Yeh matrices
Yeh matrices represent boundary systems and can be used to construct the structural models using the Yeh matrix formalism. There are available boundary and transfer matrices as well as more complicated constructs that can be used to model more complicated phenomena.
Boundary matrices
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Simple boundary matrix
B(left_medium, right_medium[, roughness_RMS, rougness_corelation_length])
This is a simple boundary matrix to model boundary between two media. The first two parameters are the corresponding definitions from media section. Optionalroughness_RMS
androugness_corelation_length
are describing the boundary roughness. If they are omitted, a flat boundary model will be used. If onlyroughness_RMS
is added a simple Drude model will be used for roughness. If both are specified, the roughness will be modeled using the Rayleigh-Rice theory.
Transfer matrices
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Simple transfer matrix
T(medium, thickness_parameter[, right_medium])
This is a simple transfer matrix through film withmedium
and thicknessthickness_parameter
. If the optionalright_medium
is selected, the linear inhomogeneous model will be used, modeling a linear interpolation of the optical constants between the left and right medium over the film thickness.
Advanced matrices
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Scalar Difraction Theory (SDT)
BSDT(left_medium, Boundary1, right_medium, sigma[, tau])
Rougness modeled by the Scalar Difraction Theory (SDT). The
Boundary1
can be any of the other boundary matrices, so you can use this for example to combine SDT with RRT to model surface with both long and short range roughness.BSDT
can be also used to model layer roughness from both sides, use the following syntax:BSDT(left_medium, Boundary1, right_medium, Boundary2, middle_medium, d, sigma1[, tau1])
In this case the SDT will be applied on both sides of the medium
middle_medium
with thicknessd
. To model correlated roughness with different RMS use:BSDT(left_medium, Boundary1, right_medium, Boundary2, middle_medium, d, sigma1, sigma2, C12)
whereC12
is the cross-correlation coefficient of the top and bottom boundaries. -
Identical rough layer
BIRL(left_medium, middle_medium, right_medium, sigma, tau[, tau2, eta])
This is the advanced matrix for the special case of rough boundary, film and a second rough boundary with identical roughness parameters.
Examples of model construction using the Yeh matrix formalism
Flat boundary:
B(ambient_medium, substrate_medium)
Flat thin film:
B(ambient_medium, film_medium)*T(film_medium, thickness_parameter)*B(film_medium, substrate_medium)