Mirrors

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:

• 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 desired 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 operating 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-13830B: 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 10110-7, 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.

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.

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.

Most curved mirrors have a spherical surface, characterized by some radius of curvature ($R$). A mirror with a concave (inwards-curved) surface acts as 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:

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.