8 CHAPTER 1:AN INTRODUCTION TO LASERS. The Discovery of Helium Helium was first identified as a new element by its fluorescence spectrum in the solar corona.During the solar eclipse of 1868 a bright yellow line was observed in the emission spectrum of the Sun's prominences by at least six different observers.This line could be explained in relation to the known spectral lines of already identified elements only by postulating the existence of a new element,helium,named after the Greek word Helios, the Sun.This same element was later,of course.identified and isolated on Earth Quantum Energy Levels Figure 1.7 shows the rather complex set of quantum energy levels possessed by even so simple an atom as the He atom.The solid arrows in this diagram designate some of the spontaneous-emission transitions that are responsible for the stronger lines in the visible spectrum of helium.The dashed arrows indicate a few of the many additional transitions that produce spontaneous emission at longer or shorter wavelengths in the infrared or ultraviolet portions of the spectrum,lines which we can "see"only with the aid of suitable instruments. Every atom in the periodic table,as well as every molecule or ion,has its own similar characteristic set of quantum energy levels,and its own characteristic spectrum of fluorescent emission lines,just as does the helium atom.Understand- ing and explaining the exact values of these quantum energy levels for different atoms and molecules,through experiment or through complex quantum analy- ses,is the task of the spectroscopist.The complex labels given to each energy level in Figure 1.7 are part of the working jargon of the spectroscopist or atomic physicist.In this text we will not be concerned with predicting the quantum energy levels of laser atoms,or even with understanding their complex labeling schemes,except in a few simple cases.Rather,we will accept the positions and properties of these levels as part of the data given us by spectroscopists,and will concentrate on understanding the dynamics and the interactions through which laser action is obtained on these transitions. Planck's Law The relationship between the frequency w2 emitted on any of these tran- sitions and the energies E2 and E of the upper and lower atomic levels is given by Planck's Law 1=B-马 (1) h where h=h/2m,and Planck's constant h=6.626 x 10-34 Joule-second. In this text,as in real life,optical and infrared radiation will sometimes be characterized by its frequency w,and sometimes by its wavelength Ao expressed in units such as Angstroms (A),nanometers (nm),or microns (um).Quantum transitions and the associated transition frequencies are also very often charac- terized by their transition energy or photon energy,measured in units of electron volts(eV),or their inverse wavelength 1/Ao measured in units of "wavenumbers
1.2 ATOMIC ENERGY LEVELS AND SPONTANEOUS EMISSION 9 200 Su Helium ion:Is 6So 6D: 6 Pa.1.0 195 D.: 55 65 5'P 5'D 5'F 55 5P1. 5Da.3. 5E13 D. E 4P,0 D32.1 4Faa 190 Weak green-blue 1 Strong violet 4922A Weak violet 4471A 3'P1 3D生 4713A 3 .0 D31 185 3 Strong red 180 6678A Very strong yellow Weak 5876A far red 7065A 173 170 20,582A=2.064 2P10 2S6 3883A 165 /10,829A=1.084 i584A 160 2 Helium atom:Is nl 155 Energy levels:L Singlets Triplets 06 1'S Ground energy level FIGURE 1.7 An energy-level diagram for the helium atom,showing the transitions responsible for the strong visible spectrum,as well as various ultraviolet and infrared transitions. or cm-1.Since we will be jumping back and forth between these units,it will be worthwhile to gain some familiarity with their magnitudes.Some useful rules of
10 CHAPTER 1:AN INTRODUCTION TO LASERS thumb to remember are that 14m(“one micron”)≡1,000nm三10000A (2) and that,in suitable energy units, 1.24 [transition energy E2-Ei in ev] wavelength Ao in microns (3) Hence 10000A or 1 um matches up with 10,000 cm-1or ~1.24 eV.A visible wavelength of 500 nm or 5000A or 0.5 um thus corresponds to a photon energy of 20,000 cm-1 or ~2.5 eV.Note that this also corresponds to a transition frequency of w21/2m=6 x 1014 Hz,expressed in the conventional units of cycles per second,or Hertz. Energy Levels in Solids:Ruby or Pink Sapphire As another simple illustration of energy levels,try shining a small ultravio- let lamp (sometimes called a "mineral light")on any kind of fuorescent mineral, such as a piece of pink ruby or a sample of glass doped with a rare-earth ion, or on a fluorescent dye such as Rhodamine 6G.These and many other materials will then glow or fluoresce brightly at certain discrete wavelengths under such ul- traviolet excitation.A sample of ruby,for example,will fluoresce very efficiently atA694 nm in the deep red,a sample of crystal or glass doped with,say,the rare-earth ion terbium,Tb3+,will fuoresce at540 nm(bright green),and a liquid sample of Rhodamine 6G dye will fluoresce bright orange. Since ruby was the very first laser material,and is still a useful and instructive laser system,let us examine its fluorescence in more detail.Figure 1.8 shows a more sophisticated version of such an experiment,in which a scanning monochro- mator plus an optical detector are used to examine the ruby fluorescent emission in more detail.The lower trace shows the two very sharp (for a solid)and very closely spaced deep-red emission lines that will be observed from a good-quality ruby sample cooled to liquid-helium temperature.(At higher temperatures these lines will broaden and merge into what appears to be a single emission line.) Figure 1.9 shows the crystal structure of ruby.Ruby consists essentially of lightly doped sapphire,Al2O3,with the darker spheres in the figure indicating the Al3+ions.(The lattice planes shown in the figure are ~2.16A apart.)Sap- phire is a very hard,colorless (when pure),transparent crystal which can be grown in large and optically very good samples by fame-fusion techniques.The transparency of pure sapphire in the visible and infrared means that its Al3+ and O2-atoms,when they are bound into the sapphire crystal lattice,have no absorption lines from their ground energy levels to levels anywhere in the in- frared or visible regions.Indeed,no optical absorption appears in pure sapphire below the insulating band gap of the crystal in the ultraviolet. We can,however,replace a significant fraction(several percent)of the Al3+ ions in the lattice by chromium or Cr3+ions.The sapphire lattice as a result acquires a pink tint at low chromium concentrations,or a deeper red color at higher concentrations,and becomes what is called "pink ruby."The individual chromium ions,when they are bound into the sapphire lattice,have a set of quantum energy levels that are associated with partially filled inner electron shells in the Cr3+ion.These energy levels are located as shown in Figure 1.10
1.2 ATOMIC ENERGY LEVELS AND SPONTANEOUS EMISSION 11 Exciting radiation Ruby sample Fluorescent -30 GHz emission Ruby R lines 6934 A Scanning optical 52 Optical 53 54 5453 501 Frequency FIGURE 1.8 Fluorescent emission from a ruby crystal.The numbers under the spectrum indicate the slightly shifted transition frequencies corresponding to different isotopes of chromium. The chromium ions can then absorb incident light in broad wavelength bands extending across much of the visible and near ultraviolet,by making transitions upward from the ground or A2 Crs+energy level to the series of broad bands or groups of levels labeled 4F and 2F in Figure 1.10.The chromium ions that are excited up into these levels then drop down by rapid nonradiative processes (which we will discuss shortly)to the two sharp 2E levels shown in the figure. From there,these ions relax across the remaining energy gap down to the ground state by almost totally radiative relaxation,emitting the deep-red fluorescent emission characteristic of ruby.(The two sharp 2E levels are often called the R and R2 levels,with most of the fluorescent emission coming from the lower or R level.The two very sharp emission lines shown in Figure 1.10 then represent the separate transitions from the R level down to the two closely spaced sublevels of the 4A2 ground level.) Synthetic Sources of Pink Ruby Sapphire,or rather pink ruby,was first grown in large amounts for use as jewels in the Swiss watch industry (it is said the pink color was added to make the tiny jewels easier to see and handle).Note that the energy levels of the Cr ion in ruby are very strongly shifted by Stark effects associated with the bonding of the Cr ion to the surrounding lattice ions.Hence these levels are very different from what would be the energy levels of an isolated Cr3+ion in free space.Many other colors of sapphire can also be created by adding other impurities,such as Fe,Mn,or Co,but only chromium-doped sapphire makes a good laser material
12 CHAPTER 1:AN INTRODUCTION TO LASERS C axis [1010] 2 6 1.44 1.661 FIGURE 1.9 Sapphire crystal lattice. Energy Levels in Solids:Rare Earth lons Figures 1.11 and 1.12 show how a typical rare-earth ion such as Nd3+or Tb3+can be bonded into an irregular glassy lattice structure,together with the quantum energy levels associated with a trivalent terbium Tb3+ion when such an ion is dispersed at low concentration,either in a glass or in a crystal structure (for example,.CaF2）. Note that the energy levels of rare-earth ions such as Tb3+or Nd3+are associated with the electrons in the partially filled 4f inner shell of the rare-earth atom.In nearly all solid materials,these inner electrons are well shielded,by surrounding outer filled electron shells,from the crystalline Stark effects caused by the bonds to surrounding atoms in the crystal or glass material.Hence the quantum energy levels of such rare-earth ions are almost unchanged in many different crystalline or glass host materials. Almost any material containing small amounts of Tb3+,for example,will fluoresce with the same brilliant green color around 540 nm,and materials con- taining Nd3+all fluoresce strongly around 1.06 um in the near infrared.There are also several other such rare-earth ions,including Dy2+,Tm2+,Ho3+,Eu3+, and Er3+,that make good to excellent laser materials