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Encyclopedia of Laser Physics and Technology

© Dr. Rüdiger Paschotta

Last update: 2008-05-08

Definition: mirrors consisting of multiple thin layers of different transparent optical materials

A dielectric mirror consists of multiple thin layers of (usually two) different transparent optical materials (→ dielectric coatings, thin-film coatings, interference coatings). Even if the Fresnel reflection coefficient from a single interface between two materials is rather small (due to a small difference in refractive indices), the reflections from many interfaces can (in a certain wavelength range) constructively interfere to result in a very high overall reflectivity of the device. The simplest and most common design is that of a Bragg mirror, where all optical layer thickness values are just one-quarter of the design wavelength. This design leads to the highest possible reflectivity for a given number of layer pairs and given materials. It is also possible to design dichroic mirrors with controlled properties for different wavelengths.

More complicated multilayer structure designs can be used for to obtain certain functions, as for example

• a broader reflection bandwidth
• a combination of desirable reflectivity values in different wavelength ranges
• special polarization properties (for non-normal incidence) (→ thin-film polarizers, polarizing beamsplitters)
• non-polarizing beamsplitters
• edge filters, e.g. long-pass filters, high-pass filters, band-pass filters
• tailored chromatic dispersion properties (see e.g. the article on chirped mirrors)

The number of thin-film layers required depends very much on the required function and on the refractive index difference between the coating materials. Few layer pairs are sufficient in some cases, whereas more than 100 layers are required in other cases.

The resonator mirrors of a laser are almost always dielectric mirrors, because such devices routinely achieve a very high reflectivity of >99.9%, and their limited reflection bandwidth can be convenient because it allows the transmission of pump light (at a shorter wavelength) through a folding mirror of the resonator (→ dichroic mirrors). Because of this use, dielectric mirrors are often called laser mirrors.

Optimized Bragg mirrors, also called supermirrors, can even have much higher reflectivities – in extreme cases, even larger than 99.9999%, allowing e.g. the construction of optical resonators (cavities) with extremely high Q factor.

As dielectric mirrors usually provide a high reflectivity at most in a smaller part of the visible spectrum, they often do not appear like other mirrors such as silver mirrors, as used in households: dielectric mirrors are usually transparent to visible light and shine in colors which depend on the angle of view. It can even be difficult to determine which side of the substrate has the mirror coating.

Dielectric multilayer mirrors can be made on both plane and curved surfaces. In the latter case, the mirrors are focusing or defocusing. For example, a concave surface with radius of curvature R focuses with a focal length R / 2 for normal incidence. For small radii of curvature (e.g. below 10 mm), there may be problems with the coating quality in terms of homogeneity and stability.

Calculating Mirror Properties

The reflection properties (including the dispersion) of a dielectric multilayer mirror can be calculated with modeling software e.g. based on a matrix method, where each layer is associated with a 2-by-2 complex matrix, and all matrices are multiplied together to result in a matrix of the whole layer structure. From this matrix, the complex amplitudes of reflected and transmitted waves can be calculated, and also the field distribution within the structure. The chromatic dispersion properties result from the frequency dependence of the complex reflection or transmission coefficients.

Some non-trivial mathematical aspects come into play when materials are absorbing. A problem can be to obtain sufficiently precise material data, particularly for materials where the obtained refractive index has a significant dependence on the fabrication method (see below).

Generally, the features of the reflection spectrum move towards shorter wavelengths as the angle of incidence is increased; this is because the projection of the k vectors perpendicular to the mirror surface are reduced in magnitude.

Designing Dielectric Mirrors

It can be a difficult task to find a dielectric mirror design which satisfies certain criteria, such as

• a combination of reflectivities at different wavelengths
• very broadband reflection ranges
• anti-reflection properties
• certain polarization properties (for non-normal incidence; → thin-film polarizers)
• a certain chromatic dispersion profile
• minimum sensitivity to growth errors

Such dielectric mirror designs can often only be found by using numerical optimization algorithms, although analytical design strategies are known for some design targets (e.g. chirped mirror designs for dispersive mirrors). Technical challenges arise from the high dimensionality of the searched parameter space, and from the myriads of local optima which make it difficult to find the global optimum. An efficient optimization requires refined software, utilizing advanced multi-dimensional optimization, Monte Carlo methods, needle methods, and the like.

Beyond the technical optimization problems, there are of course also fundamental limitations. In many cases, the design involves a compromise between the obtained optical properties, the required number of layers, and the required growth precision.

For details on the fabrication of dielectric mirrors, see the article on dielectric coatings.

Bibliography

See also: laser mirrors, Bragg mirrors, dichroic mirrors, chirped mirrors, dielectric coatings, anti-reflection coatings, Spotlight article 2006-11-02, Spotlight article 2006-10-26

Category: photonic devices