Fundamentals of Materials Science and Engineering: An Integrated Approach, 3e

GTBL042-19 GTBL042-Callister-v2 September 17, 2007 17:39

Revised Pages

19.13 Lasers • 779

Energy

Electron

excitation

Excited state

Spontaneous decay

(nonradiative,

phonon emission)

Metastable state

Incident photon

(xenon lamp)

Spontaneous and

stimulated

emission

Laser photon

E

M

G

Ground state

(Cr3+)

Figure 19.14 Schematic

energy diagram for the ruby

laser, showing electron

excitation and decay paths.

by two different paths. Some fall back directly; associated photon emissions are not

part of the laser beam. Other electrons decay into a metastable intermediate state

(pathEM, Figure 19.14), where they may reside for up to 3 ms (milliseconds) before

spontaneous emission (pathMG). In terms of electronic processes, 3 ms is a relatively

long time, which means that a large number of these metastable states may become

occupied. This situation is indicated in Figure 19.15b.

The initial spontaneous photon emission by a few of these electrons is the stim-

ulus that triggers an avalanche of emissions from the remaining electrons in the

metastable state (Figure 19.15c). Of the photons directed parallel to the long axis of

the ruby rod, some are transmitted through the partially silvered end; others, inci-

dent to the totally silvered end, are reflected. Photons that are not emitted in this

axial direction are lost. The light beam repeatedly travels back and forth along the

rod length, and its intensity increases as more emissions are stimulated. Ultimately,

a high intensity, coherent, and highly collimated laser light beam of short duration

is transmitted through the partially silvered end of the rod (Figure 19.15e). This

monochromatic red beam has a wavelength of 0.6943μm.

Semiconducting materials such as gallium arsenide may also be used as lasers

that are employed in compact disk players and in the modern telecommunications

industry. One requirement of these semiconducting materials is that the wavelength

λassociated with the band gap energyEgmust correspond to visible light. That is,

from a modification of Equation 19.3, namely

λ=

hc

Eg

(19.20)

λmust lie between 0.4 and 0.7μm. A voltage applied to the material excites electrons

from the valence band, across the band gap, and into the conduction band; corre-

spondingly, holes are created in the valence band. This process is demonstrated in

Figure 19.16a, which shows the energy band scheme over some region of the semicon-

ducting material, along with several holes and excited electrons. Subsequently, a few

of these excited electrons and holes spontaneously recombine. For each recombina-

tion event, a photon of light having a wavelength given by Equation 19.20 is emitted