# Electromagnetic Wave

## Electromagnetic Wave

Electromagnetic Waves Maxwell’s equations predict the propagation of electromagnetic energy away from time-varying sources (current and charge) in the form of waves. Consider a linear, homogeneous, isotropic media characterized by (:, ,, F) in a source-free region (sources in region 1, source-free region is region 2).

We start with the source-free, instantaneous Maxwell’s equations written in terms of E and H only. Note that conduction current in the source-free region is accounted for in the FE term.

Taking the curl of â

and inserting ã gives

Taking the curl of ã

and inserting â yields

Using the vector identity

in æ and ç gives

For time-harmonic fields, the instantaneous (time-domain) vector F is related to the phasor (frequency-domain) vector Fs by

Using these relationships, the instantaneous vector wave equations are transformed into the phasor vector wave equations:

If we let the phasor vector wave equations reduce to

The complex constant ( is defined as the propagation constant.

The real part of the propagation constant (") is defined as the attenuation constant while the imaginary part (\$) is defined as the phase constant. The attenuation constant defines the rate at which the fields of the wave are attenuated as the wave propagates. An electromagnetic wave propagates in an ideal (lossless) media without attenuation (" = 0). The phase constant defines the rate at which the phase changes as the wave propagates.

Separate but equivalent units are defined for the propagation, attenuation and phase constants in order to identify each quantity by its units [similar to complex power, with units of VA (complex power), W (real power) and VAR (reactive power)].

Given the properties of the medium (:, ,, F), we may determine equations for the attenuation and phase constants.

Properties of Electromagnetic Waves The properties of an electromagnetic wave (direction of propagation, velocity of propagation, wavelength,...