Three-layer interferometer

In the symmetric, three-layer interferometer, only even-order fringes are sensitive to refractive index and it is possible to obtain spectral infonnation of the confined film by comparison of the difierent intensities of odd-and even-order fringes. The absorption spectmm of tliin dye layers between mica was investigated by Muller and Machtle [M, M] using this method. 

Figure Bl.20.4. Cross-sectional sideview of a symmetric, three-layer interferometer illustrating the origin of primary, secondary, tertiary and gap FECOs. (Reproduced with permission from [M])...

Fig. 3.16. The Surface Force Apparatus. Inset the crossed-cylinders three-layers interferometer.

Knowing the optical properties and the orientation of the mica layers, a conversion chart can be calculated to determine the separation D from the measured A, as shown in Fig. 3.17. The conversion chart is calculated from the equations of a three-layer interferometer [39], possibly modified to include birefringence of the mica layers [40]. As a general rule, A is always shifted towards smaller values with decreasing D. As X depends also on the index n, measurements for two or more transmission wavelengths are sufficient to calculate D and n at the same time. To do that, one has to invert a set of interferometric equations giving A as a function of D and n. The resulting tjrpical resolution in separation D is about 0.2 nm and the sensitivity to n is about 0.01. We stress however that the equations are nonlinear and the solutions may become unreliable for some D, due to an instability with respect to the error in A (see Fig. 3.21 for an example). 

An optical interferometric technique is used to measure the separation D, simultaneously providing also the liquid refractive index n and the curvature R. The mica sheets are made partially reflecting by evaporating a 40 -f 50 nm silver layer on the inner sides of the mica sheets. The cell is then illuminated by a collimated white light beam, in a direction perpendicular to both axis of the cylinders. The two partially reflective silver layers form a sort of three-layer curved interferometer selective transmission occurs only for the spectral components resonating with the mica/liquid/mica cavity . The transmitted wavelengths A are analyzed by an interferometer with a resolution better than 0.1 nm, to get information about the optical properties of the layers, especially the thickness D and the index n of the liquid. 

The (I33 coefficient of a lower molecular weight (13,000 g/mol) version of 6 was measured using the methods described in the previous section (25). After poling at 170°C with a similar time-temperature protocol, the d33 was found to be 27 pm/V close to the value found for 1. The electro-opdc coefficient of 6, as measured in a three layer Mach-Zehnder interferometer, is essentially the same as that found for 1 (8.2pmA0(26). 

Beam dividers, or beamsplitters, which divide reflected and transmitted waves nearly equally, are essential components in Michelson interferometers, but are also used in other instruments. Since they are based on thin film technology we discuss such dividers in this section. The solution for a two-interface (three-layer) stack, Eq. (5.6.15), is squared to derive the reflected intensity. After a straightforward, although tedious, calculation, one finds... 

The thin film theory developed in Subsection 5.6.a is directly applicable to the design of interference filters and Fabry-Perot interferometers. These devices are similar in concept and, therefore, are treated together. The normalized reflected amplitude for a three layer film of refractive indices 2, and no [see Eq. (5.6.21)] is applied first... 

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