Mie Calculations of Single Nanosphere Cross-Sections Tool uses Mie theory to calculate absorption, scattering, and extinction cross-sections for an isolated spherical nanoparticle of a given radius. The user also defines the nanosphere material and refractive index of the surrounding environment. Calculations are performed for dipoles, quadrupoles, octupoles, and higher-order multipoles.

The tool includes the following functionality:

• The nanoparticle material can be defined through either a constant refractive index or dispersive permittivity.
• The number of multipoles considered in the calculations is either the default value or defined by the user (up to 100). To perform calculations with satisfactory accuracy, Wiscombe criterion is used for the default number of selected multipoles.
• The absorption, scattering, and extinction cross-sections are presented individually, separately for electric and magnetic multipoles, with up to 10 multipoles each. 

In Mie calculations, for an accurate representation of the scattered field, a sufficient number of multipole terms must be considered. In practice, there is a threshold number above which the Mie coefficients’ values drop almost to zero. To estimate the number of significant coefficients for dielectric nanoparticles, Wiscombe criterion is used to choose a multipole number. This number depends on the nanoparticle radius, the refractive index of the media, and the wavelength range of the incident light. As a rule of thumb, for metallic nanoparticles, one can expect the number of significant coefficients to be greater than the corresponding number used for a dielectric particle of the same size.

The tool will be advanced in future releases by adding more materials in the refractive index category, allowing users to upload data files with their desired refractive index or permittivity, and extending calculation to the case of multilayer nanoparticles. The verification of actual solution convergence will be included in each case to establish the number of coefficients that need to be retained.

Vahid Karimi, Viktoriia E. Babicheva

Department of Electrical and Computer Engineering,  University of New Mexico, Albuquerque NM

The University of New Mexico Research Allocations Committee, award RAC2022

Mie theory and Wiscombe's criterion:

Jones, P. H., Maragò, O. M., & Volpe, G. (2015). Optical tweezers: Principles and applications. Cambridge University Press.

Material parameters are taken from:

Ag, Au and Cu: Johnson, P. B., & Christy, R. W. (1972). Optical constants of the noble metals. Physical Review B, 6(12), 4370.

Al: Rakić, A. D. (1995). Algorithm for the determination of intrinsic optical constants of metal films: application to aluminum. Applied Optics, 34(22), 4755-4767.

Si: Aspnes, D. E., & Studna, A. A. (1983). Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV. Physical Review B, 27(2), 985.

Researchers should cite this work as follows:

• Vahid Karimi, Viktoriia E. Babicheva, 2021, "Mie Calculations of Single Nanosphere Cross-Sections" https://nanohub.org/resources/extcs

   

• Vahid Karimi, Viktoriia E. Babicheva (2021), "Mie Calculations of Single Nanosphere Cross-Sections," https://nanohub.org/resources/extcs. (DOI: 10.21981/8QEY-MN47).

  BibTex | EndNote

1. absorption spectra
2. electromagnetic fields
3. Mie Scattering
4. nanoparticles
5. nanophotonics
6. nanosensors/sensing
7. Plasmonic Nanostructures
8. sensors/sensing
9. surface plasmons