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The Science and Engineering of

Materials, 4

th

ed

Chapter 20 – Photonic Materials

Objectives of Chapter 20

• To present a summary of fundamental principles that

have guided applications of optical materials.

• To explore two avenues by which we can use the

optical properties of materials: emission of photons

from materials and interaction of photons with

materials.

• Light is energy, or radiation, in the form of waves or particles called photons that can be emitted from a material.
• The important characteristics of the photons—their energy E , wavelength λ , and frequency ν —are related by the equation

Section 20.

The Electromagnetic Spectrum

Figure 20.1 The electromagnetic spectrum of radiation; the bandgaps and cutoff frequencies for some optical materials are also shown. ( Source: From Optoelectronics: An Introduction to Materials and Devices, by J. Singh. Copyright © 1996 The McGraw-Hill Companies. Reprinted by permission of The McGraw-Hill Companies .)

• Index of refraction - Relates the change in velocity and direction of radiation as it passes through a transparent medium (also known as refractive index).
• Dispersion - Frequency dependence of the refractive index.
• Reflectivity - The percentage of incident radiation that is reflected.
• Linear absorption coefficient - Describes the ability of a material to absorb radiation.
• Photoconduction - Production of a voltage due to the stimulation of electrons into the conduction band by light radiation.

Section 20.

Refraction, Reflection, Absorption,

and Transmission

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

Figure 20.2 (a) Interaction of photons with a material. In addition to reflection, absorption, and transmission, the bream changes direction, or is refracted. The change in direction is given by the index of refraction n****. (b) The absorption index ( k ) as a function of wavelength.

Optical fibers are commonly made from high-purity silicate glasses. They consist of a core that has refractive index (~ 1.48) that is higher than a region called cladding (refractive index ~ 1.46). This is why even a simple glass fiber in air (refractive index 1.0) can serve as an optical fiber. In designing a fiber optic transmission system, we plan to introduce a beam of photons from a laser into a glass fiber whose index of refraction of is 1.5. Design a system to introduce the beam with a minimum of leakage of the beam from the fiber.

Example 20. Design of a Fiber Optic System

Figure 20.3 (b) Diagram a light beam in glass fiber for Example 20.1.

Example 20.1 SOLUTION

To prevent leakage of the beam, we need the total internal reflection and thus the angle θ t must be at least 90o. Suppose that the photons enter at a 60o^ angle to the axis of the fiber. From Figure 20.3(b), we find that θ i = 90 - 60 = 30o. If we let the glass be Material 1 and if the glass fiber is in air (n = 1.0), then

Because θ t is less than 90o, photons escape from the fiber. To prevent transmission, we must introduce the photons at a shallower angle, giving θ t = 90o.

Example 20. Light Transmission in Polyethylene Suppose a beam of photons in a vacuum strikes a sheet of polyethylene at an angle of 10o^ to the normal of the surface of the polymer. Calculate the index of refraction of polyethylene and find the angle between the incident beam and the beam as it passes through the polymer. Example 20.2 SOLUTION The index of refraction is related to the high-frequency dielectric constant. For this material the high-frequency

dielectric constant k = 2.3:

The angle θ t is:

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learninglicense. ™ is a trademark used herein under

Figure 20.4 The linear absorption coefficient relative to wavelength for several metals. Note the sudden decrease in the absorption coefficient for wavelengths greater than the absorption edge.

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning

is a trademark used herein under license.™

Figure 20. Relationships between absorption and the energy gap: (a) metals, (b) Dielectrics and intrinsic semiconductors, and (c) extrinsic semiconductors.

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning

is a trademark used herein under license.™

Figure 20.7 (a) Photoconduction in semiconductors involves the absorption of a stimulus by exciting electrons from the valence band to the conduction band. Rather than dropping back to the valence band to cause emission, the excited electrons carry a charge through an electrical circuit. (b) A solar cell takes advantage of this effect.

Determine the critical energy gaps that provide complete transmission and complete absorption of photons in the visible spectrum.

Example 20.3 SOLUTION

The visible light spectrum varies from 4  10 -5^ cm to 7  10 - cm. The minimum Eg required to assure that no photons in the visible spectrum are absorbed is:

Example 20. Determining Critical Energy Gaps

Example 20.3 SOLUTION (Continued)

The maximum Eg below which all of the photons in the visible spectrum are absorbed is:

For materials with an intermediate Eg , a portion of the photons in the visible spectrum will be absorbed.