Photographic Method for Determining the Dispersion of Optical Constants of Metals

The determination of the optical constants of metals is usually reduced to measuring the elliptic polarization that arises when light is reflected from the surface of the metal under investigation. Photoelectric methods, while providing a sufficiently high degree of accuracy, nevertheless have the disadvantage that measurements carried out successively for each wavelength take a rather long time, during which the measured specimen may undergo changes (surface corrosion, aging of thin films, etc.). On the other hand, in a number of cases it is more important to establish the general course of the dispersion curve than to obtain very precise values of the constants for several wavelengths. In this case, photographic methods become useful, allowing, with a certain modification, some degree of reproduction of the dispersion curve even without photometric processing. Examples of such methods are the so-called Rozhdestvenskii “hook method,” or Dorgelo’s method for obtaining absorption curves. Among them belongs also the method for determining the optical constants of metals developed by the author of the paper under review*).

The optical scheme of the apparatus is shown in Fig. 1. A parallel beam of light reflected from the metal passes through a compensator, an analyzer, and a dispersing system (a prism), and is focused by a pair of crossed cylindrical lenses on a photographic plate covered by a striped mask. The compensator consists of two right- and left-rotating quartz prisms in optical contact. Therefore elliptically polarized light, passing through the compensator, does not change the character of its polarization (the ellipse is not deformed), but the principal axes of the ellipse are rotated, with the direction and degree of rotation depending on the distance of the light beam from the neutral section of the compensator: above the central section the rotation occurs clockwise, below it—counterclockwise (Fig. 2, a).

Fig. 1. Optical scheme of the apparatus.

The analyzer selects the vertical component of the electric-field strength, as a result of which the intensity of the light passing through it

) J. Bör, Proc. Phys. Soc. 65B*, No. 394, 753 (1952).

of light turns out to be a periodic function of the distance from the central cross section (Fig. 2, b). The cylindrical lens \(L_1\), with focal length \(20\ \mathrm{cm}\), gives on the plate an image of the vertical section of the light beam emerging from the compensator, while the cylindrical lens \(L_2\) (with focal length \(65\ \mathrm{cm}\)), in the focus of which the photographic plate is located, brings the light beam into a narrow vertical line in the horizontal plane, which is spread out into a spectrum by the prism.

Fig. 2. Rotation of the polarization ellipse by the compensator (a) and the change in the intensity of light passing through the analyzer (b), as a function of the distance from the central cross section of the compensator.

It is not difficult to see that the intensity of the line oscillates along its length; moreover, the ratio of the maximum intensity to the minimum intensity is equal to the square of the ratio of the semiaxes of the polarization ellipse, while the angle of rotation of the major semiaxis of the ellipse relative to the vertical is equal to \(\left(\dfrac{AC}{AB}\right)\pi\), where the points \(A\) and \(B\) correspond to the horizontal positions of the ellipse (i.e., to intensity minima), and the point \(C\) to that place of the compensator where the light passes through without experiencing birefringence (this place is marked on the compensator by a thin thread \(W\), appearing in the photograph as a thin black stripe cutting across the spectrum).

Fig. 3. Shaped slit.

To pass from blackening to intensities, the author uses the following procedure. The compensator and analyzer are replaced by a shaped slit (Fig. 3), as a result of which a spectrum is obtained whose intensity increases linearly on both sides of the central cross section.

The measurement procedure is reduced, therefore, to 1) photographing the spectrum of radiation reflected from the metal through the compensator and analyzer, and 2) photographing the same spectrum through the shaped slit, with the photographing

this is accomplished after moving the plate in the horizontal direction behind the striped mask \(G\) by the width of one stripe. (The exposure time, according to the author, was about 5 sec.)

As a result, a photograph of the type shown in Fig. 4 is obtained, representing a spectrum divided into alternating bands corresponding to photographs taken with the slit and with the compensator (analogously to the Dorgelo photometric method), and giving a fairly clear picture of the course of dispersion of the optical constants of the metal.

Fig. 4. Example of the image obtained on the photographic plate. Reflection from aluminum.

The only serious requirement for obtaining reliable data is the requirement of parallelism of the light beam—the divergence angle must not exceed approximately \(10'\). The processing of such photographs proves to be quite simple.

The ratio of the semiaxes of the ellipse is equal to the square root of the ratio of the distances from the central section, on which the blackenings of the stripe obtained with the slit are equal, respectively, to the blackenings at the maximum and minimum of the neighboring stripe obtained with the compensator and analyzer. The angle of rotation of the ellipse is easily found from the displacement of the stripes relative to the central section. The author notes that the accuracy of the measurements proves to be quite satisfactory.

V. Yu.