Validation and Benchmark
Before applying an electromagnetic (EM) solver to any practical problems, it is important for the user to first validate the tool to gain the confidence that it produces the right and accurate results. One way of validating an EM solver is to benchmark it against analytical solutions. Although only a handful EM problems have analytical solutions, they provide the absolute standard in terms of correctness and accuracy. This page documents some of the benchmark results of EMXP.
- Reflection & transmission at the interface of two dielectrics - the simplest EM problem
- Anti-reflective coating - demonstration of EMXP's sub-grid resolution capability
- Multi-film stack with lossy materials - demonstration of EMXP's dynamic range
Planewave scattering by infinite circular cylinders
Performance of EMXP's analytic and PML ABC's [>>>]
Planewave Reflection & Transmission at the Interface of Two Dielectrics
This is perhaps the simplest EM problem having analytical solutions. The resolutions are described by Snell's law and Fresnel equations. If an EM solver cannot benchmark well in this simple problem, the user should look for other alternatives.
(1) Reflection & Transmission Coefficients of TE Polarization (or S-polarization)
(2) Reflection & Transmission Coefficients of TM Polarization (or P-polarization)
Note EMXP generally shows very good agreement with Fresnel's equations (with ~1% or less error), except for at glancing angles where the planewave propagates nearly parallel to the interface plane and the error is about 5%. Finer grid size is needed if higher accuracy is required for glancing angles.
(3) Field Distribution in Films
(4) Field Distribution in Films With Total Internal Reflection (TIR)
Note the evanescent wave in the 2nd film and the field discontinuity of the normal component at the interface.
It is well known that zero reflection can be achieved for a planewave of normal incidence if the coating film satisfies the following conditions.
The following shows the reflected e-field amplitude as a function of coating film thickness. Note the Yee cell size used in the EMXP simulations was 0.005, much larger than the thickness increment of 0.001. Due to its sub-grid resolution capability EMXP was able to accurately capture the thickness effect continuously, no staircase artifacts as in standard FDTD simulations.
Planewave Propagation in Planar Films with Lossy Materials
This is a slightly more complex planar problem than the previous two. It involves four thin films (some are lossy materials with artificial n&k) and oblique angle of incidence.
(1) E-Field Amplitude Distribution in Stack
Note the plots are in logarithmic scale to show that EMXP is accurate over a large dynamic range.
(2) E-Field Phase Distribution in Stack
Planewave Propagation in Planar Films with Lossy Materials
This is a slightly more complex planar problem than the previous two. It involves four thin films (some are lossy materials with artificial n&k) and oblique angle of incidence.
(1) E-Field Amplitude Distribution in Stack
Note the plots are in logarithmic scale to show that EMXP is accurate over a large dynamic range.
(2) E-Field Phase Distribution in Stack
Planewave Scattering by an Infinite Dielectric Cylinder
EMXP is currently designed for periodic structures. A large pitch is used in this benchmark to mimic an isolated cylinder.
(1) TE Polarization (Incident E-field parallel to cylinder orientation)
 |
 |
|
Total E-Field - Analytic |
Total E-Field - EMXP |
(2) TM Polarization (Incident H-field parallel to cylinder orientation)
 |
 |
|
Total H-Field - Analytic |
Total H-Field - EMXP |
Planewave Scattering by an Infinite Lossy Cylinder
Like the previous one, a large pitch is used in this benchmark to mimic an isolated lossy cylinder.
(1) TE Polarization (Incident E-field parallel to cylinder orientation)
 |
 |
|
Total E-Field - Analytic |
Total E-Field - EMXP |
(2) TM Polarization (Incident H-field parallel to cylinder orientation)
 |
 |
|
Total H-Field - Analytic |
Total H-Field - EMXP |
Two types of absorbing boundary conditions (ABC) are implemented in EM Explorer. One is analytic and the other is based on Perfectly Matched Layer (PML). The performance of the ABC was evaluated using the test case of planewave propagation in free air space.
In the above simulations, wavelength = 0.2, Yee cell size = 0.01. PML parameters: No. of layers = 10 (1/2 of wavelength), s (real) = 9, s (imaginary) = 34, and grading power = 3. The refection error was measured in the scattered field region after the steady state was reached. The analytic ABC outperformed the PML ABC by 10-30 dB.
It is generally recommended to use analytic ABC for its low reflection error. However stability problem may occur in some rare cases in which the user may have to resort to PML. Under different conditions the user may need to tune the PML parameters for the optimum performance. Note the real s is to attenuate evanescent waves and the imaginary s is to attenuate propagation waves. In general, the higher the s, the greater the attenuation. However too high s can cause stability problems too and degrade PML performance.
Copyright (c) 2007 www.emexplorer.net All rights reserved