Interference on a thin dielectric layer

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delay it N

Waves reflected (to the left) from two layer borders cancel each other and you see non-reflected wave (after transient while multi-scattered waves go to the left border). The wave is fully transmitted to the right if the optical path difference is equal to an integer multiple of the wavelength of light N λ. Set N = 4.5 to get minimum wave transmission. See also EM pulse reflection from a thin dielectric layer.

To get 1D incident electromagnetic wave a "soft" oscillating source is added near at the left border
    E[1] += A(t) sin ωt,     A(t) = 1/[1 + exp((to - t)/τ))]

Reflection and transmission coefficients

The Fresnel coefficients for normal incidence reflection and transmission are
r12 =   Er   =   ε1½ - ε2½   =   - 1
—— —————— ——
E ε1½ + ε2½ 2
t12 =   Et   =   2 ε1½   =   1
—— —————— ——
E ε1½ + ε2½ 2
where ε1 = 1 and ε2 = 9.
Electromagnetic wave simulation
updated 26 Mar 2014