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# Index Matching Fluids

Author: the photonics expert

Definition: fluids with a refractive index similar to that of other optical materials, typically used for suppressing light reflections

Alternative term: refractive index fluids

Index matching fluids (sometimes also called refractive index fluids) are liquid substances which are selected or optimized such that their refractive index approximately matches that of some other optical materials. The more closely the refractive index is matched, the weaker are light reflections at the interface between the fluid and the other optical material. For normal incidence, the reflectivity of such an interface can be calculated with the following equation:

$$R = {\left( {\frac{{{n_1} - {n_2}}}{{{n_1} + {n_2}}}} \right)^2}$$

where <$n_1$> and <$n_2$> are the refractive indices of the two materials. Obviously, the reflection vanishes if the two refractive indices are equal.

More general relations for other angles of incidence can be derived from the Fresnel equations.

The main application of index matching fluids is to achieve an optical contact even in situation where an extremely high surface quality cannot be ensured. Below, applications are discussed in more detail.

## Example: Fabry–Pérot Effect at a Fiber Joint

As an example, consider an interface between two optical fibers, where the normally cleaved fiber ends are placed close together, but with a small gap between them. If that gap is filled with air, the substantial Fresnel reflections at the two glass–air interfaces form a Fabry–Pérot interferometers. That configuration exhibits reflection losses which for a given optical wavelength vary periodically with the gap width (as long as the gap is not too wide, so that beam divergence effects stay negligible). This can be seen in Figure 1.

## Available Fluids

Water is typically not usable as an index matching fluid, since its refractive index (≈1.333 at 589 nm) is substantially lower than that of most optical materials. For example, fused silica has an index of ≈1.458 at the same wavelength, and crown glasses have even substantially higher values. By solving some substances in water, the refractive index can be increased only to a limited extent. Further, water would evaporate too quickly for many applications.

For such reasons, other index matching fluids has been developed, which have higher refractive indices (mostly between 1.4 and 1.7) and evaporate much more slowly.

Some index matching fluids have a substantially higher viscosity, which can be convenient for applications. High-viscosity fluids are called index matching gels. An important practical advantage of using optical gels instead of low-viscosity fluids is that they stay at their place without special measures for encapsulation. However, liquids may be more convenient for short-term applications, e.g. for a proof of concept after which the components can be reused for other purposes.

Silicone-based fluids are often used with visible and near-ultraviolet light because they are chemically quite inert, can be made with high purity and can be used in wide temperature ranges. Their refractive index and viscosity can be controlled to some degree via the chemical composition.

Some silicone-based matching fluids are curable, i.e., their viscosity can be strongly increased. They are delivered as two components which are mixed before heat. The curing can be accelerated with a heat treatment.

There are also optical component adhesives, which are initially liquid but can be completely solidified (usually by polymerization, which is induced thermally or by UV irradiation). For example, certain types of optical prisms (e.g. Wollaston and Nicol prisms) are made from two different prisms which are put together with such an index matching adhesive. For permanent applications, one usually prefers index matching materials which can be solidified and thus more long-term stable, not requiring any encapsulation.

Various other index matching fluids are commercially available, often without their chemical composition being revealed by the manufacturer. It may be difficult to judge which fluid is best suited for an application, or which other fluids may be used as satisfactory replacements. The available specifications are often not sufficiently precise for such purposes.

Index matching fluids are usually sold either in small bottles (with applicator caps) or in syringes. With the latter, they can be conveniently applied without exposing them to air before use. The content is often only a few milliliters, which however may last long in a laboratory, since normally one requires only quite small volumes.

## Applications of Index Matching Fluids

Here are some examples of the use of index matching fluids:

• As shown above, parasitic reflections due to small air gaps can be virtually eliminated by filling such a gap was a suitable index matching fluid. For example, the performance of a mechanical fiber splice can be substantially improved with a tiny droplet of index matching fluid filling the gap between the fibers. A high quality optical contact is then achieved without a critical influence of the gap width, i.e., the thickness of the fluid layer. However, this method is not very practical for non-permanent splices, since it is difficult to clean the fiber ends after removal from the splice; one may have to cleave them again.
• If an optical fiber is used where the coating has been stripped off, there is very little attenuation of cladding modes. If this is a problem, a droplet of index matching fluid somewhere on the fiber can induce strong attenuation of the cladding modes, since light can now easily leak out into the droplet and will mostly not find the way back into the cladding.
• Some high-resolution microscopes are operated with an immersion oil between the objective and the object under investigation. Such oils effectively increase the numerical aperture of the objective and in that way allow one to achieve a higher image resolution. Because such an immersion oil usually has a refractive index close to that of the glass material of the objective, it can also be regarded as an index matching fluid.

One may be tempted to mix different index matching fluids in order to obtain some intermediate value of the refractive index. However, this does not work for various combinations; for example, the mixture may not be optically homogeneous. Therefore, mixing should be done only as far as explicitly permitted by the manufacturer. An applicator cap must be used only for one specific substance.

## Important Properties of Index Matching Fluids

Various properties of an index matching fluid can be relevant for applications:

• A primary performance figure is the refractive index at the optical wavelengths of interest. Various fluids have been developed for matching certain common optical materials like fused silica, BK7 or certain crown glasses. Depending on how strongly reflections must be suppressed, there is a larger or smaller tolerance for the refractive index. The fluids should be optically very homogeneous.
• There should not be any substantial absorption or scattering of light in the relevant wavelength region. This can be a challenge for infrared and ultraviolet applications. Suppliers should provide absorption spectra for the relevant wavelength regions.
• Such fluids should ideally not exhibit any significant rate of evaporation at the intended operation temperatures, and they should be chemically stable over long times. Ideally, they should also not react e.g. with metallic parts (causing corrosion) with which they may get into contact.
• Some degree of viscosity can be convenient for applications. If such a fluid exhibits good adhesion to optical surfaces (if they are sufficiently clean), it is easier to avoid any air bubbles.
• For temporary applications, it is often desirable that an index matching fluid can be completely removed from optical surfaces after use, restoring the full optical quality without cumbersome cleaning procedures. One will often require some solvent (e.g. isopropanol or acetone) – ideally, one which is easy to obtain and safe to use. Tentatively, low-viscosity fluids are easier to remove.
• Ideally, the used fluids are not flammable and non-toxic, thus completely safe to use.

There is also a choice of optical adhesives with different refractive indices, often allowing one to reasonably match the refractive index of the parts to be joined. The key difference to index matching fluids is that after application of the adhesive its viscosity rises substantially, e.g. as a result of applying ultraviolet light for curing, and finally a stable solid connection is achieved. That connection can often not be removed later on without destroying the parts.

Despite their relatively low viscosity, index matching fluids can also provide some limited stability of an optical contact by surface tension.

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