Classical Electrodynamics

Chapter 8

Waveguides, Resonant Cavities,

and Optical Fibers

Contents

§8.1 Fields at the Surface of and Within a Conductor

§8.2Metallic Cavities and Waveguides

A. The definition of and in terms of and

B. of TM mode, TE mode and in the

C.

Contents

§8.3 Energy Flow and Attenuation in Waveguides

A.

B. The field energy per unit time

C. 、 、

D. Attenuation；

§8.4 Multimode Propagation in Optical Fibers

A. 、 、

C.

D. 、 、 、

Contents

§8.5 Modes in Dielectrics Waveguides

A. Find

B. in geometrical optics

C. Find by Helmholtz equation

§8.1 Fields at the Surface of and Within a Conductor

From the boundary conditions we see that just outside the surface of a perfect

conductor only normal E and tangential H fields can exist, and that the fields drop

abruptly to zero inside the perfect conductor.

The fields in the neighborhood of the surface of a good, but not perfect, conductor

must behave approximately the same as for a perfect conductor. In Section 5.18 we

saw that inside a conductor the fields are attenuated exponentially in a characteristic

length δ, called the skin depth.

The existence of a small tangential component of E outside the surface, in addition to

the normal E and tangential H, means that there is a power flow into the conductor.

The time-averaged power absorbed per unit area is power loss

：

Let

：

For conductor ( ) :

inserted into

For a not perfect conductor :

§8.2Metallic Cavities and Waveguides

A. The definition of and in terms of and

：

：

Let

：

Let

From (b), (c) :

Transverse components :

From (e) :

B. of TM mode, TE mode and in the

For TM mode ( ):

For TE mode ( ):

For ( ):

C.

Rectangular waveguide :

§8.3 Energy Flow and Attenuation in Waveguides

A.

For TM mode ( ):

For TE mode ( ):

B. The field energy per unit time:

C. 、 、

There will be a spectrum of eigenvalues and corresponding solutions ,

D. Attenuation； :

：

For TM mode ( ):

For TE mode ( ):

:

、

§8.4 Multimode Propagation in Optical Fibers

A. 、 、

C.

※

D. 、 、 、

2D :

For :

Physical and optical path lengths along a ray from A to B

§8.5 Modes in Dielectrics Waveguides

A. Find

s wave (TE mode):

p wave (TM mode):

B.

C.

TE mode: only

General solution:

B.C.

B.C.