Yat Hei Lo

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.

Generalized Modal Expansion and Reduced Modal Representation of 3-D Electromagnetic Fields

A generalized modal expansion theory for investigating arbitrary 3-D bounded and unbounded electromagnetic fields is presented. When an inhomogeneity is enclosed with impenetrable boundaries, the field excited by arbitrary sources is expanded with a complete set of eigenmodes, which are classified into trapped modes and radiation modes. As the boundaries tend to infinity, trapped modes remain unchanged, while radiation modes form a continuum. To illustrate the theory, several real-life structures are investigated with a conformal finite-difference technique in the frequency domain. Perfectly matched layers (PMLs) are imposed at finite extent to emulate the unbounded problems. Numerical examples show that, only a few system modes are prominent in expanding an excited field, leading to a reduced modal picture which provides a quick guidance as well as useful physical insight for engineering design and optimization of electromagnetic devices and components.

Finite-width gap excitation and impedance models

In this paper, we present a new method for the feed model for the method of moments (MoM). It is derived from a more accurate model with the realistic size of the excitation, in order to replace the commonly-used delta-gap excitation model. This new model is formulated around the electric field integration equations (EFIE) where the terms for magnetic current and magnetic field can be removed. Hence it is much simpler to implement and reduces the numerical complexity. In addition, a variational formulation is derived to provide second order accuracy of the input admittance calculation. Moreover, this new formulation can be easily extended such that one can insert passive load elements of finite size onto the distributive network, without complicated modification of the MoM analysis. This allows simulation of many realistic networks which include load elements such as resistors, capacitors and inductors.

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.

Generalized Modal Expansion of Electromagnetic Field in 2-D Bounded and Unbounded Media

A generalized modal expansion theory is presented to investigate and illustrate the physics of wave-matter interaction within arbitrary two-dimensional (2-D) bounded and unbounded electromagnetic problems. We start with the bounded case where the field excited by any sources is expanded with a complete set of biorthogonal eigenmodes. In regard to non-Hermitian or nonreciprocal problems, an auxiliary system is constructed to seek for the modal-expansion solution. We arrive at the unbounded case when the boundary tends to infinity or is replaced by the perfectly matched layer (PML). Modes are approximately categorized into two types: trapped modes and radiation modes, which respond differently to environment variations. When coupled with the source, these modes contribute to the modal-expansion solution with different weights, which leads to a reduced modal representation of the excited field in some geometries.

Finite-Width Feed and Load Models

We demonstrate a new method of applying the feed model for the method of moments (MoM) formulation for the electric field integral equation (EFIE). The model is based around a previously reported magnetic ribbon current model which is accurate and allows for a finite width of the feed port. However, with proper approximations, one can reduce the formulation such that the magnetic field operator can be removed in order to simplify computations arising from the curl of the dyadic Greens function and its singularities. We show here that the new feed model can also be used to model a lumped element.

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.

An Efficiently Preconditioned Eigenanalysis of Inhomogeneously Loaded Rectangular Cavities

In this letter, we demonstrate an efficient preconditioning scheme for the eigenanalysis of inhomogeneously loaded rectangular cavities. Modeling the entire structure with the finite-difference frequency-domain (FDFD) method yields a large sparse eigenvalue problem. The desired interior eigen-spectrum is sought for by Arnoldi iterations with the shift-and-invert operation, where the inversion can only be performed iteratively in large-scale applications. A preconditioner is constructed to speed up the inversion. It can effectively shrink the spectrum of the governing matrix and can be solved for by using fast discrete sine and cosine transforms (DSTs and DCTs). Several numerical examples are included to illustrate the efficiency of the preconditioned eigenanalysis.

Second-harmonic generation in metal nanoparticles modeling by surface integral equation

Metals are centrosymmetric materials which only posse local surface second-harmonic (SH) nonlinearities due to the symmetry broken at the surface. In this work the surface integral equation (SIE) is used for evaluating SH radiation generated from metal nanoparticles with arbitrary shapes. The whole SIE system is solved by employing the Galerkin testing procedure and Rao-Wilton-Gillson (RWG) basis functions. The mutual coupling between fundamental and second harmonic field is captured. The method is validated by comparisons with the analytic SH-Mie solution. This method paves the way for accurate and efficient design of general SH nonlinear nanoplasmonic structures.

Sum-frequency and second-harmonic generation from plasmonic nonlinear nanoantennas

Plasmonic nanostructures that support surface plasmon (SP) resonance potentially provide a route for the development of nanoengineered nonlinear optical devices. In this work, second-order nonlinear light scattering, specifically sum-frequency generation (SFG) and second-harmonic generation (SHG), from plasmonic nanoantennas is modeled by the boundary element method (BEM). Far-field scattering patterns are compared with the results calculated by the Mie theory to validate the accuracy of the developed nonlinear solver. The SFG from a multi-resonant nanoantenna (MR-NA) and the SHG from a particle-in-cavity nanoantenna (PIC-NA) are analyzed by using the developed method. Enhancements of the scattering signals due to double-resonance of the MR-NA and gap plasmonic mode of the PIC-NA are observed. Unidirectional nonlinear radiation for the PIC-NA is realized. Moreover, its emission direction can be controlled by the location of the nanosphere. This work provides new theoretical tools and design guidelines for plasmonic nonlinear nanoantennas.