Optical phase shift

Derive Eq. (13.17). Note that the condition is 1 < n < n2 and that there is an optical phase shift of tt if light is reflected from a material with higher optical density and a phase shift of 0 if the reflecting material has a lower optical density. What is the condition for destructive interference in the case 1 < n > n2 ... 

Fig. 15. In the Sa phase, the mesogenic parts (depicted as ellipsoids) of the elastomeric macromolecule stand upright (9 = 0°) inside the single smectic layers. By applying a lateral electric field (perpendicular to the plane of the paper), a tilt angle 6 that is proportional to the electric field E can be induced (electroclinic effect). The sign of the tilt depends on the sign of the electric field E. Hence, each smectic layer shrinks by Ak/z twice during one period of the electric field. The shrinkage Ah of the whole film is measured by the interferometer as an optical phase shift between the sample beam and the reference beam.

We have recently shown that the presence of phase-separated structures in polymer-blend microparticles can be indicated qualitatively by a distortion in the two-dimensional diffraction pattern. The origin of fringe distortion from a multi-phase composite particle can be understood as a result of refraction at the boundary between domains of different polymers, which typically exhibit large differences in refractive index. Thus, the presence of separate sub-domains introduces optical phase shifts and refraction resulting in a randomization (distortion) in the internal electric field intensity distribution that is manifested as a distortion in the far-field diffraction pattern. 

Side view of device showing various positions of electrically controlled liquid crystal molecules used to generate the quadratic optical phase shifts required to form a variable focal length cylindrical lens. Source Riza, N.A. and M.C. Dejule. 1994. Optics Letters, 19(14), 1013-1015. With permission.)... 

Equation (21.3) reduces to the optical model used for foam films by replacing A with 1 — A to account for differences in optical phase shifts upon reflection, and by setting K = —Y2. As with the symmetric case, Duyvis optical corrections for the adsorbed surfactant layers can be applied to extract specific distances within the film. 

The situation of displacement determination stands in evident contrast. Given careful optical beam preparation, the interval between two positions of a retroreflecting mirror can be determined with considerable refinement. Simply stated, almost all questions about optical phase shift, surface location and certain classes of imperfection disappear when the same surface is illuminated at each terminus (and, if appropriate, during the "scan). There are important questions about illumination averaging but these can be controlled as has been already demonstrated below the 10 level. 

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