sin2t. This can be written, using trigonometric methods, as
Lasers and Applications
Isaac D. Abella
The University of Chicago
Laser Principles
The enormous growth of laser technology mentioned in Section 42.9 has stimulated a broad range of scientific and engineering applications that exploit some of the unique properties of laser light. These properties derive from the distinctive way laser light is produced in contrast to the generation of ordinary light. In an ordinary sodium vapor street lamp for example, the atoms spontaneously emit in random directions and at irregular times, over a broad spectrum, resulting in isotropic illumination of incoherent light. Laser light originates from atoms, ions, or molecules through a process of stimulated emission of radiation. The active laser medium is contained in an enclosure or cavity which organizes the normally random emission process into an intense directional, monochromatic and coherent wave. The end mirrors provide the essential optical feedback which selectively builds up the stimulating wave along the tube axis. Laser light has a well-defined phase, permitting a wide variety of applications based on interference or wave modulation.
Currently operating laser systems utilize a variety of gases, solids, or liquids as the working laser substance. These devices are designed to emit either continuous or pulsed monochromatic beams, and operate over a broad range of the optical spectrum (ultraviolet, visible, infrared) with output powers ranging from microwatts to megawatts. The particular application determines the choice of laser system, wavelength, power level, or other relevant variables, since no one laser has all the desirable properties. As noted in Section 42.9, several conditions on populations of states in atoms must be satisfied for a laser to operate successfully. Population ratios of energy states of atoms in thermal equilibrium at temperature T are normally described by the Boltzmann factor,
where ∆E is the energy difference between two given levels, and k is Boltzmann's constant. Thus, the ratio of upper-state (2) to lower-state (1) populations for any reasonable laboratory temperature is always less than unity. This is the normal net absorptive case where stimulated emission does not play a dominant role. When the above ratio exceeds unity, an inverted population results, which permits net stimulated emission. This is sometimes described as a negative temperature condition, a non-physical temperature referring to a situation not in thermal equilbrium.
The requirement for population inversion, that is, more atoms in a particular excited state than in a lower state, essentially means that energy must be supplied from outside the system. Otherwise, atoms would eventually radiate, fall to the lowest energy state, and stop emitting altogether. Therefore, as required by conservation of energy, all laser systems must be connected to external energy sources, usually electrical, to maintain this non-thermal equilibrium situation as indicated in Figure 1. For example, atoms can be energized by electron impact in gaseous discharges (so called "electrical pumping"). We can also supply energy to lamps whose light populates excited states by photon absorption ("optical pumping") for those solids or liquids which do not conduct electric charge. These pumping mechanisms tend to have low efficiency (ratio of laser energy output to electric energy supplied), typically a few percent, with the balance discharged as heat into cooling water or circulating air.
Controlling the electrical input into the laser system provides a variable laser energy output, which may be important in many applications. Thus, the argon ion laser system can emit up to about 10 W in the green optical beam by adjustment of the electric current in the argon gas, which in turn controls the degree of population inversion. Chemical lasers, on the other hand, operate without direct electrical input. Several highly reactive gases are mixed in the laser chamber, with the energy released in the ensuing reaction populating the excited levels in the molecule. In this case, the reactants need to be resupplied for the laser to operate for any length of time.
Some laser systems have fluid media, containing dissolved dye molecules. The dye lasers are usually pumped to excited levels by an external laser. The advantage of this arrangement is that dye lasers can be continuously "tuned" over a wide range of wavelengths, using prisms or gratings, whereas the pump source has a fixed wavelength. Color variability is important for those cases where the laser is directed at materials whose absorption depends on wavelength. Thus, the laser can be tuned into exact coincidence with selected energy states. For example, blood does not absorb red light to any extent, which excludes red light use for most surgical applications on blood-rich tissue.
Recent developments in tunable solid state materials have permitted the design of tunable lasers without the need for unstable dye molecules; most notable are sapphire crystals containing titanium ions. These materials are optically pumped by flashlamps or fixed wavelength lasers acting to populate the upper state directly.
A variety of laser systems are in general use today. They include the 1 mW helium-neon laser (Fig. 2), usually operating in the red at 632.8 nm (although yellow and green beams are available); the argon ion laser, which operates in the green or blue up to 10 W; the carbon dioxide gas laser, which emits in the infrared at 10 m m and can produce several hundred watts; the neodymium doped yttrium aluminum garnet (YAG) laser, a powerful solid-state optically-pumped system which emits at 1.06 m m either continuous or pulsed. The recently perfected diode junction-laser illustrated in Figure 3 emits in the near infrared and operates by passage of current through the semiconductor material. The recombination radiation is essentially direct conversion of electrical energy to laser light and is a very efficient process. The diodes can emit up to 5 W and can be used to energize other laser materials.
Non-Linear Optical Effects
Some of the first scientific applications for laser light were devoted to the study of non-linear effects. The usual assumption made prior to the invention of the laser was that the intensity of light, and the corresponding optical electric field E, was weak relative to electric fields already present in matter. This is equivalent to assuming that the effect of light on an atom is simply proportional to the optical electric field.
In the study of electricity and magnetism, we note that the property of matter is often included in the linear auxiliary equation P = E , where the induced polarization P in a dielectric medium is taken to be linear in the electric field, and is the dielectic constant or the polarizability of the matter. In general, this does not hold for arbitrary field strength and a more general equation, a power series in E, needs to written:
P = 1E 1 + 2E 2 + 3E 3 + . . .
The consequence of including the second term in the series is significant. Suppose a strong red beam of laser light is introduced into a transparent crystal such as quartz. The effect of the non-linear term is to produce blue light at precisely the second harmonic of the incident light. To see why this should be so, consider the input light as a sinusoid, E = E0 sin t, where E0 is the amplitude of the light field in the crystal. An induced polarization now exists given by P = 2E sin2t. This can be written, using trigonometric methods, as
Thus, a new polarization appears consisting of two terms: a constant(DC) field, and more importantly, a term oscillating at twice the input frequency, or half the wavelength. For laser light at 694 nm, the harmonic is in the ultraviolet at 347 nm. By way of analogy, harmonic distortion of sound often occurs in vibrating mechanical systems when non-linear responses are present. The optical Second Harmonic Generation (SHG) effect was observed very soon after the invention of the ruby laser and Second Harmonic Generation is now a standard method for increasing the frequency of laser light into the UV and soft x-ray region.
There are some subtle points that must be noted. For one thing, not all materials exhibit SHG. The effect is restricted to a class of crystals having a lack of inversion symmetry in their crystal structures, such as piezoelectric crystals. Materials that do not exhibit SHG are cubic crystals, water, or glass. Another complication is that the speed of light at different wavelengths is not the same (a consequence of dispersion), which leads to inefficient SHG. The driving field at the fundamental gets out of phase with the second harmonic field and some cancellation occurs. To solve this problem, a method known as phase matching is employed, where for special directions in some birefringent crystals, the wave speeds can be matched for orthogonal polarizations of light. When light is propagated along these phase matching directions, very efficient conversion to the second harmonic can be observed.
A second important application of non-linearity comes to atomic physics and quantum mechanics. In the Bohr theory of the atom, and its subsequent modern development, transitions between atomic energy levels occur with the emission or absorption of a single quantum of light, the photon. Thus for the Bohr atom, D E = hf implies a single photon transition. This holds for the case of weak light beams as described above, since the optical electric field is treated as a weak first-order perturbation on the fields already present in an atom.
A more detailed quantum mechanical treatment shows that non-linear absorption can take place with the simultaneous absorption of two quanta so long as the sum of the energies of the two photons carries the electron between two real atomic levels. This effect has been observed in atoms and molecules, for double or triple quantum absorption, and the effect is used to populate very highly energetic states of atoms with light that is not normally resonant with the state in question. Multiphoton effects usually require focussed laser beams where the optical electric fields are comparable to atomic fields.
Holography
A method of lensless photography called holography has been developed with the advent of coherent laser sources, although the first holograms were made with ordinary monochromatic sodium yellow light. The basic ideas of holography can be understood on the basis of diffraction theory. In Section 38.4, we saw that a diffraction grating consisting of many narrow identical apertures produces various maxima in different orders; the grating equation was given as ml = d sinq . For a single laser beam incident on a grating of this sort we observe a number of diffracted beams, according to the order number m. These can be thought of as the multiple "images" of the original beam. Another view is that the beams represent a spatial Fourier analysis of the square aperture, which leads to many diffracted Fourier components.
Now consider a "grating" formed by the intersection of two plane waves incident on a photographic film. In such circumstances, one observes the stable bright and dark interference fringes. After the film is developed, a series of interference fringes is observed, which have a sinusoidal modulation of opacity, instead of the sharp-edge or "square" aperture of a ruled grating. If a laser beam is sent through a sinusoidal grating, only the first order beam is seen, corresponding to a single point image of the input beam. In Fourier terms, the spatial decomposition of a sinusoidal grating is a single Fourier component.
Simply stated, holography consists of exposing a photographic film to laser light scattered from an object, together with a reference laser beam interfering with the scattered light on the plate. The "image" on the film is a sum of sinusoidal interference gratings each of which corresponds to some point on the object. The image is reconstructed by sending laser light through the film to produce the diffracted first-order image. Early holograms required laser reconstruction of the image.
Several conditions must be satisfied to generate successful holographic plates. If the laser is low power, say at the ten milliwatt level, exposures must be long enough to get reasonable film response. During this time, the coherent phases of the interfering waves must be stable. Vibrations and moving air currents could lead to a washout of the desired effect. Higher intensity lasers reduce the time constraints. For this reason, holograms tend to be made of stationary objects, although pulsed-laser holograms can also be made.
Many technological improvements on this scheme have been made, including thick holograms where the interference is distributed in three dimensions in the film. Ordinary white light can now be scattered in reflection from these thick films in analogy to the Bragg scattering that occurs in crystal x-ray diffraction (Section 38.5). We observe thick holograms in use on credit cards, viewed in ordinary white light, where they are intended to improve security.
Other Applications
We shall describe several other applications that should serve to illustrate the wide variety of laser uses. First, lasers are used in precision long-range distance measurement (range-finding). It has become important, for astronomical and geophysical purposes, to measure as precisely as possible the distance from various points on the surface of the earth to a point on the moon's surface. To facilitate this, the Apollo astronauts set up a compact array, a 0.5 m square of reflector prisms on the moon, which allows laser pulses directed from an earth station to be retro-reflected to the same station. (See Section 35.7 on prism reflectors.) Using the known speed of light and the measured round-trip travel time of a 1 ns pulse, one can determine the earth-moon distance, 380 000 km, to a precision of better than 10 cm. Such information would be useful, for example, in making more reliable earthquake predictions and for learning more about the motions of the earth-moon system. This technique requires a high-power pulsed laser for its success, since a sufficient burst of photons must return to a collecting telescope on earth and be detected. Variations of this method are also used to measure the distance to inaccessible points on the earth.
The low-power helium-neon laser is the basis for a widespread technical innovation involving product labels. The laser beam can be focussed with a lens to a very small bright spot, which is then reflected from an oscillating mirror producing a swiftly moving dot image. If this spot is scanned over the product identification bar-code printed on supermarket products, the variation of the reflected light can be detected and decoded for speed and accuracy at the checkout counter. The spot of light must be small enough to resolve the different widths of the individual bars and bright enough to be "seen" in reflection by the optical detector below the counter. Since this laser is operated in public, the power must be low enough to be safe to the eye for any reasonable use of the system. This puts stringent limits on the type of laser used in this application.
Similarly, a laser (light-emitting diode) is used to decode the digital information on the compact audio laser-disc, the so-called CD. On the compact disc, the music has been digitized as pits and grooves embedded into a plastic-covered metal foil. The fluctuating reflection of the weak laser spot from the foil surface is detected by a photocell and decoded by digital to analog circuits to reproduce music with extremely high fidelity, without the noise or hiss associated with regular long-playing records or magnetic tape. There are also video versions of the laser disc. In all of these decoding applications, the essential laser properties that are exploited are: the accurate focusing of the beam, the monochromaticity (to be able to operate in the presence of background illumination), and enough power to observe the diffusely reflected light. High power lasers could lead to damage in these applications and are not employed.
The amount of information stored on a compact audio disc as digital data is estimated to be about 1 gigabyte (109 characters), which is enormously high density data storage. By way of comparison, the data storage on magnetic "floppy" discs in personal computers is typically 800 kilobytes (8 x 105 characters). Developments are under way to transfer this optical storage technology to computer disc readers having both read and write capability. The CD disc as a read-only device with prerecorded computer data requires very little modification and is already in use to store encyclopedia or dictionary volumes. However, the optically erasable feature would require a combination of optical and magnetic methods. The reason the data density is so high on a CD has to do with the fine size of the optical spot that can be produced from a laser beam.
Novel medical applications utilize the fact that the different laser wavelengths can be absorbed in specific biological tissues. A widespread eye condition, glaucoma, is manifested by a high fluid pressure in the eye, which can lead to destruction of the optic nerve. A simple laser operation (iridectomy) can "burn" open a tiny hole in a clogged membrane, relieving the destructive pressure. Along the same lines, a serious side effect of diabetes is the formation of weak blood vessels (neovascularization), which often leak blood into extremities. When this occurs in the eye, vision deteriorates (diabetic retinopathy) leading to blindness in diabetic patients. It is now possible to direct the green light from the argon ion laser through the clear eye lens and eye fluid, focus on the retina edges, and photo-coagulate the leaky vessels. These procedures have greatly reduced cases of blindness due to glaucoma and diabetes.
Laser surgery is now a practical reality. Infrared light at 10 m m from a carbon dioxide laser can cut through muscle tissue, primarily by heating and evaporating the water contained in cellular material. Laser power of about 100 W is required in this technique. The advantage of the "laser knife" over conventional methods is that laser radiation cuts and coagulates at the same time, leading to substantial reduction of blood loss. In addition, the technique virtually eliminates cell migration, which is very important in tumor removal. Furthermore, a laser beam can be trapped in fine glass-fiber light-guides (endoscopes) by means of total internal reflection (Sec. 35.7). The light fibers can be introduced through natural orifices, conducted around internal organs and directed to specific interior body locations, eliminating the need for massive surgery. For example, bleeding in the gastrointestinal tract can be optically cauterized by fiberoptic endoscopes inserted through the mouth.
Finally, we describe an application to biological and medical research. It is often important to isolate and collect unusual cells for study and growth. A laser cell-separator exploits the fact that specific cells can be tagged with fluorescent dyes. All cells are then dropped from a tiny charged nozzle and laser scanned for the dye tag. If triggered by the correct light-emitting tag, a small voltage applied to parallel plates deflects the falling electrically charged cell into a collection beaker. This is an efficient method for extracting the proverbial needles from the haystack.
For communications applications of lasers, see the essay on fiber optics in Chapter 35.
Suggested Readings
Demtroder, W., The Laser Spectroscopy, New York, Springer, 1982.
O'Shea, D., R. Callen, and W.T. Rhodes, Introduction to Lasers and Their Applications, Reading, Mass., Addison-Wesley, 1977.
Shawlow, A.L., "Laser Light," Sci. American, September 1968, 120 - 126.
Siegman, A.E., An Introduction to Lasers and Masers, New York, McGraw-Hill, 1979.
Physics Today, Vol. 30, no. 5, May 1977, Special issue on Applications of Lasers in Research.
Questions
Problems
(b) What precision in timing is required, that is, how small a time change needs to be detectable, to be able to measure the distance to an error of 10 cm? What effect does the Earth's atmosphere have on this measurement?
(b) Estimate how many kilograms each of hydrogen and chlorine gas would be needed to make an HCl laser operate for an hour at 1-kW output.
Figure Legends
Figure 1 A schematic of a laser design. The tube contains atoms, which represent the active medium. An external source of energy, (optical, electrical, etc.) is needed to "pump" the atoms to excited energy states. The paralel end mirrors provide the feedback of the stimulating wave.
Figure 2 A typical He-Ne gas laser.
Figure 3 A gallium arsenide p-n junction laser
Scientist checking the performance of an experimental laser-cutting device mounted on a robot arm. The laser is being used to cut through a metal plate. (Courtesy of Philippe Plailly, Science Photo Library/Photo Researchers, Inc.)
An argon laser passing through a cornea and lens during eye surgery. (© Alexander Tsiaras, Science Source/Photo Researchers, Inc.)