Xiaoyan Y. Z. Xiong

Compact Nonlinear Yagi-Uda Nanoantennas

Nanoantennas have demonstrated unprecedented capabilities for manipulating the intensity and direction of light emission over a broad frequency range. The directional beam steering offered by nanoantennas has important applications in areas including microscopy, spectroscopy, quantum computing, and on-chip optical communication. Although both the physical principles and experimental realizations of directional linear nanoantennas has become increasingly mature, angular control of nonlinear radiation using nanoantennas has not been explored yet. Here we propose a novel concept of nonlinear Yagi-Uda nanoantenna to direct second harmonic radiation from a metallic nanosphere. By carefully tuning the spacing and dimensions of two lossless dielectric elements, which function respectively as a compact director and reflector, the second harmonic radiation is deflected 90 degrees with reference to the incident light (pump) direction. This abnormal light-bending phenomenon is due to the constructive and destructive interference between the second harmonic radiation governed by a special selection rule and the induced electric dipolar and magnetic quadrupolar radiation from the two dielectric antenna elements. Simultaneous spectral and spatial isolation of scattered second harmonic waves from incident fundamental waves pave a new way towards nonlinear signal detection and sensing.

Surface waves in three-dimensional electromagnetic composites and their effect on homogenization

Reflection and transmission of electromagnetic waves at the boundaries of periodic composites (electromagnetic/optical metamaterials) depends in general on both bulk and surface waves. We investigate the interplay of these two contributions using three-dimensional full-wave numerical simulations and a recently developed non-asymptotic homogenization theory.

Strongly enhanced and directionally tunable second-harmonic radiation from a plasmonic particle-in-cavity nanoantenna

Second-harmonic (SH) generation is tremendously important for nonlinear sensing, microscopy, and communication systems. One of the great challenges of current designs is to enhance the SH signal and simultaneously tune its radiation direction with a high directivity. In contrast to the linear plasmonic scattering dominated by a bulk dipolar mode, a complex surface-induced multipolar source at the doubled frequency sets a fundamental limit to control the SH radiation from metallic nanostructures. In this work, we harness a plasmonic hybridization mechanism together with a special selection rule governing the SH radiation to achieve the high-intensity and tunable-direction emission by a metallic particle-in-cavity nanoantenna (PIC-NA). The nanoantenna is modelled with a first-principle, self-consistent boundary element method, which considers the depletion of pump waves. The giant SH enhancement arises from a hybridized gap plasmon resonance between the small particle and the large cavity that functions as a concentrator and reflector. Centrosymmetry breaking of the PIC-NA not only modifies the gap plasmon mode boosting the SH signal, but also redirects the SH wave with a unidirectional emission. The PIC-NA has a significantly larger SH conversion efficiency compared to existing literature. The main beam of the radiation pattern can be steered over a wide angle by tuning the particles position.

Mixing of spin and orbital angular momenta via second-harmonic generation in plasmonic and dielectric chiral nanostructures

We present a theoretical study of the characteristics of the nonlinear spin-orbital angular momentum coupling induced by second-harmonic generation in plasmonic and dielectric nanostructures made of centrosymmetric materials. In particular, the connection between the phase singularities and polarization helicities in the longitudinal components of the fundamental and second-harmonic optical fields and the scatterer symmetry properties are discussed. By in-depth comparison between the interaction of structured optical beams with plasmonic and dielectric nanostructures, we have found that all-dielectric and plasmonic nanostructures that exhibit magnetic and electric resonances have comparable second-harmonic conversion efficiency. In addition, mechanisms for second-harmonic enhancement for single and chiral clusters of scatterers are unveiled and the relationships between the content of optical angular momentum of the incident optical beams and the enhancement of nonlinear light scattering is discussed. In particular, we formulate a general angular momenta conservation law for the nonlinear spin-orbital angular momentum interaction, which includes the quasi-angular-momentum of chiral structures with different-order rotational symmetry. As a key conclusion of our study relevant to nanophotonics, we argue that all-dielectric nanostructures provide a more suitable platform to investigate experimentally the nonlinear interaction between spin and orbital angular momenta, as compared to plasmonic ones, chiefly due to their narrower resonance peaks, lower intrinsic losses, and higher sustainable optical power.

FULL HYDRODYNAMIC MODEL OF NONLINEAR ELECTROMAGNETIC RESPONSE IN METALLIC METAMATERIALS (Invited Paper)

Applications of metallic metamaterials have generated significant interest in recent years. Electromagnetic behavior of metamaterials in the optical range is usually characterized by a local-linear response. In this article, we develop a finite-difference time-domain (FDTD) solution of the hydrodynamic model that describes a free electron gas in metals. Extending beyond the local-linear response, the hydrodynamic model enables numerical investigation of nonlocal and nonlinear interactions between electromagnetic waves and metallic metamaterials. By explicitly imposing the current continuity constraint, the proposed model is solved in a self-consistent manner. Charge, energy and angular momentum conservation laws of high-order harmonic generation have been demonstrated for the first time by the Maxwell-hydrodynamic FDTD model. The model yields nonlinear optical responses for complex metallic metamaterials irradiated by a variety of waveforms. Consequently, the multiphysics model opens up unique opportunities for characterizing and designing nonlinear nanodevices.

Efficient Calculation of Large Finite Periodic Structures Based on Surface Wave Analysis

The electromagnetic modeling of practical finite periodic structures is a topic of growing interest. Due to the truncation of infinite periodic structures, surface waves will be excited and localized near discontinuous interfaces leading to the edge effect. In this work, surface waves are numerically extracted and their magnitudes and decay rates are analyzed for different materials and geometries. Based on the exponential decay of the surface wave, a novel method is developed by connecting the solution to the large finite array problem with that to a relatively small one to achieve low complexity and memory consumption. The method numerically reconstructs propagating Bloch waves and surface waves according to the Bloch-Floquet theorem of periodic structures and translation invariant properties of semi-infinite periodic structures, respectively. Numerical examples are shown for near-field distributions and far-field radiation patterns. The results obtained from small finite periodic structures capture the edge effect and agree well with the results by the rigorous element-by-element approach.

A New EFIE Method Based on Coulomb Gauge for the Low-Frequency Electromagnetic Analysis

To solve the low-frequency breakdown inherent from the electric fleld integral equation (EFIE), an alternative new form of the EFIE is proposed by using the Coulomb-gauge Greens function of quasi-static approximation. Difierent from the commonly adopted Lorentz-gauge EFIE, the Coulomb-gauge EFIE separates the solenoidal and irrotational surface currents explicitly, which captures inductive and capacitive responses through electrodynamic and electrostatic Greens functions, respectively. By applying existing techniques such as the loop-tree decomposition, frequency normalization, and basis rearrangement, the Coulomb-gauge EFIE also can remedy the low-frequency breakdown problem. Through comparative studies between the Lorentz-gauge and Coulomb-gauge EFIE approaches from mathematical, physical and numerical aspects, the Coulomb-gauge EFIE approach shows the capability of solving low-frequency problems and achieves almost the same accuracy and computational costs compared to the Lorentz-gauge counterpart.

Volterra Series-Based Time-Domain Macromodeling of Nonlinear Circuits

Volterra series (VS) representation is a powerful mathematical model for nonlinear circuits. However, the difficulties in determining higher order Volterra kernels limited its broader applications. In this paper, a systematic approach that enables a convenient extraction of Volterra kernels from X-parameters is presented. A concise and general representation of the output response due to arbitrary number of input tones is given. The relationship between Volterra kernels and X-parameters is explicitly formulated. An efficient frequency sweep scheme and an output frequency indexing scheme are provided. The least square linear regression method is employed to separate different orders of Volterra kernels at the same frequency, which leads to the obtained Volterra kernels complete. The proposed VS representation based on X-parameters is further validated for time-domain verification. The proposed method is systematic and general-purpose. It paves the way for time-domain simulation with X-parameters and constitutes a powerful supplement to the existing blackbox macromodeling methods for nonlinear circuits.

Blackbox macro-modeling of the nonlinearity based on Volterra series representation of X-parameters

Volterra series representation is a powerful mathematical model for nonlinear devices. However, the difficulties in determining higher-order Volterra kernels limited its broader applications. This paper proposed a systematic approach that enables a convenient extraction of Volterra kernels from X-parameters for the first time. Then the Vandermonde method is employed to separate different orders of Volterra kernels at the same frequency, which leads to a highly efficient extraction process. The proposed Volterra series representation based on X-parameters is further benchmarked for verification. The proposed new algorithm is very useful for the blackbox macro-modeling of nonlinear devices and systems.

The Error Control of Mixed-form Fast Multipole Algorithm Based on the High Order Multipole Rotation

In this letter, the mixed-form fast multipole algorithm (MF-FMA) with feasible error controllability is implemented through high-order multipole rotation that can make the translation matrices very sparse. The saving of both storage and CPU time makes it attainable to increase the number of harmonics in the middle frequency regime, thus shifting up the transition region of MF-FMA. Consequently, the broadband accuracy of the MF-FMA can be improved significantly.