3.1 Prisms Producing Polarized Light

3.1.1 Uniaxial double-refracting crystals

Certain types of crystals, such as calcite (Iceland spar or calcium carbonate) exhibit the property of double refraction or birefringence, as first observed in calcite by Erasmus Bartholinus in 1669. For the class of crystals called uniaxial, there is only one direction where all light rays travel along the same path at a constant velocity. This direction defines the optic axis or principal axis, and any plane that contains the optic axis is called a principal plane (sometimes called a principal section). The optic axis is not a specific line, but indicates a direction in the crystal where there is no double refraction. For all rays not traveling along the optic axis, the velocity is determined by a pair of refractive indices called the ordinary refractive index n_o and the extraordinary refractive index n_e, and the path of an incident ray is split into two rays, the so-called o-rays and e-rays. Birefringence is specified by the number (n_o − n_e). Moreover, these o-rays and e-rays are polarized and vibrate in mutually perpendicular planes. Only rays traveling parallel to the optic axis will not be split, and n_o is therefore assigned to this direction. One way to represent this refractive index variation is by use of the indicatrix.¹ Figure 3.1(a) shows a positive uniaxial indicatrix in the shape of an oblate spheroid, where n_e > n_o, and Fig. 3.1(b) shows a negative uniaxial indicatrix in the shape of a prolate spheroid, where n_o > n_e. Both have circular symmetry in planes normal to the optic axis, and when the indicatrix has a spherical shape, n_e = n_o, and the crystal is isotropic.

3.1.2 Nicol polarizing prism

One of the first prism polarizers to utilize a birefringent crystal was developed by William Nicol in 1828 and is known as the Nicol prism. The Nicol prism shown in Fig. 3.2 is constructed from negative uniaxial calcite, where n_o = 1.6584 and n_e = 1.4864 for λ = 589.3 nm. Calcite is a widely used material because of its clarity, stability, high spectral transmission range (200-5000 nm), and high birefringence. Two triangular sections are optically coupled at the hypotenuse by a thin coating of optically clear cement such as Canadian balsam (n_cement ≈ 1.54) with the optic axis direction as shown.