Plane wave reflection and transmission

Reflection of uniform plane waves at normal incidence

Boundary conditions (at the interface, z =0)

Reflection from perfect electric conductor (at the interface, z =0)

Example

Wave reflection from multiple interfaces

Example : radome Reflection Transmission

Example : anti-reflection coating Calculate the refractive index and minimum thickness for the glass coating to provide total transmission from air to the glass at a free space wavelength of 570nm. refractive index of the glass is n3=1.45. (n: refractive index)

Plane wave refraction at oblique incidence angles

Plane of incidence

If an EM wave approaches a surface obliquely, it is easier to decompose the field into two components, s-polarization and p-polarization. s-polarization (perpendicular) p-polarization (parallel)

p-polarization (E-field parallel to the plane of incidence)

E-field tangential component continuity

phase matching condition (Snell’s law)

H-field tangential component continuity

Reflection coefficient for parallel polarization

Reflection coefficient for perpendicular polarization (s)

Example

Total reflection

Optical fiber

Wave propagation TV antenna TV signal transmitting antenna TV signals are transmitted as EM wave with horizontal polarization.

Polarization of EM waves Source current Source current

Reflection from ionosphere

Reflection from ground and troposphere EM waves undergo reflections and diffractions while propagating toward receivers.

2-Ray Ground Reflection For d>> hr, ht, low angle of incidence allows the earth to act as a reflector the reflected signal is 180 out of phase Pr  1/d4 R T ht hr Phase shift! d