# 5: Wave Reflection and Transmission

• 5.1: Plane Waves at Normal Incidence on a Planar Boundary
When a plane wave encounters a discontinuity in media, reflection from the discontinuity and transmission into the second medium is possible. In this section, we consider the scenario of a uniform plane wave which is normally incident on the planar boundary between two semi-infinite material regions. By “normally-incident” we mean the direction of propagation is perpendicular to the to the boundary.
• 5.2: Plane Waves at Normal Incidence on a Material Slab
In this section, we consider the problem of a uniform plane wave normally incident on a “slab” sandwiched between two semi-infinite media. This scenario arises in many practical engineering problems, including the design and analysis of filters and impedance-matching devices at RF and optical frequencies, the analysis of RF propagation through walls, and the design and analysis of radomes.
• 5.3: Total Transmission Through a Slab
The “single-slab” problem is comprised of three material regions: A semi-infinite Region 1, from which a uniform plane wave is normally incident; Region 2, the slab, defined by parallel planar boundaries; and a semi-infinite Region 3, through which the plane wave exits. This section focus on a particular class of applications involving this structure that involve total transmission through the slab. i.e., 100% of power incident on the slab is transmitted through the slab.
• 5.4: Propagation of a Uniform Plane Wave in an Arbitrary Direction
The ray-fixed representation accommodates all possible combinations of direction of propagation and reference polarization.
• 5.5: Decomposition of a Wave into TE and TM Components
A broad range of problems in electromagnetics involve scattering of a plane wave by a planar boundary between dissimilar media. For the general case in which the incident wave is obliquely incident, the directions of the field vectors will generally be different and we take the effort to represent the incident wave as the sum of two waves having particular polarizations. These polarizations are referred to as transverse electric and transverse magnetic.
• 5.6: Plane Waves at Oblique Incidence on a Planar Boundary- TE Case
In this section, we consider the problem of reflection and transmission from a planar boundary between semi-infinite media for a transverse electric (TE) uniform plane wave.
• 5.7: Plane Waves at Oblique Incidence on a Planar Boundary- TM Case
In this section, we consider the problem of reflection and transmission from a planar boundary between semi-infinite media for a transverse magnetic (TM) uniform plane wave.
• 5.8: Angles of Reflection and Refraction
Phase matching is essentially a boundary condition that enforces continuity of the phase of the electric and magnetic fields across the boundary. Since the same requirement emerges independently in the TE and TM cases, and since any plane wave may be decomposed into TE and TM components, the requirement must apply to any incident plane wave regardless of polarization.
• 5.9: TE Reflection in Non-magnetic Media
Many materials of practical interest are non-magnetic; that is, they have permeability that is not significantly different from the permeability of free space. In this section, we consider the behavior of the reflection coefficient for this class of materials.
• 5.10: TM Reflection in Non-magnetic Media
Many materials of practical interest are non-magnetic; that is, they have permeability that is not significantly different from the permeability of free space. In this section, we consider the behavior of the reflection coefficient for this class of materials.
• 5.11: Total Internal Reflection
Total internal reflection refers to a particular condition resulting in the complete reflection of a wave at the boundary between two media, with no power transmitted into the second region. One way to achieve complete reflection with zero transmission is simply to require the second material to be a perfect conductor. However, total internal reflection is a distinct phenomenon in which neither of the two media are perfect conductors.
• 5.12: Evanescent Waves
When total internal reflection occurs, the transmitted field is an evanescent wave; i.e., a surface wave which conveys no power and whose magnitude decays exponentially with increasing distance into the next region.

Thumbnail: Sinusoidal traveling plane wave entering a region of lower wave velocity at an angle, illustrating the decrease in wavelength and change of direction (refraction) that results. (CC BY-SA 3.0 Unported; Richard F. Lyon via Wikipedia)