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Longitudinal-section mode

There is an analogy between the way transverse modes (TE and TM modes) are arrived at and the definition of longitudinal section modes (LSE and LSM modes). When determining whether a structure can support a particular TE mode, one sets the electric field in the z direction (the longitudinal direction of the line) to zero and then solves Maxwell's equations for the boundary conditions set by the physical structure of the line. One can just as easily set the electric field in the x direction to zero and ask what modes that gives rise to. Such modes are designated LSE^{x} modes. Similarly there can be LSE^{y} modes and, analogously for the magnetic field, LSM^{x} and LSM^{y} modes. When dealing with longitudinal-section modes, the TE and TM modes are sometimes written as LSE^{z} and LSM^{z} respectively to produce a consistent set of notations and to reflect the analogous way in which they are defined.^[2]

Both LSE and LSM modes are a linear superposition of the corresponding TE and TM modes (that is, the modes with the same suffix numbers). Thus, in general, the LSE and LSM modes have a longitudinal component of both electric and magnetic field. Likewise the LSM modes are found by setting one of the transverse components of magnetic field to zero with analogous results.^[2]

Occurrence[edit]

LSE and LSM modes can occur in some types of planar transmission line with non-homogeneous transmission media. There are some structures that are unable to support a pure TE or TM mode and consequently the transmission mode must necessarily be hybrid.^[3]

References[edit]

Bibliography[edit]

• Zhang, Kequian; Li, Dejie, Electromagnetic Theory for Microwaves and Optoelectronics, Springer, 2013 ISBN 3-662-03553-7.