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en:fitting [2012/10/15 18:32]
deinega
en:fitting [2012/10/15 18:37] (current)
deinega
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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.
-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>) 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
-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)  ((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]] [[http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-37-1-112|http]]
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The way to substitute Debye, Drude and Lorentz terms into FDTD scheme is described in  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) )). ((A. Taflove and S. H. Hagness, Computational Electrodynamics: The Finite Difference Time-Domain Method, Artech House, Boston (2005) )).
-FDTD scheme for <tex>a_{p,1} \ne 0</tex> terms using ADE (auxliliary differential equation) technique can be found in our work+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)  ((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]] [[http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-37-1-112|http]] 