Mirrors – properties, optical specifications, metal-coated ...

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Author: the photonics expert Dr. Rüdiger Paschotta

A mirror is an optical device which can reflect light. Usually, only those devices are meant where the reflection is of specular type and the angle of reflection equals the angle of incidence (see Figure 1). This means that reflective diffusers and diffraction gratings, for example, are not considered as mirrors, although they also reflect light in a way.

A somewhat more general term is reflector. While all mirrors are reflectors, there are reflectors which are somewhat more complex than a simple mirror. For example, there are prisms used as retroreflectors, using more than one total internal reflection at a prism surface.

Mirror surfaces are not necessarily flat; there are mirrors with a curved (convex or concave) reflecting surface (see below), which have focusing or defocusing properties..

This article deals mostly with optical mirrors as used in optics and laser technology, for example, and in other areas of photonics.

Properties of a Mirror

Various basic properties characterize a mirror:

Figure 1:

Reflection of light on a mirror.

• The reflectivity (or reflectance) is the percentage of the optical power which is reflected. Generally, it depends on the wavelength and the angle of incidence, for non-normal incidence often also on the polarization direction.
• Mirrors often work only in a limited wavelength range, i.e., they exhibit the wanted reflectivity only within that range. The width of that range is called the reflection bandwidth. Of course, its exact value generally depends on the angle of incidence, the polarization and on the tolerance for the reflectivity.
• Similarly, there can be a limited range of angles of incidence, particularly for dielectric mirrors.
• The reflection phase is the phase shift of reflected light, i.e., the change in optical phase obtained when comparing light directly before and directly after the reflection. The phase shift can depend on the wavelength and the polarization direction. If the phase change is different between s and p polarization (for non-normal incidence), the polarization state of incident light will in general be modified, except if it is purely s or p polarization. That is exploited in phase-retarding mirrors, e.g. for converting linearly polarized light into circularly polarized light.
• The surface shape (e.g. spherically convex curved) is also relevant, see below.

Additional properties can be relevant in various applications:

• A high surface quality is often important in laser technology. The surface flatness of laser mirrors and others is often specified in wavelengths, e.g. λ / 10, at some given operation wavelength. As surface defects are largely a random phenomenon, worst-case or statistical specifications can be given. For small localized defects, it is common to give &#;scratch & dig&#; specifications according to the US standard MIL-REF-B: there are two numbers, quantifying the severity of scratches (shallow markings or tearings) and digs (pit-like holes) basically by a comparison of their visual appearance with those of defects in certain standard parts. A quality figure of simple parts could be 80-50, a commercial quality is 60-40, laser mirrors should normally have 20-10 or better, and high precision parts can have 10-5. There is also the standard ISO -7, which also contains a more rigorous definition based on the size of defects rather than only their visual appearance.
• For use with high-power lasers, the optical damage threshold may be of interest &#; particularly in conjunction with pulsed lasers, as these tend to have high peak powers. It is often specified for nanosecond pulses.
• Chromatic dispersion properties are relevant in some applications, particularly those involving ultrashort pulses of light.

Types of Mirrors

Metal-coated Mirrors &#; Back Side and First Surface Mirrors

Ordinary mirrors as used in households are often silver mirrors on glass. These basically consist of a glass plate with a silver coating on the back side. The silver coating is thick enough to suppress any significant transmission. Nevertheless, the reflectivity is substantially below 100%, since there are absorption losses of a few percent (for visible light) in the silver layer, apart from typically smaller losses in the glass. The essential advantage of such back side mirrors is that one has a robust glass surface outside, which can be cleaned easily, and the coating on the back side (with an additional layer) is well protected. For other applications, one uses first surface mirrors, where the light is incident directly on the coating and does not reach the mirror substrate. Here, one avoids the additional light transmission through glass.

For use in laser technology and general optics, more advanced types of first surface metal-coated mirrors have been developed. These often have additional dielectric layers on top of the metallic coating in order to improve the reflectivity and/or to protect the metallic coating against oxidation (enhanced and protected mirrors). Different metals can be used, e.g. gold, silver, aluminum, copper, beryllium and nickel/chrome alloys. Silver and aluminum mirrors are particularly popular. Others are mostly used as infrared mirrors.

The article on metal-coated mirrors gives more details.

Dielectric Mirrors

The most important type of mirror in laser technology and general optics is the dielectric mirror. This kind of mirror contains multiple thin dielectric layers. One exploits the combined effect of reflections at the interfaces between the different layers. A frequently used dielectric mirror design is that of a Bragg mirror (quarter-wave mirror), which is the simplest design and leads to the highest reflectivity at a particular wavelength (the Bragg wavelength). The reflectivity is high only within a limited wavelength band, which depends on the angle of incidence.

Figure 2:

The reflectance spectrum of a Bragg mirror for different incidence angles from normal incidence (red) up to 60° (blue) in steps of 10°.

In contrast to some metal-coated mirrors, dielectric mirrors are usually made as first surface mirrors, which means that the reflecting surface is at the front surface, so that the light does not propagate through some transparent substrate before being reflected. That way, not only possible propagation losses in the transparent medium are avoided, but most importantly additional reflections at the front surface, which could be particularly relevant for non-normal incidence.

Generally, dielectric mirrors have a limited reflection bandwidth. (If that is outside the visible region, one may not even visually recognize the device as a mirror.) However, there are specially optimized broadband dielectric mirrors, where the reflection bandwidth can be hundreds of nanometers. Some of those are used in ultrafast laser and amplifier systems; they are sometimes called ultrafast mirrors, and they also need to be optimized in terms of chromatic dispersion.

Laser mirrors as used to form laser resonators, for example, are also usually dielectric mirrors, having a particularly high optical quality and often a high optical damage threshold. Some of them are used as laser line optics, i.e., only with certain laser lines. Also, there are supermirrors with a reflectivity extremely close to 100%, and dispersive mirrors with a systematically varied thin-film thickness. They can be used for high-Q optical resonators, for example.

In some cases, dielectric mirrors should also be polished on the back side &#; in particular, when some amount of light transmission is required, e.g. for output couplers of lasers.

Dielectric mirrors can be designed as cold mirrors or hot mirrors, which both can be used for removing unwanted infrared radiation &#; usually for reducing the thermal load on an optical system.

See the article on dielectric mirrors for more details.

Dichroic Mirrors

Dichroic mirrors are mirrors which have substantially different reflection properties for two different wavelengths. They are usually dielectric mirrors with a suitable thin-film design. For example, they can be used as harmonic separators in setups for nonlinear frequency conversion.

Figure 3:

Reflectance spectrum of a dichroic mirror coating, designed with the software RP Coating for high transmittance (low reflectance) around 800&#;950 nm and high reflectance at  nm.

Curved Mirrors

While many mirrors have a plane reflecting surface, many others are available with a curved (convex or concave) surface, for example for focusing laser beams or for imaging applications.

Figure 4:

A ring resonator containing two curved mirrors. This feature is essential for defining resonator modes with an appropriate mode size and low power losses.

Most curved mirrors have a spherical surface, characterized by some radius of curvature <$R$>. A mirror with a concave (inwards-curved) surface acts a focusing mirror, while a convex surface leads to defocusing behavior. Apart from the change in beam direction, such a mirror acts like a lens. For normal incidence, the focal length (disregarding its sign) is simply <$R / 2$>, i.e., half the curvature radius. For non-normal incidence with an angle <$\theta$> against the normal direction, the focal length is <$(R / 2) \cdot \cos \theta$> in the tangential plane and <$(R / 2) / \cos \theta$> in the sagittal plane.

There are also parabolic mirrors, having a surface with a parabolic rather than spherical shape, which can be advantageous. For tight focusing, one often uses off-axis parabolic mirrors, which allow one to have the focus well outside the incoming beam.

Deformable Mirrors

There are deformable mirrors, where the surface shape can be controlled, often with many degrees of freedom (possibly several thousands). Such mirrors are mostly used in adaptive optics for correcting wavefront distortions.

Variable Reflectivity Mirrors

While most mirrors have a uniform reflectance across their reflecting area, there are also variable reflectivity mirrors, where the reflectance depends on the position. These are also called graded reflectivity mirrors. They are used in lasers with unstable resonators, also as variable optical attenuators.

Mirrors for Special Functions

Some types of mirrors are used for special functions:

Phase-retarding Mirrors

Phase-retarding mirrors are made such that they introduce a well defined phase difference for s- and p-polarized components of a beam. For example, they can be used for converting linearly polarized light into circularly polarized light if that phase difference is <$\pi /2$>.

Absorbing Thin-film Reflectors

Absorbing thin-film reflectors are metal-coated mirrors which are designed to reflect e.g. s-polarized light at 45° angle of incidence while absorbing p-polarized light with the same direction of incidence. They work e.g. at the common CO2 laser wavelength of 10.6 μm and can be used in conjunction with a phase-retarding mirror to build a kind of polarization-based optical isolator. Such a device can e.g. be used for preventing light reflected on a workpiece from getting back to the laser. However, it can be used only for moderate power levels because otherwise the absorbed power would destroy the mirror or at least degrade its performance.

Substrate Shapes

Mirror substrates in optics and laser technology often have a cylindrical form, for example with a diameter of 1 inch and a thickness of a couple of millimeters. However, there are also substrates with a rectangular, elliptical or D-shaped front surface, for example. Besides, there are prism mirrors, where a reflecting coating is placed on a prism, and retroreflectors.

For special applications, a mirror substrate with a tiny hole is used. This can be useful, for example, for combining two laser beams, one of which is sent in a focused fashion through the hole while the other beam, having a substantially larger diameter, is reflected on the mirror surface.

Mirrors in Fiber Optics

In fiber optics, it is also often required to reflect light &#; in most cases back into the fiber where the light came from. That can be achieved simply by butting a normal kind of mirror (e.g. a dielectric mirror) to a normally cleaved fiber end. Alternatively, one may apply a dielectric coating directly on a fiber end.

There are also completely different types of fiber reflectors, e.g. fiber loop mirrors which are strictly speaking no mirrors but another type of reflectors.

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A mirror is an important element in many optical systems. Its basic function is to redirect light, often with the purpose of making an optical system more compact. This article discusses the kinds of thin-film coatings that can be used for mirrors. The choice of coating depends on the application, including the spectral range of interest, the optical wavefront quality desired and the cost limitations.

JDSU

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.

TABLE 1.
n AND k FOR SELECTED METALS

                     Wavelength (µm):

       

0.2

     

0.3    

 

0.4

     

0.5

     

0.6

     

0.7

     

1.0

     

2.0

     

4.0

     

10.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                    Aluminum*       n:
                                           k:

 

0.12
2.30

 

0.28
3.61

 

0.49
4.86

 

0.77
6.08

 

1.20
7.26

 

1.83
8.31

 

1.35
9.58

 

2.15
20.7

 

6.43
39.8

 

25.3
89.8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                    Beryllium          n:
                                           k:

 

0.84
2.52

 

2.42
3.09

 

2.89
3.13

 

3.25
3.17

 

3.43
3.18

 

3.47
3.25

 

3.28
3.87

 

2.44
7.61

 

2.38
16.7

 

8.3
41.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                    Chromium        n:
                                           k:

 

0.89
1.69

 

0.98
2.67

 

1.50
3.59

 

2.61
4.45

 

3.43
4.37

 

3.84
4.37

 

4.50
4.28

 

4.01
6.31

 

3.08
13.7

 

14.2
27.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                    Copper             n:
                                           k:

 

1.01
1.50

 

1.39
1.67

 

1.18
2.21

 

1.13
2.56

 

0.40
2.95

 

0.21
4.16

 

0.33
6.60

 

0.85
10.6

 

2.41
21.5

 

11.6
49.1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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                    Gold                 n:
                                           k:

 

1.43
1.22

 

1.80
1.92

 

1.66
1.96

 

0.85
1.90

 

0.22
2.97

 

0.16
3.95

 

0.26
6.82

 

0.85
12.6

 

2.60
24.6

 

12.4
55.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                    Molybdenum    n:
                                          k:

 

0.81
2.50

 

2.86
3.70

 

3.03
3.22

 

3.41
3.74

 

3.68
3.47

 

3.82
3.56

 

2.58
4.02

 

1.38
10.4

 

2.32
23.0

 

12.6
56.7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Nickel n:

 

1.00
1.54

 

1.74
2.00

 

1.61
2.36

 

1.68
2.96

 

1.88
3.54

 

2.18
4.05

 

2.81
5.00

 

3.78
8.17

 

4.15
14.6

 

6.83
37.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                    Platinum          n:
                                          k:

 

1.24
1.34

 

1.46
2.17

 

1.72
2.84

 

1.97
3.44

 

2.25
3.97

 

2.54
4.49

 

3.44
5.79

 

5.27
6.72

 

3.74
15.5

 

10.4
38.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                    Rhodium          n:
                                          k:

 

0.78
1.85

 

0.84
3.00

 

1.41
4.20

 

1.88
4.68

 

2.07
5.37

 

2.33
6.11

 

3.41
7.83

 

3.83
13.1

 

5.71
25.1

 

14.4
57.3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                    Silver               n:
                                          k:

 

1.07
1.24

 

1.51
0.96

 

0.17
1.95

 

0.13
2.92

 

0.12
3.73

 

0.14
4.52

 

0.21
6.76

 

0.65
12.2

 

2.30
24.3

 

13.3
54.0

                                         

                    Tungsten          n:
                                           k:

 

1.47
3.24

 

2.98
2.36

 

3.39
2.41

 

3.40
2.69

 

3.56
2.85

 

3.84
2.88

 

3.04
3.44

 

1.28
7.52

 

1.77
17.6

 

9.5
45.0

*Aluminum has a reflectance dip at 0.8 µm:        for λ = 0.8 µm, n = 2.80 and k = 8.45
                                                                              for λ = 0.9 µm, n = 2.06 and k = 8.30

SOURCE: Handbook of Optical Constants of Solids

Across the visible spectrum, silver is the most reflective (Figure 1). For UV applications, such as astronomical telescope mirrors, silver is unacceptable and aluminum is the best choice. Unfortunately, aluminum suffers in the region from 0.8 to 1.0 μm, where the reflectance dips well below 90 percent. In an optical system with several mirrors, this can be detrimental to performance. For a reflectance of 85 percent, a system with five mirrors would have a throughput of only 44 percent.



Figure 1. The reflectance of several shiny metals vs. wavelength from 0.2 to 1.2 μm. The reflectance values are calculated using equation 1 with data from references 1 and 2.
Copper and gold are useful only in the red and IR spectral regions. For situations involving higher durability, less shiny metals are adequate. For example, rhodium is used for dental mirrors and chromium is used for rearview mirrors in cars.



A solution to degradation is overcoating the mirror with a dielectric material that is harder than the metal surface. A common overcoat material for visible mirrors is silicon monoxide (SiO). A mirror with a simple dielectric overcoat is called a protected metal mirror. Environmentally stable silver mirrors can be made by including various overcoat layers.4

A more complicated coating can be used to increase the reflectance of a metal mirror. Such a coating would consist of several dielectric layers with alternating high and low indices of refraction. The first layer usually has a low index and the last layer, a high index. This type of mirror is called an enhanced metal mirror or an enhanced reflector. With four layers, the reflectance can be enhanced several percent over a limited spectral region (Figure 2).


Figure 2. The reflectance of an enhanced aluminum mirror vs. wavelength compared with the reflectance of an uncoated aluminum surface. The enhanced mirror includes four alternating layers of silicon dioxide and titanium dioxide.

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.
A λ/4 stack reflector also can be used to filter out or remove a selected portion of the spectrum from an optical system. Such a filter is called a dichroic filter because it separates light of two spectral regions.

A broadband all-dielectric mirror can be made by combining two or more λ/4 stack reflectors with central wavelengths close enough together that the edges of the reflectance bands overlap. Such a mirror is durable and nonconductive and can have more than 99 percent reflectance over the entire visible spectrum. A mirror with such performance might involve as many as 100 layers. The buyer is left with the trade-off between the higher cost of a 100-layer mirror with 99+ percent reflectance and a much less expensive three- or four-layer enhanced aluminum mirror with about 97 percent reflectance.

A final word about optical figure: In cases where optical figure or flatness is important, choose a mirror with fewer layers. The figure of a surface that has been polished to 1/10 of a wavelength will not be adversely affected by a -Å-thick aluminum layer that has thickness variations of several percent. However, a 100-layer coating with thickness variations of 2 percent across the surface (a typical coating uniformity tolerance) would distort the wavefront of the reflected beam by several wavelengths. Amateur astronomers who polish their own telescope mirrors &#; often to a surface accuracy of λ/10 &#; must be careful that the figure is not ruined by an aluminum coating with a protective layer that has poor uniformity.

References

1. Handbook of Optical Constants of Solids. Edward D. Palik, ed. (). Academic Press.

2. Handbook of Optical Constants of Solids II. Edward D. Palik, ed. (). Academic Press.

3. Handbook of Optical Constants of Solids III. Edward D. Palik, ed. (). Academic Press.

4. Wolfe, Jesse D., Ronald E. Laird, C.K. Carniglia and J.P. Lehan (). Durable silver-based antireflection coatings and enhanced mirrors. OPTICAL INTERFERENCE COATINGS, Technical Digest Series, 17:115-117.

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