Sophisticated Material Models

FDTD++ includes a number of sophisticated material models that can be used to accurately describe the optical properties of any material, ranging from dielectrics and conductors to dispersive materials to even those exhibiting nonlocality^1,2. Not only these provide accurate fits, but they also correctly describe the physics behind the optical responses.

A database of predefined material models are included with FDTD++³, which provide the most accurate and physically-meaningful fits to experimental optical data than can be found anywhere else.

Dielectrics and Conductors

FDTD++ can easily model any dielectric, using the dielectric model shown to the right. This includes perfect (lossless) dielectrics, conductive (lossy) materials, and perfect electric conductors.

Dispersive Materials

Dispersive (frequency-dependent) materials can also be easily modeled in FDTD++. A number of material models are included for this purpose, which also correctly describe the physics behind the optical responses. Some of these models include (which are also shown to the left):

• The Drude model: Describes intraband electron motion.
• The Lorentz oscillator model: Describes interband electron transitions.
• The Debye model: Describes the relaxation of atomic vibrations.

Arbitrarily-accurate Models

Single material models can be combined in any fashion, including any number of terms, in FDTD++. By doing so, arbitrarily-accurate (albeit, perhaps unphysical) fits to experimental optical data can be obtained.

A particularly powerful model for fitting experimental optical data, for example, is a Drude model in combination with two Lorentz oscillator poles. The image to the right shows the permittivities of silver and gold fit to such a model⁴, demonstrating the accuracy that can be achieved.

Nonlocal Materials

Spatially-nonlocal effects arise when electrons are confined to small regions of space. Examples include junctions between structures, the areas around the edges of small structures, etc. These can significantly modify the electromagnetic fields, relative to classical (local) effects. The implementation of nonlocal effects into the finite-difference time-domain (FDTD) method was developed by the creator of FDTD++, and the nonlocal hydrodynamic Drude model has been incorporated into FDTD++⁵.

As an example of nonlocal effects, the images to the left shows the permittivity of gold as a function of energy and wavevector, using a physical fit to a hydrodynamic Drude model plus two Lorentz poles^1,2. As can be seen by the image to the far right, as the wavevector is increased (smaller regions of space), the permittivity is significantly modified.

 

Materials Database

A materials database is included with FDTD++, containing a large number of the most accurate and physically-meaningful fits to experimental data than can be found anywhere else³.

Fits to additional materials can be requested on the discussion forums, and fits for sensitive experimental data can be requested by emailing support@fdtdxx.com.

 

Notes and references

1. J. M. McMahon, G. C. Schatz, and S. K. Gray, “Plasmonics in the ultraviolet with the poor metals Al, Ga, In, Sn, Tl, Pb, and Bi,” Phys. Chem. Chem. Phys. 15, 5415 (2013).
2. J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal Optical Response of Metal Nanostructures with Arbitrary Shape,” Phys. Rev. Lett. 103, 097403 (2009).
3. The materials database is only available to licensed users of the commercial version of FDTD++.
4. J. M. McMahon, S. K. Gray, and G. C. Schatz, “Calculating nonlocal optical properties of structures with arbitrary shape,” Phys. Rev. B 82, 035423 (2010).
5. FDTD++ is one of the only (if not the only) FDTD software capable of modeling nonlocal effects.