We propose a new method to measure within a high accuracy both the electro-optic properties and the birefringence changes in bulk crystals. This technique is based upon the frequency doubling electro-optic modulation (FDEOM) method in which an external modulator is inserted in the experimental Sénarmont setup. We present a complete analysis of the optical response of a Sénarmont setup within Jones formulation. The FDEOM method possesses as main advantages a high accuracy and sensitivity in the measurements due to a direct determination of the electric field-induced phase retardation in the crystal under study. The measurements are recorded with an adjustment of the shape of the output beam at a frequency double the frequency of the ac applied voltage. The external modulation version of this method allows us to perform measurements with a higher modulation depth and to avoid any additional dynamical perturbation in the electro-optic crystal under study. Therefore, even small values of the electro-optic coefficients can be accurately measured. Moreover, the new method is able to measure with a high accuracy the variations of the birefringence in any crystal, even if it does not present an electro-optic effect. Some significative results in LiNbO3 point out the large advantages of the method.

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This article addresses the problem of the Non Unitary Joint Block Diagonalization (NU − JBD) of a given set of complex matrices for the blind separation of convolutive mixtures of sources. We propose new different iterative optimization schemes based on Conjugate Gradient, Preconditioned Conjugate Gradient, Levenberg-Marquardt and Quasi-Newton methods. We perform also a study to determine which of these algorithms offer the best compromise between efficiency and convergence speed in the studied context. To be able to derive all these algorithms, a preconditioner has to be computed which requires either the calculation of the complex Hessian matrices or the use of an approximation to these Hessian matrices. Furthermore, the optimal stepsize is also computed algebraically to speed up the convergence of these algorithms. Computer simulations are provided in order to illustrate the behavior of the different algorithms in various contexts: when exactly block-diagonal matrices are considered but also when these matrices are progressively perturbed by an additive Gaussian noise. Finally, it is shown that these algorithms enable solving the blind separation of the convolutive mixtures of sources problem. Keywords

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