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All-dielectric mirror coatings Mirrors can be made by depositing a stack of alternate high- and low-index dielectric layers on a glass substrate. If one wishes to make a mirror for a given wavelength of light, usually denoted λ0, the thickness of each layer is chosen so that the product of the thickness and the index of refraction of the layer is λ0/4. This is called a λ/4 stack reflector. The first and last layers of the stack are of the high-index material. Increasing the number of layers can increase the reflectance at λ0, but the spectral width of the high-reflectance region is limited. If the λ/4 stack reflector consists of p+1 high-index layers with refractive index nH and p low-index layers with index nL on a substrate with refractive index nS, the maximum reflectance is given by: where the effective index nE of the λ/4 stack is given by: For the 11-layer stack whose reflectance is shown in Figure 3, the following values were used: nH = 2.5, nL = 1.46 and nS = 1.52 with p = 5. The wavelength λedge at each edge of the high-reflectance region defines the width of the reflectance band, as indicated in Figure 3. The two values of λedge are given by: where For the reflectance curve in Figure 3, the calculated edge wavelengths are 0.727 and 1.034 μm. Because of the limited width of the high-reflectance region, λ/4 stack mirrors have specific applications. The most common is their use as laser reflectors, either as a part of the laser cavity itself or for the optics that direct the laser beam through the optical system. For example, the 0.85-μm reflector might be used with the laser diode in a CD player. The typical laser reflector usually has between 21 and 27 layers and a maximum reflectance of more than 99.9 percent. Figure 3. The reflectance of a λ/4 stack, all-dielectric mirror vs. wavelength. The mirror consists of 11 alternating layers of titanium dioxide and silicon dioxide. The reflectance band is centered at λ0 = 0.85 μm and the width of the high-reflectance region is between the two wavelengths marked λedge given by equations 4 and 5.
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The basic difference between the household mirror and the optical mirror is that one is coated on the back surface and the other is coated on the front. For optical applications, a front-surface mirror must be used. This means that the reflective surface is subject to environmental degradation, even though it is usually in an enclosed environment and not exposed to the harsh conditions of the household mirror. An important part of mirror technology is providing a durable front-surface mirror that is stable and can be cleaned. A mirror’s substrate surface should be flat and smooth. The flatness is usually specified in terms of how many wavelengths of light the surface deviates from being a perfect plane. For many applications, the glass can be flat to a few wavelengths of visible light. For the most stringent applications, the surface must be flat to a quarter of a wavelength or less. The surface quality of a mirror, or its smoothness, is measured in terms of scratches and digs that are still present after polishing. A scratch/dig specification of 80/50 is fairly routine, while a specification of 20/10 is much better, but more expensive. For some applications, a mirror’s ability to conduct heat is important. In these cases, metal substrates are often used because metal is much more conductive than glass. Optical-quality metal surfaces can be fabricated by polishing or single-point diamond turning. The most common metals used are copper and aluminum. Although beryllium is highly toxic, it is used when especially light weight, stiff mirrors are required. In the case of metal substrates, the coating improves the reflectance and makes the surface more durable and resistant to scratches. Metal mirror coatings The simplest and most common mirror coating is a thin layer of metal. A 100-nm layer of aluminum or silver makes an excellent reflector for the visible spectrum. Aluminum reflects about 90 percent of the light across the visible spectrum, while silver reflects about 95 percent. The reflectance of a metal mirror can be calculated from the index of refraction n and the extinction coefficient k of the metal. The reflectance of a metal surface in air is given by: An extensive list of n and k values over a wide range of wavelengths and for many metals is available.1,2,3 Table 1 contains an abbreviated list, with data given for ultraviolet (0.2 and 0.3 μm), visible (0.4 to 0.7 μm) and infrared wavelengths (1 to 10 μm). In general, metals with k>>n are shiny, while those with k ≈ n ≈ 3 are gray. Thus, silver with n = 0.13 and k = 2.92 at 0.5 μm is shiny, while tungsten with n = 3.4 and k = 2.69 is not. As the wavelength increases into the IR region, n and k increase, leading to high reflectance in this spectral region.
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation.