Neutral beam splitters

A device which divides a beam of light into two parts is known as a beam splitter.

The functional part of a beam splitter generally consists of a plane surface coated to have a specified reflectance and transmittance over a certain wavelength range.

The incident light is split into a transmitted and a reflected portion at the surface, which is usually tilted so that the incident and reflected beams are separated. The ideal values of reflectance and transmittance may vary from one application to another. The beam splitters considered in this section are known as neutral beam splitters, because reflectance and transmittance should ideally be constant over the wavelength range concerned.

Neutral beam splitters are usually specified by the ideal values of transmittance and reflectance expressed as a percentage and written T/R. 50/50 beam splitters are probably the most common.

4.2.1 Beam splitters using metallic layers

Apart from a single uncoated surface, which is sometimes used, the simplest type of beam splitter consists of a metal layer deposited on a glass plate. Silver,

Figure 4.7. Reflectance and transmittance curves for a platinum film on glass, calculated from the optical constants on the bulk metal. (After Heavens [13].)

which has least absorption of all the common metals used in the visible region, is traditionally the most popular material for this. 50/50 beam splitters are frequently referred to as being ‘half-silvered’, although commercial beam splitters nowadays are usually constructed from metals such as chromium which are less prone to damage by abrasion and corrosion.

All metallic beam splitters suffer from absorption. The transmission of a metal film is the same, regardless of the direction in which it is measured. This is not so for reflectance, and that measured at the air side is slightly higher than that measured at the glass side. This effect does not appear with a transparent film. Since T + A + R = 1, the reduction in reflectance at the substrate side means that the absorption from that side must always be higher. Figure 4.7 shows curves for platinum demonstrating this behaviour [13]. Because of this difference in reflection, metallic beam splitters should always be used in the manner shown in figure 4.8 if the highest efficiency is to be achieved.

It is possible to decrease the absorption in metallic beam splitters by adding an extra dielectric layer. The method has been applied to chromium films by Pohlack [14] and figure 4.9 gives some of the measurements made.

The first pair of results is for a simple chromium film on glass of index 1.52 measured both from the air side and the glass side. The second pair of results shows how the absorption in the chromium can be reduced by the presence of a quarter-wave layer of high refractive index material (zinc sulphide of index approximately 2.4 in this case) between the metal and the glass. This layer forms an antireflection coating on the rear surface of the metal, and the effect can be seen particularly strongly in the results for reflectance and transmission from the glass side. There, the transmission remains exactly as before, but the reflectance

Figure 4.8. Correct use of a metallic beam splitter.

Figure 4.9. Values of reflectance, transmittance and absorptance at 550 nm and normal incidence for semi-reflecting films of chromium on glass showing the effect of adding a quarter-wave layer of zinc sulphide. (After Pohlack [13].)

is considerably reduced. Results are also given for a chromium layer protected by a glass cover cemented on the front surface with and without the antireflecting layer. The metallic absorption again is very much less when the antireflection layer is on the side of the metal remote from the incident light.

Shkliarevskii and Avdeenko [15] increased the transparency and decreased the absorption in metallic coatings using an antireflection coating in a similar manner. The antireflection coating in this case, instead of being dielectric, was a thin metallic layer. They found that a layer of silver deposited on a substrate heated to around 300^◦C increased the transparency of an aluminium coating, deposited on top of the silver at room temperature, by a factor as high as 3.5 at 1µm and 2.5 at 700 nm without any decrease in reflectance at the aluminium–air interface.

If the beam splitter is used correctly, the reduction in reflectance at the glass–

film interface can be useful in reducing the stray light derived from reflection, first from the back surface of the glass blank and then from the glass–film interface.

Figure 4.10. A cube beam splitter.

One complication found with beam splitters is a difference in the values of reflectance for the two planes of polarisation when the beam splitter is tilted. The

TE (or s-) reflectance is higher than the TM(or p-) reflectance. In calculating the efficiency of a beam splitter this must be taken into account. Anders [16]

describes a method for calculating efficiency and stray light performance.

It is not always possible to use the flat plate beam splitter in some optical systems. Reflections from the rear surface can be a problem in spite of the antireflection layer behind the metal film, and in applications where the light passing through the plate is not collimated, aberrations are introduced. To overcome these difficulties a beam-splitting cube, as shown in figure 4.10, can be used, although the absorption in the metal is greater in this configuration because both surfaces, instead of just one, are now in contact with a medium whose index is greater than unity. Since the cemented assembly protects the metal layers the choice of materials is wide. Silver is probably most frequently used, although chromium, aluminium and gold are also popular.

Chromium gives almost neutral beam splitting over the visible region, with an absorption of approximately 0.55 for both planes of polarisation, the TE

reflectance being approximately 0.30 and theTM0.15. Silver varies more with wavelength, the reflectance falling towards the blue end of the spectrum, but the absorption is rather less than for chromium, around 0.15 at 550 nm, with TE

reflectance 0.50 and TM 0.30. Curves of the performance of several different metallic beam splitters are given by Anders [16].

4.2.2 Beam splitters using dielectric layers

There are many optical instruments where the light undergoes a transmission followed by a reflection, or vice versa, both at the same, or at the same type

of, beam splitter. In two-beam interferometers, for example, the beams are first of all separated by one pass through a beam splitter and then combined again by a further pass either through the same beam splitter, as in the Michelson interferometer, or through a second beam splitter, as in the Mach–Zehnder interferometer. The effective transmittance of the instrument is given by the product of the transmission and the reflectance of the beam splitter, taking into account the particular polarisation involved. For a perfect beam splitter, T R would be 0.25; for most metallic beam splitters it is around 0.08 or 0.10. The absorption in the film is the primary source of loss.

A beam splitter of improved performance, as far as the T R product is concerned, can be obtained by replacing the metallic layer with a transparent high-index quarter-wave. At normal incidence the reflectance of a quarter-wave is given by

At 45^◦angle of incidence in air the position of the peak is shifted to a shorter wavelength, and the appropriate optical admittances must be used in calculating peak reflectance.

R=

η0− (η₁²/η2) η0− (η₁²/η2)

2

and sinceη varies with the plane of polarisation, R will have two values, RTEand R_TM.

Figure 4.11 shows the peak reflectance of a quarter-wave of index between 1.0 and 3.0 on glass of index 1.52 for both 45^◦incidence and normal incidence.

At 45^◦, the peak reflectance for unpolarised light, ¹₂(RTE+ RTM), is within 1.5%

of the peak value for normal incidence.

Zinc sulphide, with index 2.35, is a popular material for beam splitters. At 45^◦we have

(T R)TE = (0.46 × 0.54) = 0.248 (T R)TM= (0.185 × 0.815) = 0.151 and

(T R)unpolarised= ¹₂(0.248 + 0.151) = 0.200.

((T R)unpolarised cannot be calculated using T_meanR_mean (= 0.219) because the light, after having undergone one reflection or transmission, is then partly polarised.)

If a more robust film is required, cerium oxide, with an index approximately 2.25, is a good choice. Here

(T R)TE = (0.423 × 0.577) = 0.244

Figure 4.11. Peak reflectance in air of a quarter-wave of index n₁on glass of index 1.52 at normal and 45^◦incidence.

Figure 4.12. Measured transmittance curve of a dielectric 70/30 beam splitter at 45^◦angle of incidence. (Courtesy of Sir Howard Grubb, Parsons & Co. Ltd.)

(T R)TM= (0.158 × 0.842) = 0.133 (T R)unpolarised= 0.189.

Clearly the dielectric beam splitter, even if it does tend to have characteristics which more nearly correspond to 70/30 rather than 50/50, has a considerably better performance than the metallic beam splitter. The reflectance curve of a typical 70/30 beam splitter in figure 4.12 shows how the reflectance varies on either side of the peak.

Beam splitters with 55/45 characteristics can be made by evaporating pure titanium in a good vacuum and subsequently oxidising it to TiO₂by heating at 420^◦C in air at atmospheric pressure. The titanium oxide thus formed has rutile structure and a refractive index of 2.8. Titanium films produced in a poor vacuum oxidise subsequently to the anatase form, having rather lower refractive index.

The production of very large beam splitters, of this type, 17× 13 inches, is described in a paper by Holland et al [17].

The single-layer beam splitter suffers from a fall in reflectance on either side