OPTICAL FILTER DESIGN APPLICATION NOTE THIN-FILM THEORY each other by producing a wave of zero amplitude. When two such lightwaves are Light is known to have both particle-like and exactly in phase with each other, they inter- wave-like characteristics. Optical thin-film fere constructively, producing a lightwave of theory is based principally upon the wave- higher amplitude. An optical thin-film coat- like characteristics of light. Key among these ing is designed so that the distances are reflection, refraction, and interference. between the boundaries (often integral quar- All boundaries between media in which ter-wavelengths) will control the phase differ- lightwaves travel create a division of reflect- ences of the multiple reflected and transmit- ed and transmitted portions of the energy. ted components. When this “stack of bound- Those lightwaves not reflected are transmit- aries” is placed in a light path, constructive ted across the boundary to a medium with interference is induced at some selected different electric and magnetic properties. wavelengths, while destructive interference These differences cause a refraction, or a is induced at others. change in the speed and angle of the light- waves. A material’s refractive index is With the aid of thin-film design software, we derived by comparing the velocity of a light- apply optical thin-film theory to optimize var- wave in that medium to the velocity in a vac- ious coating performance characteristics uum. such as: a) the degree of transmission and reflection; b) the size of the spectral range The amount of light reflected is related to the over which transmission, reflection, and the difference between the refractive indices of transition between them occur; and c) the the media on either side of the boundary; polarization effects at off-normal angles of greater differences create greater reflectivity. incidence. These characteristics are influ- If there is an increase in refractive index enced by the number of boundaries, the dif- across the boundary, the reflected lightwave ference in refractive index across each undergoes a phase change of 180º; if there is boundary, and the various distances between a decrease, no phase change occurs. An opti- the boundaries within a coating. cal thin-film coating is a stack of such bound- aries, each producing reflected and transmit- The Coating Process ted components that are subsequently We select coating materials for their trans- reflected and transmitted at other bound- missive, refractive, and absorptive character- aries. If each of these boundaries is located istics at those wavelengths critical to at a precise distance from the other bound- the filter’s application. The coating process aries, the reflected and transmitted compo- requires that materials be selected for their nents are enhanced by interference. evaporation and condensation properties as well. Unlike “solid” particles, two or more light- waves can occupy the same space. When A coating is produced in a vacuum chamber lightwaves of equal wavelength occupy the at a pressure typically less than 10-5 torr. The same space, they interfere with each other in coating materials are vaporized by a resistive a manner determined by their difference in heating source or an electron beam. With phase and amplitude. When two such light- careful control of conditions such as vapor- waves are exactly out of phase with each ization rate, pressure, temperature, and other—by 180°—they interfere destructively, chamber geometry, the vapor cloud con- and if their amplitudes are equal, they cancel denses uniformly onto rotating substrates, OPTICAL FILDER DESIGN APPLICATION NOTE 2 returning to the solid state. reflectors made of dielectric materials. The spacer, which is a single layer of dielectric As a layer of material is deposited, its material having an optical thickness corre- increasing thickness is monitored optically. sponding to an integral-half of the principal With exacting response to anticipated wavelength, induces transmission rather changes in the monitor signal, the operator than reflection at the principal wavelength. stops deposition by shielding the material Light with wavelengths longer or shorter and turning off the thermal source (or than the principal wavelength undergoes a electron beam), thereby precisely controlling phase condition that maximizes reflectivity the thickness of the layer. A multi-layer coat- and minimizes transmission. The result is a ing is produced by alternating this cycle (typ- passband filter. The size of the passband ically 20 to 70 times) with two or more mate- region, the degree of transmission in that rials. region, and the degree of reflection outside that region are determined by the number Quarter-Wave Stack Reflector and arrangement of layers. A narrow pass- The quarter-wave stack reflector is a basic band region is created by increasing the building block of optical thin-film products. reflection of the quarter-wave stacks as well Composed of alternating layers of two or as increasing the thickness of the thin-film more dielectric materials—each layer with an spacer. optical thickness corresponding to one-quar- ter of the principal wavelength—this coating In a metal-dielectric-metal (MDM) cavity, the has highest reflection at the principal wave- reflectors of the solid Fabry-Perot interferom- length and transmission both higher and eter are thin-films of metal and the spacer is lower than the principal wavelength. At the a layer of dielectric material with an integral principal wavelength, constructive interfer- half-wave thickness. These are commonly ence of the multiple reflected rays maximizes used to filter UV light that would be the overall reflection of the coating; destruc- absorbed by all-dielectric coatings. tive interference among the transmitted rays minimizes the overall transmission. 100 Figure 1 illustrates the spectral performance of a quarter-wave stack reflector. Designed for maximum reflection of 550nm light 50 waves, each layer has an optical ransmission thickness corresponding to one quarter % T of 550nm. This coating is useful for three types of filters: cut-on filters, rejection band 0 filters, and blockers. 400 500 600 700 800 900 Wavelength (nm) Fabry-Perot Interferometer Figure 1: Quarter-Wave Stack Reflector The solid Fabry-Perot interferometer, also Twenty-three layers alternating between zinc known as a single-cavity coating, is formed sulfide (n=2.35) and cryolite (n=1.35), at a princi- by separating two thin-film reflectors with a pal wavelength of 550nm. A slight design modifi- thin-film spacer. In an all-dielectric cavity, the cation could be used to eliminate the dips in the transmission regions, optimizing the element for thin-film reflectors are quarter-wave stack use as a longpass or a shortpass cut-on filter. OPTICAL FILDER DESIGN APPLICATION NOTE 3 Multi-Cavity Passband Coatings trates the spectral performance of a 3-cavity The multi-cavity passband coating is made bandpass filter. Three features used to identi- by coupling two or more single-cavities with fy bandpass filters are center wavelength a matching layer. The transmission at any (CWL); full width at half maximum transmis- given wavelength in and near the band is sion (FWHM), which characterizes the width roughly the product of the transmission of of the passband; and peak transmission the individual cavities. Therefore, as the (%T). number of cavities increases, the cut-off edges become steeper and the degree of Anti-Reflective Coatings reflection becomes greater. The anti-reflective coating is a thin-film that does the opposite of a reflector. At the princi- When this type of coating is made of all- pal wavelength(s), it creates destructive dielectric materials, out-of-band reflection interference for the multiple reflected light- characteristically ranges from about waves and constructive interference for the (.8 x CWL) to (1.2 x CWL). If thin-films of multiple transmitted lightwaves. This type of metal, such as silver, are substituted for coating is commonly applied to the surfaces some of the dielectric layers, the metal’s of optical components such as lenses, mir- reflection and absorption properties extend rors, and windows. When deposited on the the range of attenuation far into the IR. surface of an interference filter, the anti- These properties cause loss in the transmis- reflective coating increases net transmission sion efficiency of the band. and reduces the intensity of ghost images. It should be noted that a properly designed The multi-cavity coating is used in many longpass or shortpass filter is anti-reflective variations on bandpass filters. Figure 2 illus- in its transmission. 100 CWL 90 T peak = 90% λ1 λ2 50 45 ransmission % T T peak = 45% 2 FWHM 0 571.3 576.1 580.9 550 560 570 580 590 600 Wavelength (nm) Figure 2: Multi-Cavity Passband Coating A bandpass filter that was made by depositing alternating layers of zinc sulfide and cryolite on a glass substrate according to a 3-cavity Fabry-Perot interferometric design. The filter’s CWL is located at 576.1nm; its FWHM is 9.6nm. OPTICAL FILDER DESIGN APPLICATION NOTE 4 Partial Reflectors material to increase their durability. When made from all dielectric materials, the partial reflector is similar to the quarter-wave Refractory oxide surface coatings, while stack reflector except that fewer layers trans- eliminating additional substrates and their mit only a given portion of the incident light. related problems, are inherently unstable as The portion not transmitted is reflected, a result of coating densification and inconsis- since virtually none of the light is absorbed. tent reduction. The reactive coating process Partial beamsplitters used at off-normal for oxides is critically dependent on deposi- angles of incidence are common to all dielec- tion parameters at the physical chemistry tric partial reflectors. A 50/50 beamsplitter level. Methods such as ion beam, sputtering, will reflect 50% and transmit 50% of the inci- and plasma coating have been developed to dent light over a given spectral range.