a generalization of Steady-State Ab Initio Laser Theory (SALT) to treat complex gain media. The generalized theory (C-SALT) is able to treat atomic and molecular gain media with diffusion and multiple lasing transitions, and semiconductor gain media in the free carrier approximation including fully the effect of Pauli blocking. The key assumption of the theory is stationarity of the level populations, which leads to coupled self-consistent equations for the populations and the lasing modes that fully include the effects of openness and non-linear spatial hole-burning. These equations can be solved efficiently for the steady-state lasing properties by a similar iteration procedure as in SALT, where a static gain medium with a single transition is assumed. The theory is tested by comparison to much less efficient Finite Difference Time Domain (FDTD) methods and excellent agreement is found. Using C-SALT to analyze the effects of varying gain diffusion constant we demonstrate a cross-over between the regime of strong spatial hole burning with multimode lasing to a regime of negligible spatial hole burning, leading to gain-clamping, and single mode lasing. The effect of spatially inhomogeneous pumping combined with diffusion is also studied and a relevant length scale for spatial inhomogeneity to persist under these conditions is determined. For the semiconductor gain model, we demonstrate the frequency shift due to Pauli blocking as the pumping strength changes., Comment: 15 pages, 5 figures

An unusual form of symmetry breaking in coupled microresonators with balanced optical gain and loss is now exploited to realize a novel type of optical isolator. Accepted version

We demonstrate the simulation of optical analog of topological edge states in honeycomb lattice composed of ring resonators. Three kinds of edges, zig-zag, armchair, and beard, support edge states for the same working frequency.

A photonic topological insulator can be constructed from a lattice of ring resonators, without using aperiodic couplers or metamaterials. With gain and loss, the system can function as an optical diode for coupled resonator modes.

The performance of a coherent perfect absorber (time-reversed laser) is limited by quantum and thermal noise. At zero temperature, the quantum shot noise dominates the signal for frequencies close to the resonance frequency, and both vanish exactly at the resonance frequency. We compute the sensitivity of the absorbing cavity as a background-free detector, limited by finite signal or detector bandwidth., Comment: 6 pages, 3 figures

We identify a family of unusual slow-light modes occurring in lossy multimode grating waveguides, for which either the forward or backward mode components, or both, are degenerate. In the fully degenerate case, the response can be modulated between coherent perfect absorption (zero reflection) and perfect reflection by varying the wave amplitudes in a uniform input waveguide. The perfectly absorbed wave has anomalously short absorption length, scaling as the inverse one-third power of the absorptivity. Published version

High-order stationary points in a dispersion relation, giving rise to frozen light, lead to efficient coupling into slow modes. Here we show that frozen light also enables low-threshold nonlinear effects and strongly enhanced optical absorption. Article not available.

Electrically pumped random lasers, operating in the mid-infrared regime at λ ≈ 10 μm, are realized for the first time. Randomly distributed air holes are patterned onto a quantum cascade wafer emitting in the transverse-magnetic (TM) polarization. The advantage of employing TM polarized gain medium is that TM modes are more effectively confined in the gain region, and thus improve lasing efficiency and vertical confinement compared to TE modes. ASTAR (Agency for Sci., Tech. and Research, S’pore)

A photonic network, such as a periodic lattice of coupled ring resonators, can act as a photonic topological insulator. Using transfer-matrix and FDTD calculations, we demonstrate the existence and properties of the topologically-protected edge states.

We perform a theoretical study of nonlinear optical isolator devices based on coupled microcavities with gain and loss. Using coupled-mode theory, we derive a correspondence between the boundary of asymptotic stability in the nonlinear regime, where gain saturation is present, and the PT-breaking transition in the underlying linear system. For zero detuning and weak input intensity, the onset of optical isolation can be rigorously derived, and corresponds precisely to the PT transition point. When the couplings to the external ports are unequal, the isolation ratio exhibits an abrupt jump at the transition point, determined by the ratio of the couplings. This could be exploited to realize an actively controlled nonlinear optical isolator, in which strong optical isolation can be switched on or off using tiny variations in the inter-resonator separation., Comment: 15 pages, 8 figures

We perform a numerical study of two-dimensional amorphous photonic structures consisting of dielectric rods in a close-packed honeycomb-like structure, with nearest-neighbor rods joined by dielectric veins of various widths. For vein widths comparable to the rod radius, the in-plane Q factors for the transverse magnetic (TM) modes are enhanced by around two orders of magnitude, due to the presence of short-range order in the amorphous lattice, even though the density of states has a weak dip rather than a prominent gap. Such structures may be useful for realizing multi-mode random quantum cascade lasers, which lase in the TM polarization.

A formula for the laser linewidth of arbitrary cavities in the multimode non-linear regime is derived from a scattering analysis of the solutions to semiclassical laser theory. The theory generalizes previous treatments of the effects of gain and openness described by the Petermann factor. The linewidth is expressed using quantities based on the non-linear scattering matrix, which can be computed from steady-state ab initio laser theory; unlike previous treatments, no passive cavity or phenomenological parameters are involved. We find that low cavity quality factor, combined with significant dielectric dispersion, can cause substantial deviations from the Schawlow-Townes-Petermann theory., 5 pages, 2 figures

A general theory of the laser linewidth is presented, which holds for lasers of arbitrary spatial complexity, including those operated far above threshold with multiple modes and/or strong spatial hole-burning.

A lattice of optical ring resonators can exhibit a topological insulator phase, with the role of spin played by the direction of propagation of light within each ring. Unlike the system studied by Hafezi et al., topological protection is achieved without fine-tuning the inter-resonator couplings, which are given the same periodicity as the underlying lattice. The topological insulator phase occurs for strong couplings, when the tight-binding method is inapplicable. Using the transfer matrix method, we derive the bandstructure and phase diagram, and demonstrate the existence of robust edge states. When gain and loss are introduced, the system functions as a diode for coupled resonator modes., Comment: 10 pages, 9 figures

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., 10 pages, 10 figures

We discuss a class of lasing modes created by a spatially inhomogeneous gain profile. These lasing modes are "extra modes", in addition to, and very different from, conventional lasing modes, which arise from the passive cavity resonances. These new modes do not have high intensity across the entire gain region, but instead are localized at the gain boundary and throughout the gain-free region. They are surface modes, originating from the transmission resonances of the gain-free region. Using an S-matrix description we connect these surface modes to the lasing modes in PT-symmetric (balanced gain-loss) cavities., Comment: 8 pages, 7 figures

The ideal elastic limit is the upper bound to the stress and elastic strain a material can withstand. This intrinsic property has been widely studied for crystalline metals, both theoretically and experimentally. For metallic glasses, however, the ideal elastic limit remains poorly characterized and understood. Here we show that the elastic strain limit and the corresponding strength of submicron-sized metallic glass specimens are about twice as high as the already impressive elastic limit observed in bulk metallic glass samples, in line with model predictions of the ideal elastic limit of metallic glasses. We achieve this by employing an in situ transmission electron microscope tensile deformation technique. Furthermore, we propose an alternative mechanism for the apparent 'work hardening' behaviour observed in the tensile stress–strain curves., National Science Foundation (U.S.) (CMMI-0728069), National Science Foundation (U.S.) (DMR-1008104), National Science Foundation (U.S.) (DMR-1120901), United States. Air Force Office of Scientific Research (FA9550-08-1-0325)

We show that a weakly absorbing, strongly scattering (white) medium can be made very strongly absorbing at any frequency within its strong-scattering bandwidth by optimizing the input electromagnetic field. For uniform absorption, results from random matrix theory imply that the reflectivity of the medium can be suppressed by a factor ~(l_a/lN^2), where N is the number of incident channels and l,l_a are the elastic and absorption mean free paths respectively. It is thus possible to increase absorption from a few percent to > 99%. For a localized weak absorber buried in a non-absorbing scattering medium, we find a large but bounded enhancement., 4 pages, 4 figures

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., Comment: 4 pages, 4 figures

A scattering theory of lasing and absorption in arbitrary complex and random systems is presented, leading to tractable computational methods to describe multimode lasing, as well as time-reversed lasing and coherent control of absorption.

We study the general scattering properties of balanced gain/loss (PT-symmetric) optical structures, without restriction to the paraxial approximation. The scattering eigenstates exhibit a PT-symmetry breaking transition, with experimentally accessible consequences.

Based on the concept of time-reversing a laser, we develop two schemes of 100% coupling of light into individual nanoparticles, either a dielectric nanoparticle buried in a scattering medium or a single metallic nanoparticle in vacuum.

We demonstrate a novel mechanism for controlling absorption of coherent light bytwo orders of magnitude. By varying the phase of incident laser light in a two-port geometry, the absorption is greatly enhanced or reduced.

We show theoretically that coherent light can be completely absorbed in a two-dimensional or three-dimensional metallic nanostructure by matching the frequency and field pattern of an incident wave to that of a localized surface plasmon resonance. This can be regarded as critical coupling to a nano-plasmonic cavity, or as an extension of the concept of time-reversed laser to the spaser. Light scattering is completely suppressed via impedance matching to the nano-objects, and the energy of incoming wave is fully transferred to surface plasmon oscillations and evanescent electromagnetic fields. Perfect coupling of light to nanostructures has potential applications to nanoscale probing as well as background-free spectroscopy and ultrasensitive detection of environmental changes., Comment: 10 pages, 4 figures

We present two photonic crystal enabled platforms, exhibiting novel active optical phenomena. First, using a detailed theoretical and numerical analysis, we show how a Purcell-effect inspired nonlinear nanophotonic scheme could enable optimal and compact THz sources via optical difference frequency generation. Second, we show how electromagnetic one-way edge modes analogous to quantum Hall edge states, originally predicted by Raghu and Haldane in gyroelectric photonic crystals, can appear in more general settings. In gyromagnetic YIG photonic crystals operating at microwave frequencies, time-reversal breaking is strong enough that the effect is readily observable. We present our experimental results on this novel phenomenon.

The semiclassical equations of motion for a Bloch electron include an anomalous velocity term analogous to a $k$-space "Lorentz force", with the Berry connection playing the role of a vector potential. By examining the adiabatic evolution of Bloch states in a monotonically-increasing vector potential, I show that the anomalous velocity can be explained as the difference in the Berry's phase acquired by adjacent Bloch states within a wavepacket., 2 pages, 1 figure