Due to a large index contrast and near-wavelength dimensions, there exists a wide wavelength range where only two waveguide-array modes have real propagation constants in the z direction and, hence, carry energy.
32.
In these cases, solutions to the wave equation resulting in imaginary propagation constants are likewise termed " evanescent " and have the essential property that no net energy is transmitted even though there is a non-zero field.
33.
To achieve this a phase matching condition is required between the propagation constant of the mth mode in the waveguide \ beta _ m and the incident light at an angle \ theta _ m normal from the waveguide surface.
34.
When the wave propagates in inhomogeneous seismic media the propagation constant k must be a complex value that includes not only an imaginary part, the frequency-dependent attenuation coefficient, but also a real part, the dispersive wavenumber.
35.
When the wave propagates in inhomogeneous seismic media the propagation constant k must be a complex value that includes not only an imaginary part, the frequency-dependent attenuation coefficient, but also a real part, the dispersive wave number.
36.
According to this method we will apply the resonance condition along a separability which links the wavenumbers in the various directions and the frequency, it is possible to obtain the values of the longitudinal propagation constant k z for the various modes.
37.
The formal solution to the wave equation can describe modes having an identical form, but the change of the propagation constant from real to imaginary as the frequency drops below the cut-off frequency totally changes the physical nature of the result.
38.
The propagation constant, symbol " ? ", for a given system is defined by the ratio of the complex amplitude at the source of the wave to the complex amplitude at some distance " x ", such that,
39.
Basically we have to try different values of frequency with pre-selected values of propagation constant and propagation direction-through trial and error-until we find a combination that produces the desired zero field condition on the surface of the array of scatterers.
40.
Where is the propagation constant and \ Gamma _ L = \ left ( Z _ L-Z _ 0 \ right ) / \ left ( Z _ L + Z _ 0 \ right ) is the voltage reflection coefficient at the load end of the transmission line.
