What is the difference between TE and TM mode?

TE (Transverse Electric) and TM (Transverse Magnetic) modes are terms used in the field of electromagnetics and waveguide theory to describe different types of electromagnetic wave propagation within waveguides, which are structures that guide and confine electromagnetic waves. These modes are typically associated with rectangular or cylindrical waveguides, but the concepts can also be applied to other structures.

TE Mode (Transverse Electric Mode):

In TE modes, there is no electric field component in the direction of wave propagation (usually the z-axis). This means that the electric field is purely transverse, i.e., it lies entirely in the xy-plane, perpendicular to the direction of wave propagation.
TE modes have non-zero magnetic field components in both the transverse and longitudinal directions. The magnetic field lines circulate around the direction of propagation.
The lowest-order TE mode is usually called TE10, and it has a single nodal plane in the xy-plane, with the electric field perpendicular to it.
TM Mode (Transverse Magnetic Mode):

In TM modes, there is no magnetic field component in the direction of wave propagation (usually the z-axis). This means that the magnetic field is purely transverse, i.e., it lies entirely in the xy-plane, perpendicular to the direction of wave propagation.
TM modes have non-zero electric field components in both the transverse and longitudinal directions. The electric field lines circulate around the direction of propagation.
The lowest-order TM mode is usually called TM11, and it has a single nodal plane in the xy-plane, with the magnetic field perpendicular to it.
In waveguide theory, TE and TM modes represent different possible field configurations that can exist within the waveguide. The specific mode(s) supported in a waveguide depend on the geometry of the waveguide and the operating frequency. Each mode has its own set of boundary conditions and dispersion characteristics, which affect how electromagnetic waves propagate within the waveguide.

In addition to TE and TM modes, there are also hybrid modes (e.g., TE-TM hybrid modes) that exhibit a combination of both electric and magnetic field components in various directions. Understanding these modes is essential for the design and analysis of waveguide-based devices such as antennas, microwave components, and optical waveguides.