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Singularities on the two-sheeted complex plane of the longitudinal wavenumber k z = b - j a for a wave-guiding structure open on one side, as in Fig. 1(c), (d), and Fig. 2 (if the waveguide 

Singularities on the two-sheeted complex plane of the longitudinal wavenumber k z = b - j a for a wave-guiding structure open on one side, as in Fig. 1(c), (d), and Fig. 2 (if the waveguide 

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Leaky waves have been among the most active areas of research in microwave engineering over the second half of the 20th century. They have been shown to dominate the near-field of several open wave-guiding structures, of great interest to tailor their radiation, guidance and filtering properties. The elegant theoretical analyses and deep physical i...

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... provided by the fundamental works of Marcuvitz [1] and Oliner [4], [5]. While in closed systems the eigenmodal spectrum is purely discrete, in open systems a continuous eigenmodal spectrum arises, determined by the branch cuts of (2) that emanate from the branch points k z ¼ AEk 0 . For a wave- guiding structure open on one side, the sketch in Fig. 3 shows the complex plane of the longitudinal wavenumber k z , with the typical choice of branch cuts. A proper spectral solution of the source-excited electromagnetic problem implies an integration over the top Riemann sheet associated with waves decaying at infinity, namely, Im½k x Š G 0, or x > 0, (radiation condition). However, as ...
Context 2
... shows the complex plane of the longitudinal wavenumber k z , with the typical choice of branch cuts. A proper spectral solution of the source-excited electromagnetic problem implies an integration over the top Riemann sheet associated with waves decaying at infinity, namely, Im½k x Š G 0, or x > 0, (radiation condition). However, as indicated in Fig. 3, pole singularities may also be present in the bottom Riemann sheet, and in this case they are denoted as nonmodal, or improper source-free solutions of the field equation. As shown by Marcuvitz [1], these complex poles can actually correspond to leaky modes. Although they do not directly contribute to the proper spectral solution, and ...

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