RESULTS Comparison with 2D ResultsTo test our code, we simulate the same problem as [8], used there to check focus properties of LHM. The problem consists of an infinitely long line source located 0 /2 above an LHM slab with thickness d ϭ 0 / 2, which is surrounded by free space. The LHM slab was located exactly in the middle of our domain, occupying x ϭ [0 120], y ϭ [40 80], and z ϭ [0 30] cells, including the PML region. The line source was located at (60, 100, [0 30]), 20 cells away from the slab and the resonant frequency used for expression (3) was set to be p ϭ 266.6 ϫ 10 11 rad/s, which gives r ϭ r Ӎ Ϫ1. The computational domain for this example is 120 ϫ 120 ϫ 30 grid points, in the x, y, and z directions, respectively. With the PML approach, we were able to reproduce the results in [8] in a much smaller domain. Figure 2 shows the E z -field distribution corresponding to the time t ϭ 1250⌬t. The field is shown down to 40 dB below its maximum. In order to compare our simulation to [8], we did not place a PML layer on the front and back faces, perpendicular to the z axis, in the 2D simulations. It should be noted that the field distribution is the same as in Fig. 7 in [8], even with a different precision due to larger time steps and larger cell sizes in our simulation. The same field distribution is also seen in [12].Another simulation was done in comparison with rad/s. The field is plotted down to 40 dB below its maximum and at a time t ϭ 1250⌬t. As shown in Figure 3, paraxial foci are located at the center of the slab and at the opposite side from the source. 3D Simulation of a /2 DipoleFinally, we apply our code to 3D problems. The problem is to simulate a 0 /2 dipole 0 /2 above an LHM slab with thickness d ϭ 0 / 2. We reproduced similar geometry to the 2D problems, but with a finite line source. The computational domain for all 3D examples has 120 ϫ 120 ϫ 120 grid points. Figure 4 illustrates the problem's geometry, with the xy-plane cutting at the middle of our domain and the yz-and zx-planes cutting along the dipole. All the fields are plotted down to 60 dB below their maxima.For the first example, the dipole was located at ( Figure 6.For all the examples presented here, the colored animation can be found at http://iris-lee3.ece.uiuc.edu/ ϳ jjin/jin_home.html, where the wave propagation and focus property are shown more clearly. CONCLUSIONA complete 3D formulation, adding the PML approach to the previous formulation of the Drude medium model, has been developed in this paper. The simulation results show good accuracy as compared to the previously published results. The phenomenon of backward-wave propagation can now be analyzed in any arbitrary direction inside an LHM and more complex and realistic structures can be simulated with our code.

The optical characteristic of the nanohole array film is analyzed by using rigorous coupled wave, and the nanohole array film is proposed to serve as photovoltaic device anti-reflection film to improve the device absorption and efficiency. According to theoretical analysis, nanohole array anti-reflection film has a better anti-reflection effect than the monofilm and can better enhance the photovoltaic device's efficiency, especially in a speetral range of 400 nm600 nm; the optimal period of the nanohole array is 500 nm, the optimal filling factor of the nanohole array is 0.2 and the optimal thickness of the nanohole array is 110 nm. In order to testify the optical effect of nanohole array, the nanohole arrays of different sizes are made by the micro-nano processing technology in the anti-reflection film of the 200 m Si Detector, and a relevant experimental system is set up. With the optimized nanohole arrays, the short circuit currents of the experimental sample are increased ～6% in a 4001100 nm spectral range, especially, increased ～15% in a 400 nm-600 nm spectral range.