On field representations in terms of leaky modes or Eigenmodes

Travelling Planar Wave Antenna for Wireless Communications

“…These microwave and millimeter leaky wave antennas, have the same properties of the waveguide leaky wave antennas described previously. In addition, when opening a waveguide to free space, a discrete spectrum is not enough to express an arbitrary solution [16].…”

“…According to (16) we can observe that the leaky mode leaks away in the form of space wave when 0 K   , therefore we can define the radiation leaky region, from the cutoff frequency to the frequency at which the phase constant equals the free-space wavenumber…”

“…Therefore, if we know the begin width and the end width of the antenna, from the curves of normalized phase and attenuation constant at fixed frequency, we can determine the beam radiation range from (16), and the main beam angle through (20). ) [25].…”

The Response of a Two-Wire Transmission Line to Incident Field and Voltage Excitation, Including the Effects of Higher Order Modes

“…C', may now be deformed into a new path C", as shown in Figure 4, with the purpose of improving the convergence of the integral [2,6,7]. In the process of carrying out the last step, we cross the poles of the integrand in (37).…”

Analysis of Leaky Modes in Photonic Crystal Fibers Using the Surface Integral Equation Method

“…In classical optical fibers, two types of leaky modes are known: tunneling leaky modes that arise because of the curvature of the boundary between the core and the cladding and refracting leaky modes that arise from the beams that fall within the boundary with angles smaller than the critical angle [1]. From historical records, the leaky mode concept was first described in 1956 by Marcuvitz [2], who noted the close analogy to quantum-mechanical tunneling. He stated that this solution to the wave equation gives a field representation in a center range with a complex propagation constant, but that the field becomes infinite at the infinite transverse spatial limit [3].…”