# Complex reflection and transmission coefficient of EM waves

• OmeRogie
In summary, the discussion is about complex reflection and transmission coefficients in the context of a wave traveling through two mediums with different permittivity values. The phases of the electric and magnetic fields are affected by the reflection and transmission on the boundary between the two mediums, due to the boundary conditions set by Maxwell's equations. This is manifested in the emergence of phase lag in the second medium.
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 traveled 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?

OmeRogie said:
does a reflection or transmission on the boundary between medium 1 and 2 affect the phases of E and H fields in this case?
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.

## 1. What is the complex reflection coefficient of an EM wave?

The complex reflection coefficient of an EM wave is a ratio of the reflected amplitude to the incident amplitude, taking into account both the amplitude and phase of the reflected wave. It is represented by the symbol ρ and is a complex number with both real and imaginary components.

## 2. How is the complex reflection coefficient calculated?

The complex reflection coefficient is calculated by dividing the reflected amplitude by the incident amplitude. This calculation takes into account the phase shift between the incident and reflected waves, resulting in a complex number.

## 3. What is the significance of the complex reflection coefficient in EM wave analysis?

The complex reflection coefficient is significant in EM wave analysis because it provides information about the behavior of the wave at a boundary between two media. It takes into account not only the amplitude of the reflected wave, but also the change in phase, which can affect the overall behavior of the wave.

## 4. How is the complex reflection coefficient related to the reflection coefficient?

The complex reflection coefficient is related to the reflection coefficient by its magnitude. The absolute value of the complex reflection coefficient is equal to the magnitude of the reflection coefficient. However, the complex reflection coefficient also includes information about the phase shift, which the reflection coefficient does not.

## 5. Can the complex reflection coefficient be used to determine the properties of a medium?

Yes, the complex reflection coefficient can be used to determine the properties of a medium. By analyzing the magnitude and phase of the complex reflection coefficient, we can gather information about the refractive index, conductivity, and permittivity of the medium. This can be useful in various applications, such as in remote sensing or material characterization.

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