Formalism of optical coherence and polarization based on material media states

Abstract

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...

Snapshot circular dichroism measurements

“…To handle such processes, one must start with the coherent Jones formalism and then switch to the Mueller one. The formalism based on 4×4 Z states that we developed recently [29,30] is particularly suitable for this kind of evaluation since it allows for a direct calculation. If we consider the system setup of Fig.…”

Light scattering by coupled oriented dipoles: Decomposition of the scattering matrix

“…As it was discussed in Refs. [19,20] the outer product |h h| generates a 4 × 4 covariance scattering matrix of rank 1 that can be considered as an analog of a pure state in quantum mechanics. In terms of covariance vectors we can, alternatively, write the decomposition in Eq.…”

“…(26) and (27) are symmetric, the fourth component of these covariance vectors is always zero. This reads as an absence of circular polarization effects [19,21].…”

Mueller Quaternion with Matrix Coefficients for Depolarizing and Nondepolarizing Media

“…In previous works [1], [2] there were two different representations of Mueller-Jones states: the covariance vector |h and the Z matrix.…”

“…The same depolarization scheme given in [2] applies to this quaternion formulation as well. But, in the following it will be shown that there exists a Mueller quaternion with matrix coefficients which can transform the Stokes quaternion for depolarizing and nondepolarizing processes.…”