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Guided wave propagation in a rectangular waveguide refers to the controlled transmission of electromagnetic waves along a confined path defined by conducting walls. A rectangular waveguide consists of a hollow metallic structure with cross-sectional dimensions (a) (width) and (b) (height), where (a > b), and the wave propagates primarily along the longitudinal axis, usually designated as the (z)-axis. The metallic boundaries impose boundary conditions on the electric and magnetic fields, restricting the modes that can exist in the waveguide and determining their propagation characteristics. Unlike free-space propagation, guided waves in a waveguide do not exist at all frequencies; only specific modes above a certain frequency, called the cut-off frequency, can propagate without attenuation. These modes are classified as Transverse Electric (TE) and Transverse Magnetic (TM) modes, where in TE modes the electric field has no longitudinal component ((E_z = _____ _______ _________ ______ _________ ____ ______.
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