1.2 ATOMIC ENERGY LEVELS AND SPONTANEOUS EMISSION 13 energy (103cm1) 30外 "blue band" 20 "green band" R levels” FIGURE 1.10 10 optical pumping Quantum-mechanical energy strong red fluorescence levels of the Cr3+ions in a ruby 694nm crystal. 11.6 GHz Optical Pumping of Atoms All of these minerals illustrate another basic method for pumping or excit- ing atoms into upper energy levels,that is,through the absorption of light at an appropriate pumping wavelength.The high-pressure mercury lamp used as the excitation source in a "mineral light"emits a broad continuum of visible and ultraviolet wavelengths.As shown in Figures 1.8 and 1.12,some of these wave- lengths will coincide with the transition frequencies from the lowest or ground levels of the chromium or terbium ions(nearly all the ions are located at ground level when in thermal equilibrium)up to some of the higher energy levels of these ions. These ions can thus absorb radiation ("absorb photons")from the UV light source at these particular frequencies,and as a result be lifted up to various of the upper levels.This excitation is enhanced by the fact that in solids the higher energy levels are often rather broad bands of levels.The absorption linewidths of the ruby and terbium absorption lines are thus relatively broad,permitting reasonably efficient absorption of the continuum radiation from the mercury lamp. Once they are lifted upward by this so-called "optical pumping,"the ions in each case then relax or fluoresce down to lower energy levels,as shown in Figure 1.12,emitting a relatively sharp fluorescence at two or three visible wavelengths as they drop from upper to lower levels. Spontaneous Energy Decay or Relaxation Let us discuss a little more the spontaneous decay or relaxation process we have introduced here.Suppose that a certain number N2 of such atoms have been pumped into some upper energy level E2 of an atom or molecule,whether
1.2 ATOMIC ENERGY LEVELS AND SPONTANEOUS EMISSION 15 30 nonradiative relaxation 20 visible-uv strong green excltatlon fluorescence -540nm 10 0 FIGURE 1.12 Optical pumping of the upper quantum-mechanical energy levels in the rare-earth ion terbium,Tb3+. The lifetime of the R levels in the ruby crystal happens to be long enough (about 4 msec),and the visible fluorescence strong enough,that we can rather easily demonstrate this kind of exponential decay by using the simple apparatus shown in Figure 1.15.The pulsed stroboscopic light source emits a broadband flash of visible and ultraviolet light about 60 usec long.This flash of light optically pumps the Cr3+ions in the ruby sample up to upper levels,from which they very rapidly decay to the metastable R levels.These levels then decay to the ground level by emitting visible red fluorescence with a decay timer4.3 msec. (Similar fluorescence lifetime measurements can also be made for any of the other materials we have mentioned,but some of the lifetimes are much shorter,and the fluorescent intensities much smaller,making the experiment more difficult.) Radiative and Nonradiative Relaxation There are actually two quite separate kinds of downward relaxation that occur in these solid-state materials,as well as in most other atomic systems. One mechanism is radiative relaxation,which is to say the spontaneous emission of electromagnetic or fluorescent radiation,as we have already discussed.We
16 CHAPTER 1:AN INTRODUCTION TO LASERS relaxation by fluorescence or nonradiative relaxation 2 0w89R excltation by electron impact or optlcal pumping FIGURE 1.13 3903092806882 28000 General concept of upper-level excitation by electron impact or optical pumping. atomic energy levels 88888838X can usually measure this emitted radiation directly,with some suitable kind of photodetector. The other mechanism is what is commonly called nonradiative relaxation. In terbium,for example,when the terbium ions relax from higher energy levels shown in Figure 1.12 down into the 5D4 level,they get rid of the transition en- ergy not by radiating electromagnetic radiation somewhere in the infrared,but by setting up mechanical vibrations of the surrounding crystal lattice.To put this in another way,the excess energy is emitted as lattice phonons,or as heat- ing of the surrounding crystal lattice,rather than as electromagnetic radiation or photons-hence the term nonradiative relaxation.This kind of nonradiative emission is usually difficult to measure directly,since it mostly goes into a very small warming up of the surrounding medium.This same kind of nonradiative relaxation process also allows excited ruby atoms to relax down into the2E levels. The total relaxation rate y on any given transition will thus be,in general,the sum of a radiative or fluorescent or electromagnetic part,described by a purely radiative decay rate that we often write as Yrad;plus a nonradiative part,with a nonradiative decay rate that we often write as Yar.The total or measured decay rate for atoms out of the upper level will then be the sum of these,or ot Yrad +Tnr.The actual numerical values for these rates,and the balance between radiative and nonradiative parts,will in general be different for every different atomic transition,and may depend greatly on the immediate surroundings of the atoms,as we will discuss in much more detail later.The one certain thing is that atoms placed in an upper level will decay downward,by some combination of radiative and/or nonradiative decay processes. Nonradiative relaxation can be a particularly rapid process for relaxation across some of the smaller energy gaps for rare-earth ions and other absorbing ions in solids,as we will see in more detail later.For example,in terbium as in many other rare-earth ions,there may be many rather closely spaced levels or bands at higher energies;but then the energy gap down from the lowest of these
1.2 ATOMIC ENERGY LEVELS AND SPONTANEOUS EMISSION 17 energy population Na E2 d=-Y22 d N2(t) N2o FIGURE 1.14 e2' Spontaneous energy decay rate. 专么1 料 upper levels (the D4 level in terbium)to the next lower group of levels may be larger than the frequency hw of the highest phonon mode that the crystal lattice can support. As a result,the terbium ion cannot relax across this gap very readily by nonradiative processes,i.e.,by emitting lattice phonons,since the lattice cannot accept or propagate phonons of this frequency.Instead the atoms relax across this gap almost entirely by radiative emission,i.e.,by spontaneous emission of visible fuorescence.Across other,smaller gaps,however,the nonradiative relax- ation rate is so fast that any radiative decay on these transitions is completely overshadowed by the nonradiative rate. This behavior is typical for many other rare-earth ions in crystals and glasses. Following optical excitation to high-lying levels,the atoms relax by rapid nonra- diative relaxation into some lower metastable level,from which further nonradia- tive relaxation is blocked by the size of the gap to the next lower level.Efficient fluorescent emission from here to the lower levels then occurs,followed by fur- ther fast nonradiative relaxation across any remaining energy gaps to the ground level.The nonradiative decay time of the atoms via phonon emission across the smaller energy gaps may be in the subnanosecond to picosecond range-too fast