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plane wave reflection and refracting

i r t 1 , 1 2 , 2 E i E t E r H i H r H t z x O 平行极化 i r t 1 , 1 2 , 2 E i E t E r H i H r H t z x O 垂直极化
constants:c epsilon0 mu0

Parameters
Incident angle
`theta_i` \(^{\circ}\)
incident permittivity
`epsilon_1` \(\)
incident permeability
`mu_1` \(\)
refracted permitivity
`epsilon_2` \(\)
refracted permeability
`mu_2` \(\)
Output
incident reflect index `n_1`

`n_1=(ck_1)/omega=sqrt(epsilon_1 mu_1)`

incident wave impedance  `Z_1`

`Z=abs(E/H)={omega mu}/k=sqrt(mu/epsilon)`

refracted reflect index `n_2`

`n_2=(ck_2)/omega=sqrt(epsilon_2 mu_2)`

relative reflect index `n_21`

`n_21=n_2/n_1`

refracted wave impedance `Z_2`

`Z=abs(E/H)={omega mu}/k=sqrt(mu/epsilon)`

refracted angle `theta_r`

`n_1 sin(theta_i)=n_2 sin(theta_r)`

Parallel polarization
reflect coefficient `R_p`

`R_p=(Z_1 cos(theta_i)-Z_2 cos(theta_t))/(Z_1 cos(theta_i)+Z_2 cos(theta_t))`

refract coefficient `T_p`

`T_p=(2 Z_2 cos(theta_i))/(Z_1 cos(theta_i)+Z_2 cos(theta_t))`

Brewster angle `theta_b`

`tan(theta_b)=n_21`

Perpendicular polarization
reflect coefficient `R_bot`

`R_bot=(Z_2 cos(theta_i)-Z_1 cos(theta_t))/(Z_2 cos(theta_i)+Z_1 cos(theta_t))`

refract coefficient `T_bot`

`T_bot=(2 Z_2 cos(theta_i))/(Z_2 cos(theta_i)+Z_1 cos(theta_t))`

reflect vs incident angle 

Figure