Melles Griot Optics Guide - Multilayer Antireflection Coatings

Coating Theory

Multilayer Antireflection Coatings

Previously, we discussed basic principles of thin-film design and operation for a simple antireflection coating of magnesium fluoride. It is useful to also discuss multilayer antireflection coatings in order to understand the operation of multilayer coatings. It is beyond the scope of this chapter to cover all aspects of modern thin-film design and operation; however, it is hoped that this section will provide the reader with insight into thin films that will be useful when considering system designs and specifying cost-effective coatings. Two basic types of antireflection coating are worth examining in detail: the quarter/quarter coating and the multilayer broadband coating.
The Quarter/Quarter Coating
This coating is used as an alternative to the single-layer antireflection coating. It was developed because of the lack of suitable materials available to improve the performance of single-layer coatings. The basic problem of a single-layer antireflection coating is that the refractive index of the coating material is too high, resulting in too strong a reflection from the first surface which cannot be completely canceled by interference of the weaker reflection from the substrate surface. In a two-layer coating, the first reflection is canceled by interference with two weaker reflections. A quarter/quarter coating consists of two layers, both of which have an optical thickness of a quarter wave at the wavelength of interest. The outer layer is made of a low-refractive-index material, and the inner layer is made of a high-refractive-index material (compared to the substrate). As illustrated in the figure below, the second and third reflections are both exactly 180 degrees out of phase with the first reflection.

Interference in a typical quarter/quarter coating
As with any multilayer coating, performance and design are calculated in terms of relative amplitudes and phases which are then summed to give the overall (net) amplitude of the reflected beam. The overall amplitude is then squared to give the intensity. How does one calculate the required refractive index of the inner layer? Several methodologies have been developed over the last 40 to 50 years to calculate thin-film coating properties and converge on optimum designs. The whole field has been revolutionized in recent years with the availability of powerful microcomputers. Among the most sophisticated and effective programs are those developed by Professor H. A. Macleod, which are used by Melles Griot. With a two-layer quarter/quarter coating optimized for one wavelength at normal incidence, the required refractive indices can easily be calculated by hand. The formula for exact zero reflectance for such a coating is

where n₀ is the refractive index of air (approximated as 1.0), n₃ is (the refractive index of the substrate material, and n₁ and n ₂ are the refractive indices of the two film materials, as indicated in the figure above. If the substrate is crown glass with a refractive index of 1.52 and if the first layer is the lowest possible refractive index, 1.38 (MgF₂), the refractive index of the high-index layer needs to be 1.70. Either beryllium oxide or magnesium oxide could be used for the inner layer, but both are soft materials and will not produce very durable coatings. Although it allows some freedom in the choice of coating materials and can give very low reflectance, the quarter/quarter coating is very restrictive in its design. In principle, it is possible to deposit two materials simultaneously to achieve layers of almost any required refractive index, but such coatings are not very practical. As a consequence, thin-film engineers have developed multilayer antireflection coatings and two-layer coating designs to allow the refractive index of each layer to be chosen.
Two-Layer Coatings of Arbitrary Thickness
Interference is often thought of in terms of constructive or destructive interference, where the phase shift between interfering wavefronts is either 0 or 180 degrees. For two wavefronts to completely cancel, as in a single-layer antireflection coating, a phase shift of exactly 180 degrees is required. Where three or more reflecting surfaces are involved, complete cancellation can be achieved by carefully choosing arbitrary phase and relative intensities. This is the basis of a two-layer antireflection coating, where the layers are adjusted to suit the refractive index of available materials, instead of vice versa. For a given combination of materials, there are usually two combinations of layer thicknesses that will give zero reflectance at the design wavelength. These two combinations are of different overall thickness. For any type of thin-film coating, the thinnest possible overall coating is used since it will have better mechanical properties (less stress). In this case, the thinner combination is also less wavelength sensitive. Two-layer antireflection coatings are the simplest of the so-called V-coatings. The term V-coating arises from the shape of the reflectance curve as a function of wavelength, as shown in the figure below, which is a skewed V shape with a reflectance minimum at the design wavelength.

Characteristic performance curve of a V coating
V-coatings are very popular, economical coatings for near monochromatic applications, such as optical systems using nontunable laser radiation (e.g., helium neon lasers at 632.8 nm).
Broadband Antireflection Coatings
Many optical systems (particularly imaging systems) use polychromatic (more than one wavelength) light. In order for the system to have a flat spectral response, transmitting optics are coated with a broadband or dichroic antireflection coating. The main technique used in designing antireflection coatings that are highly efficient at more than one wavelength is to use absentee layers within the coating. There are two additional techniques that can be used for shaping performance curves of high-reflectance coatings and wavelength-selective filters, but these are not applicable to antireflection coatings.
Absentee Layers
An absentee layer is a film of dielectric material that does not change the performance of the overall coating at one particular wavelength, usually the wavelength for which the coating is being principally optimized. This results from the fact that the coating has an optical thickness of a half wave at that wavelength. The effects of the "extra" reflections cancel out at the two interfaces since no additional phase shifts are introduced. In theory, the performance of the coating is the same at that wavelength whether the absentee layer is present or not. At other wavelengths, the absentee layer starts to have an effect, for two reasons. The ratio between physical thickness of the layer and the wavelength of light changes with wavelength. Also, dispersion of the coating material causes optical thickness to change with wavelength.
Multilayer Broadband Antireflection Coatings
The complex, computer-design techniques used by Melles Griot for multilayer antireflection coatings are based on the simple principles of interference and phase shifts described in the preceding text. All methods consider the combined effect of various film elements. Because of the extensive properties of coherent interference, it is meaningless to consider individual layers in a multilayer coating. Each layer is influenced by the optical properties of the layer next to it. The properties of that layer are influenced by its environment. Clearly, this represents at least a complex series of matrix multiplications, where each matrix corresponds to a single layer. An important aspect that is often overlooked in simple theory is that there are multiple "reflections" in the coatings. In the previous discussions, only first-order reflections have been considered. This oversimplified approach is unable to predict correctly the behavior of multilayer coatings. Second, third, and higher order terms must be considered if real behavior is to be modeled accurately. The exact behavior of an antireflection coating is clearly dependent on the refractive index of the substrate to which it is applied. In order to simplify the task of choosing and ordering coatings for optics of different glass types, Melles Griot has listed the coatings in this catalog according to performance. Actual coatings applied by Melles Griot are adjusted for different glass types in order to achieve the specified performance.

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