Yu Mao Wu

Optical and electrical study of organic solar cells with a 2D grating anode

We investigate both optical and electrical properties of organic solar cells (OSCs) incorporating 2D periodic metallic back grating as an anode. Using a unified finite-difference approach, the multiphysics modeling framework for plasmonic OSCs is established to seamlessly connect the photon absorption with carrier transport and collection by solving the Maxwells equations and semiconductor equations (Poisson, continuity, and drift-diffusion equations). Due to the excited surface plasmon resonance, the significantly nonuniform and extremely high exciton generation rate near the metallic grating are strongly confirmed by our theoretical model. Remarkably, the nonuniform exciton generation indeed does not induce more recombination loss or smaller open-circuit voltage compared to 1D multilayer standard OSC device. The increased open-circuit voltage and reduced recombination loss by the plasmonic OSC are attributed to direct hole collections at the metallic grating anode with a short transport path. The work provides an important multiphysics understanding for plasmonic organic photovoltaics.

The Numerical Steepest Descent Path Method for Calculating Physical Optics Integrals on Smooth Conducting Quadratic Surfaces

In this paper, we use the numerical steepest descent path (NSDP) method to analyze the highly oscillatory physical optics (PO) integral on smooth conducting parabolic surfaces, including both monostatic and bistatic cases. Quadratic variations of the amplitude and phase functions are used to approximate the integrand of PO integral. Then the surface PO integral is reduced into several highly oscillatory line integrals. By invoking the NSDP method, these highly oscillatory PO line integrals are defined on the corresponding NSDPs. Furthermore, the critical point contributions for the PO integral are exactly extracted and represented based on the NSDPs. The proposed NSDP method for calculating the PO integral on the smooth conducting surfaces is frequency-independent and error-controllable. Compared with the traditional asymptotic expansion approach, the NSDP method significantly improves the PO integral accuracy by around two digits when the working wave frequencies are not extremely large. Numerical results are given to validate the NSDP method.

Dirichlet-to-Neumann map method for analyzing interpenetrating cylinder arrays in a triangular lattice

An efficient numerical method is developed for computing the transmission and reflection spectra of finite two-dimensional photonic crystals composed of circular cylinders in a triangular lattice. Our method manipulates a pair of operators defined on a set of curves, and it remains effective when the radius of the cylinders is larger than sqrt 3/4 of the lattice constant—a condition where different arrays of cylinders cannot be separated by planes without intersecting the cylinders. The method is efficient since it never calculates the wave field in the interiors of the (hexagon) unit cells and it approximates the operators by small matrices. This is achieved by using the Dirichlet-to-Neumann (DtN) maps of the unit cells, which map the wave field on the boundaries of the unit cells to its normal derivative.

Computing highly oscillatory physical optics integral on the polygonal domain by an efficient numerical steepest descent path method

In this work, the computation of physical optics (PO) type integral with the integrand of quadratic phase and amplitude is studied. First, we apply the numerical steepest descent path (NSDP) method to calculate the highly oscillatory PO integral on the triangular patch. Then, we rigorously extend the proposed NSDP method to analyze the PO integral on polygonal domains. Furthermore, the contributions of critical points on polygonal domains, including the stationary phase point, resonance and vertex points, are comprehensively studied in terms of the NSDP method. Compared to the traditional high frequency asymptotic (HFA) method, when the wave frequency is not very high but in the high frequency regime, the NSDP method has improved the PO integral accuracy by one to two digits. Meanwhile, the computational cost by using the proposed NSDP method is independent of the wave frequency.

Analyzing diffraction gratings by a boundary integral equation Neumann-to-Dirichlet map method.

For analyzing diffraction gratings, a new method is developed based on dividing one period of the grating into homogeneous subdomains and computing the Neumann-to-Dirichlet (NtD) maps for these subdomains by boundary integral equations. For a subdomain, the NtD operator maps the normal derivative of the wave field to the wave field on its boundary. The integral operators used in this method are simple to approximate, since they involve only the standard Greens function of the Helmholtz equation in homogeneous media. The method retains the advantages of existing boundary integral equation methods for diffraction gratings but avoids the quasi-periodic Greens functions that are expensive to evaluate.

Dirichlet-to-Neumann map method for analyzing periodic arrays of cylinders with oblique incident waves

For finite two-dimensional photonic crystals given as periodic arrays of circular cylinders in a square or triangular lattice, we develop an efficient method to compute the transmission and reflection spectra for oblique incident plane waves. The method relies on vector cylindrical wave expansions to approximate the Dirichlet-to-Neumann (DtN) map for each distinct unit cell and uses the DtN maps to derive an efficient method that works on the edges of the unit cells only. The DtN operator maps the two longitudinal field components to their derivatives on the boundary of the unit cell.

The Contour Deformation Method for Calculating the High-Frequency Scattered Field by the Fock Current on the Surface of the 3-D Convex Cylinder

In this paper, the high-frequency diffracted waves like the creeping waves are comprehensively analyzed by the Fock currents. On invoking the contour deformation method, the highly oscillatory Fock currents are efficiently calculated. Furthermore, the workload for the calculation of Fock currents is frequency-independent. To capture the high-frequency wave physics phenomenon, the Fock current is separated into the classical physical optics (PO) current and the nonuniform (NU)-Fock current along the shadow boundary and in the deep shadow region. To calculate the highly oscillatory scattered wave fields from the Fock current, quadratic approximations of the phase functions in the integrand are adopted. On invoking the numerical steepest descent path (NSDP) method, the scattered wave fields are efficiently calculated with frequency-independent computational effort and error controllable accuracy in each frequency-independent segment. Meanwhile, the high-frequency creeping wave coming from the NU-Fock current is efficiently captured by the NSDP method. Numerical results for the Fock currents, the high-frequency NU-diffracted and scattered far fields on the convex cylinders are given to validate the efficiency of the proposed method. Furthermore, the contour deformation method for computing the Fock currents offers a clear physical picture for the high-frequency wave fields on the convex scatterer.

Dirichlet-to-Neumann map method for analyzing crossed arrays of circular cylinders

An efficient and accurate computational method is developed for analyzing finite layers of crossed arrays of circular cylinders, including woodpile structures as special cases. The method relies on marching a few operators (approximated by matrices) from one side of the structure to another. The marching step makes use of the Dirichlet-to-Neumann (DtN) maps for two-dimensional unit cells in each layer where the structure is invariant in the direction of the cylinder axes. The DtN map is an operator that maps two wave field components to their normal derivatives on the boundary of the unit cell, and they can be easily constructed by vector cylindrical waves. Unlike existing numerical methods for crossed gratings, our method does not require a discretization of the structure. Compared with the multipole method that uses vector cylindrical wave expansions and scattering matrices, our method is relatively simple since it does not need sophisticated lattice sums techniques.

Methods for fast evaluation of self-energy matrices in tight-binding modeling of electron transport systems

Simulation of quantum carrier transport in nanodevices with non-equilibrium Green’s function approach is computationally very challenging. One major part of the computational burden is the calculation of self-energy matrices. The calculation in tight-binding schemes usually requires dealing with matrices of the size of a unit cell in the leads. Since a unit cell always consists of several planes (for example, in silicon nanowire, four atomic planes for [100] crystal orientation and six for [111] and [112]), we show in this paper that a condensed Hamiltonian matrix can be constructed with reduced dimension (∼1/4 of the original size for [100] and ∼1/6 for [111] and [112] in the nearest neighbor interaction) and thus greatly speeding up the calculation. Examples of silicon nanowires with sp3d5s* basis set and the nearest neighbor interaction are given to show the accuracy and efficiency of the proposed methods.

Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction

Boundary integral equation methods for diffraction gratings are particularly suitable for gratings with complicated material interfaces but are difficult to implement due to the quasi-periodic Greens function and the singular integrals at the corners. In this paper, the boundary integral equation Neumann-to-Dirichlet map method for in-plane diffraction problems of gratings [Y. Wu and Y. Y. Lu, J. Opt. Soc. Am. A26, 2444 (2009)] is extended to conical diffraction problems. The method uses boundary integral equations to calculate the so-called Neumann-to-Dirichlet maps for homogeneous subdomains of the grating, so that the quasi-periodic Greens functions can be avoided. Since wave field components are coupled on material interfaces with the involvement of tangential derivatives, a least squares polynomial approximation technique is developed to evaluate tangential derivatives along these interfaces for conical diffraction problems. Numerical examples indicate that the method performs equally well for dielectric or metallic gratings.