FDTD Solutions Specifications Sheet

FDTD Solutions can be used to obtain accurate results for a wide range of problems. The following results show the comparison between analytic and simulated results for a series of complex, wavelength-scale scattering problems in two and three dimensions.

Dispersive Materials

In the following, reflection and transmission coefficients are calculated as a function of wavelength for two different structures: a 500 nm layer of silicon (left) and a 50 nm layer of silver (right). In each case, the coefficients are calculated using a broadband plane wave source in a single FDTD simulation that incorporates the dispersive material properties as shown below. The simulated wavelength range is 400 to 2000 nm for silicon and 280 to 600 nm for silver. For comparison, the reflection and transmission coefficients are also calculated analytically using a standard a Fabry-Perot analysis. The analytic and simulated (FDTD) results are so close that a residual difference plot is also calculated.

The complex refractive index for silicon (left) and silver (right) as a function of wavelength. The data points show experimental data and the lines show the refractive index as simulated by FDTD Solutions using a combination of Plasma (Drude) and Lorentz dispersive models.

Reflection and transmission coefficients for a plane wave incident on a 500 nm layer of silicon (left) and a 50 nm layer of silver (right) at normal incidence calculated by FDTD Solutions (FDTD) and a standard Fabry-Perot analysis (theory).

Percentage difference between the simulated and theoretical values for the reflectance and transmission coefficients for silicon (left) and silver (right).

LED Light Extraction

There is current interest in calculating the light extraction efficiency of LEDs and OLEDs, particularly when subwavelength scattering structures are added near the emission layer. In order to simulate the extraction efficiencies and enhancements that can be obtained, it is necessary to accurately simulate the power radiate by a point dipole source into a half-space. Furthermore, it is necessary to calculate the angular distribution of radiated power from an isotropic ensemble of incoherent dipole emitters. We show the comparison between simulated and analytic results for the case of a dipole emitting in a dielectric half-space, where analytical solutions can be easily calculated.

The total emitted power as a function of point source distance from a dielectric interface, calculated in three dimensions, for an isotropic dipole source at a wavelength of 614nm.  The results were obtained using ~20 mesh points per wavelength with FDTD Solutions, as well as the analytic solution Wasey et al, "Efficiency of spontaneous emission from planar microcavities", Journal of Modern Optics, 47, 725-741, (2000).

Far-field radiation pattern as a function of angle, for an incoherent, isotropic ensemble of dipole emitters in two dimensions at wavelength of 500 nm. The radiating dipoles are located in a half-space of refractive index 2, and the farfield projection of |E|2 is calculated into a half-space of air. The results are then compared to a theoretical calculation using Fresnel reflection and transmission coefficients (theory). The agreement is very good up to angles of approximately 85 degrees.

Mie Theory in Cylinder

The scattering from a dielectric cylinder can be calculated in two dimensions and compared to the analytic model. In the following figures, we compare simulated and theoretical scattering intensity versus angle. Excellent agreement is achieved over six orders of magnitude.

Theoretical (analytic) and simulated (FDTD) far field intensity (|E|2) vs angle on a logarithmic scale using a Total Field Scatter Field (TFSF) source with a 1 micron wavelength scattering from a cylinder of index 1.02 and a radius of 2 um.  The simulated near field is projected to the far field.

Theoretical (analytic) and simulated (FDTD) far field intensity (|E|2) vs angle on a logarithmic scale using a Total Field Scatter Field (TFSF) source with a 2 micron wavelength scattering from a cylinder of index 1.02 and a radius of 2 um.  The simulated near field is projected to the far field.

Mie Theory for Three Dimensional Gold Nanoparticle

The three dimensional absorption and scattering cross sections for gold nanoparticles can be calculated with FDTD Solutions and compared to the analytical results.

Screenshot of three dimensional mie scattering with a gold nanoparticle.

The mie absorption cross section versus size parameter (2πradius/λ), theoretical and experimental for a 50 nm radius gold nanoparticle.

The mie scattering cross section versus size parameter (2πradius/λ), theoretical and experimental for a 50 nm radius gold nanoparticle.

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