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
violet Blue Green Yellow Red Visible 丫kays X Ultraviolet>kNear Infirared Microwave FIGURE 31.2 Electromagnetic spectrum showing visible and optical wavelengths (31.1) where c is the velocity of light in a vacuum(c= 299, 796 km/s). The denominator in Eq. (31. 1)is a term in optics called the refractive index of the medium where e is the dielectric constant(permittivity)and u is the magnetic permeability. The wavelength of light A, which is the distance between phase fronts is 入 where no is the wavelength in vacuum and u is the light frequency. The refractive index varies with wavelength and this is referred to as the dispersive property of a medium. Another parameter used to describe light frequency is wave number. This is given by 入 and is usually expressed in cm-l, giving the number of waves in a 1-cm path. Group velocity When traveling in a medium, the velocity of energy transmission(e.g, a light pulse)is less than c and is given by (31.5) In vacuum the phase and group velocities are the same. c2000 by CRC Press LLC
© 2000 by CRC Press LLC (31.1) where c is the velocity of light in a vacuum (c = 299,796 km/s). The denominator in Eq. (31.1) is a term in optics called the refractive index of the medium (31.2) where e is the dielectric constant (permittivity) and m is the magnetic permeability. The wavelength of light, l, which is the distance between phase fronts is (31.3) where l0 is the wavelength in vacuum and u is the light frequency. The refractive index varies with wavelength, and this is referred to as the dispersive property of a medium. Another parameter used to describe light frequency is wave number. This is given by (31.4) and is usually expressed in cm–1, giving the number of waves in a 1-cm path. Group Velocity When traveling in a medium, the velocity of energy transmission (e.g., a light pulse) is less than c and is given by (31.5) In vacuum the phase and group velocities are the same. FIGURE 31.2 Electromagnetic spectrum showing visible and optical wavelengths. v c = em n = em l l u = = 0 n v s l = 1 u v dv d = -l l
polarization Light polarization is defined by the direction of the electric field vector. For isotropic media this direction is perpendicular to the propagation direction. It can exist in a number of states, described as follows Unpolarized. The electric field vector has a random and constantly changing direction,and when there are multiple frequencies the vector directions are different for each frequenc Linear. The electric field vector is confined to one direction EllipticaL. The electric field vector rotates, either left hand or right hand, at the light frequency The magnitude of the vector(intensity of the light) traces out an ellipse Circular. Circular is the special case of the above where the electric field vector traces out a Absorption Light in traveling through media can be absorbed. This can be represented in two ways. The light flux ting through a medium can be written as (31.6) where x is the distance through the medium with incident light flux Io. a is the absorption coefficient, usually stated in cm-l. An alternative way of describing absorption is to use the imaginary term in the media refractive index. The complex refractive index is n=n(1+认) (317) where k is the attenuation index. a and k are related 4π (31.8) Coherence Light can be partially or fully coherent or incoherent, depending on the source and subsequent filtering operations. Common sources of light are incoherent because they consist of many independent radiators. An example of this is the fluorescent lamp in which each excited atom radiates light independently. There is fixed phase relationship between the waves from these atoms. In a laser the light is generated in a resonant e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Polarization Light polarization is defined by the direction of the electric field vector. For isotropic media this direction is perpendicular to the propagation direction. It can exist in a number of states, described as follows. Unpolarized. The electric field vector has a random and constantly changing direction, and when there are multiple frequencies the vector directions are different for each frequency. Linear. The electric field vector is confined to one direction. Elliptical. The electric field vector rotates, either left hand or right hand, at the light frequency. The magnitude of the vector (intensity of the light) traces out an ellipse. Circular. Circular is the special case of the above where the electric field vector traces out a circle. Absorption Light in traveling through media can be absorbed. This can be represented in two ways. The light flux propagating through a medium can be written as (31.6) where x is the distance through the medium with incident light flux I0. a is the absorption coefficient, usually stated in cm–1. An alternative way of describing absorption is to use the imaginary term in the media refractive index. The complex refractive index is (31.7) where k is the attenuation index. a and k are related as (31.8) Coherence Light can be partially or fully coherent or incoherent, depending on the source and subsequent filtering operations. Common sources of light are incoherent because they consist of many independent radiators. An example of this is the fluorescent lamp in which each excited atom radiates light independently. There is no fixed phase relationship between the waves from these atoms. In a laser the light is generated in a resonant I Ie x = - 0 a n n ik = + ( ) 1 a p l = 4 0 nk
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
Medium 1 Reflected Medium 1 Medium 2 FIGURE 31.3 (a)Diagram of a light ray in medium I incident at angle 0, on the surface to medium 2. The ray is refracted at angle 8,(b)Diagram of the situation when the ray in medium 2 is incident at an angle greater than the critical angle 0 and totally internally reflected Planes FIGURE 31.4 Schematic of an optical system forming an image of an object. Light rays from the object are cap the lens which focuses them to form the image. EFL, effective focal length, f, of the lens; FFL and BFL, distances from the focal points to the outer lens surface. Principal planes are the positions to which the focal points, object distance, and image Image formation with a lens Many applications require a lens to focus light or to form an image onto a detector. A well-corrected lens usually consists of a number of lens elements in a mount, and this can be treated as a black box system. The haracteristics of this lens are known as the cardinal points. Figure 31. 4 shows how a lens is used to form an image from an illuminated object. The equation which relates the object, image, and lens system (31.13) The image magnification is given by M=s/s,. When the object is very far away s, is infini is formed at the back focal plane Incoherent Light When two or more incoherent light beams are combined, the resulting light flux is the sum of their energies For coherent light this is not necessarily true and the resulting light intensity depends on the phase relationships between the electric fields of the two beams, as well as the degree of coherence e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Image Formation with a Lens Many applications require a lens to focus light or to form an image onto a detector. A well-corrected lens usually consists of a number of lens elements in a mount, and this can be treated as a black box system. The characteristics of this lens are known as the cardinal points. Figure 31.4 shows how a lens is used to form an image from an illuminated object. The equation which relates the object, image, and lens system is (31.13) The image magnification is given by M = s2/s1. When the object is very far away s1 is infinite and the image is formed at the back focal plane. Incoherent Light When two or more incoherent light beams are combined, the resulting light flux is the sum of their energies. For coherent light this is not necessarily true and the resulting light intensity depends on the phase relationships between the electric fields of the two beams, as well as the degree of coherence. FIGURE 31.3 (a) Diagram of a light ray in medium 1 incident at angle q1 on the surface to medium 2. The ray is refracted at angle q2. (b) Diagram of the situation when the ray in medium 2 is incident at an angle greater than the critical angle qc and totally internally reflected. FIGURE 31.4 Schematic of an optical system forming an image of an object. Light rays from the object are captured by the lens which focuses them to form the image. EFL, effective focal length, ƒ, of the lens; FFL and BFL, distances from the focal points to the outer lens surface. Principal planes are the positions to which the focal points, object distance, and image distance are measured; in a simple lens they are coincident. 1 1 1 1 2 f s s = +