Complex Permittivity and Refractive Index for Metals Aaron Webster Last Update: November 9, 2012 The following figures plot the frequency dependent complex permittivity = 0 +i00 and refractive index n = n 0 +in 00 for silver, aluminum, gold, copper, chromium, nickel, tungsten, titanium, beryl- lium, palladium, and platinum using either the Drude (Equation 3), Lorentz-Drude (Equation 4), or Brendel-Bormann (Equation 5 models in the range 200 nm to 2000 nm. The material parameters and mathematical formalism detailed in [1]. These tables are generated programmatically. Three different models for the complex permittivity are tabulated. The first two are the Drude and Lorentz-Drude (LD) models. D = D (1) LD = D + L (2) where D is contribution from the Drude model, representing free electron effects D =1 - √ f 0 ω 02 p ω(ω - iΓ 0 0 ) (3) and L is the Lorentz contribution, representing the bound electron effects L = k X j=0 f j ω 02 p ω 02 j - ω 2 +iωΓ 0 j (4) The third is the Brendel-Bormann model which is based instead on an infinite superposition of oscillators BB = 1 √ 2π σ n Z ∞ -∞ exp - (x - ω 0 n ) 2σ 2 n f j ω 2 p (x 2 - ω 2 )+iωΓ 0 n dx (5) 1
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Complex Permittivity and Refractive Index for Metals
Aaron Webster
Last Update: November 9, 2012
The following figures plot the frequency dependent complex permittivity ε = ε′ + iε′′ and refractiveindex n = n′ + in′′ for silver, aluminum, gold, copper, chromium, nickel, tungsten, titanium, beryl-lium, palladium, and platinum using either the Drude (Equation 3), Lorentz-Drude (Equation 4), orBrendel-Bormann (Equation 5 models in the range 200 nm to 2000 nm. The material parameters andmathematical formalism detailed in [1]. These tables are generated programmatically. Three differentmodels for the complex permittivity are tabulated. The first two are the Drude and Lorentz-Drude (LD)models.
εD = εD (1)
εLD = εD + εL (2)
where εD is contribution from the Drude model, representing free electron effects
εD = 1−√f0 ω
′2p
ω(ω − iΓ′0)(3)
and εL is the Lorentz contribution, representing the bound electron effects
εL =
k∑j=0
fjω′2p
ω′2j − ω2 + iωΓ′j(4)
The third is the Brendel-Bormann model which is based instead on an infinite superposition of oscillators