Topologically enhanced nonlinear optical response of graphene nanoribbon heterojunctions.

We study the nonlinear optical properties of heterojunctions made of graphene nanoribbons (GNRs) consisting of two segments with either the same or different topological properties. By utilizing a quantum mechanical approach that incorporates distant-neighbor interactions, we demonstrate that the presence of topological interface states significantly enhances the second- and third-order nonlinear optical response of GNR heterojunctions that are created by merging two topologically inequivalent GNRs. Specifically, GNR heterojunctions with topological interface states display third-order harmonic hyperpolarizabilities that are more than two orders of magnitude larger than those of their similarly sized counterparts without topological interface states, whereas the second-order harmonic hyperpolarizabilities exhibit a more than ten-fold contrast between heterojunctions with and without topological interface states. Additionally, we find that the topological state at the interface between two topologically distinct GNRs can induce a noticeable red-shift of the quantum plasmon frequency of the heterojunctions. Our results reveal a general and profound connection between the existence of topological states and an enhanced nonlinear optical response of graphene nanostructures and possible other photonic systems.

All-optical control of topological valley transport in graphene metasurfaces.

We demonstrate that the influence of Kerr effect on valley-Hall topological transport in graphene metasurfaces can be used to implement an all-optical switch. In particular, by taking advantage of the large Kerr coefficient of graphene, the index of refraction of a topologically-protected graphene metasurface can be tuned via a pump beam, which results in an optically controllable frequency shift of the photonic bands of the metasurface. This spectral variation can in turn be readily employed to control and switch the propagation of an optical signal in certain waveguide modes of the graphene metasurface. Importantly, our theoretical and computational analysis reveals that the threshold pump power needed to optically switch ON/OFF the signal is strongly dependent on the group velocity of the pump mode, especially when the device is operated in the slow-light regime. This study could open up new routes towards active photonic nanodevices whose underlying functionality stems from their topological characteristics.

Nonlinear optics in diamond-fin photonic nanowires: soliton formation and frequency comb generation.

We present a detailed study of the nonlinear optical properties of newly developed subwavelength diamond-fin waveguides, along with an analysis of soliton generation and pulse spectral broadening in these structures. Our rigorous mathematical model includes all the key linear and nonlinear optical effects that govern the pulse dynamics in these diamond waveguides. As a relevant application of our investigations, we demonstrate how these waveguides can be employed to efficiently generate frequency combs in the visible spectral domain.

Reprogrammable plasmonic topological insulators with ultrafast control.

Topological photonics has revolutionized our understanding of light propagation, providing a robust way to manipulate light. So far, most of studies in this field are focused on designing a static photonic structure. Developing a dynamic photonic topological platform to switch multiple topological functionalities at ultrafast speed is still a great challenge. Here we theoretically propose and experimentally demonstrate a reprogrammable plasmonic topological insulator, where the topological propagation route can be dynamically changed at nanosecond-level switching time, leading to an experimental demonstration of ultrafast multi-channel optical analog-digital converter. Due to the innovative use of electric switches to implement the programmability of plasmonic topological insulator, each unit cell can be encoded by dynamically controlling its digital plasmonic states while keeping its geometry and material parameters unchanged. Our reprogrammable topological plasmonic platform is fabricated by the printed circuit board technology, making it much more compatible with integrated photoelectric systems. Furthermore, due to its flexible programmability, many photonic topological functionalities can be integrated into this versatile topological platform.

Topological valley plasmon transport in bilayer graphene metasurfaces for sensing applications.

Topologically protected plasmonic modes located inside topological bandgaps are attracting increasing attention, chiefly due to their robustness against disorder-induced backscattering. Here, we introduce a bilayer graphene metasurface that possesses plasmonic topological valley interface modes when the mirror symmetry of the metasurface is broken by horizontally shifting the lattice of holes of the top layer of the two freestanding graphene layers in opposite directions. In this configuration, light propagation along the domain-wall interface of the bilayer graphene metasurface shows unidirectional features. Moreover, we have designed a molecular sensor based on the topological properties of this metasurface using the fact that the Fermi energy of graphene varies upon chemical doping. This effect induces strong variation of the transmission of the topological guided modes, which can be employed as the underlying working principle of gas sensing devices. Our work opens up new ways of developing robust integrated plasmonic devices for molecular sensing.

Four-wave mixing of topological edge plasmons in graphene metasurfaces.

We study topologically protected four-wave mixing (FWM) interactions in a plasmonic metasurface consisting of a periodic array of nanoholes in a graphene sheet, which exhibits a wide topological bandgap at terahertz frequencies upon the breaking of time reversal symmetry by a static magnetic field. We demonstrate that due to the significant nonlinearity enhancement and large life time of graphene plasmons in specific configurations, a net gain of FWM interaction of plasmonic edge states located in the topological bandgap can be achieved with a pump power of less than 10 nW. In particular, we find that the effective nonlinear edge-waveguide coefficient is about γ ≃ 1.1 × 1013 W-1 m-1, i.e., more than 10 orders of magnitude larger than that of commonly used, highly nonlinear silicon photonic nanowires. These findings could pave a new way for developing ultralow-power-consumption, highly integrated, and robust active photonic systems at deep-subwavelength scale for applications in quantum communications and information processing.

Efficient C-band single-photon upconversion with chip-scale Ti-indiffused pp-LiNbO3 waveguides.

Frequency upconversion for single photons at telecom wavelengths is important to simultaneously meet the different wavelength requirements for long-distance communications and quantum memories in a quantum nodal network. It also enables the detection for the telecom "flying qubit" photons with silicon-based efficient single-photon detectors with low dark count (DC) rates. Here, we demonstrate the frequency upconversion of attenuated single photons, using a low-loss titanium-indiffused periodically poled lithium niobate waveguide, pumped with a readily available erbium-doped fiber amplifier in the L-band. Internal and conversion efficiencies up to 84.4% and 49.9% have been achieved, respectively. The DC rates are suppressed down to 44 kHz at 13.9% end-to-end quantum efficiency (including full conversion and detection), enabled by our long-wavelength pump configuration and narrow 3.5-GHz bandpass filtering.

Plasmon-induced nonlinearity enhancement and homogenization of graphene metasurfaces.

We demonstrate that the effective 3rd-order nonlinear susceptibility of a graphene sheet can be enhanced by more than 2 orders of magnitude by patterning it into a graphene metasurface. In addition, to gain deeper physical insights into this phenomenon, we introduce a versatile homogenization method, which is subsequently used to characterize quantitatively this nonlinearity enhancement effect by calculating the effective linear and nonlinear susceptibility of graphene metasurfaces. The accuracy of the proposed homogenization method is demonstrated by comparing its predictions to those obtained from the Kramers-Kronig relations. This work may open new opportunities to explore novel physics pertaining to nonlinear optical interactions in graphene metasurfaces.

Giant enhancement of the effective Raman susceptibility in metasurfaces made of silicon photonic crystal nanocavities.

We demonstrate that stimulated Raman amplification can be enhanced by more than four orders of magnitude in a silicon metasurface consisting of a periodic distribution of specially engineered photonic crystal (PhC) cavities in a silicon PhC slab waveguide. In particular, by designing the PhC cavities so as they possess two optical modes separated by the Raman frequency of silicon, one can achieve large optical field enhancement at both the pump and Stokes frequencies. As a consequence, the effective Raman susceptibility of the nonlinear metasurface, calculated using a novel homogenization technique, is significantly larger than the intrinsic Raman susceptibility of silicon. Implications to technological applications of our theoretical study are discussed, too.

A comparative analysis of surface and bulk contributions to second-harmonic generation in centrosymmetric nanoparticles.

Second-harmonic generation (SHG) from nanoparticles made of centrosymmetric materials provides an effective tool to characterize many important properties of photonic structures at the subwavelength scale. Here we study the relative contribution of surface and bulk effects to SHG for plasmonic and dielectric nanostructures made of centrosymmetric materials in both dispersive and non-dispersive regimes. Our calculations of the far-fields generated by the nonlinear surface and bulk currents reveal that the size of the nanoparticle strongly influences the amount and relative contributions of the surface and bulk SHG effects. Importantly, our study reveals that, whereas for plasmonic nanoparticles the surface contribution is always dominant, the bulk and surface SHG effects can become comparable for dielectric nanoparticles, and thus they both should be taken into account when analyzing nonlinear optical properties of all-dielectric nanostructures.

Surface modes in plasmonic Bragg fibers with negative average permittivity.

We investigate surface modes in plasmonic Bragg fibers composed of nanostructured coaxial cylindrical metal-dielectric multilayers. We demonstrate that the existence of surface modes is determined by the sign of the spatially averaged permittivity of the plasmonic Bragg fiber, ε¯. Specifically, localized surface modes occur at the interface between the cylindrical core with ε¯<0 and the outermost uniform dielectric medium, which is similar to the topologically protected plasmonic surface modes at the interface between two different one-dimensional planar metal-dielectric lattices with opposite signs of the averaged permittivity. Moreover, when increasing the number of dielectric-metal rings, the propagation constant of surface modes with different azimuthal mode numbers is approaching that of surface plasmon polaritons formed at the corresponding planar metal/dielectric interface. Robustness of such surface modes of plasmonic Bragg fibers is demonstrated as well.

Polarization control using passive and active crossed graphene gratings.

Graphene gratings provide a promising route towards the miniaturization of THz metasurfaces and other photonic devices, chiefly due to remarkable optical properties of graphene. In this paper, we propose novel graphene nanostructures for passive and active control of the polarization state of THz waves. The proposed devices are composed of two crossed graphene gratings separated by an insulator spacer. Because of specific linear and nonlinear properties of graphene, these optical metasurfaces can be utilized as ultrathin polarization converters operating in the THz frequency domain. In particular, our study shows that properly designed graphene polarizers can effectively select specific polarization states, their thickness being about a tenth of the operating wavelength and size more than 80× smaller than that of similar metallic devices. Equally important, we demonstrate that the nonlinear optical properties of graphene can be utilized to actively control the polarization state of generated higher harmonics.

Exploiting high-order phase-shift keying modulation and direct-detection in silicon photonic systems.

A computational approach to evaluate the bit-error ratio (BER) in silicon photonic systems employing high-order phase-shift keying (PSK) modulation formats is presented. Specifically, the investigated systems contain a silicon based optical interconnect, namely a strip silicon photonic waveguide or a silicon photonic crystal waveguide, and direct-detection receivers suitable to detect PSK and amplitude-shaped PSK signals. The superposition of a PSK signal and complex additive white Gaussian noise passes through the optical interconnect and subsequently through two detection-branch receivers. To model the signal propagation in the silicon optical interconnects we used a modified nonlinear Schrödinger equation, which incorporates all relevant linear and nonlinear optical effects and the mutual interaction between free-carriers and the optical field. Finally, the BER is calculated by applying a frequency-domain approach based on the Karhunen-Loève series expansion method. Our computational studies of the BER reveal that the optical power, type of PSK modulation, waveguide length, and group-velocity are key factors characterizing the system BER, their influence on BER being more significant in a photonic system with larger nonlinearity. In particular, our analysis shows that the system performance is affected to a much larger extent when the signal propagates in the slow-light regime, despite the fact that this regime allows for a significantly reduced length of optical interconnects.

Double-resonant enhancement of third-harmonic generation in graphene nanostructures.

Intriguing and unusual physical properties of graphene offer remarkable potential for advanced, photonics-related technological applications, particularly in the area of nonlinear optics at the deep-subwavelength scale. In this study, we use a recently developed numerical method to illustrate an efficient mechanism that can lead to orders of magnitude enhancement of the third-harmonic generation in graphene diffraction gratings. In particular, we demonstrate that by taking advantage of the geometry dependence of the resonance wavelength of localized surface-plasmon polaritons of graphene ribbons and discs one can engineer the spectral response of graphene gratings so that strong plasmonic resonances exist at both the fundamental frequency and third-harmonic (TH). As a result of this double-resonant mechanism for optical near-field enhancement, the intensity of the TH can be increased by more than six orders of magnitude.This article is part of the themed issue 'New horizons for nanophotonics'.

Topological surface plasmons in superlattices with changing sign of the average permittivity.

We address the topological properties of one-dimensional plasmonic superlattices composed of alternating metallic and dielectric layers. We reveal that the Zak phase of such plasmonic lattices is determined by the sign of the spatial average of their permittivity, ε¯, and as such the topology and their associated interfacial (edge) states are extremely robust against structural disorder. Our study shows that the topologically protected interfacial modes occurring at the interface between two plasmonic lattices with opposite signs of ε¯ can be viewed as the generalization of the conventional surface plasmon polaritons existing at metallic-dielectric interfaces.

Rigorous theoretical analysis of a surface-plasmon nanolaser with monolayer MoS2 gain medium.

Lasers based on monolayer (ML) transition-metal dichalcogenide semiconductor crystals have the potential for low threshold operation and a small device footprint; however, nanophotonic engineering is required to maximize the interaction between the optical fields and the three-atom-thick gain medium. Here, we develop a theoretical model to design a direct bandgap optically pumped nanophotonic integrated laser. Our device utilizes a gap-surface-plasmon optical mode to achieve subwavelength optical confinement and consists of a high-index GaP nanowire atop an ML MoS2 film on an Ag substrate. The optical field and material medium are analyzed using a three dimensional finite-difference time-domain method and a first-principles calculation based on the density functional theory, respectively. The nanolaser is designed to have a threshold of ∼0.6 µW under quasi-continuous wave operation on an excitonic transition at room temperature.

Resonant mixing of optical orbital and spin angular momentum by using chiral silicon nanosphere clusters.

We present an in-depth analysis of the resonant intermixing between optical orbital and spin angular momentum of Laguerre-Gaussian (LG) beams, mediated by chiral clusters made of silicon nanospheres. In particular, we establish a relationship between the spin and orbital quantum numbers characterizing the LG beam and the order q of the rotation symmetry group 𝒞q of the cluster of nanospheres for which resonantly enhanced coupling between the two components of the optical angular momentum is observed. Thus, similar to the case of diffraction grating-mediated transfer of linear momentum between optical beams, we demonstrate that clusters of nanospheres that are invariant to specific rotation transformations can efficiently transfer optical angular momentum between LG beams with different quantum numbers. We also discuss the conditions in which the resonant interaction between LG beams and a chiral cluster of nanospheres leads to the generation of superchiral light.

Transverse Anderson localization of light near Dirac points of photonic nanostructures.

We perform a comparative study of the Anderson localization of light beams in disordered layered photonic nanostructures that, in the limit of periodic layer distribution, possess either a Dirac point or a Bragg gap in the spectrum of the wavevectors. In particular, we demonstrate that the localization length of the Anderson modes increases when the width of the Bragg gap decreases, such that in the vanishingly small bandgap limit, namely when a Dirac point is formed, even extremely high levels of disorder are unable to localize the optical modes residing near the Dirac point. A comparative analysis of the key features of the propagation of Anderson modes formed in the Bragg gap or near the Dirac point is also presented. Our findings could provide valuable guidelines in assessing the influence of structural disorder on the functionality of a broad array of optical nanodevices.

Comparative analysis of four-wave mixing of optical pulses in slow- and fast-light regimes of a silicon photonic crystal waveguide.

We present an in-depth study of four-wave mixing (FWM) of optical pulses in silicon photonic crystal waveguides. Our analysis is based on a rigorous model that includes all relevant linear and nonlinear optical effects and their dependence on the group velocity, as well as the influence of free carriers on pulse dynamics. In particular, we reveal key differences between FWM in the slow- and fast-light regimes and how they are related to the physical parameters of the pulses and waveguide. Finally, we illustrate how these results can be used to design waveguides with optimized FWM conversion efficiency.

Generation of Subwavelength Plasmonic Nanovortices via Helically Corrugated Metallic Nanowires.

We demonstrate that plasmonic helical gratings consisting of metallic nanowires imprinted with helical grooves or ridges can be used efficiently to generate plasmonic vortices with radius much smaller than the operating wavelength. In our proposed approach, these helical surface gratings are designed so that plasmon modes with different azimuthal quantum numbers (topological charge) are phase-matched, thus allowing one to generate optical plasmonic vortices with arbitrary topological charge. The general principles for designing plasmonic helical gratings that facilitate efficient generation of such plasmonic vortices are derived and their applicability to the conversion of plasmonic vortices with zero angular momentum into plasmonic vortices with arbitrary angular momentum is illustrated in several particular cases. Our analysis, based both on the exact solutions for the electromagnetic field propagating in the helical plasmonic grating and a coupled-mode theory, suggests that even in the presence of metal losses the fundamental mode with topological charge m = 0 can be converted to plasmon vortex modes with topological charge m = 1 and m = 2 with a conversion efficiency as large as 60%. The plasmonic nanovortices introduced in this study open new avenues for exciting applications of orbital angular momentum in the nanoworld.