18 CHAPTER 1:AN INTRODUCTION TO LASERS 6943A Fluorescence optical hlter Photo detector Ruby crystal Stroboscopic light source Sweep trigger Oscilloscope FIGURE 1.15 Measurement of ruby fluorescent lifetime. to be easily measured-and the average lifetime of the same rare-earth ions in their metastable levels,before they radiate away their energy and drop down,is typically between a few hundred usec and a few msec. We will see later that in many rare-earth samples it is possible,by pumping hard enough,to actually build up enough of a population inversion between the metastable level and lower levels to permit laser action on these transitions. Several different rare-earth atoms can thus be used as good optically pumped solid-state lasers (though terbium itself is not among the best of these). REFERENCES Brief but useful introductions to the whole range of spectroscopy,on many different kinds of atomic systems,in widely different frequency ranges and using widely different experimental techniques,can be found in D.H.Whiffen,Spectroscopy (John Wiley, 1966),or in Oliver Howarth,Theory of Spectroscopy(Halsted Press,John Wiley,1973). There exist innumerable books on the theory and practice of atomic and molecular spectroscopy,of which two recent examples are H.G.Kuhn,Atomic Spectra(Academic Press,1969),and J.I.Steinfeld,Molecules and Radiation:An Introduction to Modern Molecular Spectroscopy (Harper and Row,1974). For tables of detailed data on energy levels of isolated atoms,the standard reference sources are the National Bureau of Standards Tables of Atomic Energy Levels,edited by Charlotte E.Moore (U.S.Government Printing Office,1971). 1.3 STIMULATED ATOMIC TRANSITIONS Having introduced spontaneous(downward)transitions,we will now look at the stimulated (upward and downward)transitions that are the essential processes in all kinds of laser and maser action
1.3 STIMULATED ATOMIC TRANSITIONS 19 absorption sample detector collimating mirrors grating broadband light source FIGURE 1.16 An elementary grating spectrometer. Atomic Absorption Lines Suppose we now examine more carefully the absorption of radiation by a collection of atoms as a function of the wavelength of the incident radiation. Figure 1.16 shows a very elementary example of a grating spectrometer such as might be used for such measurements.(A tunable laser would be a very useful alternative,if one were conveniently available.) In this spectrometer the radiation from a broadband continuum light source is collected into a roughly parallel beam by a collimating mirror,and is then reflected from a diffraction grating located on a rotatable mount.At any one orientation of the grating,only one wavelength(rather,a finite but narrow band of wavelengths)is reflected at the correct angle to be collected by another curved mirror,focused down through a narrow slit,and passed through the experimen- tal sample onto a detector.By rotating the grating,we can tune the wavelength of the radiation that passes through the sample and thereby measure the trans- mission through the sample as a function of frequency or wavelength.(Figure 1.17 shows a more compact in-line version of such an instrument.) The result of such an experiment will often appear as shown schematically in Figure 1.18.The atomic sample will have absorption transitions from the lowest energy level to higher energy levels;so it will exhibit discrete absorption lines- that is,narrow bands of frequency in which the sample exhibits more or less strong absorption-at exactly those wavelengths.These wavelengths will corre- spond through Planck's law to the energy gaps between the lowest and higher levels.If there happen to be some atoms already located in higher-lying levels, then absorption lines from those levels to still higher levels may also be seen,as illustrated by transition C in the figure.These excited-state absorptions,how-
20 CHAPTER 1:AN INTRODUCTION TO LASERS collimating mirror FIGURE 1.17 A compact in-line grating monochromator. grating transmitted energy optical frequency FIGURE 1.18 Absorption transitions (top)and absorption lines (bottom). ever,will usually appear substantially weaker,simply because there will normally be many fewer atoms in the higher energy levels. As a specific illustration of atomic absorption,Figure 1.19 shows some of the sharp absorption lines observed when radiation at wavelengths around 540 nm in the visible is transmitted through a crystal of lanthanum fluoride (LaF2)
1.3 STIMULATED ATOMIC TRANSITIONS 21 Er+in LaFs 5340 5360 5380 5400 5420 5440 Wavelength,A 1,high-pressure Hg-lamp spectrum 品 个 GdP+in SrF: % Total instrumental width,50u 3060 3055 3050 9045 Wavelength,A FIGURE 1.19 Light transmission versus wavelength through crystals of lanthanum fluoride (LaF2)con- taining a small amount of the rare-earth ion erbium E(upper trace),and strontium fluoride(SrF2)containing a small amount of the rare-earth ion gadolinium Gd3+(lower trace). containing a small percentage of the rare-earth ion erbium,or when radiation at wavelengths around 300 nm in the near ultraviolet is transmitted through a crystal of strontium Aluoride(SrF2)containing a small percentage of the rare- earth ion gadolinium.These absorption lines all represent different transitions from the lowest or ground levels of the Er3+or Gd3+ions to higher-lying levels, exactly analogous to the terbium levels shown in Figure 1.13.Of course,if a pure lanthanum or strontium Auoride crystal is grown without any erbium or gadolinium present,no such absorption lines are observed
22 CHAPTER 1:AN INTRODUCTION TO LASERS Absorption Lines in Gases,and Molecular Spectroscopy Absorption experiments of this sort are,of course,by no means limited to solids or to rare earths.Isolated atoms or ions in gases will exhibit such absorption lines in the visible,and especially the UV.Molecules in gases,liquids, and solids will exhibit an extremely rich spectrum of absorption lines,notably in the infrared as well as in the visible and ultraviolet.The absorption lines of atoms and molecules in gases are typically sharper or narrower than those in solids or liquids,since the energy levels in gases are not subject to some of the perturbing influences that tend to broaden,or smear out the energy levels in liquids or solids. As just one more example to illustrate absorption spectroscopy,Figure 1.20 shows a few of the sharp absorption lines characteristic of the formaldehyde molecule H2CO in a narrow range of wavelengths near 3.57 um.This particular spectrum was taken by using a continuously tunable laser source (a cw injec- tion diode laser using a lead/cadmium sulfide diode)rather than an incoherent spectrometer.The dashed envelope in Figure 1.20(a)is the power output of the tunable laser versus wavelength,over a tuning range that is extremely large in absolute terms (~3x 1010 Hz),yet extremely narrow (~0.04%)relative to the center frequency.The solid line is the power transmitted through the vapor-filled cell. Many different molecules exhibit exactly such characteristic sharp lines,spe- cific to the individual molecules,in rich profusion through the near and middle infrared regions.These sharp lines are extremely useful not only as potential laser lines,but as characteristic signatures of different molecules,for use in chemical diagnostics or in identifying the presence of specific pollutant molecules or haz- ardous chemicals.Note that the sensitivity and the laser scanning rate in the experiment allow a small portion of the formaldehyde absorption spectrum to be displayed on an oscilloscope in real time. Emission spectroscopy,using the spontaneous emission lines radiated from an excited sample as in Figure 1.5,is thus one way of observing and learning about the discrete transitions and the quantum'energy levels of atoms,ions, and molecules.Absorption spectroscopy,as briefly described here,is another and complementary method of obtaining the same kind of information.These methods are in fact complementary in their utility,since emission spectroscopy tends to give information about downward transitions emanating from high-lying levels,whereas absorption spectroscopy tends to give information about upward transitions from the ground level or low-lying atomic levels.The formaldehyde example illustrates the possibilities for applying tunable lasers to spectroscopy, to analytical chemistry,and to practical applications such as pollution detection. Stimulated versus Spontaneous Atomic Transitions We have now seen that there are two basically different kinds of transition processes that can occur in atoms or molecules. First,there are spontaneous emission or relaxation transitions,in which atoms spontaneously drop from an upper to a lower level while emitting electro- magnetic and/or acoustic radiation at the transition frequency.Fluorescence,en- ergy decay,and energy relaxation are other names for this process.When atoms emit this kind of fluorescence or spontaneous electromagnetic radiation,each in- dividual atom acts almost exactly like a small randomly oscillating antenna-in