Nondepolarizing Mueller matrices contain up to seven independent parameters. However, these seven parameters typically do not appear explicitly among the measured 16 parameters of a Mueller matrix, so that they are not directly accessible for physical interpretation. This work shows that all the information contained in a nondepolarizing Mueller matrix can be conveniently expressed in terms of a four component covariance vector state or a generating 4×4 matrix, which can be understood as a matrix state. The generating matrix, besides being directly related to the nondepolarizing Mueller matrix, mimics all properties of the Jones matrix and provides a powerful mathematical tool for formulating all properties of nondepolarizing systems, including the Mueller symmetries and the anisotropy coefficients.

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The fluctuations or disordered motion of the electromagnetic fields are described by statistical properties rather than instantaneous values. This statistical description of the optical fields is underlying in the Stokes-Mueller formalism that applies to measurable intensities. However, the fundamental concept of optical coherence, that is assessed by the ability of waves to interfere, is not treatable by this formalism because it omits the global phase. In this work we show that, using an analogy between deterministic matrix states associated to optical media and quantum mechanical wavefunctions, it is possible to construct a general formalism that accounts for the additional terms resulting from the coherency effects that average out for incoherent treatments. This method generalizes further the concept of coherent superposition to describe how deterministic states of optical media can superpose to generate another deterministic media state. Our formalism of coherency is used to study the combined polarimetric response of interfering plasmonic nanoantennas.In optics, interference is the phenomena that occurs when two coherent waves superpose. The celebrated example is the Young's double slit experiment with a beam of light, but quantum coherence and interference is not restricted to photons. Any moving particle is susceptible to interfere with another if they keep a well-defined and constant phase relation, as it can occur for example in between two oscillating dipoles [1]. In optics, this is one of the most fundamental interactions. When a material medium is irradiated by an electromagnetic wave, molecular electric charges are set in oscillatory motion by the electric field of the wave, producing secondary radiation in a form of refracted, reflected, diffracted or scattered light with certain polarization attributes.In quantum mechanics, the observable values are the eigenvalues of Hermitian operators associated to the observable quantity. The observable corresponding to the optical phenomena occurring in light-matter interactions is the 4×4 scattering matrix with sixteen real elements also known as the Mueller matrix that describes the linear transformation of the Stokes parameters of a light beam upon interaction with a linear medium. In this work, we first demonstrate how alternative representations of nondepolarizing (deterministic) optical systems that were recently presented [2] can be used to make the analogy between the scattering matrix states of optical systems and the quantum mechanical wavefuction. We also show that quantum coherence in material media can be represented by a coherent linear superposition of matrix (or vector) states associated to non-depolarizing Mueller matrices. This linear combination is generally understood as a convex sum of Jones matrices of nondepolarizing component systems [3,4]. But here, instead of Jones matrices, we propose a linear combination of matrix (or vector) states with complex coefficients that play the role of probability amplitudes of quantum mechanics. Despi...

In this Letter we describe an experiment in which coherent light is sent through a calcite crystal that separates the photons by their polarization. The two beams are then let to superpose, and this recombined beam is used to measure the Mueller matrix of the system. Results are interpreted according to our recent formalism of coherent superposition in material media. This is the first experimental implementation of a Young's experiment with complete polarimetry, and it is demonstrated that our method can be used for the experimental synthesis of optical devices with on-demand optical properties.

It is shown that the Stokes-Mueller formalism can be reformulated in terms of quaternions, and the quaternion approach is more suitable for the formalism of Mueller-Jones states that we have recently described. In terms of quaternions it can be shown that the vector and matrix states and the Jones matrix associated to nondepolarizing optical systems are different representations isomorphic to the same quaternion state, and this quaternion state turns out to be the rotator of the Stokes quaternion. It is also shown that the coherent linear combination of nondepolarizing optical media states and depolarization phenomena can be reformulated in terms of quaternion states.

A procedure for the parallel decomposition of a depolarizing Mueller matrix with an associated rank 2 covariance matrix into its two nondepolarizing components is presented. We show that, if one of the components agrees with certain symmetry conditions, the arbitrary decomposition becomes unique, and its calculation is straightforward. Solutions for six different symmetries, which are relevant for the physical interpretation of polarimetric measurements, are provided. With this procedure, a single polarimetric measurement is sufficient to fully disclose the complete polarimetric response of two different systems and evaluate their weights in the overall response. The decomposition method we propose is illustrated by obtaining the ellipsometric responses of a silicon wafer and a holographic grating from a single measurement in which the light spot illuminates sectors of both materials. In a second example, we use the decomposition to analyze an optical system in which a polarizing film is partially covered by another misaligned film.

Conversión de un microscopio de polarización en un microscopio de matriz de Mueller. Aplicación a la medida de fibras textiles. ABSTRACT:This work reports the conversion of a commercial polarization microscope (Zeiss Jenaval) into an automatized Mueller matrix microscope. A Mueller matrix measurement provides the value of all the optical properties of a specimen (linear dichroism, linear birefringence, circular dichroism etc.) at a specific wavelength. In contrast to traditional polarization microscopes, which use white light and crossed polarizers to generate colored interference patterns that are analyzed by the microscope user and give only semi-quantitative results, here we demonstrate that it is possible to convert a polarization microscope into a Mueller microscope by only adding two motorized rotating compensators into the optical path without altering the optics or other opto-mechanical elements of the microscope. To our knowledge this is the most compact, fast and handy Mueller microscope ever developed. The performance of this new Mueller matrix microscope is illustrated with some birefringence measurements on textile fibers.Key words: microscopy, polarimetry, Mueller matrix, birefringence. RESUMEN:Este trabajo describe la conversión de un microscopio de polarización comercial (Zeiss Jenaval) en un microscopio de matriz de Mueller automatizado. Una medida de la matriz de Mueller proporciona todas las propiedades ópticas de una muestra (dicroísmo lineal, birrefringencia lineal, dicroísmo circular, etc) para una longitud de onda dada. Los microscopios de polarización tradicionales usan luz blanca y polarizadores cruzados para generar un patrón de colores interferencia que debe ser interpretado por el usuario del microscopio y proporciona resultados sólo semi-cuantitativos. En este trabajo demostramos que añadiendo dos compensadores rotatorios actuados por sendos motores es posible convertir un microscopio de polarización en un microscopio de matriz de Mueller sin alterar la óptica u otros elementos opto-mecánicos del microscopio. Creemos que este es el microscopio de matriz de Mueller más compacto, rápido y práctico que se ha desarrollado. El funcionamiento de este microscopio se demuestra con algunas medidas de birrefringencia en fibras textiles.Palabras clave: microscopía, polarimetría, matriz de Mueller, birrefringencia.

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