Numerical Solutions of Finite Well in Two Dimensions Using the Finite Difference Time Domain Method

The higher excited states for two dimensional finite rectangular well potential are calculated numerically,by solving the Schrödinger equation using the finite difference time domain method.Although,this method is suitable to calculate the ground state of the quantum systems,it has been improved to calculate the higher excited states directly.The improvement is based on modifying the iterative process involved in this method to include two procedures.The first is known as cooling steps and the second is known as a heating step.By determining the required length of the cooling iteration steps using suitable excitation energy estimate,and repeating these two procedures using suitable initial guess function for sufficient times.This modified iteration will lead automatically to the desired excited state.In the two dimensional finite rectangular well potential problem both of the suitable excitation energy and the suitable initial guess wave function are calculated analytically using the separation of variables technique.

Finite-difference time-domain studies of low-frequency stop band in superconductor-dielectric superlattice

The transmission coefficients of electromagnetic （EM） waves due to a superconductor-dielectric superlattice are numerically calculated. Shift operator finite difference time domain （SO-FDTD） method is used in the analysis. By using the SO-FDTD method, the transmission spectrum is obtained and its characteristics are investigated for different thicknesses of superconductor layers and dielectric layers, from which a stop band starting from zero frequency can be apparently observed. The relation between this low-frequency stop band and relative temperature, and also the London penetration depth at a superconductor temperature of zero degree are discussed, separately. The low-frequency stop band properties of superconductor-dielectric superlattice thus are well disclosed.

High Precision Time Domain Forward Modeling for Crosshole Electromagnetic Tomography

To improve the resolution of crosshole electromagnetic tomography, high precision of forward modeling is necessary. A pseudo-spectral time domain （PSTD） forward modeling was used to simulate electromagnetic wave propagation between two boreholes. The PSTD algorithm is based on the finite difference time domain （FDTD） method and uses the fast Fourier transform （FFT） algorithm for spatial derivatives in Maxwell＇s equations. Besides having the strongpoint of the FDTD method, the calculation precision of the PSTD algorithm is higher than that of the FDTD method under the same calculation condition. The forward modeling using the PSTD method will play an important role in enhancing the resolution of crosshole electromagnetic tomography.

Design of the sample cell in near-field surface-enhanced Raman scattering by finite difference time domain method

The rational design of the sample cell may improve the sensitivity of surface-enhanced Raman scattering （SERS） detection in a high degree. Finite difference time domain （FDTD） simulations of the configuration of Ag film-Ag particles illuminated by plane wave and evanescent wave are performed to provide physical insight for design of the sample cell. Numerical solutions indicate that the sample cell can provide more ＂hot spots＂ and the massive field intensity enhancement occurs in these ＂hot spots＂. More information on the nanometer character of the sample can be got because of gradient-field Raman （GFR） of evanescent wave. OCIS codes： 290.5860, 240.0310, 240.6680, 999.9999 （surface-enhanced Raman scattering）.

Photocurrent improvement of an ultra-thin silicon solar cell using the localized surface plasmonic effect of clustering nanoparticles

The cluster-shaped plasmonic nanostructures are used to manage the incident light inside an ultra-thin silicon solar cell.Here we simulate spherical,conical,pyramidal,and cylindrical nanoparticles in a form of a cluster at the rear side of a thin silicon cell,using the finite difference time domain(FDTD)method.By calculating the optical absorption and hence the photocurrent,it is shown that the clustering of nanoparticles significantly improves them.The photocurrent enhancement is the result of the plasmonic effects of clustering the nanoparticles.For comparison,first a cell with a single nanoparticle at the rear side is evaluated.Then four smaller nanoparticles are put around it to make a cluster.The photocurrents of 20.478 mA/cm2,23.186 mA/cm2,21.427 mA/cm2,and 21.243 mA/cm2 are obtained for the cells using clustering conical,spherical,pyramidal,cylindrical NPs at the backside,respectively.These values are 13.987 mA/cm2,16.901 mA/cm2,16.507 mA/cm2,17.926 mA/cm2 for the cell with one conical,spherical,pyramidal,cylindrical NPs at the backside,respectively.Therefore,clustering can significantly improve the photocurrents.Finally,the distribution of the electric field and the generation rate for the proposed structures are calculated.

Main Factors for Affecting Photonic Bandgap of Photonic Crystals

The factors affecting one dimensional （1D） and two dimensional （2D） photonic crystals （PhCs） are systemically analyzed in this paper by numerical simulation. Transfer matrix method （TMM） is employed for 1D PCs, both finite difference time domain method （FDTD） and plane wave expansion method （PWE） are employed for 2D PCs. The result shows that the photonic bandgaps （PBG） are directly affected by crystal type, crystal lattice constant, modulation of refractive index and periodicity, and it is should be useful for design of different type photonic crystals with the required PBG and functional devices. Finally, as an example, a near-IR 1D PCs narrow filter was designed.

Optimizing bowtie structure parameters for specific incident light

We investigate optical properties of a bowtie-shaped aperture using the finite difference time domain method to optimize its geometric parameters for specific incident lights. The influence of the parameters on local field enhancement and resonant wavelength in the visible frequency range is numerically analysed. It is found that the major resonance of the spectrum is exponentially depended on the bowtie angle but independent of the whole aperture size. The simulation also demonstrates that increasing the aperture size raises the local field intensity on the exit plane due to an enlarged interaction area between the light and the metal medium. And the near-field spot size is closely related to the gap. Based on these results, the design rules of the bowtie structure can be optimized for specific wavelengths excited.

Optimization of Short-Pulse GPR Transmit Antenna

By analyzing the current distribution of Bow-Tie antenna used in short-pulse ground penetrating radar, the methods of antenna load and driving are presented in this paper to reduce strength of reflective wave both at antenna end and excitation point. The numerical simulation results show the strength of reflective wave is smaller than ?55 dB comparing with the driving wave when the methods are adopted. Key words short-pulse GPR - resistive loading - finite difference time domain method CLC number TN 820 Foundation item: Supported by the National Natural Science Foundation of China (49984001)Biography: LI Tai-quan (1961-), male, Ph. D candidate, research direction: antenna model and design

Numerical investigation of the enhanced unidirectional surface plasmon polaritons generator

A unidirectional surface plasmon polaritons(SPPs) generator with greatly enhanced generation efficiency is proposed. The SPPs generator consists of an asymmetric single nanoslit coated with a polyviny alcohol(PVA) film and a silver rectangle block. The generation efficiency of this SPPs generator is investigated using the finite difference time domain method. Due to the presence of the silver rectangle block, the SPPs generation efficiency of the asymmetric single nanoslit with PVA film can be greatly enhanced and the corresponding wavelength with the maximum enhancement factor can be tuned flexibly. The influence of the structural parameters on the generation efficiency is also investigated for the enhanced unidirectional SPPs generator.

A functional probe with bowtie aperture and bull's eye structure for nanolithograph

The bowtie aperture surrounded by concentric gratings(the bull’s eye structure) integrated on the near-field scanning optical microscopy(NSOM) probe(aluminum coated fiber tip) for nanolithography has been investigated using the finite-difference time domain(FDTD) method.By modifying the parameters of the bowtie aperture and the concentric gratings,a maximal field enhancement factor of 391.69 has been achieved,which is 18 times larger than that obtained from the single bowtie aperture.Additionally,the light spot depends on the gap size of the bowtie aperture and can be confined to sub-wavelength.The superiority of the combination of the bowtie aperture and the bull’s eye structure is confirmed,and the mechanism for the electric field enhancement in this derived structure is analyzed.

Solution of the time-dependent Schrdinger equation with absorbing boundary conditions

The performances of absorbing boundary conditions （ABCs） in four widely used finite difference time domain （FDTD） methods, i.e. explicit, implicit, explicit staggered-time, and Chebyshev methods, for solving the time-dependent Schrodinger equation are assessed and compared. The computation efficiency for each approach is also evaluated. A typical evolution problem of a single Gaussian wave packet is chosen to demonstrate the performances of the four methods combined with ABCs. It is found that ABCs perfectly eliminate reflection in implicit and explicit staggered-time methods. However, small reflection still exists in explicit and Chebyshev methods even though ABCs are applied.

Analysis of directional emission in square resonator lasers with an output waveguide

Square microcavity laser with an output waveguide is proposed and analyzed by the finite-difference time-domain （FDTD） technique. For a square resonator with refractive index of 3.2, side length of 4μm, and output waveguide of 0.4μm width, we have got the quality factors （Q factors） of 6.7 ×10^2 and 7.3 × 10^3 for the fundamental and first-order transverse magnetic （TM） mode near the wavelength of 1.5μm, respectively. The simulated intensity distribution for the first-order TM mode shows that the coupling efficiency in the waveguide reaches 53%. The numerical simulation shows that the first-order transverse modes have fairly high Q factor and high coupling efficiency to the output waveguide. Therefore the square resonator with an output waveguide is a promising candidate to realize single-mode directional emission microcavity lasers.

Investigation of mode radiation loss for microdisk resonators with pedestals by FDTD technique

Mode radiation loss for microdisk resonators with pedestals is investigated by three-dimensional（3D） finite-difference time-domain（FDTD） technique.For the microdisk with a radius of 1μm,a thickness of 0.2μm,and a refractive index of 3.4,on a pedestal with a refractive index of 3.17,the mode quality（Q） factor of the whispering-gallery mode（WGM） quasi-TE_（7.1） first increases with the increase of the radius of the pedestal,and then quickly decreases as the radius is larger than 0.75μm.The mode radiation loss is mainly the vertical radiation loss induced by the mode coupling between the WGM and vertical radiation mode in the pedestal,instead of the scattering loss around the perimeter of the round pedestal.The WG M can keep the high Q factor when the mode coupling is forbidden.

High speed sub-micrometric microscopy using optical polymer microlens

We report the high speed scanning submicronic microscopy （SSM） using a low cost polymer microlens integrated at the extremity of an optical fiber. These microlenses are fabricated by a free-radical photopolymerization method. Using a polymer microlens with a radius of curvature of 250 nm, a sub-micrometric gold pattern is imaged experimentally by SSM. Different distances between the tip and the sample are used with a high scanning speed of 200 cm/s. In particular, metallic absorption contrasts are described with an optical spatial resolution of 250 nm at the wavelength of 532 nm. Moreover, finite-difference time-domain （FDTD） simulations concerning the focal lengths of microlenses with different geometries and heights support the experimental data.

Positive-negative birefraction phenomenon for TM polarization in annular photonic crystal

We propose a two-dimensional （2D） annular photonic crystal （APC） with dual equi-frequency contours （EFCs） in one band. The refractive behaviors of a Gaussian beam incident from air to the APC are analyzed by the EFC analysis and finite-diflerence time-domain （FDTD） method. The results show the positive-negative birefraction phenomenon for the transverse magnetic （TM） polarization in the same band occurs at the interface between air and the APC, and the surface termination of the APC has a large effect on the strength of the negatively refracted beam.

A concave photonic crystal waveguide with a corrugated surface for high-quality focusing

A concave two-dimensional （2D） photonic crystal waveguide （PCW） with corrugated surface is theoret- ically used as a focusing structure. To design this structure, a genetic algorithm is combined with the finite-difference time-domain method. For PCWs with different degrees of concaveness, the power reaches about 80% at different focusing points when the morphology of the concave surface is optimized. More importantly, the focusing location is easily controlled by changing the location of the detector placed in the outout field.

Influence of incident light polarization on photonic nanojet

Dielectric microspheres can confine light in a three-dimensional （3D） region called photonic nanojet is shown when they are illuminated by different polarized beams. The influence of incident light polarization on photonic nanojet using the finite-difference time-domain （FDTD） method is demostrated. The axial field intensity profiles of photonic nanojets for both the linear and circular polarization incident beams are very similar. Azimuthal polarization incident beam induces a doughnut beam along the optical axis, while the radial polarization incident beam permits one to reach an effective volume as small as 0.7（λ/n）3.

Bragg reflection in a quantum periodic structure

We investigate the reflected field for few-cycle ultra-short laser pulses propagating through resonant media embedded within wavelength-scale structures. Full-wave Maxwell–Bloch equations are solved numerically by using the finite-difference time-domain method. The results show that the spectral feature of the reflected spectrum is determined by the Bragg reflection condition, and that the periodic structure of a dense atomic system can be regarded as a one-dimensional photonic crystal and even as a highly reflective multilayer film. Our study explains the suppression of the frequency shifts in the reflected spectrum based on the Bragg reflection theory and provides a method to control the frequency and frequency intervals of the spectral spikes in the reflected spectrum.

Optimization of T-shaped waveguide branches in two-dimensional photonic crystals

The interval and the radius of a pair of defect dielectric rods in waveguide channels near the branching region of a T-shaped waveguide branches are simultaneously varied, and their effects on the transmission properties are investigated using the finite-difference time-domain （FDTD） method. Numerical results show that there is an optimized region where the relative bandwidth of high-transmission （total transmittance ≥0.95） band of the branches is larger than 17%, which is higher than that of the existing same structures （11.60%） with fixed interval. These results provide for engineering application of simple T-shaped waveguide branches with high transmission.

Novel periodic dielectric ring waveguide and design of compact dual wavelength demultiplexer

A novel one dimensional periodic dielectric ring waveguide （PDRWG） is proposed and its dispersion properties are studied in details. Based on the proposed waveguide structure, a compact dual wavelength demultiplexer is designed. By a finite-difference time-domain （FDTD） simulation method, the performance of the designed device is calculated and analyzed. The dual wavelength demultiplexer can split the communication wavelengths of 1.31 and 1.55 μm into different waveguides and output from different ports with relative high transmittances of about 98% and 92%, respectively. The PDRWG may find applications in multi-wavelength demultiplexers or other novel integrated photonic devices.