= Electromagnetic waveguide
An <electromagnetic waveguide> confines an <electromagnetic wave> across its axis while allowing it to travel along the axis. Conducting walls or changes of <refractive index> select transverse <normal modes>: reproducible cross-sectional field patterns with their own longitudinal <wavenumbers>. A hollow metal pipe and an <optical fiber> are different realizations of this principle. Their usefulness is to deliver <electromagnetic energy> along a chosen route instead of letting it spread freely.
For a uniform <vacuum>-filled conducting guide, write a <normal mode>'s axial and time dependence as $e^{i(\beta z-\omega t)}$. Here $\omega>0$ is <angular frequency>, $\beta$ is the longitudinal <wavenumber>, and $k_\perp^2$ is the transverse <eigenvalue> selected by the wall <boundary conditions>. The <electromagnetic wave equation> separates into
$$
\beta^2=\frac{\omega^2}{c^2}-k_\perp^2.
$$
The geometry consumes part of the available squared <wavenumber>: when $\omega/c<k_\perp$, this branch is an <evanescent wave> rather than a propagating <normal mode>. The <waveguide cutoff frequency> is therefore a property of a specified branch and geometry. A <transverse electromagnetic mode> in a suitable two-conductor geometry can have $k_\perp=0$ and no positive geometric cutoff. An <optical fiber> needs its own <dielectric> <boundary conditions>, rather than the metal-wall formulas below.
The <rectangular electromagnetic waveguide> makes these ideas explicit with a single <sine> profile. The <scalar-potential conducting waveguide modes> give a broader construction. At an open <aperture>, a confined field can radiate into the <electromagnetic aperture angular spectrum>; it need not remain one guided <normal mode>.
Back to article page
