Jinjie Liu

Classical theory for second-harmonic generation from metallic nanoparticles

In this paper, we develop a classical electrodynamic theory to study the optical nonlinearities of metallic nanoparticles. The quasi free electrons inside the metal are approximated as a classical Coulomb-interacting electron gas, and their motion under the excitation of an external electromagnetic field is described by the plasma equations. This theory is further tailored to study second-harmonic generation. Through detailed experiment-theory comparisons, we validate this classical theory as well as the associated numerical algorithm. It is demonstrated that our theory not only provides qualitative agreement with experiments but it also reproduces the overall strength of the experimentally observed second-harmonic signals.

Generalization of the FDTD algorithm for simulations of hydrodynamic nonlinear Drude model

In this paper we present a numerical method for solving a three-dimensional cold-plasma system that describes electron gas dynamics driven by an external electromagnetic wave excitation. The nonlinear Drude dispersion model is derived from the cold-plasma fluid equations and is coupled to the Maxwells field equations. The Finite-Difference Time-Domain (FDTD) method is applied for solving the Maxwells equations in conjunction with the time-split semi-implicit numerical method for the nonlinear dispersion and a physics based treatment of the discontinuity of the electric field component normal to the dielectric-metal interface. The application of the proposed algorithm is illustrated by modeling light pulse propagation and second-harmonic generation (SHG) in metallic metamaterials (MMs), showing good agreement between computed and published experimental results.

A Conservative Front Tracking Method in N-Dimensions

We propose a fully conservative Front Tracking algorithm for systems of nonlinear conservation laws. The algorithm can be applied uniformly in one, two, three and N dimensions. Implementation details for this algorithm and tests of fully conservative simulations are reported.

General properties of two-dimensional conformal transformations in electrostatics

Electrostatic properties of two-dimensional nanosystems can be completely described by their non-trivial geometry modes. In this paper we prove that these modes as well as the corresponding eigenvalues are invariant under any conformal transformation. This invariance suggests a new way to study electrostatic conformal transformations, while also providing an in-depth interpretation of the behavior exhibited by singular plasmonic nanoparticles.

Overlapping Yee FDTD Method on Nonorthogonal Grids

We propose a new overlapping Yee (OY) method for solving time-domain Maxwell’s equations on nonorthogonal grids. The proposed method is a direct extension of the Finite-Difference Time-Domain (FDTD) method to irregular grids. The OY algorithm is stable and maintains second-order accuracy of the original FDTD method, and it overcomes the late-time instability of the previous FDTD algorithms on nonorthogonal grids. Numerical examples are presented to illustrate the accuracy, stability, convergence and efficiency of the OY method.

Transformation optics based local mesh refinement for solving Maxwell's equations

In this paper, a novel local mesh refinement algorithm based on transformation optics (TO) has been developed for solving the Maxwell@?s equations of electrodynamics. The new algorithm applies transformation optics to enlarge a small region so that it can be resolved by larger grid cells. The transformed anisotropic Maxwell@?s equations can be stably solved by an anisotropic FDTD method, while other subgridding or adaptive mesh refinement FDTD methods require time-space field interpolations and often suffer from the late-time instability problem. To avoid small time steps introduced by the transformation optics approach, an additional application of the mapping of the material matrix to a dispersive material model is employed. Numerical examples on scattering problems of dielectric and dispersive objects illustrate the performance and the efficiency of the transformation optics based FDTD method.

Subpixel smoothing finite-difference time-domain method for material interface between dielectric and dispersive media

In this Letter, we have shown that the subpixel smoothing technique that eliminates the staircasing error in the finite-difference time-domain method can be extended to material interface between dielectric and dispersive media by local coordinate rotation. First, we show our method is equivalent to the subpixel smoothing method for dielectric interface, then we extend it to a more general case where dispersive/dielectric interface is present. Finally, we provide a numerical example on a scattering problem to demonstrate that we were able to significantly improve the accuracy.

Finite-difference time-domain simulation of spacetime cloak

In this work, we present a numerical method that remedies the instabilities of the conventional FDTD approach for solving Maxwells equations in a space-time dependent magneto-electric medium with direct application to the simulation of the recently proposed spacetime cloak. We utilize a dual grid FDTD method overlapped in the time domain to provide a stable approach for the simulation of a magneto-electric medium with time and space varying permittivity, permeability and coupling coefficient. The developed method can be applied to explore other new physical possibilities offered by spacetime cloaking, metamaterials, and transformation optics.

A diagonal split-cell model for the overlapping Yee FDTD method

Abstract In this paper, we present a nonorthogonal overlapping Yee method for solving Maxwells equations using the diagonal split-cell model. When material interface is presented, the diagonal split-cell model does not require permittivity averaging so that better accuracy can be achieved. Our numerical results on optical force computation show that the standard FDTD method converges linearly, while the proposed method achieves quadratic convergence and better accuracy.

Implicit high-order unconditionally stable complex envelope algorithm for solving the time-dependent Maxwell's equations

Based on the Padé approximation and multistep method, we propose an implicit high-order unconditionally stable complex envelope algorithm to solve the time-dependent Maxwells equations. Unconditional numerical stability can be achieved simultaneously with a high-order accuracy in time. As we adopt the complex envelope Maxwells equations, numerical dispersion and dissipation are very small even at comparatively large time steps. To verify the capability of our algorithm, we compare the results of the proposed method with the exact solutions.