Yongpin P. Chen

A New Green's Function Formulation for Modeling Homogeneous Objects in Layered Medium

A new Greens function formulation is developed systematically for modeling general homogeneous (dielectric or magnetic) objects in a layered medium. The dyadic form of the Greens function is first derived based on the pilot vector potential approach. The matrix representation in the moment method implementation is then derived by applying integration by parts and vector identities. The line integral issue in the matrix representation is investigated, based on the continuity property of the propagation factor and the consistency of the primary term and the secondary term. The extinction theorem is then revisited in the inhomogeneous background and a surface integral equation for general homogeneous objects is set up. Different from the popular mixed potential integral equation formulation, this method avoids the artificial definition of scalar potential. The singularity of the matrix representation of the Greens function can be made as weak as possible. Several numerical results are demonstrated to validate the formulation developed in this paper. Finally, the duality principle of the layered medium Greens function is discussed in the appendix to make the formulation succinct.

Study on spontaneous emission in complex multilayered plasmonic system via surface integral equation approach with layered medium Green’s function

A rigorous surface integral equation approach is proposed to study the spontaneous emission of a quantum emitter embedded in a multilayered plasmonic structure with the presence of arbitrarily shaped metallic nanoscatterers. With the aid of the Fermis golden rule, the spontaneous emission of the emitter can be calculated from the local density of states, which can be further expressed by the imaginary part of the dyadic Greens function of the whole electromagnetic system. To obtain this Greens function numerically, a surface integral equation is established taking into account the scattering from the metallic nanoscatterers. Particularly, the modeling of the planar multilayered structure is simplified by applying the layered medium Greens function to reduce the computational domain and hence the memory requirement. Regarding the evaluation of Sommerfeld integrals in the layered medium Greens function, the discrete complex image method is adopted to accelerate the evaluation process. This work offers an accurate and efficient simulation tool for analyzing complex multilayered plasmonic system, which is commonly encountered in the design of optical elements and devices.

Optical design of organic solar cell with hybrid plasmonic system

We propose a novel optical design of organic solar cell with a hybrid plasmonic system, which comprises a plasmonic cavity coupled with a dielectric core-metal shell nanosphere. From a rigorous solution of Maxwells equations, called volume integral equation method, optical absorption of the active polymer material has a four-fold increase. The significant enhancement mainly attributes to the coupling of symmetric surface wave modes supported by the cavity resonator. The dispersion relation of the plasmonic cavity is characterized by solving an 1D eigenvalue problem of the air/metal/polymer/metal/air structure with finite thicknesses of metal layers. We demonstrate that the optical enhancement strongly depends on the decay length of surface plasmon waves penetrated into the active material. Furthermore, the coherent interplay between the cavity and the dielectric core-metal shell nanosphere is undoubtedly confirmed by our theoretical model. The work offers detailed physical explanations to the hybrid plasmonic cavity device structure for enhancing the optical absorption of organic photovoltaics.

An Augmented Electric Field Integral Equation for Layered Medium Green's Function

This paper proposes an augmented electric field integral equation (A-EFIE) for layered medium Greens function. The newly developed matrix-friendly formulation of layered medium Greens function is applied in this method. By separating charge as extra unknown list, and enforcing the current continuity equation, the traditional EFIE can be cast into a generalized saddle-point system. Frequency scaling for the matrix-friendly formulation is analyzed when frequency tends to zero. Rank deficiency and the charge neutrality enforcement of the A-EFIE for layered medium Greens function is discussed in detail. The electrostatic limit of the A-EFIE is also analyzed. Without any topological loop-searching algorithm, electrically small conducting structures embedded in a general layered medium can be simulated by using this new A-EFIE formulation. Several numerical results are presented to validate this method at the end of this paper.

A Novel Implementation of Discrete Complex Image Method for Layered Medium Green's Function

A novel implementation of discrete complex image method (DCIM) based on the Sommmerfeld branch cut is pro posed to accurately capture the far-field behavior of the layered medium Greens function as a complement to the traditional DCIM. By contour deformation, the Greens function can be naturally decomposed into branch-cut integration (radiation modes) and pole contributions (guided modes). For branch-cut integration, matrix pencil method is applied, and the alternative Sommerfeld identity in terms of kz integration is utilized to get a closed-form solution. The guided modes are accounted for with a pole-searching algorithm. Both one-branch-cut and two-branch-cut cases are studied. Several numerical results are presented to validate this method.

Graphene plasmonics for tuning photon decay rate near metallic split-ring resonator in a multilayered substrate

Study of photon decay rate is essential to various optical devices, where graphene is an emerging building block due to its electrical tunability. In this paper, we study photon decay rate of a quantum emitter near a metallic split-ring resonator, which is embedded in a multilayered substrate incorporating a graphene layer. Analyzing photon decay rate in such a complex multilayered system is not only computationally challenging but also highly important to experimentally realizable devices. First, the dispersion relation of graphene plasmonics supported at a dieletric/graphene/dielectric structure is investigated systematically. Meanwhile, the dispersion relation of metallic plasmonics supported at a dielectric/metal structure is studied comparatively. According to our investigation, graphene offers several flexible tuning routes for manipulating photon decay rate, including tunable chemical potential and the emitters position and polarization. Next, considering plasmonic waves in a graphene sheet occur in the infrared regime, we carefully design a metallic split ring resonating around the same frequency range. Consequently, this design enables a mutual interaction between graphene plasmonics and metallic plasmonics. The boundary element method with a multilayered medium Greens function is adopted in the numerical simulation. Blue-shifted and splitting resonance peaks are theoretically observed, which suggests a strong mode coupling. Moreover, the mode coupling has a switch on-off feature via electrostatically doping the graphene sheet. This work is helpful to dynamically manipulate photon decay rate in complex optical devices.

A Calderón Preconditioner for the Electric Field Integral Equation With Layered Medium Green's Function

A Calderón preconditioner is developed for the analysis of electromagnetic scattering of perfect electrically conducting (PEC) objects embedded in a layered medium. The electric field integral equation (EFIE) is formulated with the kernel of layered medium Greens function to account for the effects from the multilayered background. The Calderón projector is derived based on the general source-field relationship and the extinction theorem for inhomogeneous environment in electromagnetic theory. The Calderón identities can be naturally deduced based on this projector, which is then leveraged to precondition the EFIE with layered kernel. An alternative implementation is then proposed to make the implementation of the preconditioner as efficient as the one in free space. Different numerical examples are designed to show the performance of the preconditioner, where the objects are located in different positions with respect to the layered medium, or different types of excitation are adopted. It is shown that the proposed effective and robust preconditioner makes the EFIE system converge rapidly in all cases, independent of the discretization density.

Fast Analysis of Electromagnetic Scattering From Three-Dimensional Objects Straddling the Interface of a Half Space

The electromagnetic scattering from 3-D perfectly electrically conducting (PEC) objects straddling the interface of a half-space is analyzed in this letter. The adaptive cross approximation (ACA) algorithm is adopted to enhance the computational efficiency. As the object is naturally separated into two parts by the interface of the half-space, two different mesh densities are required due to the contrast of the two background materials. Therefore, two multilevel tree structures are set up individually in the two regions. When the source and field points are in the same region, which corresponds to the primary terms and reflection terms, the implementation is similar to the free-space case. However, when considering the mutual coupling of the two regions, which corresponds to the transmitted terms, difficulties arise since the two trees are independent and the numbers of levels are, in general, different. In this case, a z-dependent grouping strategy is proposed to redefine the well-separated interactions and match the abrupt changes at the interface. Three clustering strategies are proposed and discussed carefully to account for the mutual coupling in the two different regions of the half-space. The combined field integral equation (CFIE) formulation is further applied to improve the convergence of the system. Several numerical examples are demonstrated to validate the proposed schemes.

A Mixed-Form Thin-Stratified Medium Fast-Multipole Algorithm for Both Low and Mid-Frequency Problems

A mixed-form thin-stratified medium fast-multipole algorithm is proposed for fast simulation of general microstrip structures at both low and mid-frequencies. The newly developed matrix-friendly formula of layered medium Greens function is applied in this algorithm. For well-separated interactions, the path deformation technique is implemented to achieve a smoother and exponentially convergent integral. The two-dimensional addition theorem is then incorporated into the integrand to expedite the matrix-vector product. In our approach, multipole expansion (low-frequency fast-multiple algorithm) as well as the plane wave expansion (mid-frequency fast-multipole algorithm) of the translational addition theorem are combined into a single multilevel tree to capture quasi-static physics and wave physics simultaneously. The outgoing wave is represented first in terms of multipole expansion at leafy levels, and then switched to plane wave expansion automatically at higher levels. This seamless connection makes the algorithm applicable in simulations, where subwavelength interaction and wave physics both exist.

A Hybrid FEM/MoM Method for 3-D Electromagnetic Scattering in Layered Medium

Accurate and efficient prediction of electromagnetic scattering from inhomogeneous objects in layered medium is one of the most challenging issues in engineering applications. This paper presents the first 3-D higher order hybrid finite-element method (FEM) and method of moments (MoM) for the accurate modeling of inhomogeneous dielectric objects in multilayered medium. The main challenges of this paper include: 1) the integration of these algorithms for layered medium and 2) the higher order computational approach involved in layered medium for high efficiency. In the proposed method, the MoM with the layered medium dyadic Greens function is used as the exact radiation boundary condition in an inhomogeneous background, and the FEM is applied to model the inhomogeneous objects. Furthermore, the higher order maximally orthogonal basis functions with curl-conforming and divergence-conforming properties are used in the FEM and MoM, respectively to improve the modeling capability of this algorithm. For 3-D inhomogeneous objects scattering in multilayered medium, this new method requires a much more tightly truncated simulation domain than the traditional FEM, and provides much higher flexibility than the pure surface integral equation method. Finally, some numerical results are provided to validate the accuracy, efficiency, and flexibility of this method.