# Nicol-Type Prisms

This is a continuation from the previous tutorial - ** an introduction to the fundamentals of coherent fiber optic transmission technology**.

Nicol-type prisms are not generally used at the present time, as Glan types are optically preferable. However, they were the first kind made and were once so common that Nicol became a synonym for polarizer.

There is much more calcite wastage in making Glan-type prisms than in making the simpler Nicol types so that, even though Glan polarizers were developed in the nineteenth century, it was only following the recent discoveries of new calcite deposits that they became popular. Many of the older instruments are still equipped with Nicol prisms so they will be briefly described here.

### Conventional Nicol Prism

The first polarizing prism was made in 1828 by William Nicol a teacher of physics in Edinburgh. By cutting a calcite rhomb diagonally and symmetrically through its blunt corners and then cementing the pieces together with Canada balsam, he could produce a better polarizer than any known up to that time.

A three-dimensional view of Nicol’s prism is shown in Fig. 3d.

The cut is made perpendicular to the principal section, and the angle is such that the ordinary ray is totally reflected and only the extraordinary ray emerges. When the rhomb is intact, the direction of polarization can be determined by inspection. However, the corners are sometimes cut off, making the rhomb difficult to recognize.

The principal section of Nicol’s original prism is similar to that shown in Fig. 2 except that the ordinary ray is internally reflected at the cut along diagonal \(BH\).

The cut makes an angle of \(19^\circ8'\) with edge \(BF\) in Fig. 2 and an angle of about \(90^\circ\) with the end face of the rhomb. Since the obtuse angle is \(109^\circ7'\) (Fig. 3d), the angle between the cut and the optic axis is \(44^\circ36'\).

The field of the prism is limited on one side by the angle at which the ordinary ray is no longer totally reflected from the balsam film, about \(18.8^\circ\) from the axis of rotation of the prism, and on the other by the angle at which the extraordinary ray is totally reflected by the film, about \(9.7^\circ\) from the axis. Thus the total angle is about \(28.5^\circ\) but is not by any means symmetric about the axis of rotation; the field angle is only \(2\times9.7^\circ=19.4^\circ\).

In order to produce a somewhat more symmetric field and increase the field angle, the end faces of Nicol prisms are usually trimmed to an angle of \(68^\circ\). This practice was apparently started by Nicol himself. If the cut is made at \(90^\circ\) to the new face, as shown in Fig. 8, the new field angle is twice the smaller of \(\theta_1\) and \(\theta_1'\).

### Trimmed Nicol-Type Prisms

The angle at which the cut is made in a Nicol-type prism is not critical. The field angle is affected, but a useful prism will probably result even if the cut is made at an angle considerably different from \(90^\circ\). The conventional trimmed Nicol is shown again in Fig. 9a. In this and the other five parts of the figure, principal sections of various prisms are shown superimposed on the principal section of the basic calcite rhomb (Fig. 2). Thus, it is clear how much of the original rhomb is lost in making the different types of trimmed Nicols.

In the Steeg and Reuter Nicol shown in Fig. 9b, the rhomb faces are not trimmed, and the cut is made at \(84^\circ\) to the faces instead of \(90^\circ\), giving a smaller L/A ratio. The asymmetry of the field which results is reduced by using a cement having a slightly higher index than Canada balsam.

Alternately, in the Ahrens Nicol shown in Fig. 9c, the ends are trimmed in the opposite direction, increasing their angles with the long edges of the rhomb from \(70^\circ53'\) to \(74^\circ30'\) or more. By also trimming the long edges by \(3^\circ30'\), the limiting angles are made more symmetric about the prism axis.

**Thompson Reversed Nicol**

In the Thompson reversed Nicol shown in Fig. 9d, the ends are heavily trimmed so that the optic axis lies nearly in the end face. As a result, the blue fringe is thrown farther back than in a conventional Nicol, and although the resulting prism is shorter, its field angle is actually increased.

**Nicol Curtate, or Halle, Prism**

The sides of the calcite rhomb may also be trimmed so that they are parallel or perpendicular to the principal section. Thus, the prism is square (or sometimes octagonal). This prism is of the Halle type and was shown in Fig. 3e.

Halle, in addition, used thickened linseed oil instead of Canada balsam and altered the angle of the cut. In this way he reduced the length-to-aperture ratio from about 2.7 to 1.8 and the total acceptance angle from \(25^\circ\) to about \(17^\circ\). Such shortened prisms cemented with low-index cements are often called Nicol curtate prisms (curtate means shortened).

**Square-ended Nicol**

The slanting end faces on conventional Nicol prisms introduce some difficulties, primarily because the image is slightly displaced as the prism is rotated. To help correct this defect, the slanting ends of the calcite rhomb can be squared off, as in Fig. 9e, producing the so-called square-ended Nicol prism.

The angle at which the cut is made must then be altered since the limiting angle \(\theta_1\) for an ordinary ray depends on the angle of refraction at the end face in a conventional prism, in which the limiting ray travels nearly parallel to the prism axis inside the prism (ray A in Fig. 8).

If the cut remained the same, the limiting value of \(\theta_1\) would thus be zero. However, if the cut is modified to be \(15^\circ\) to the sides of the prism, the total acceptance angle is in the 24 to \(27^\circ\) range, depending on the type of cement used.

Some image displacement will occur even in square-ended Nicol prisms since the optic axis is not in the plane of the entrance face. Therefore, the extraordinary ray will be bent even if light strikes the entrance face of the prism at normal incidence. There is considerable confusion on this point in the literature.

**Hartnack-Prazmowski Prism**

A reversed Nicol which has the cut at \(90^\circ\) to the optic axis is shown in Figs. 3f and 9f. If it is cemented with linseed oil, the optimum cut angle calculated by Hartnack is \(17^\circ\) to the long axis of the prism, giving a total acceptance angle of \(35^\circ\) and an L/A ratio of 3.4. If Canada balsam is used, the cut should be \(11^\circ\), in which case the total acceptance angle is \(33^\circ\) and the L/A ratio is 5.2.

**Foucault Prism**

A modified Nicol prism in which an air space is used between the two prism halves instead of a cement layer consists of a natural-cleavage rhombohedron of calcite which has been cut at an angle of \(51^\circ\) to the face.

The cut nearly parallels the optic axis. Square-ended Foucault-type prisms, such as the Hofmann prism, have also been reported. The angle at which the cut is made can be varied slightly in both the normal Foucault prism and the Hofmann variation of it.

In all designs the L/A ratio is 1.5 or less, and the total acceptance angle about \(8^\circ\) or less. The prisms suffer somewhat from multiple reflections, but the principal trouble, as with all Nicol prisms, is that the optic axis is not in the plane of the entrance face. This defect causes various difficulties, including nonuniform polarization across the field and the occurrence of a Landolt fringe when two Nicol-type prisms are crossed.

**Landolt Fringe**

If an intense extended light source is viewed through crossed polarizing prisms, careful observation will reveal that the field is not uniformly dark. In Nicol-type prisms the darkened field is crossed by a darker line whose position is an extremely sensitive function of the angle between the polarizer and analyzer. Other types of polarizing prisms also exhibit this anomaly but to a lesser extent.

The next tutorial introduces ** polarizing beam-splitter prisms**.