ABSTRACT
The dispersive characteristics of a photonic crystal fiber enhanced with a liquid crystal core are studied using a planewave expansion method. Numerical results demonstrate that by appropriate design such fibers can function in a single-mode/single-polarization operation, exhibit high- or low- birefringence behavior, or switch between an on-state and an off-state (no guided modes supported). All of the above can be controlled by the application of an external electric field, the specific liquid crystal anchoring conditions and the fiber structural parameters.
ABSTRACT
A method for reconstructing the constitutive parameters of two-dimensional (2-D) penetrable scatterers from scattered field measurements is presented. This method is based on the differential formulation of the forward scattering problem, which is solved by applying the finite-element method (FEM). Given a set of scattered field measurements, the objective is to minimize a cost function which consists of two terms. The first is the standard error term, which is related to the measurements and their estimates, while the second term, which is related to the Tikhonov regularization, is used to heal the ill posedness of the inverse problem. The iterative Polak-Ribière nonlinear conjugate gradient algorithm is applied to the minimization of the cost function. During each iteration of the algorithm, the direction of correction is computed by using a sensitivity analysis approach, which is carried out by an elaborate finite-element scheme. The adoption of the finite-element method results in sparse systems of equations, while the computational burden is further reduced by applying the adjoint state vector methodology. Finally, a microwave medical imaging application, which is related to the detection of proliferated bone marrow, is examined, while the robustness of the proposed technique in the presence of noise and for different regularization levels is investigated.