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| Mie scattering | |
|---|---|
| Name | Mie scattering |
| Field | Optics, Atmospheric physics, Electromagnetism |
| Discovered by | Gustav Mie |
| Year | 1908 |
Mie scattering Mie scattering describes the interaction of electromagnetic waves with spherical particles whose sizes are comparable to the wavelength of the incident radiation. It provides an exact solution to Maxwell's equations for homogeneous spheres and underpins interpretations in atmospheric science, optical engineering, astronomy, biomedical optics, and remote sensing.
Mie scattering arose from efforts to explain light interactions with particles such as aerosols, droplets, and biological cells, linking empirical observations from Gustav Mie to developments in Maxwell's equations, James Clerk Maxwell's electromagnetic theory, and earlier optical studies by Lord Rayleigh, John William Strutt, 3rd Baron Rayleigh, and Hendrik Lorentz. Its significance spans many disciplines including atmospheric optics studied by researchers at institutions like NASA, NOAA, ESA, and universities such as Harvard University, Massachusetts Institute of Technology, University of Cambridge, University of Oxford, and California Institute of Technology. Mie theory contrasts with approximations used by scientists at laboratories like Bell Labs and national facilities including NIST and Max Planck Institute for Meteorology.
The mathematical foundation rests on solving Maxwell's equations with boundary conditions on a sphere, employing expansions in spherical harmonics developed by Pierre-Simon Laplace-era mathematics and furthered by contributors linked to Johann Carl Friedrich Gauss and Adrien-Marie Legendre. Key theoretical constructs reference vector spherical harmonics, Bessel functions studied by Friedrich Bessel, and Hankel functions associated with Hermann Hankel. The formulation yields infinite series for scattering coefficients derived from determinants related to work by Gustav Mie and contemporaries like Lorentz, building on dielectric theory from Hendrik Antoon Lorentz and dispersion concepts related to Arnold Sommerfeld. The solution connects to optical constants catalogued in compilations by researchers at Bell Labs and material data used by groups at Kirsten and Matsuura-style labs; analytic limits reduce to Rayleigh scattering and geometrical optics explored by Lord Rayleigh and Wilhelm C. Röntgen contexts. Advanced links to plasma physics and photonics tie to studies by Lev Landau, Evgeny Lifshitz, and optics texts used at Stanford University and Princeton University.
Practical computation employs truncated series, recurrence relations, and stable algorithms developed at centers such as IBM Research, Microsoft Research, and universities like University of Chicago and University of Tokyo. Numerical approaches use continued fractions, fast convergence strategies inspired by work at Argonne National Laboratory and Lawrence Livermore National Laboratory, and software implementations in libraries maintained by groups at NCAR and ECMWF. Approximations include Rayleigh, anomalous diffraction approximation referenced in aerosol studies at Scripps Institution of Oceanography and geometric optics approximations applied by teams at JPL. High-performance computing for large size parameters leverages resources from Oak Ridge National Laboratory, Los Alamos National Laboratory, and cloud services provided by Amazon Web Services used in astrophysics at STScI.
Mie solutions predict size-dependent scattering efficiency, absorption efficiency, phase functions, and polarization patterns, influencing observations across spectra from ultraviolet campaigns by ESA missions to infrared surveys by Spitzer and WISE. The wavelength dependence is central to aerosol retrievals used by MODIS teams at NASA Goddard Space Flight Center and by climate modelers at IPCC-associated researchers. Optical constants from databases compiled at NIST and material optical research at Rijksuniversiteit Groningen inform refractive index inputs spanning visible, microwave, and radio regimes studied by Karl Jansky-linked radio astronomy groups at NRAO.
Applications include atmospheric optics phenomena observed by photographers and scientists at Royal Society-affiliated observatories, remote sensing of clouds and aerosols by NOAA and NASA satellites, cometary coma studies by teams at ESO and Keck Observatory, biomedical imaging in centers like Mayo Clinic and Johns Hopkins University, and nanophotonics research at ETH Zurich and University of California, Berkeley. Observational signatures appear in sky color analyses by historical researchers such as Augustin-Jean Fresnel and modern climate studies referenced in IPCC reports. Instruments on platforms from HST to ground-based lidar networks at MPLNET exploit Mie-based retrievals.
Laboratory measurements use spectrophotometers, integrating nephelometers, and polarimeters manufactured by companies that serve research labs at Toshiba, Siemens, and scientific suppliers used by groups at Riken and Chinese Academy of Sciences. Field instruments including sun photometers from networks like AERONET (operated in collaboration with NASA and Oregon State University) implement inversion algorithms to retrieve size distributions and refractive indices. Experimentalists at facilities such as Lawrence Berkeley National Laboratory and Max Planck Institute for Chemistry conduct optical trapping and single-particle scattering experiments, while beamlines at ESRF and Diamond Light Source provide characterization of optical properties at high resolution.
The origin traces to work by Gustav Mie in 1908, influenced by contemporaneous advances by Hendrik Lorentz, Albert Einstein's electromagnetic studies, and earlier scattering theory by Lord Rayleigh. Subsequent development involved mathematicians and physicists across Europe and North America, including contributions from Arnold Sommerfeld, Ludwig Lorenz, Max Born, Eugene Wigner, and modern computational advances credited to researchers at IBM, Bell Labs, and national laboratories. The field matured through collaborations at institutions like University of Vienna, University of Göttingen, Sorbonne University, Columbia University, and through international programs coordinated by UNESCO and space agencies such as NASA and ESA.