A boundary can surprise you.
Can a nonzero field carry no power across an interface? Can adding a layer remove reflection? Predict first, then change one parameter and inspect what Maxwell's boundary conditions require.
Set the interface
Angles are measured from the normal. Both media have positive real indices and μ = μ₀. Coefficients use the same tangential electric-field direction for incident and reflected waves.
The TM reflection sign can differ from textbooks that rotate the reflected p-polarization basis. The reflected power is unchanged.
Add one coherent layer
Normal incidence; one uniform lossless layer; real constant indices. The phase is referenced from the layer entrance to its exit. These are coherent plane-wave amplitudes.
Draw a field with two components
Jones vector: [cos α, sin α exp(iδ)]. The total incident power is normalized to 1. A perfect linear analyzer projects the vector onto its transmission axis.
The drawing uses x to the right and y upward at one fixed point. V = 2 Im(Eₓ*Eᵧ) is an explicit coordinate convention; no ambiguous right/left circular label is used.
Give a zero-thickness sheet an admittance
g = η₀Yₛ = G + iB is dimensionless. Equal exterior indices n₁ = n₂ = 1; normal incidence; electric current sheet only. G ≥ 0 makes the sheet passive.
Inputs (1, exp(iφ))/√2 keep total incident power at 1.
Two-beam absorption:
The main R, T, A metrics below still describe one-sided illumination. Changing illumination changes the relevant absorption limit.
ReflectedTransmittedAbsorbed
What changed, and why?
Complex field coefficients
| Quantity | Real part | Imaginary part |
|---|