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en:fitting [2012/02/01 13:00]
deinega
en:fitting [2012/10/15 18:37] (current)
deinega
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 Number of terms <tex>P</tex> and coefficients <tex>\varepsilon_{\infty}</tex>, <tex>a_{p,j}</tex>, <tex>b_{p,j}</tex> should be chosen in order to approximate given <tex>\varepsilon(\omega)</tex> with sufficient accuracy and do not necessary have a physical meaning. Number of terms <tex>P</tex> and coefficients <tex>\varepsilon_{\infty}</tex>, <tex>a_{p,j}</tex>, <tex>b_{p,j}</tex> should be chosen in order to approximate given <tex>\varepsilon(\omega)</tex> with sufficient accuracy and do not necessary have a physical meaning.
 +
 +You can fit arbitrary dielectric function with {{:fitting.zip|fitting program}} written on MatLab.
 +This program is well commented and easy to understand.
 +You should specify all necessary parameters (number of terms <tex>P</tex>, file with tabular dielectric function, etc.) in file 'fitting.m' .
 +Initial settings in 'fitting.m' were used to fit experimental data for silicon dielectric permittivity.
  
 In physical literature following models are commonly used: In physical literature following models are commonly used:
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   *Drude term <tex>\frac{\Delta \varepsilon \omega_p^2}{-2i\omega\gamma_p-\omega^2}</tex>   *Drude term <tex>\frac{\Delta \varepsilon \omega_p^2}{-2i\omega\gamma_p-\omega^2}</tex>
   *Lorentz term <tex>\frac{\Delta \varepsilon \omega_p^2}{\omega_p^2-2i\omega\gamma_p-\omega^2}</tex>   *Lorentz term <tex>\frac{\Delta \varepsilon \omega_p^2}{\omega_p^2-2i\omega\gamma_p-\omega^2}</tex>
 +  *modified Lorentz term <tex>\frac{\Delta \varepsilon (\omega_p^2 - i\omega\gamma_p')}{\omega_p^2-2i\omega\gamma_p-\omega^2}</tex>
 +
 +Using modified Lorentz term allows to obtain more accurate fittings.
 +For example, two (<tex>P=2</tex>) modified Lorentz terms are sufficient to fit silicon dielectric function over the wavelength range from 300 to 1000 nm, whereas even a large number of Debye, Drude or Lorentz terms (<tex>a_{p,1}=0</tex>) is inadequate there 
 +((A. Deinega and S. John, "Effective optical response of silicon to sunlight in the finite-difference time-domain method," Opt. Lett. 37, 112-114 (2012) 
 +[[http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-37-1-112|http]]
 +{{:deinega_-_effective_optical_response_of_silicon_to_sunlight_in_the_fdtd_method.pdf|PDF}})).
 +Previous fitting for silicon by 3 Lorentz terms (see paper on textured antireflective coatings 
 +((A. Deinega, I. Valuev, B. Potapkin and Yu. Lozovik, "Minimizing light reflection from dielectric textured surfaces," JOSA A 28, 770-777 (2011) 
 +[[http://www.opticsinfobase.org/abstract.cfm?URI=josaa-28-5-770|http]] 
 +{{:deinega_-_minimizing_light_reflection_from_dielectric_textured_surfaces.pdf|PDF}}))) 
 +is accurate only for the visible range and no fitting with Lorentz terms was found for both visible and near ultraviolet ranges.
 +
 +The way to substitute Debye, Drude and Lorentz terms into FDTD scheme is described in 
 +((A. Taflove and S. H. Hagness, Computational Electrodynamics: The Finite Difference Time-Domain Method, Artech House, Boston (2005) )).
 +FDTD scheme for modified Lorentz terms using ADE (auxliliary differential equation) technique can be found in our work
 +((A. Deinega and S. John, "Effective optical response of silicon to sunlight in the finite-difference time-domain method," Opt. Lett. 37, 112-114 (2012) 
 +[[http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-37-1-112|http]]
 +{{:deinega_-_effective_optical_response_of_silicon_to_sunlight_in_the_fdtd_method.pdf|PDF}})).
 +
  
 +/* ((M. A. Green and M. Keevers, Optical properties of intrinsic silicon at 300 K, Progress in Photovoltaics 3, 189 (1995)
 +[[http://onlinelibrary.wiley.com/doi/10.1002/pip.4670030303/abstract|http]]))
 +(see file 'si.dat' in archive) with two terms <tex>a_{p,1} \ne 0</tex>. */
  
-Case <tex>a_{p,1} \ne 0</tex> does not correspond to any of physical model, but allows to obtain more accurate fittings. 
-For example, two (<tex>P=2</tex>) terms of this case are sufficient to fit silicon dielectric function over the wavelength range from 300 to 1000 nm, whereas even a large number of Debye, Drude or Lorentz terms (<tex>a_{p,1}=0</tex>) is inadequate there ((A. Deinega and S. John, "Effective optical response of silicon to sunlight in the finite-difference time-domain method," Opt. Lett. 37, 112-114 (2012) [[http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-37-1-112|http]]{{: 
-deinega_-_effective_optical_responce_of_silicon_to_sunlight_in_the_fdtd_method.pdf|PDF}})). 
-Previous fitting for silicon by 3 Lorentz terms (see paper on textured antireflective coatings ((A. Deinega, I. Valuev, B. Potapkin and Yu. Lozovik, "Minimizing light reflection from dielectric textured surfaces," JOSA A 28, 770-777 (2011) [[http://www.opticsinfobase.org/abstract.cfm?URI=josaa-28-5-770|http]] {{:deinega_-_minimizing_light_reflection_from_dielectric_textured_surfaces.pdf|PDF}}))) is accurate only for the visible range and no fitting with Lorentz terms was found for both visible and near ultraviolet ranges. 
  
 
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