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## DDSCAT Discrete Dipole Approximation

Calculate scattering and absorption of light by targets with arbitrary geometries and complex refractive index.

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#### Abstract

This tool is useful for calculating the plasmonic properties of nanostructures and composites containing dielectric heterostructures. Spectra (absorption and scattering) and electrical (near) fields can be readily calculated using classical electrodynamics. This tool is useful for people building bio-sensors based on refractive index sensing and plasmonic coupling, as well as people who wish to compute fields for SERS or other field enhanced spectroscopies.

Through the use of Discrete Dipole Approximation (this tool uses DDSCAT version 7.3) users are able to study absorption, scattering, and electric fields around arrays of nanostructures, including nanobio systems, with varied properties. This tool provides a platform for allowing user-input for the DDSCAT (Discrete Dipole Scattering) software package through an interactive interface. There are a number of geometries supported within this tool including: rectangular prism, anisotropic ellipsoid, ellipsoid, concentric ellipsoids, isotropic cylinder, isotropic cylinder with hemispherical end-caps, cylinder with unixial anisotropic dielectric tensor.

The way that an electromagnetic field interacts with small metallic nanoparticles can be very surprising and yield great insights into the particle itself. This phenomenon can be observed on the macro scale – the precise way a halo forms around a solar eclipse, the combination of colors in a rainbow that forms after a rain storm or emerges from a spray hose on a sunny day, or even the changing colors of the sky at sunset. Each of these physical consequences of light scattering can tell us a great deal about the underlying systems. Light scattering has been used to make gains in biological understanding, study entire galaxies and even understand light itself.

Some of the interesting properties of light (e.g. evanescent fields, light extinction, scattering, absorption, and others) can be leveraged for medical and engineering applications. Surface Plasmon Resonance (SPR), Surface Enhanced Raman Spectroscopy (SERS), are two examples of high impact bionanotechnology in the field of medicine. In order to harness the full power of these phenomena, however, scientists need to understand the interactions of light with nanoparticles at very small length scales.

This principle can be extended and applied in a rigorous laboratory setting to attain very detailed information regarding a variety of particles. Scientists have used light and more generally electromagnetic radiation to study everything from cells and soybeans to planets and stars. As we’ve mentioned, however, this ability to use light as a scientific tool is dependent on our understanding of the interaction between light (and electromagnetic radiation in general) with particles.

Many scientists have worked to understand the behavior of electromagnetic radiation. In the nineteenth century, however, a Scottish physicist, James Clerk Maxwell, developed a mathematical description of the behavior of electric and magnetic fields. This set of partial differential equations, known as Maxwell’s equations, is an approximation of electrodynamic behavior, which nonetheless has formed the foundation for the field since their creation. Many phenomena can be predicted and explained by these equations. Many more, however, cannot. Maxwell’s equations are well characterized and excellent approximations for very common and simple shapes such as spheres and infinite cylinders. For a more general class of geometries, however, exact solutions are not known.

Scientists, of course, are still interested in these non-common geometries. New ways, such as using numerical methods, have arisen to meet the challenge of determining the interaction of electromagnetic radiation with particles arranged in uncommon ways. Mie scattering, for example, has been developed to describe scattering by particles that are larger than a wavelength. Conversely, Rayleigh scattering was developed to understand scattering smaller than a wavelength.

Another very powerful method is known as Discrete Dipole Approximation (DDA). Here, the target is discretized into a collection of dipoles, or polarizable points. This method then uses various algorithms to solve the equations for how the incoming beam interacts with each of the dipoles individually. The resulting data can be used to compute scattering and absorption properties of the target. This method relies on the assumption that the dielectric properties (and hence the interaction between the particle and incoming beam) are directly related to the polarizability of dipoles.

Once the target is converted to a collection of dipoles, the scattering problem can be solved exactly for each dipole. Note that the calculation of interaction with many individual dipoles means that this method lends itself well to parallel processing.

A popular software package for conducting DDA calculations is called DDSCAT. DDSCAT allows for the computation of scattering properties with arbitrary shapes and geometries, and provide graphs of light extinction, absorption, and scattering properties. Using software like DDSCAT, scientists can determine properties of, as mentioned before, everything from space dust to red blood cells (RBCs).

The simulation methods can be used to not only understand properties of these systems but design diagnostic platforms as well. A very exciting area of research involves Surface Plasmon Resonance (SPR), which deals with the changing properties of scattering based on the ordering of gold nanoparticles on some surface. This technology can be used to determine the presence and concentrations of certain proteins in solution or find detect very small quantities of other substances. DDSCAT can be used to design the surface and optimize it for maximal sensitivity. In astrochemistry, scientists can use telescope imaging data and use DDSCAT to find geometries of space targets that most closely match the data in order to determine the most probable geometry.

Clearly, light scattering has been and will be a primary target of research relevant to a variety of fields. Many methods, tools, and approaches exist to conduct light scattering studies. Here, we present an implementation of a popular tool, DDSCAT, which may be used with another tool, DDACONVERT, to determine the light scattering properties of a variety of irregular particles and targets. Please see the instructions file to learn more about using this tool

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#### References

- "Discrete Dipole Approximation." Wikipedia. Wikimedia Foundation, 27 Oct. 2013. Web. 27 Jan. 2014. (link)
- Draine, Bruce T., and Piotr J. Flatau. "Discrete-dipole Approximation for Scattering Calculations." Journal of the Optical Society of America A 11.4 (1994): 1491. Web. (pdf)
- Draine, Bruce T., and Piotr J. Flatau. User Guide for the Discrete Dipole Approximation Code DDSCAT 7.2. N.p., 2012. Web. (pdf)
- Jain, Prashant K., Kyeong Seok Lee, Ivan H. El-Sayed, and Mostafa A. El-Sayed. "Calculated Absorption and Scattering Properties of Gold Nanoparticles of Different Size, Shape, and Composition: Applications in Biological Imaging and Biomedicine." The Journal of Physical Chemistry B 110.14 (2006): 7238-248. Web. (pdf)
- Jain, Prashant K. "Plasmons in assembled metal nanostructures: radiative and nonradiative properties, near-field coupling and its universal scaling behavior." (2008). (pdf)

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