Model & Assumptions Stable
- Model
- Exact Mie theory — analytical solution to Maxwell's equations for a homogeneous sphere in a uniform host medium.
- Assumptions
- Spherical geometry, isotropic and local dielectric functions, plane-wave or electron-beam excitation, no substrate or inter-particle coupling.
- Validity
- Valid for any sphere size relative to wavelength. Optical constants from tabulated experimental data (Johnson & Christy, Palik, etc.) via cubic-spline interpolation.
- Limitations
- No non-local or quantum-size corrections. EELS uses the non-retarded analytical model for the homogeneous sphere (retardation effects missing for large particles or high energies).
- References
-
- C. F. Bohren & D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
- F. J. García de Abajo, Optical excitations in electron microscopy, Rev. Mod. Phys. 82, 209 (2010).
- Y. S. Kim, P. T. Leung & T. F. George, Classical decay rates for molecules in the presence of a spherical surface: A complete treatment, Surf. Sci. 195, 1 (1988).
References
- [1]C. F. Bohren & D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
- [2]F. J. García de Abajo, Relativistic energy loss and induced photon emission in the interaction of a dielectric sphere with an external electron beam, Phys. Rev. B 59, 3095 (1999), doi:10.1103/PhysRevB.59.3095.
- [3]P. E. Stamatopoulou, W. Zhao, A. Rodríguez Echarri, N. A. Mortensen, K. Busch, C. Tserkezis & C. Wolff, Electron beams traversing spherical nanoparticles: analytic and numerical treatment, Phys. Rev. Research 6, 013239 (2024), doi:10.1103/PhysRevResearch.6.013239.
- [4]Optical constants: refractiveindex.info. Au, Ag: Johnson & Christy (1972); Si: Aspnes & Studna (1983); Al: Rakić (1995); TiO2: Sarkar et al. (2019).
- [5]L. Meng, R. Yu, M. Qiu & F. J. García de Abajo, Plasmonic nano-oven by concatenation of multishell photothermal enhancement (Thermal view), ACS Nano 11, 7915–7924 (2017), doi:10.1021/acsnano.7b02426.
- [6]Y. S. Kim, P. T. Leung & T. F. George, Classical decay rates for molecules in the presence of a spherical surface: A complete treatment, Surf. Sci. 195, 1 (1988), doi:10.1016/0039-6028(88)90776-5.