Basics Of Spectroscopy Dec 2006 - SPIE

Figure 1-2 The basic operation of a simple prism spectrometer. In other optical instruments fordisplaying or recording spectra, the prism is replaced by a diffraction grating or interferometer.(Adapted from Physical Science, Robert Dixon, 1979)A Brief History of SpectroscopyBefore we begin a review of electromagnetic spectra, photons, and the process of lightabsorption and emission in matter, let us outline briefly the development of spectroscopy as ascience of detection in modern technologies.In ancient times, Egyptians and Greeks thought about light and color and considered light to bemostly “something” that emanated from the eyes. The great minds of Ptolemy, Plato, andAristotle failed to perceive of possible applications that might involve light as we know it.Following the Middle Ages (400–1350 AD) and the Renaissance period (1350–1700 AD),ancient, classical ways of thinking gave way to more creative, academic analyses and crudeoptical instruments began to appear. Scientists like Johann Kepler, Willebrord Snell, andGalileo Galilei used combinations of lenses in telescopes to see distant objects. And Sir IsaacNewton, in the latter half of the 17th century, showed how a prism “broke” white light passingthrough it into a rainbow of separate and distinct colors.All through these years, the best scientific minds puzzled over the question “what is light?” Thecorpuscular or particle theory of light was championed by Isaac Newton and seemed securelyentrenched in the mid-1700s. Later, the work of Christiaan Huygens, Thomas Young, andAugustin Fresnel lent considerable support to the wave theory of light. So the battle between“light as particle” and “light as wave” continued on into the 20th century with intellectual giantssuch as James Clerk Maxwell and Albert Einstein providing significant evidence for one or theother model.In the midst of all the theoretical turbulence on the nature of light, the science of spectroscopywas nevertheless taking shape. In 1802 a physicist named W. H. Wolleston used a prism, lenses,and a narrow beam of light to produce an image of a single wavelength of the light. Followingthis work, with the help of a different light dispersing element—a diffraction grating—scientistsproduced similar monochromatic images of “split light.”The spectroscope as an instrument, like that sketched in Figure 1-2, became a practicallaboratory instrument in the hands of German physicists such as Josef Fraunhofer, G. R.Kirchoff, and Robert Bunsen, during the first half of the 1800s. With Fraunhofer’s study of solar4Optics and Photonics Series, Spectroscopy

energy and the discovery of narrow dark lines in the solar spectrum, and with the ongoinganalysis of light sources based on flames produced with Bunsen burners, there appeared brightlines as well as dark lines, and the science of spectroscopy was launched.Scientists understood then that the dark and bright lines seen in absorption and emission wereuniquely characteristic of the internal makeup of chemical elements. They assumed, correctly,that the energy in light could somehow excite the internal motions of atoms and molecules,extracting energy from the light at certain wavelengths, thereby giving rise to the narrowabsorption lines. Similarly, heat or electrical energy could excite internal motions in matterwhich would then radiate away the absorbed energy as light, accounting for the bright oremission lines in the spectra. In every instance, the energy that was directed onto the targetsubstance—to excite the internal motions of the electrons, atoms, and molecules—could bedescribed as a well-known part of the electromagnetic spectrum.Creating Electromagnetic (EM) WavesAll electromagnetic (EM) waves are created by accelerating electric charges. Thus thefrequency, wavelength, and energy of EM waves all depend on charge acceleration and just howthis acceleration changes with time. For example, for a charge moving with simple harmonicmotion, the frequency f of the EM wave emitted by the accelerating charge is equal to thefrequency f of the charge’s motion. If the charge oscillates back and forth with a frequency ofthree times per second, it will emit a wave with a frequency of 3 cycles/sec, or 3 hertz.To create light waves in the visible part of the electromagnetic spectrum—a wavelength rangeof 0.4 μm to 0.7 μm—an electric charge must accelerate at a rate high enough to generate wavesof lengths around 0.5 10–6 meters. Now we know that for any wave,v fλ(1-1)where v wave speed in meters per second (m/s)f frequency in cycles per second or hertz (Hz)λ wavelength in meters (m)Thus, for light in free space, where v 3 108 m/s, and for the mid-visible region of lightaround 0.5 10–6 m, the frequency from Equation 1-1 would bef v3 108 ms 6 1014 Hz 0.5 10 6 mλa tremendously high value! Clearly, there are no ordinary “mechanical motions” of chargedsubstances at our disposal that can attain such high frequencies. Only in regions inside atomsand molecules—where the electrons move very rapidly around the nucleus and where atomsvibrate and oscillate very rapidly in molecules—can such high frequencies of moving electriccharges be realized. Figure 1-3a depicts the creation of a single wave by an oscillating charge,and Figure 1-3b shows how such charge made to oscillate along the arms of an antenna givesrise to EM waves moving outwardly in regions surrounding the antenna.Basics of Spectroscopy5

(a)(b)Figure 1-3 (a) Accelerating charge e– creates an EM wave of wavelength λ and frequency f as shown in(b). A wire antenna subjected to an AC voltage sends out an EM wave. In the propagating EM wave onlythe E-field is shown; the magnetic B-field not shown is perpendicular to the E-field. The developing EMfield is shown in stages 1, 2, and 3, ultimately reaching a receiving antenna.The opposite terminals of an AC power supply, connected respectively to the upper and lowerarms of the antenna, generate electrons e– that accelerate up and down the two arms. In stage 1,the accelerating electrons are moving downward in both arms and create the outward-movingEM field with the E-field directed downward. As the applied AC voltage changes polarity, sodoes the direction of electron flow in the arms and so then the outward moving E-fields changedirections, as shown in stage 2. As the electron flow in the arms of the antenna continues tochange directions, the newly produced electric fields are created next to the antenna and theprevious fields are forced further outward as shown in stage 3, where finally they may bedetected by a similar receiving antenna.The Electromagnetic SpectrumAs we have just seen, accelerating charges produce electromagnetic waves. There are manylevels in the structure of matter where moving (accelerating) charges exist. Some of the moreobvious are electrons in an atom, freely-moving electrons in conducting metals, vibrating atomsin molecules, and charged particles in a nucleus. Thus, two factors result in the many differenttypes of electromagnetic waves we observe—the source of the charge motions and theaccelerations inherent in the motions. The many different types of EM waves are categorizedaccording to their origins and their frequency/wavelength values. A typical organization of the6Optics and Photonics Series, Spectroscopy

electromagnetic spectrum is shown in Figure 1-4a with special emphases given to the locationof the infrared, visible, and ultraviolet regions, Figures 1-4b, c.Figure 1-4 The electromagnetic spectrum and its principal regionsThe span of wavelengths and frequencies shown in Figure 1-4a extends from 104 meters and105 hertz in the radio region to 10–12 meters and 1020 hertz in the gamma ray region. The visibleregion, bracketed by the infrared and ultraviolet regions, extends from 0.7 10–6 m (4.3 1014Hz) in the deep red down to 0.4 10–6 m (7.5 1014 Hz) in the violet.Devices that produce or detect electromagnetic waves must be designed to operate at thefrequency of the waves they emit or receive. For example, radio AM and FM transmitters andsimilar receivers operate at frequencies in the 103 to 107 Hz range and are designed to emit orrespond to these frequencies. X-ray tubes and films are designed for use in the 1017 to 10l9 Hzfrequency range. Lasers generally produce laser light in the frequency and wavelength rangeindicated by Figure 1-4b, extending from the infrared to the ultraviolet.Basics of Spectroscopy7

Particle Properties of Electromagnetic EnergyIn Figure 1-4 we have emphasized the wave properties of light. We treat light as a wave todescribe its propagation from one point to another and to explain its behavior in interference,diffraction, and polarization phenomena. To describe its behavior in the process of reflectionand refraction of light, or in the emission and absorption of light by atoms, we find it useful totreat light as a “particle”—a localized EM wave packet. We refer to this wave packet as aphoton.A photon is the smallest division of a light beam that retains the properties of the beam. Thecharacteristics of a photon include its frequency, its wavelength, and its energy. A photonshould not be visualized merely as a particle that has physical dimension or a specific locationin space. More accurately, a photon is viewed as a “wave packet” that has a specific energycontent.The energy of a photon is directly proportional to the frequency of light in its wave packet and isgiven by Equation 1-2.E hf (1)where:(1-2)E Energy of photon in joules (J)f Frequency in hertz (Hz)h Planck’s constant 6.625 10–34 joule-seconds. (This famous constant wasidentified by the German physicist Max Planck in 1900, during his attempt toexplain the spectral distribution of black-body radiation. His work introduced theconcept of a “quantum of action,” involving the constant h. The “quantum ofaction” led eventually to the idea of a photon.)c(Eq. 1-1), the energy E can be expressed in terms of the wavelength λλand speed c of the photon as in Equation 1-3.Alternatively, since f E where:Ecλh hcλ(1-3)Energy of photon in joulesSpeed of light in vacuum in m/sWavelength of light in metersPlanck’s constant 6.625 10–34 joule-secondsExamples 1, 2, and 3 illustrate the use of these two equations.(1)Note that we are using the letter f to represent frequency, as we did in Equation 1-1. Be alert, however, sinceauthors vary in their use of symbols and often the Greek letter ν (nu) is used to denote frequency.8Optics and Photonics Series, Spectroscopy

Example 1Calculation of the energy of a photon of given frequencyGiven: The frequency of a photon of HeNe laser light is 4.74 1014 Hz.Find: The energy of the photonSolution:E hf (Eq. 1-2)E (6.625 10 –34 J sec)(4.74 1014 /sec)E 3.14 10 –19 JExample 2Calculation of the energy of a photon of a given wavelengthGiven: The wavelength of a HeNe laser light is near 633 nm.Find: The energy of the photon of this wavelengthSolution:E E hc(Eq. 1-3)λ(6.625 10 –34 J sec)(3 108 m/sec)6.33 10 –7 mE 3.14 10 J (Same as the photon energy calculated in Example 1 for aphoton of frequency 4.74 1014 Hz)–19Example 3Calculation of wavelength and frequencyof a photon of given energyGiven: A photon has an energy of 1.875 10–19 J.Find: The frequency and the wavelength of the photonSolution:From Equation 1-2,f Eh(1.875 10 –19 J)(6.625 10 –34 J sec)f 2.83 1014 /sec 283 THzNote: One terahertz (THz) equals (1 1012) Hertz.Basics of Spectroscopy9

From Equation 1-3,λ hcE(6.625 10 –34 J sec)(3 108 m/sec)(1.875 10 –19 J)λ 1.06 10 –6 m 1.06 μmEnergy Levels and PhotonsThe interaction of light with matter is best understood by treating light energy as if it were madeup of photons—more like localized wave packets of energy rather than like the waves describedby Thomas Young and Christiaan Huygens. The details of the interaction—including theabsorption and emission of light—involve atoms, energy levels, and photons. Let us reviewbriefly how Niels Bohr’s model of the atom provides us with helpful insights to theseinteractions. All matter is made upof atoms. Recall that an atom is thesmallest unit of matter that retainsthe characteristics of a chemicalelement. It consists of a positivenucleus surrounded by negativeelectrons arranged in distinct energyshells designated by the letters Kthrough O, as shown in Figure 1-5.The notation K(2) indicates that theK-shell is complete when it has 2electrons. Similarly, L(8) indicatesthat the L-shell is complete with 8electrons and M(18) indicates thatthe M-shell is complete with 18, andso on. Different chemical elementscorrespond to atoms with variousnumbers of electrons in the availableshells. For example, hydrogen hasone electron in the K-shell, heliumhas two electrons in the K-shell,lithium has two in the K-shell andone in the L-shell, beryllium has twoFigure 1-5 Atomic model of energy shellsin the K-shell and two in the L-shell,according to Bohrand so on until all chemical elementsare accounted for. The drawing of shells in Figure 1-5 depicts an element with 11 electrons—2in the K-shell, 8 in the L-shell, and 1 (another electron called a valence electron) in the M-shell.The chemical element with 11 electrons would have to be sodium, a very active chemicalelement. It is “active” because its lone outer electron can absorb energy easily and combine withother elements that need an electron to fill a shell or a subshell. This figure also shows an10Optics and Photonics Series, Spectroscopy

absorption of energy (E2 – E1) which moves the valence electron from the M-shell to the Nshell.We model the energy of an atom according to the different positions of its electrons. When allthe electrons are in an unexcited, or ground, state, the atom is assumed to be in its lowest energylevel. When the atom absorbs energy, electrons can be “excited” and moved into higher energyshells. As electrons move from one shell to another, unique amounts, or quanta, of energy areabsorbed or emitted as we have noted earlier. A photon is such a quantum of energy.An atomic energy-level diagram shows the unique electron energies available in a given atom.An energy-level diagram for hydrogen is shown in Figure 1-6a. Hydrogen has only one electron,and so it can exist in only one of the available energy levels shown at a time. The lowest level,E1, is the ground state. Energy must be added to the atom for the electron to move to a higherlevel. Note that energy levels range from a negative value of –13.6 eV (electron volts) for thelowest energy level (n 1) to a value of 0.0 eV for the very highest energy level (n )—whenthe electron breaks free from the atom. Next to the energy level diagram for hydrogen, we show(Figure 1-6b) the available energy shells and principal energy transition from higher energylevels down to the energy level marked n 2 or E2. There we see Hα for the 3-to-2 transition,Hβ for the 4-to-2 transition, and Hγ for the 5-to-2 transition.Figure 1-6 Energy levels, shells, and line spectra for the hydrogen atom. In (a) transitions from levelsn 5, 4, 3 to n 2 yield the energy emissions (spectral lines) Hγ , Hβ , Hα respectively, as shown in (b),the energy shell view, and in (c), the line spectra view as seen on film—with colors shown in the visibleEM region.Basics of Spectroscopy11

Suppose a hydrogen atom is in an excited energy state that corresponds to the n 3 level. Theatom can make a transition to the n 2 level by emitting a photon. The energy of the emittedphoton equals the decrease in energy of the atom (in going from E3 to E2), as illustrated below.Ephoton E3 – E2 –1.51 eV – (–3.4 eV) 1.89 eV(2)(Be sure to pay close attention tonegative signs for the energies.)The atom can also absorb photons. This happens when the energy of a photon exactly matchesthe difference between two electron energy levels. For example, a hydrogen atom in the n 2state can absorb a photon whose energy is 1.89 eV. The electron in the atom will then movefrom energy level E2 to energy level E3.Spectra of Light SourcesWe see in Figure 1-6c the partial line spectra of a glowing hydrogen light source formed with aprism spectrometer. The sources of electromagnetic radiation are many. Usually sources aredivided into two categories, natural and man-made. Examples of natural sources of radiationinclude the sun, observable stars, radio stars, lightning, and, in fact, any living body. Some ofthe man-made sources of radiation are incandescent and fluorescent lights, heaters, lasers,masers, radio and television antennas, radar, and X-ray tubes.As we have already indicated, two types of spectra are especially important in spectroscopy:emission and absorption spectra. An emission spectrum is formed by light emitted from asource of radiation. An absorption spectrum is formed when light that passes through an opticalmedium is partially absorbed by the optical medium.All materials with temperatures above absolute zero degrees Kelvin emit electromagneticradiation. As we have noted, every atom and molecule has its own characteristic set of spectrallines. The specific wavelengths and energies produce a unique spectral trace that depends on theatomic and molecular structure of the material. The line spectra observed early in the scientificage led to a significant understanding of the structure of atoms and eventually to thedevelopment of modern quantum theory. This theory holds that light emitted by an atom ormolecule has a discrete wavelength, corresponding to a specific energy level change within theatom or molecule, as indicated by Equation 1-3.To observe a line or band spectrum, light is passed first through a slit, as shown earlier inFigure 1-2. The image

2 Optics and Photonics Series, Spectroscopy Describe the infrared (IR), ultraviolet (UV), and visible regions of the electromagnetic spectrum. Describe how atoms and molecules absorb, store, and emit energy. Describe how electromagnetic energy is separated into different wavelengths by prisms and gratings. Describe how prisms, diffraction gratings, and interferometers are used .