Propagation in multilayered media with the transfer-matrix method

Reflectance calculation using Fresnel equations involves determining the reflection of light when it hits an interface between two different media. The Fresnel equations provide the reflectance for both perpendicular (s-polarized) and parallel (p-polarized) light components.

Fresnel Equations

For an interface between two media with refractive indices $n_1$ and $n_2$, and an incident angle ${\theta }_i$:

Perpendicular (s-polarized) Light

The reflectance $R_{\mathrm{s }}$is given by: $R_s = \left| \frac{n_1 \cos \theta_i - n_2 \cos \theta_t}{n_1 \cos \theta_i + n_2 \cos \theta_t} \right|^2$

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Parallel (p-polarized) Light

The reflectance $R_p$ is given by: $R_p = \left| \frac{n_2 \cos \theta_i - n_1 \cos \theta_t}{n_2 \cos \theta_i + n_1 \cos \theta_t} \right|^2$

Here, $\theta_t$ is the angle of transmission (refraction), which can be found using Snell's Law: $n_1 \sin \theta_i = n_2 \sin \theta_t$

Total Reflectance

For unpolarized light, the total reflectance $R$ is the average of $R_s$ and $R_p$: $R = \frac{R_s + R_p}{2}$

R=(Rs​+Rp)/2​​​​