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I dont think I have enough backgrounds for optics.

I am sorry for asking this elementary question.

I am reading a paper Phyc Rev A, Vol 59 # 6, 1999

they introduces discontinuity matrix $$\Delta_{ij}$$ which describes the boundary condition for the transfer of the electric field from left to right across a discontinuous $$n_i --> n_j$$ interface, accounting for the Fresnel reflection and transmission coefficients.

The incidence angle is 0

they introduces this matrix as

$$\Delta_{ij}=\begin{bmatrix} \delta_{ij}^+ & \delta_{ij}^- \\ \delta_{ij}^- & \delta_{ij}^+ \\ \end{bmatrix}$$

where $$\delta_{ij}^+=\frac12(1+\frac{n_j}{n_i})$$ and $$\delta_{ij}^-=\frac12(1-\frac{n_j}{n_i})$$

note that $$n_i$$ and $$n_j$$ are complex numbers.

I know the Fresnel equation with respect to the incidence angle.

I think the Fresnel coefficient should be $$(\frac{n_i-n_j}{n_i+n_j})^2$$ for R... but it is different

how can I get that coefficient

I actually want to know how the $$\Delta_{ij}$$ changes with respect to the incidence angle.

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  • $\begingroup$ Are you looking at isotopic and homogeneous materials? In this cast $\Delta_{ij}$ is not a function of angle. Can you link to the actual paper, this would help. $\endgroup$
    – boyfarrell
    Mar 20, 2015 at 18:29
  • $\begingroup$ journals.aps.org/pra/pdf/10.1103/PhysRevA.59.4736 $\endgroup$
    – eric
    Mar 20, 2015 at 18:56
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    $\begingroup$ Pay wall. Maybe you can summarise by adding a bit more context. $\endgroup$
    – boyfarrell
    Mar 20, 2015 at 18:57
  • $\begingroup$ Thanks boyfarrell, metrix delra is not a function of theta because the paper considers only 0 incidence angle, please see the 4739 page $\endgroup$
    – eric
    Mar 20, 2015 at 18:58
  • $\begingroup$ You need to add more context to this question. For example I didn't even understand why it would be a function of angle because the refractive index doesn't change with angle (see my above point about isotropic and homogeneous materials). $\endgroup$
    – boyfarrell
    Mar 20, 2015 at 19:00

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