# Chapter 8 Wave Reflection and Transmission

# Chapter Contents

1. EM Waves at Boundaries

2. 8.1 Wave Reflection and Transmission at Normal Incidence

3. TB 15 Lasers

4. 8.2 Snell’s Laws

5. 8.3 Fiber Optics

6. 8.4 Wave Reflection and Transmission at Oblique Incidence

7. TB 16 Bar-Code Readers

8. 8.5 Reflectivity and Transmissivity

9. 8.6 Waveguides

10. 8.7 General Relations for E and H

11. 8.8 TM Modes in Rectangular Waveguide

12. 8.9 TE Modes in Rectangular Waveguide

13. 8.10 Propagation Velocities

14. 8.11 Cavity Resonators

1. Chapter 8 Summary

2. Problems

# Objectives

Upon learning the material presented in this chapter, you should be able to:

1. Characterize the reflection and transmission behavior of plane waves incident upon plane boundaries for both normal and oblique incidence.

2. Calculate the transmission properties of optical fibers.

3. Characterize wave propagation in a rectangular waveguide.

4. Determine the behavior of resonant modes inside a rectangular cavity.

# EM Waves at Boundaries

Figure 8-1 depicts the propagation path traveled by a signal transmitted by a shipboard antenna and received by an antenna on a submerged submarine. Starting from the transmitter (denoted Tx in Fig. 8-1), the signal travels along a transmission line to the transmitting antenna. The relationship between the transmitter (generator) output power, P t, and the power supplied to the antenna is governed by the transmission-line equations of Chapter 2. If the transmission line is approximately lossless and properly matched to the transmitting antenna, then all of P t is delivered to the antenna. If the antenna itself is lossless too, it will convert all of the power P t in the guided wave provided by the transmission line into a spherical wave radiated outward into space. The radiation process is the subject of Chapter 9. From point 1, denoting the location of the shipboard antenna, to point 2, denoting the point of incidence of the wave onto the water’s surface, the signal’s behavior is governed by the equations characterizing wave propagation in lossless media, which was covered in Chapter 7. As the wave impinges upon the air–water boundary, part of it is reflected by the surface while another part gets transmitted across the boundary into the water. The transmitted wave is refracted, wherein its propagation direction moves closer toward the vertical, compared with that of the direction of the incident wave. Reflection and transmission processes are treated in this chapter. Wave travel from point 3, representing a point just below the water surface, to point 4, which denotes the location of the submarine antenna, is subject to the laws of wave propagation in lossy media, which also was treated in Chapter 7. Finally, some of the power carried by the wave traveling in water towards the submarine is intercepted by the receiving antenna. The received power, P r, is then delivered to the receiver via a transmission line. The receiving properties of antennas are covered in Chapter 9. In summary, each wave-related aspect of the transmission process depicted in Fig. 8-1 is treated in this book, starting with the transmitter and ending with the receiver.

# Figure 8-1 Signal path between a shipboard transmitter (Tx) and a submarine receiver (Rx).

Figure 8 1 Full Alternative Text

This chapter begins by examining the reflection and transmission properties of plane waves incident upon planar boundaries and concludes with sections on waveguides and cavity resonators. Applications discussed along the way include fiber and laser optics.