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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.
Various basic properties characterize a mirror:
Figure 1:
Reflection of light on a mirror.Additional properties can be relevant in various applications:
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.
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 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.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.
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.
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.
Some types of mirrors are used for special functions:
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 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.
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.
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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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:
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
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:
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