《电子工程师手册》学习资料（英文版）chapter 31 Optoelectronics.pdf_大学文库

31 optoelectronics Jeff Hecht 31.1 Laser Differences from Other Light Sources. The Laser Industry Laurence s. Watkins 2 Sources and Detectors Properties of Light. Absorption Coherence. Geometric Optics.Incoherent Light. Detectors, RA Becker Semiconductor. Detectors, Photoemissive. Imaging ed Optical Circui Detectors Noise and detecti 31.3 Circuits 31.1 Lasers Jeff hecht The word laser is an acronym for "light amplification by the stimulated emission of radiation, a phrase that covers most, though not all, of the key physical processes inside a laser. Unfortunately, that concise definition may not be very enlightening to the nonspecialist who wants to use a laser and cares less about its internal physics than its external characteristics From a practical standpoint, a laser can be considered as a source of a narrow beam of monochromatic, coherent light in the visible, infrared, or ultraviolet parts of the spectrum. The power in a continuous beam can range from a fraction of a milliwatt to around 25 kilowatts(kw)in commercial lasers, and up to more than a megawatt in special military lasers. Pulsed lasers can deliver much higher peak powers during a pulse, although the power averaged over intervals while the laser is off and on is comparable to that of continuous lasers. The range of laser devices is broad. The laser medium, or material emitting the laser beam, can be a gas, liquid, glass, crystalline solid, or semiconductor crystal and can range in size from a grain of salt to filling the nside of a moderate-sized building. Not every laser produces a narrow beam of monochromatic, coherent light Semiconductor diode lasers, for example, produce beams that spread out over an angle of 20 to 40 degrees, of wavelengths, the optics used with them. Other types emit at a number of spectral lines, producing light that is neither truly monochromatic nor coherent. Table 31. 1 summarizes important commercial lasers Practically speaking, lasers contain three key elements. One is the laser medium itself, which gen berates the laser light. A second in the power supply, which delivers energy to the laser medium in the form needed to excite it to emit light. The third is the optical cavity or resonator, which concentrates the light to stimulate the emission of laser radiation. All three elements can take various forms, and although they are not always immediately evident in all types of lasers, their functions are essential. Figure 31. 1 shows these elements in a ruby and a helium-neon laser. Laser-like devices called optical parametric oscillators have come into sing use. They are more costl and complex than lasers, but can be tuned across a broad range, with wavelengths from 0.2 to 4 micrometers. "Modified from J. Hecht, The Laser Guidebook, 2nd ed, New York: McGraw-Hill, 1991. With permission. c 2000 by CRC Press LLC

© 2000 by CRC Press LLC 31 Optoelectronics 31.1 Lasers Differences from Other Light Sources • The Laser Industry 31.2 Sources and Detectors Properties of Light • Absorption • Coherence • Geometric Optics • Incoherent Light • Detectors, Semiconductor • Detectors, Photoemissive • Imaging Detectors • Noise and Detectivity 31.3 Circuits Integrated Optics • Device Fabrication • Packaging • Applications 31.1 Lasers1 Jeff Hecht The word laser is an acronym for “light amplification by the stimulated emission of radiation,” a phrase that covers most, though not all, of the key physical processes inside a laser. Unfortunately, that concise definition may not be very enlightening to the nonspecialist who wants to use a laser and cares less about its internal physics than its external characteristics. From a practical standpoint, a laser can be considered as a source of a narrow beam of monochromatic, coherent light in the visible, infrared, or ultraviolet parts of the spectrum. The power in a continuous beam can range from a fraction of a milliwatt to around 25 kilowatts (kW) in commercial lasers, and up to more than a megawatt in special military lasers. Pulsed lasers can deliver much higher peak powers during a pulse, although the power averaged over intervals while the laser is off and on is comparable to that of continuous lasers. The range of laser devices is broad. The laser medium, or material emitting the laser beam, can be a gas, liquid, glass, crystalline solid, or semiconductor crystal and can range in size from a grain of salt to filling the inside of a moderate-sized building. Not every laser produces a narrow beam of monochromatic, coherent light. Semiconductor diode lasers, for example, produce beams that spread out over an angle of 20 to 40 degrees, hardly a pencil-thin beam. Liquid dye lasers emit at a broad or narrow range of wavelengths, depending on the optics used with them. Other types emit at a number of spectral lines, producing light that is neither truly monochromatic nor coherent. Table 31.1 summarizes important commercial lasers. Practically speaking, lasers contain three key elements. One is the laser medium itself, which generates the laser light. A second in the power supply, which delivers energy to the laser medium in the form needed to excite it to emit light. The third is the optical cavity or resonator, which concentrates the light to stimulate the emission of laser radiation. All three elements can take various forms, and although they are not always immediately evident in all types of lasers, their functions are essential. Figure 31.1 shows these elements in a ruby and a helium-neon laser. Laser-like devices called optical parametric oscillators have come into increasing use. They are more costly and complex than lasers, but can be tuned across a broad range, with wavelengths from 0.2 to 4 micrometers. 1 Modified from J. Hecht, The Laser Guidebook, 2nd ed., New York: McGraw-Hill, 1991. With permission. Jeff Hecht Laser Focus World Laurence S. Watkins Lucent Technologies R.A. Becker Integrated Optical Circuit Consultants

© 2000 by CRC Press LLC TABLE 31.1 Important Commercial Lasers Wavelength (mm) Type Output Type and Power 0.157 Molecular fluorine (F2) Pulsed, avg. to a few watts 0.192 ArF excimer Pulsed, avg. to tens of watts 0.2–0.35 Doubled dye Pulsed 0.235–0.3 Tripled Ti-sapphire Pulsed 0.24–0.27 Tripled alexandrite Pulsed 0.248 KrF excimer Pulsed, avg. to over 100 W 0.266 Quadrupled Nd Pulsed, watts 0.275–0.306 Argon-ion CW, 1-W range 0.308 XeCl excimer Pulsed, to tens of watts 0.32–1.0 Pulsed dye Pulsed, to tens of watts 0.325 He-Cd CW, to tens of milliwatts 0.337 Nitrogen Pulsed, under 1 W avg. 0.35–0.47 Doubled Ti-sapphire Pulsed 0.351 XeF excimer Pulsed, to tens of watts 0.355 Tripled Nd Pulsed, to tens of watts 0.36–0.4 Doubled alexandrite Pulsed, watts 0.37–1.0 CW dye CW, to a few watts 0.442 He-Cd CW, to over 0.1 W 0.45–0.53 Ar-ion CW, to tens of watts 0.51 Copper vapor Pulsed, tens of watts 0.520–0.569 Kryption ion CW, >1W 0.523 Doubled Nd-YLF Pulsed, watts 0.532 Doubled Nd-YAG Pulsed to 50 W, or CW to watts 0.5435 He-Ne CW, 1-mW range 0.578 Copper vapor Pulsed, tens of watts 0.594 He-Ne CW, to several milliwatts 0.612 He-Ne CW, to several milliwatts 0.628 Gold vapor Pulsed 0.6328 He-Ne CW, to about 50 mW 0.635–0.66 InGaAlP diode CW, milliwatts 0.647–0.676 Krypton ion CW, to several watts 0.67 GaInP diode CW, to 10 mW 0.68–1.13 Ti-sapphire CW, watts 0.694 Ruby Pulsed, to a few watts 0.72–0.8 Alexandrite Pulsed, to tens of watts (CW in lab) 0.75–0.9 GaAlAs diode CW, to many watts in arrays 0.98 InGaAs diode CW, to 50 mW 1.047 or 1.053 Nd-YLF CW or pulsed, to tens of watts 1.061 Nd-glass Pulsed, to 100 W 1.064 Nd-YAG CW or pulsed, to kilowatts 1.15 He-Ne CW, milliwatts 1.2–1.4 InGaAsP diode CW, to 100 mW 1.313 Nd-YLF CW or pulsed, to 0.1 W 1.32 Nd-YAG Pulsed or CW, to a few watts 1.4–1.6 Color center CW, under 1 W 1.5–1.6 InGaAsP diode CW, to 100 mW 1.523 He-Ne CW, milliwatts 1.54 Erbium-glass (bulk) Pulsed, to 1 W 1.54 Erbium-fiber (amplifier) CW, milliwatts 1.75–2.5 Cobalt-MgF2 Pulsed, 1-W range 2.3–3.3 Color center CW, under 1 W 2.6–3.0 HF chemical CW or pulsed, to hundreds of watts 3.3–29 Lead-salt diode CW, milliwatt range 3.39 He-Ne CW, to tens of milliwatts 3.6–4.0 DF chemical CW or pulsed, to hundreds of watts 5–6 Carbon monoxide CW, to tens of watts 9–11 Carbon dioxide CW or pulsed, to tens of kilowatts 40–100 Far-infrared gas CW, generally under 1 W

Flash lamp (excites laser rod) (aser medium) ∥ ower supply (drives flash lamp mixture Electrode laser cavity) Power supply drives discharge through laser gas) Figure 31.1 lified views of two common lasers,(a)ruby and(b)helium-neon, showing the basic components that Several general characteristics are common to most lasers that new users may not expect. Like most other light sources, lasers are inefficient in converting input energy into light. Efficiencies range from less than 0.001 to more than 50%, but except for semiconductor lasers, few types are much above 1% efficient. These low efficiencies can lead to special cooling requirements and duty-cycle limitations, particularly for high-power lasers. In some cases, special equipment may be needed to produce the right conditions for laser operation, such as cryogenic temperatures for lead salt semiconductor lasers Operating characteristics of individual lasers lepend strongly on structural components such as cavity optics, and in many cases a wide range is possible Packaging can also have a strong impact on laser characteristics and the use of lasers for certain applications Thus, there are wide ranges of possible characteristics, although single devices will have much more limited ranges of operation. Differences from Other Light Sources The basic differences between lasers and other light sources are the characteristics often used to describe a laser the output beam is narrow, the light is monochromatic, and the emission is coherent. Each of these features is important for certain applications and deserves more explanation. Most gas or solid-state lasers emit beams with divergence angle of about a milliradian, meaning that they spread to about 1 m in diameter after traveling a kilometer. Semiconductor lasers have much larger beam vergence, but suitable optics can reshape the beam to make it much narrower. The actual beam divergence depends on the type of laser and the optics used with it. The fact that laser light is contained in a beam serves concentrate the output power onto a small area. Thus, a modest laser power can produce a high intensity inside the small area of the laser beam; the intensity of light in a 1-mw helium-neon laser beam is comparable to that of sunlight on a clear day, for example. The beams from high-power lasers, delivering tens of watts or more of continuous power or higher peak powers in pulses, can be concentrated to high enough intensities that they can weld, drill, or cut many materials e 2000 by CRC Press LLC

© 2000 by CRC Press LLC Several general characteristics are common to most lasers that new users may not expect. Like most other light sources, lasers are inefficient in converting input energy into light. Efficiencies range from less than 0.001 to more than 50%, but except for semiconductor lasers, few types are much above 1% efficient. These low efficiencies can lead to special cooling requirements and duty-cycle limitations, particularly for high-power lasers. In some cases, special equipment may be needed to produce the right conditions for laser operation, such as cryogenic temperatures for lead salt semiconductor lasers. Operating characteristics of individual lasers depend strongly on structural components such as cavity optics, and in many cases a wide range is possible. Packaging can also have a strong impact on laser characteristics and the use of lasers for certain applications. Thus, there are wide ranges of possible characteristics, although single devices will have much more limited ranges of operation. Differences from Other Light Sources The basic differences between lasers and other light sources are the characteristics often used to describe a laser: the output beam is narrow, the light is monochromatic, and the emission is coherent. Each of these features is important for certain applications and deserves more explanation. Most gas or solid-state lasers emit beams with divergence angle of about a milliradian, meaning that they spread to about 1 m in diameter after traveling a kilometer. (Semiconductor lasers have much larger beam divergence, but suitable optics can reshape the beam to make it much narrower.) The actual beam divergence depends on the type of laser and the optics used with it. The fact that laser light is contained in a beam serves to concentrate the output power onto a small area. Thus, a modest laser power can produce a high intensity inside the small area of the laser beam; the intensity of light in a 1-mW helium-neon laser beam is comparable to that of sunlight on a clear day, for example. The beams from high-power lasers, delivering tens of watts or more of continuous power or higher peak powers in pulses, can be concentrated to high enough intensities that they can weld, drill, or cut many materials. Figure 31.1 Simplified views of two common lasers, (a) ruby and (b) helium-neon, showing the basic components that make a laser. Electrode Mirror (defines laser cavity) laser beam Helium - neon gas mixture (laser medium) Power supply (drives discharge through laser gas) Power supply (drives flash lamp) (b) (a) Mirror (defines laser cavity) Electrode Ruby rod (laser medium) Flash lamp (excites laser rod) Mirror laser beam Mirror

The laser beams concentrated light delivers energy only where it is focused. For example, a tightly focused laser beam can write a spot on a light-sensitive material without exposing the adjacent area, allowing high- resolution printing. Similarly, the beam from a surgical laser can be focused onto a tiny spot for microsurgery, without heating or damaging surrounding tissue. Lenses can focus the parallel rays in a laser beam to a much smaller spot than they can the diverging rays from a point source, a factor that helps compensate for the limited light-production efficiency of lasers ode la ems deliver a tia fo at ontains only sen row age af wht engtes an d thtursthe bit ia n much of the visible and infrared spectrum. For most applications, the range of wavelengths emitted by lasers is narrow enough to make life easier for designers by avoiding the need for achromatic optics and simplifying the task of understanding the interactions between laser beam and target. For some applications in spectroscopy and communications, however, that range of wavelengths is not narrow enough, and special line-narrowing One of the beams unique properties is its coherence, the property that the light waves it contains are in hase with one another. Strictly speaking, all light sources have a finite coherence length, or distance over which the light they produce is in phase. However, for conventional light sources that distance is essentially zero. For many common lasers, it is a fraction of a meter or more, allowing their use for applications requiring coherent light. The most important of these applications is probably holography, although coherence is useful in some types of spectroscopy, and there is growing interest in communications using coherent light. Some types of lasers have two other advantages over other light sources: higher power and longer lifetime For some high-power semiconductor lasers, lifetime must be traded off against higher power, but for most others the life vs power trade-off is minimal. The combination of high power and strong directionality makes certain lasers the logical choice to deliver high light intensities to small areas. For some applications, lasers offer longer lifetimes than do other light sources of comparable brightness and cost. In addition, despite their low lasers may be more efficient in converting energy to light than other light sources The Laser Industry There is a big difference between the world of laser research and the world of the commercial laser industr Unfortunately, many text and reference books fail to differentiate between types of lasers that can be built in the laboratory and those that are readily available commercially. That distinction is a crucial one for laser users Laser emission has been obtained from hundreds of materials at thousands of emission lines in laboratories around the world. Extensive tabulations of these laser lines are available [Weber, 1982, and even today researchers are adding more lines to the list. However, most of these laser lines are of purely academic interest. Many are weak lines close to much stronger lines that dominate the emission in practical lasers. Most of the lasers that have been demonstrated in the laboratory have proved to be cumbersome to operate, low in power, inefficient, and/or simply less practical to use than other types. Only a couple of dozen types of lasers have proved to be commercially viable on any significant scale; these are summarized in Table 31. 1. Some of these types, notably the ruby and helium-neon lasers, have been around nce the beginning of the laser era. Others, such as vibronic solid-state, are promising newcomers. The family of commercial lasers is expanding slowly, as new types such as titanium-sapphire come on the market, but with the economics of production a factor to be considered, the number of commercially viable lasers will always There are many possible reasons why certain lasers do not find their way onto the market. Some require cotic operating conditions or laser media, such as high temperatures or highly reactive metal vapors. Some emit only feeble powers. Others have only limited applications, particularly lasers emitting low powers in the far-infrared or in parts of the infrared where the atmosphere is opaque. Some simply cannot compete with materials already on the market. c2000 by CRC Press LLC

© 2000 by CRC Press LLC The laser beam’s concentrated light delivers energy only where it is focused. For example, a tightly focused laser beam can write a spot on a light-sensitive material without exposing the adjacent area, allowing highresolution printing. Similarly, the beam from a surgical laser can be focused onto a tiny spot for microsurgery, without heating or damaging surrounding tissue. Lenses can focus the parallel rays in a laser beam to a much smaller spot than they can the diverging rays from a point source, a factor that helps compensate for the limited light-production efficiency of lasers. Most lasers deliver a beam that contains only a narrow range of wavelengths, and thus the beam can be considered monochromatic for all practical purposes. Conventional light sources, in contrast, emit light over much of the visible and infrared spectrum. For most applications, the range of wavelengths emitted by lasers is narrow enough to make life easier for designers by avoiding the need for achromatic optics and simplifying the task of understanding the interactions between laser beam and target. For some applications in spectroscopy and communications, however, that range of wavelengths is not narrow enough, and special line-narrowing options may be required. One of the beam’s unique properties is its coherence, the property that the light waves it contains are in phase with one another. Strictly speaking, all light sources have a finite coherence length, or distance over which the light they produce is in phase. However, for conventional light sources that distance is essentially zero. For many common lasers, it is a fraction of a meter or more, allowing their use for applications requiring coherent light. The most important of these applications is probably holography, although coherence is useful in some types of spectroscopy, and there is growing interest in communications using coherent light. Some types of lasers have two other advantages over other light sources: higher power and longer lifetime. For some high-power semiconductor lasers, lifetime must be traded off against higher power, but for most others the life vs. power trade-off is minimal. The combination of high power and strong directionality makes certain lasers the logical choice to deliver high light intensities to small areas. For some applications, lasers offer longer lifetimes than do other light sources of comparable brightness and cost. In addition, despite their low efficiency, some lasers may be more efficient in converting energy to light than other light sources. The Laser Industry Commercial Lasers There is a big difference between the world of laser research and the world of the commercial laser industry. Unfortunately, many text and reference books fail to differentiate between types of lasers that can be built in the laboratory and those that are readily available commercially. That distinction is a crucial one for laser users. Laser emission has been obtained from hundreds of materials at many thousands of emission lines in laboratories around the world. Extensive tabulations of these laser lines are available [Weber, 1982], and even today researchers are adding more lines to the list. However, most of these laser lines are of purely academic interest. Many are weak lines close to much stronger lines that dominate the emission in practical lasers. Most of the lasers that have been demonstrated in the laboratory have proved to be cumbersome to operate, low in power, inefficient, and/or simply less practical to use than other types. Only a couple of dozen types of lasers have proved to be commercially viable on any significant scale; these are summarized in Table 31.1. Some of these types, notably the ruby and helium-neon lasers, have been around since the beginning of the laser era. Others, such as vibronic solid-state, are promising newcomers. The family of commercial lasers is expanding slowly, as new types such as titanium-sapphire come on the market, but with the economics of production a factor to be considered, the number of commercially viable lasers will always be limited. There are many possible reasons why certain lasers do not find their way onto the market. Some require exotic operating conditions or laser media, such as high temperatures or highly reactive metal vapors. Some emit only feeble powers. Others have only limited applications, particularly lasers emitting low powers in the far-infrared or in parts of the infrared where the atmosphere is opaque. Some simply cannot compete with materials already on the market

Defining Terms Coherence: The condition of light waves that stay in the same phase relative to each other; they must hav the same wavelength. Continuous wave(CW): A laser that emits a steady beam rather than pulses Laser medium: The material in a laser that emits light; it may be a gas, solid, or liquid Monochromatic: Of a single wavelength or frequency Resonator: Mirrors that reflect light back and forth through a laser medium, usually on opposite ends of a rod, tube, or semiconductor wafer. One mirror lets some light escape to form the laser beam. Solid-state laser: A laser in which light is emitted by atoms in a glass or crystalline matrix. Laser specialists do not consider semiconductor lasers to be solid-state types. Related Topic 42.1 Lightwave Waveguides References J. Hecht, The Laser Guidebook, 2nd ed, New York: McGraw-Hill, 1991; this section is excerpted from the M. J. Weber(ed ) CRC Handbook of Laser Science and Technology(2 vols. ) Boca Raton, Fla: CRC Press, 1982 M. J. Weber(ed ) CRC Handbook of Laser Science and Technology, Supplement 1, Boca Raton, Fla: CRC Press, 1989; other supplement n preparation. Further Information Several excellent introductory college texts are available that concentrate on laser principles. These include: Anthony E Siegman, Lasers, University Science Books, Mill Valley, Calif, 1986, and Orzio Svelto, Principles of Lasers, 3rd ed, Plenum, New York, 1989. Three trade magazines serve the laser field; each publishes an annual directory issue. For further information contact: Laser Focus World, Penn Well Publishing, Ten Tara Blvd., Nashua, NH 03062; Lasers d Optronics, PO Box 650, Morris Plains, N.J. 07950-0650; or Photonics Spectra, Laurin Publishing Co, Berkshire Common, PO Box 1146, Pittsfield, Mass. 01202. Write the publishers for information. 31.2 Sources and detectors laurence s. watkins Properties of light The strict definition of light is electromagnetic radiation to which the eye is sensitive Optical devices, howeve can operate over a larger range of the electromagnetic spectrum, and so the term usually refers to devices which rate in some part of the spectrum from the near ultraviolet(UV) through the visible range to the near Figure 31.2 shows the whole spectrum and delineates these ranges cal radiation is electromagnetic radiation and so obeys and can be completely described by Maxwell,s s. We will not discuss this analysis here but just review the important properties of light Phase Velocity In isotropic media light propagates as transverse electromagnetic(TEM)waves. The electric and magnetic field vectors are perpendicular to the propagation direction and orthogonal to each other. The velocity of light propagation in a medium(the velocity of planes of constant phase, i. e, wavefronts)is given by e 2000 by CRC Press LLC

© 2000 by CRC Press LLC Defining Terms Coherence: The condition of light waves that stay in the same phase relative to each other; they must have the same wavelength. Continuous wave (CW): A laser that emits a steady beam rather than pulses. Laser medium: The material in a laser that emits light; it may be a gas, solid, or liquid. Monochromatic: Of a single wavelength or frequency. Resonator: Mirrors that reflect light back and forth through a laser medium, usually on opposite ends of a rod, tube, or semiconductor wafer. One mirror lets some light escape to form the laser beam. Solid-state laser: A laser in which light is emitted by atoms in a glass or crystalline matrix. Laser specialists do not consider semiconductor lasers to be solid-state types. Related Topic 42.1 Lightwave Waveguides References J. Hecht, The Laser Guidebook, 2nd ed., New York: McGraw-Hill, 1991; this section is excerpted from the introduction. M. J. Weber (ed.), CRC Handbook of Laser Science and Technology (2 vols.), Boca Raton, Fla.: CRC Press, 1982. M. J. Weber (ed.), CRC Handbook of Laser Science and Technology, Supplement 1, Boca Raton, Fla.: CRC Press, 1989; other supplements are in preparation. Further Information Several excellent introductory college texts are available that concentrate on laser principles. These include: Anthony E. Siegman, Lasers, University Science Books, Mill Valley, Calif., 1986, and Orzio Svelto, Principles of Lasers, 3rd ed., Plenum, New York, 1989. Three trade magazines serve the laser field; each publishes an annual directory issue. For further information contact: Laser Focus World, PennWell Publishing, Ten Tara Blvd., Nashua, NH 03062; Lasers & Optronics, PO Box 650, Morris Plains, N.J. 07950-0650; or Photonics Spectra, Laurin Publishing Co., Berkshire Common, PO Box 1146, Pittsfield, Mass. 01202. Write the publishers for information. 31.2 Sources and Detectors Laurence S. Watkins Properties of Light The strict definition of light is electromagnetic radiation to which the eye is sensitive. Optical devices, however, can operate over a larger range of the electromagnetic spectrum, and so the term usually refers to devices which can operate in some part of the spectrum from the near ultraviolet (UV) through the visible range to the near infrared. Figure 31.2 shows the whole spectrum and delineates these ranges. Optical radiation is electromagnetic radiation and so obeys and can be completely described by Maxwell’s equations. We will not discuss this analysis here but just review the important properties of light. Phase Velocity In isotropic media light propagates as transverse electromagnetic (TEM) waves. The electric and magnetic field vectors are perpendicular to the propagation direction and orthogonal to each other. The velocity of light propagation in a medium (the velocity of planes of constant phase, i.e., wavefronts) is given by

ity using a light amplifier and the resulting coherent light has well-defined phase fronts and frequency Spatial and Temporal Coherence. Spatial coherence describes the phase front properties of light. A beam from a single-mode laser which has one well-defined phase front is fully spatially coherent. A collection of light aves from a number of light emitters is incoherent because the resulting phase front has a randomly indefinable form. Temporal coherence describes the frequency properties of light. A single-frequency laser output is fully temporally coherent. White light, which contains many frequency components, is incoherent, and a narrow band of frequencies is partially cohere Laser beam focusing The radial intensity profile of a collimated single-mode TEMoo(Gaussian) beam from a laser is given by I(r)=Io expl (31.9) where wo is the beam radius(1/e intensity). This beam will diverge as it propagates out from the laser, and the half angle of the divergence is given by (31.10) When this beam is focused by a lens the resulting light spot radius is given by (31.11) where I is the distance from the lens to the position of the focused spot and wa is the beam radius entering the lens. It should be noted that l=f the lens focal length, for a collimated beam entering the lens. However, I will a greater stance than f if the beam is diverging when entering the Geometric Optics The wavelength of light can be approximated to zero for many situations. This permits light to be described in terms of light rays which travel in the direction of the wave normal. This branch of optics is referred to Properties of Light Rays Refraction. When light travels from one medium into another it changes propagation velocity, Eq (31.1) This results in refraction(bending) of the light as shown in Fig. 31.3 The change in propagation direction of the light ray is given by Snells law n, sin 01=n2, sin 82 (31.12) where n, and n, are the refractive indices of media I and 2, respectively Critical Angle. When a light ray traveling in a medium is incident on a surface of a less dense medium, there incidence angle 0, where sin 0,= 1. This is the critical angle; for light incident at angles greater than 8, ight is totally internally reflected as shown in Fig. 31.3(b). The critical angle is given by 0=sin"(n/n, c2000 by CRC Press LLC

© 2000 by CRC Press LLC cavity using a light amplifier and the resulting coherent light has well-defined phase fronts and frequency characteristics. Spatial and Temporal Coherence. Spatial coherence describes the phase front properties of light. A beam from a single-mode laser which has one well-defined phase front is fully spatially coherent. A collection of light waves from a number of light emitters is incoherent because the resulting phase front has a randomly indefinable form. Temporal coherence describes the frequency properties of light. A single-frequency laser output is fully temporally coherent. White light, which contains many frequency components, is incoherent, and a narrow band of frequencies is partially coherent. Laser Beam Focusing The radial intensity profile of a collimated single-mode TEM00 (Gaussian) beam from a laser is given by (31.9) where w0 is the beam radius (1/e2 intensity). This beam will diverge as it propagates out from the laser, and the half angle of the divergence is given by (31.10) When this beam is focused by a lens the resulting light spot radius is given by (31.11) where l is the distance from the lens to the position of the focused spot and wd is the beam radius entering the lens. It should be noted that l @ f, the lens focal length, for a collimated beam entering the lens. However, l will be a greater distance than f if the beam is diverging when entering the lens. Geometric Optics The wavelength of light can be approximated to zero for many situations. This permits light to be described in terms of light rays which travel in the direction of the wave normal. This branch of optics is referred to geometric optics. Properties of Light Rays Refraction. When light travels from one medium into another it changes propagation velocity, Eq. (31.1). This results in refraction (bending) of the light as shown in Fig. 31.3. The change in propagation direction of the light ray is given by Snell’s law: (31.12) where n1 and n2 are the refractive indices of media 1 and 2, respectively. Critical Angle. When a light ray traveling in a medium is incident on a surface of a less dense medium, there is an incidence angle q2, where sin q1 = 1. This is the critical angle; for light incident at angles greater than q2 the light is totally internally reflected as shown in Fig. 31.3(b). The critical angle is given by qc = sin–1(n1/n2). I r I r w ( ) = exp Ê - Ë Á ˆ ¯ ˜ È Î Í Í ˘ ˚ ˙ ˙ 0 2 0 2 2 q l p 1 2 0 / = w w l w f d = l p n n 1 2 sin sin q1 2 = q