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Optical Interference Coatings

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Optical Interference Coatings © 1970 SCIENTIFIC AMERICAN, INC Optical Interference Coatings The same phenomenon that is responsible for the iridescence of various natural surfaces, including peacocks' tail feathers, is exploited to produce a host of modern optical components by Philip Baumeister and Gerald Pincus hat do oil slicks, soap films, oys­ counters a medium with a different re­ the air again. This phase difference de­ ter shells and peacock feathers fractive index, say glass, a portion of the pends on the film's thickness (measured Whave in common? The famil­ incident wave is reflected at the inter­ in wavelengths of the incident light) and iar iridescen t patterns of color reflected face [see top illustration on next page J. also on the film's refractive index. It is from all these surfaces are natural mani­ The amplitude of the reflected wave, convenient to express the phase differ­ festations of the same phenomenon: which is equivalent to the electric-field ence in terms of the "optical thickness" optical interference in a thin layer. Al­ strength, is computed from an equation of the film, which is defined as the prod­ though the principles of optical inter­ developed in 1816 by the French phys­ uct of its physical thickness times its ference have been understood for more icist Augustin Jean Fresnel. The equa­ refractive index. than a century, it has been only in the tion yields a value called the amplitude­ When a film's optical thickness is a past few decades that this knowledge reflection coefficient, which depends on quarter of a wavelength, the phase dif­ has been exploited for technological the ratio of the refractive indexes of the ference between the two reflected waves ends. The oldest, simplest and still the two mediums; in the case of air and glass, is 180 degrees; in other words, they are most common application of an optical for example, the amplitude of the re­ completely out of phase. This means that interference film is as a single-layer anti­ flected wave is .203 (or about 20 per­ the net amplitude of the reflected wave reflection coating, such as those used to cent) of the amplitude of the incident is a minimum because, to use the lan­ reduce the reflectance of camera lenses. wave. guage of phYSical optics, the two waves In recent years more complicated op­ The human eye and most other photo­ add destructively. The amplitude of the tical interference coatings have been de­ detectors do not respond to the ampli­ wave reflected from the air-film interface veloped in which many layers of differ­ tude of a light wave directly but rather is .16 and the amplitude at the film-glass ent materials are deposited on an optical to its intensity, which is equal to the interface is .048. The net amplitude of surface. Stacks of such films are used not square of the amplitude; thus the inten­ the reflected wave is approximately .16 only as antireflection coatings but also sity of the reflected wave in the forego­ minus .048, or .11, and its intensity is as filters, polarizers, beam-dividers and ing example is (.203)2, or 4.1 percent, of (.11)2, or .012, which is equivalent to 1.2 highly reflecting mirrors. These coatings the intensity of the incident wave. This percent of the incident wave. are indispensable components of not a is the ordinary reflection that occurs at This minimum reflectance is attained few modern optical systems, such as each surface of a pane of window glass. at only one wavelength. At wavelengths lasers, color television cameras and in­ Now, suppose one wishes to reduce shorter than the minimum the reflec­ frared missile-guidance systems. This this reflectance by coating the glass sur­ tance increases until the film's optical article explains the rudiments of optical face with an antireflection coating, say thickness is a half-wave. At this point interference and discusses in detail a a single layer of magnesium fluoride[see the phase difference is 360 degrees and number of current devices that make use bottom illustrationon next page J. A por­ the waves that reflect at the two inter­ of this phenomenon. tion of the incident wave is then reflect­ faces of the film add constructively, or in ed at each of the two interfaces. There phase, to produce a maximum ampli­ ptical interference in a thin film can is a difference in the phase of the two tude. Thus the net amplitude of the re­ Obe explained in terms of the wave waves because of the time it takes for the flected wave is approximately .16 plus theory of light. When a light wave trav­ wave to penetrate the film, reflect from .048, or .208. At other wavelengths the eling in a certain medium, say air, en- the film-glass interface and emerge into reflectance lies between the minimum and the maximum value. he wavelength at which the mini- SINGLE·LA YER ANTIREFLECTION COATINGS consisting of varying thicknesses of Tmum reflectance occurs depends on magnesium fluoride are responsible for the distinctly different colors reflected from the glass plates in the photograph on the opposite page. The thicknesses of the magnesium the thickness of the film. For example, if fluoride coatings are .073 micron (top left), .086 micron (top right), .098 micron (middle its optical thickness is a quarter-wave in left), .123 micron (middle right), .180 micron (bottom left) and .220 micron (bottom right). the green portion of the spectrum, the The coated plates are used as references to gauge the thickness of magnesium fluoride coat­ reflectance is a minimum there. Such ings applied to a variety of optical surfaces by comparing their colors in reflected light. coatings appear purplish in reflected 59 © 1970 SCIENTIFIC AMERICAN, INC light and are deposited on camera lenses for use with black-and-white film. If the lenses are to be used for color photog­ .8----------------------��--------�--+-----------------� raphy, then the magnesium fluoride lay­ er is made slightly thinner so that the .6------------------+-----------��----------------- reflectance minimum is in the blue part of the spectrum. These coatings have an amber hue in reflected light. .4------------------ �---------------- ----------------� +_ The single layer of magnesium flu­ oride reduces the reflectance to low val­ ues, but not to zero. The minimum re­ flectance depends on the refractive index of both the glass and the film. If the film's index is the square root of the index of the glass, then the waves that reflect from each interface of the film are equal in amplitude and they exactly can­ cel. This would require that the refrac­ tive index of the film equal V 1.51, or 1.23. Unfortunately it is not possible to deposit durable films with such a low refractive index, and thus magnesium fluoride represents a compromise: a film with a fairly low refractive index (1.38) that is hard and durable. In the foregoing discussion only the reflectance of the coating was consid­ UNCOATED GLASS SURFACE reflects a portion of an incident light wave at the interface ered. How is the transmittance deter­ between the air and the glass. The amplitude of the reflected wave, which is equivalent to mined? Although there are equations by the electric·field strength, is dependent on the ratio of the refractive indexes of the two which the transmittance can be com­ mediums; in this particular case the amplitude of the reflected wave is .203 (or about 20 puted, it can also be found by noting percent) of the amplitude of the incident wave. The wavelength of the transmitted wave that if the coating is nonabsorbing, then is shorter inside the glass because the wave's velocity there is less than it is in the air. the reflectance and transmittance must add to 100 percent. This follows from the conservation of energy. For example, the minimum reflectance of the coated . 8 glass mentioned above is 1.2 percent . Since the absorptance of the coating is negligible, its transmittance is 100 per­ 6 . cent minus 1.2 percent, or 98.8 percent. This method of computing the coat­ .4 ing's reflectance by adding the waves that are reflected at each interface is called "vector addition of amplitudes." .2 Although the method is used here to w 0 compute the reflectance of a single layer, � I- it can be extended to two or more layers. :::.J \ 0.. ------------------ -- Its advantage is that it furnishes an intui­ 2: <t REFLECTED WAVES tive and simple model of how the coat­ .2 \ ing functions. The disadvantage is that it is an approximation that becomes less and less accurate as the number of layers .4 increases and also as the differences in the refractive indexes get larger. How .6 good an approximation is the method in the case of the magnesium Hum'ide coat­ ing? vVe can obtain some estimate of its .8 MAG· accuracy for this material, since it can be AIR NESIUM GLASS rigorously shown that when the optical FLUORIDE thickness of the layer is a half-wave, the reflectance is the same as that of COATED GLASS SURFACE is covered by a single antireflection layer of magnesium fluo· ride with an optical thickness equal to a quarter of a wavelength of the incident light. The the bare substrate. By vector addition reflectance is rednced because the two reflected waves are exactly out of phase. The am· of amplitudes one obtains a reflectance plitnde of the wave reflected from the air·film interface is .16 and the amplitude at the film· of (.208)", or 4.3 percent, in contrast to glass interface is .048. Hence the net amplitude of the reflected wave is approximately .16 the exact result of 4.
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