Configuration of a Smectic A Liquid Crystal Due to an Isolated Edge Dislocation

We discuss the static configuration of a smectic A liquid crystal subject to an edge dislocation under the assumption the the director and layer normal fields (<b>n</b> and <b>a</b>, respectively) defining the smectic arrangement are not, in general, equivalent. After constructing the energy density for the smectic, we obtain exact solutions to the equilibrium equations which result from its minimisation at quadratic order in the variables which describe the distortion, and hence a complete description of the smectic configuration across the domain of the sample. We also examine the effect of relaxing the constraint <b>n</b> ≡ <b>a</b> for different values of the constants which characterise the response of the material to distortions, and compare these results with the "classical" case considered by previous authors, in which equivalence of <b>n</b> and <b>a</b> is enforced.