# Complex reflection and transmission coefficient of EM waves

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1. May 25, 2015

### OmeRogie

I have a question about complex reflection and transmission coefficients. For example, I am modeling a wave in air (medium 1) $\varepsilon = \varepsilon_0$ reflecting on, and transmitted to, a medium 2 with

$\varepsilon = \varepsilon' -j \varepsilon''$

If the wave would have travelled in medium 2, as most of you probably know, the phase of the magnetic (H) field would lag the electric (E) field in this media with complex impedance.

Reflection and transmission coefficients, in this case, are also complex. My question is: does a reflection or transmission on the boundary between medium 1 and 2 affect the phases of E and H fields in this case? Except for a possible inversion of the E- or H-field, does the signal change its phase because of the reflection or transmisson on this layer boundary, as a result of the complex reflection or transmission coeffs?

2. May 26, 2015

### blue_leaf77

Basically yes, because EM field needs to satisfy the boundary conditions set up by the Maxwell's equations. The emergence of phase lag in the second medium is due to the fact that Maxwell's equations connect the E and H fields through the variations in space, in particular the curls, and again this mathematical relations are then manifested in the boundary conditions.