In this paper, we present a new procedure for computing the band structure of semiconductor-based photonic crystals using the spatial finite-difference and temporal differential formulation. Unlike the conventional plane wave expansion (PWE) method where the wavelet expansion and Fourier transform are required; this new scheme only forces the finite-difference to the Maxwell's equation in the spatial domain. When applying the Bloch’s boundary condition to the algorithm for solving the band-diagram, it will result in a system of first-order differential equations in a matrix format. A band mode can be obtained directly by solving the eigen-value and the eigen-vector of this matrix. Numerical examples to demonstrate the accuracy and efficiency of the proposed approach are given.
Photonic crystal fiber (PCF) is a new type of optical fiber that adds a unique dimension to fiber design possibilities, enabling the previously unthinkable in fiber optics. The mode and the band-diagram analysis by conventional electromagnetic methods had proven the advantages of the PCF. When this new product couples to the existing optical fiber systems or vice versa, the important issue is the coupling efficiency. From among the available numerical techniques, the FDTD method seems to be the most reliable for such a task. The method does not force any assumptions on the behavior of the propagating light. It solves Maxwell’s equation in time domain and space domain directly and is readily applicable to problems like transmissions through refractive index discontinuities and multiple reflections on interfaces. The paper will present FDTD simulation results of the coupler and analysis of the calculated coupling efficiency on coupler design parameters.
Biological cells can be considered as dielectric objects with a given refractive index distribution. Light scattering simulations provide us with an efficient tool for studying cell morphology as well as the nature of scattering and its sources. The analysis of this information is the basis for a better understanding and development of new optical methods for non-invasive biomedical diagnostics. Here we demonstrate the potential of Finite-Difference Time-Domain (FDTD) method based software tools for the simulation of light scattering from single cells in situations where other approaches simply do not work or the approximations inherited in them begin to be questionable.
We present the state of the art for commercial design and simulation software in the 'front end' of photonic circuit design. One recent advance is to extend the flexibility of the software by using more than one numerical technique on the same optical circuit. There are a number of popular and proven techniques for analysis of photonic devices. Examples of these techniques include the Beam Propagation Method (BPM), the Coupled Mode Theory (CMT), and the Finite Difference Time Domain (FDTD) method. For larger photonic circuits, it may not be practical to analyze the whole circuit by any one of these methods alone, but often some smaller part of the circuit lends itself to at least one of these standard techniques. Later the whole problem can be analyzed on a unified platform. This kind of approach can enable analysis for cases that would otherwise be cumbersome, or even impossible. We demonstrate solutions for more complex structures ranging from the sub-component layout, through the entire device characterization, to the mask layout and its editing. We also present recent advances in the above well established techniques. This includes the analysis of nano-particles, metals, and non-linear materials by FDTD, photonic crystal design and analysis, and improved models for high concentration Er/Yb co-doped glass waveguide amplifiers.
Based on the exciting results recently achieved using the finite-difference time domain (FDTD) method, an explicit two dimensional FDTD package for modeling wave propagation in certain kinds of nonlinear media such as 2nd-order nonlinearity, 3rd-order nonlinearity, Kerr effect, Raman effect is proposed. The proposed scheme adopts the polarization equation (PE) philosophy, where all nonlinear effects are expressed by nonlinear polarization terms in the time-space domain Maxwell's equation. The Lorentz dispersive effect in time domain polarization term can also be easily coupled in this scheme, which will lead to a dispersive nonlinearity simulation. Typical examples for pulsed beam self-focusing, scattering, harmonic response are presented in this paper.
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