Chapter 8
Reflection and Transmission
of Electromagnetic Waves in Dielectric
Media
In Chap. 7, we considered the propagation of electromagnetic waves in an infinite
uniform dielectric medium. In this chapter, we think of a situation where two
(or more) dielectrics are in contact with each other at a plane interface. When two
dielectric media adjoin each other with an interface, propagating electromagnetic
waves are partly reflected by the interface and partly transmitted beyond the interface. We deal with these phenomena in terms of characteristic impedance of the
dielectric media. In the case of an oblique incidence of a wave, we categorize it into a
transverse electric (TE) wave and transverse magnetic (TM) wave. If a thin plate of a
dielectric is sandwiched by a couple of metal sheets, the electromagnetic wave is
confined within the dielectric. In this case, the propagating mode of the wave differs
from that of a wave propagating in a free space (i.e., a space filled by a threedimensionally infinite dielectric medium). If a thin plate of a dielectric having a large
refractive index is sandwiched by a couple of dielectrics with a smaller refractive
index, the electromagnetic wave is also confined within the dielectric with a larger
index. In this case, we have to take account of the total reflection that causes a phase
change upon the reflection. We deal with such specific modes of the electromagnetic
wave propagation. These phenomena are treated both from a basic aspect and from a
point of view of device application. The relevant devices are called waveguides in
optics.
8.1 Electromagnetic Fields at an Interface
We start with examining a condition of an electromagnetic field at the plane
interface. Suppose that two semi-infinite dielectric media D1 and D2 are in contact
with each other at a plane interface. Let us take a small rectangle S that strides the
interface (see Fig. 8.1). Taking a surface integral of both sides of (7.28) over the
strip, we have
© Springer Nature Singapore Pte Ltd. 2020
S. Hotta, Mathematical Physical Chemistry,
https://doi.org/10.1007/978-981-15-2225-3_8
295
Reflection and Transmission
of Electromagnetic Waves in Dielectric
Media
In Chap. 7, we considered the propagation of electromagnetic waves in an infinite
uniform dielectric medium. In this chapter, we think of a situation where two
(or more) dielectrics are in contact with each other at a plane interface. When two
dielectric media adjoin each other with an interface, propagating electromagnetic
waves are partly reflected by the interface and partly transmitted beyond the interface. We deal with these phenomena in terms of characteristic impedance of the
dielectric media. In the case of an oblique incidence of a wave, we categorize it into a
transverse electric (TE) wave and transverse magnetic (TM) wave. If a thin plate of a
dielectric is sandwiched by a couple of metal sheets, the electromagnetic wave is
confined within the dielectric. In this case, the propagating mode of the wave differs
from that of a wave propagating in a free space (i.e., a space filled by a threedimensionally infinite dielectric medium). If a thin plate of a dielectric having a large
refractive index is sandwiched by a couple of dielectrics with a smaller refractive
index, the electromagnetic wave is also confined within the dielectric with a larger
index. In this case, we have to take account of the total reflection that causes a phase
change upon the reflection. We deal with such specific modes of the electromagnetic
wave propagation. These phenomena are treated both from a basic aspect and from a
point of view of device application. The relevant devices are called waveguides in
optics.
8.1 Electromagnetic Fields at an Interface
We start with examining a condition of an electromagnetic field at the plane
interface. Suppose that two semi-infinite dielectric media D1 and D2 are in contact
with each other at a plane interface. Let us take a small rectangle S that strides the
interface (see Fig. 8.1). Taking a surface integral of both sides of (7.28) over the
strip, we have
© Springer Nature Singapore Pte Ltd. 2020
S. Hotta, Mathematical Physical Chemistry,
https://doi.org/10.1007/978-981-15-2225-3_8
295