Noé Ortega-Quijano

Mueller matrix differential decomposition

We present a Mueller matrix decomposition based on the differential formulation of the Mueller calculus. The differential Mueller matrix is obtained from the macroscopic matrix through an eigenanalysis. It is subsequently resolved into the complete set of 16 differential matrices that correspond to the basic types of optical behavior for depolarizing anisotropic media. The method is successfully applied to the polarimetric analysis of several samples. The differential parameters enable one to perform an exhaustive characterization of anisotropy and depolarization. This decomposition is particularly appropriate for studying media in which several polarization effects take place simultaneously.

Depolarizing differential Mueller matrices

The evolution of a polarized beam can be described by the differential formulation of Mueller calculus. The nondepolarizing differential Mueller matrices are well known. However, they only account for 7 out of the 16 independent parameters that are necessary to model a general anisotropic depolarizing medium. In this work we present the nine differential Mueller matrices for general depolarizing media, highlighting the physical implications of each of them. Group theory is applied to establish the relationship between the differential matrix and the set of transformation generators in the Minkowski space, of which Lorentz generators constitute a particular subgroup.

Experimental validation of Mueller matrix differential decomposition.

Mueller matrix differential decomposition is a novel method for retrieving the polarimetric properties of general depolarizing anisotropic media [N. Ortega-Quijano and J. L. Arce-Diego, Opt. Lett. 36, 1942 (2011), R. Ossikovski, Opt. Lett. 36, 2330 (2011)]. The method has been verified for Mueller matrices available in the literature. We experimentally validate the decomposition for five different experimental setups with different commutation properties and controlled optical parameters, comparing the differential decomposition with the forward and reverse polar decompositions. The results enable to verify the method and to highlight its advantages for certain experimental applications of high interest.

Polarimetric study of birefringent turbid media with three-dimensional optic axis orientation

Recent approaches to the analysis of biological samples with three-dimensional linear birefringence orientation require numerical methods to estimate the best fit parameters from experimental measures. We present a novel analytical method for characterizing the intrinsic retardance and the three-dimensional optic axis orientation of uniform and uniaxial turbid media. It is based on a model that exploits the recently proposed differential generalized Jones calculus, remarkably suppressing the need for numerical procedures. The method is applied to the analysis of samples modeled with polarized sensitive Monte Carlo. The results corroborate its capacity to successfully characterize 3D linear birefringence in a straightforward way.

Mueller matrix differential decomposition for direction reversal: application to samples measured in reflection and backscattering

Mueller matrix differential decomposition is a novel method for analyzing the polarimetric properties of optical samples. It is performed through an eigenanalysis of the Mueller matrix and the subsequent decomposition of the corresponding differential Mueller matrix into the complete set of 16 differential matrices which characterize depolarizing anisotropic media. The method has been proposed so far only for measurements in transmission configuration. In this work the method is extended to the backward direction. The modifications of the differential matrices according to the reference system are discussed. The method is successfully applied to Mueller matrices measured in reflection and backscattering.

Full characterization of dichroic samples from a single measurement by circular polarization orthogonality breaking

We report a novel method to unambiguously determine the magnitude and orientation of linear dichroism in a simultaneous way. It is based on the use of a dedicated dual-frequency dual-polarization coherent source providing two orthogonal circularly polarized modes at the output. We show that the interaction of such a beam with dichroic media gives rise to a beatnote signal whose amplitude and phase enable the full determination of the diattenuation coefficient and axis orientation, respectively. The application of this method to polarimetric imaging provides single-shot sample characterization by its diattenuation coefficient and optical axis angle, with potential applications in biomedical imaging.

Polarimetric contrast microscopy by orthogonality breaking

We report the design and first implementation of an active polarimetric imaging system based on the recently introduced concept of polarimetric sensing by orthogonality breaking, which involves a specific crossed-polarization dual-frequency illumination. We describe the laser source architecture and microscope set-up devoted to visible imaging at 488 nm, as well as the specific homodyne detection chain required for orthogonality breaking measurements. The first polarimetric images obtained with this non-conventional approach are presented. The polarimetric contrasts observed validate the polarimetric sensitivity of the technique.

Generalized Jones matrices for anisotropic media

The interaction of arbitrary three-dimensional light beams with optical elements is described by the generalized Jones calculus, which has been formally proposed recently [Azzam, J. Opt. Soc. Am. A 28, 2279 (2011)]. In this work we obtain the parametric expression of the 3×3 differential generalized Jones matrix (dGJM) for arbitrary optical media assuming transverse light waves. The dGJM is intimately connected to the Gell-Mann matrices, and we show that it provides a versatile method for obtaining the macroscopic GJM of media with either sequential or simultaneous anisotropic effects. Explicit parametric expressions of the GJM for some relevant optical elements are provided.

Necrosis prediction of photodynamic therapy applied to skin disorders

The great selectivity and the lack of side effects of Photodynamic Therapy make it more advantageous than radiotherapy or chemotherapy. The application of PDT to skin diseases is particularly appropriate, due to the accessibility of this tissue. Common disorders like nonmelanoma skin cancer, that includes basocelullar or squamous cell carcinomas, can be treated with PDT. Conventional procedures, like surgery or radiotherapy, are not so efficient and do not, in general, obtain the same favourable results. PDT in dermatology medical praxis uses fixed protocols depending on the photosensitizer and the optical source used. These protocols are usually provided by the photosensitizer laboratory, and every lesion is treated with the same parameters. In this work we present a photo-chemical model of PDT applied to skin disorders treated with topical photosensitizers. Optical propagation inside the tissue is calculated by means of a 3D diffusion equation, solved via a finite difference numerical method. The photosensitizer degradation or photobleaching is taken into account, as the drug looses efficiency with the irradiation time. With these data the necrosis area is estimated, so this model could be used as a predictive tool to adjust the optical power and exposition time for the particular disease under treatment.

Orthogonality-breaking sensing model based on the instantaneous Stokes vector and the Mueller calculus.

Polarimetric sensing by orthogonality breaking has been recently proposed as an alternative technique for performing direct and fast polarimetric measurements using a specific dual-frequency-dual-polarization (DFDP) source. Based on the instantaneous Stokes-Mueller formalism to describe the high-frequency evolution of the DFDP beam intensity, we thoroughly analyze the interaction of such a beam with birefringent, dichroic, and depolarizing samples. This allows us to confirm that orthogonality breaking is produced by the sample diattenuation, whereas this technique is immune to both birefringence and diagonal depolarization. We further analyze the robustness of this technique when polarimetric sensing is performed through a birefringent waveguide, and the optimal DFDP source configuration for fiber-based endoscopic measurements is subsequently identified. Finally, we consider a stochastic depolarization model based on an ensemble of random linear diattenuators, which makes it possible to understand the progressive vanishing of the detected orthogonality-breaking signal as the spatial heterogeneity of the sample increases, thus confirming the insensitivity of this method to diagonal depolarization. The fact that the orthogonality-breaking signal is exclusively due to the sample dichroism is an advantageous feature for the precise decoupled characterization of such an anisotropic parameter in samples showing several simultaneous effects.