Interferometer birefringent

The basic principle of the birefringent interferometer or Lyot filter [4.24,4.56] is founded on the interference of polarized light that has passed through a birefringent crystal. Assume that a linearly polarized plane wave 

The superposition of these two waves results, in general, in elliptically polarized light, where the principal axis of the ellipse is turned by an angle = 0/2 against the direction of o- 

The elementary Lyot filter consists of a birefringent crystal placed between two linear polarizers (Fig. 4.63a). Assiune that the two polarizers are both parallel to the electric vector E(O) of the incoming wave. The second polarizer parallel to (0) transmits only the projection 

The transmission of the Lyot filter is therefore a function of the phase retardation, i.e.. 

Note According to (4.96) the maximum modulation of the transmittance with Tmax = To and Tmin = 0 is only achieved for a = 45°  

Taking into account absorption and reflection losses, the maximum transmission Ij/Io = To 1 becomes less than 100%. Within a small wavelength interval, the difference An = no — n can be regarded as constant. Therefore (4.92) gives the wavelength-dependent transmission function, cos cp, typical of a two-beam interferometer (Fig. 4.26). For extended spectral ranges the different dispersion of no(k) and e( ) has to be considered, which causes a wavelength dependence, An(k). 

Note According to (4.96) the maximum modulation of the transmittance with 

For phase differences j) = 2mjr linearly polarized light with E(L) E(0) is obtained, while for = (2m+l)7r and a = 45 , the transmitted wave is also linearly polarized but now E(L) 1 E(0). 

E = Ey sina + E cosa = A[sin2acos(wt-kgL) + cos2acos(wt-k(,L)] of the amplitudes which yields the transmitted time averaged intensity 

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To simplify FECO evaluation, it is conmion practice to experimentally filter out one of the components by the use of a linear polarizer after the interferometer. Mica bireftingence can, however, be useftil to study thin films of birefringent molecules [49] between the surfaces. Rabinowitz [53] has presented an eigenvalue analysis of birefringence in the multiple beam interferometer. 

Fig. 1. Representative device configurations exploiting electrooptic second-order nonlinear optical materials are shown. Schematic representations are given for (a) a Mach-Zehnder interferometer, (b) a birefringent modulator, and (c) a directional coupler. In (b) the optical input to the birefringent modulator is polarized at 45 degrees and excites both transverse electric (TE) and transverse magnetic (TM) modes. The appHed voltage modulates the output polarization. Intensity modulation is achieved using polarizing components at the output.

Fabry-Perot interferometers, polarization interference, birefringence, Lyot filters... 

Fig. 1 - Three common electro-optic device configurations Top Mach-Zehnder interferometer middle birefringent modulator bottom directional coupler...

Fig. 3.11 Electro-optic device configurations, (a) Mach-Zehnder interferometer, (b) birefringent modulator. TM and TE denote transverse magnetic and transverse electric polarization, respectively.

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). 

Some interferometers utilize the optical birefringence of specific crystals to produce two partial waves with mutually orthogonal polarization. The phase difference between the two waves is generated by the different refractive index for the two polarizations. An example of such a polarization interferometer is the Lyot filter [4.23] used in dye lasers to narrow the spectral linewidth (Sect. 4.2.9). 

The three most common basic configurations of polymeric modulators are the Mach-Zehnder interferometer, the birefringent modulator, and the directional cou-... 

Fig. 8. Mach Zehnder interferometer (top), birefringent modulator (middle), and directional coupler (bottom) device configurations are shown.

The measurements were made with a nonlinear polarization interferometer (see Fig. 3). A thermostat with the liquid crystal was placed between two crossed polarizers pi and/ 2- The beam from a helium-neon laser A = 0.638 pm), whose 2 is vanishingly small, was broadened by a telescope T and passed through polarizers into a cell with the NLC. Polarized and intensity-modulated emission from a helium-cadmium laser was also guided into the cell with the crystal whose birefringence it altered on account of conformation... 

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