Longitudinal-section modes are a set of a particular kind of electromagnetic transmission modes found in some types of

transmission line In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmi ...

. They are a subset of hybrid electromagnetic modes (HEM modes). HEM modes are those modes that have both an electric field and a

magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and t ...

component longitudinally in the direction of travel of the propagating wave. Longitudinal-section modes, additionally, have a component of either magnetic or electric field that is zero in one transverse direction. In longitudinal-section electric (LSE) modes this field component is electric. In longitudinal-section magnetic (LSM) modes the zero field component is magnetic. Hybrid modes are to be compared to

transverse mode A transverse mode of electromagnetic radiation is a particular electromagnetic field pattern of the radiation in the plane perpendicular (i.e., transverse) to the radiation's propagation direction. Transverse modes occur in radio waves and microwa ...

s which have, at most, only one component of either electric or magnetic field in the longitudinal direction.

Derivation and notation

There is an analogy between the way

s (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 direction (the longitudinal direction of the line) to zero and then solves

Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. Th ...

for the

boundary condition In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to ...

s set by the physical structure of the line. One can just as easily set the electric field in the direction to zero and ask what modes that gives rise to. Such modes are designated LSE modes. Similarly there can be LSE modes and, analogously for the magnetic field, LSM and LSM modes. When dealing with longitudinal-section modes, the TE and TM modes are sometimes written as LSE and LSM respectively to produce a consistent set of notations and to reflect the analogous way in which they are defined. Both LSE and LSM modes are a

linear superposition The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So tha ...

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.Zhang & Li, pp. 294–299

Occurrence

LSE and LSM modes can occur in some types of

planar transmission line Planar transmission lines are transmission lines with electrical conductor, conductors, or in some cases dielectric (insulating) strips, that are flat, ribbon-shaped lines. They are used to interconnect components on printed circuits and integra ...

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.Zhang & Li, pp. 332

References

Bibliography

* Zhang, Kequian; Li, Dejie, ''Electromagnetic Theory for Microwaves and Optoelectronics'', Springer, 2013 {{ISBN, 3-662-03553-7. Wave mechanics Electromagnetic radiation Microwave transmission