Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix

We present a theoretical study of multi-mode scattering of light by optically random media, using the Mueller-Stokes formalism which permits to encode all the polarization properties of the scattering medium in a real 4×4 matrix. From this matrix two relevant parameters can be extracted: the depolarizing power DM and the polarization entropy EM of the scattering medium. By studying the relation between EM and DM , we find that all scattering media must satisfy some universal constraints. These constraints apply to both classical and quantum scattering processes. The results obtained here may be especially relevant for quantum communication applications, where depolarization is synonymous with decoherence.PACS numbers: 03.65. Nk, 42.25.Dd, 42.25.Fx, 42.25.Ja Introduction The polarization aspects of random light scattering have drawn quite some interest in recent years, since they present a diagnostic method of the medium involved and also help visualization of objects that are hidden inside the medium [1]. When polarized light is incident on an optically random medium it suffers multiple scattering and, as a result, it may emerge partly or completely depolarized. The amount of depolarization can be quantified by calculating either the entropy (E F ) or the degree of polarization (P F ) of the scattered field [2]. It is simple to show that the field quantities E F and P F are related by a single-valued function: E F = E F (P F ). For example polarized light (P F = 1) has E F = 0 while partially polarized light (0 ≤ P F < 1) has 1 ≥ E F > 0. When the incident beam is polarized and the output beam is partially polarized, the medium is said to be depolarizing. An average measure of the depolarizing power of the medium is given by the so called depolarization index (D M ) [3]. Non-depolarizing media are characterized by D M = 1, while depolarizing media have 0 ≤ D M < 1. A depolarizing scattering process is always accompanied by an increase of the entropy of the light, the increase being due to the interaction of the field with the medium. An average measure of the entropy that a given random medium can add to the entropy of the incident light beam, is given by the polarization entropy E M [4]. Non-depolarizing media are characterized by E M = 0, while for depolarizing media 0 < E M ≤ 1. As the field quantities E F and P F are related to each other, so are the medium quantities E M and D M with the key difference that, as we shall show later, E M is a multi-valued function of D M .

show abstract

“…A deeper characterization of the scattering medium can be achieved by using the Hermitian matrix H [14,15] defined as…”

mentioning

confidence: 99%

Physical Bounds to the Entropy-Depolarization Relation in Random Light Scattering

Aiello

Woerdman

2005

Phys. Rev. Lett.

View full text Add to dashboard Cite

show abstract

“…Assuming that the given matrix M is the sum of a perturbation ∆M and an "exact" matrix M e which is a pure Mueller matrix or a sum of pure Mueller matrices, an error bound formula is derived in terms of the given matrix M such that M passes the test whenever the error bound is less than a given threshold value. Such a procedure has been implemented for the coherency matrix test by Anderson and Barakat (1994) and by Hovenier and Van der Mee (1996). In either paper, a "corrected" pure Mueller matrix or sum of pure Mueller matrices is sought that minimizes the error bound.…”

Section: A4 Discussionmentioning

confidence: 99%

“…This is obvious, since T and N s are unitarily equivalent and therefore have the same eigenvalues. As a test for sums of pure Mueller matrices, this was clearly understood by Cloude (1992a,b) and by Anderson and Barakat (1994). The details of the "target decomposition," but not its principle, are different but can easily be transformed into each other.…”

Section: A2 Relationships For Sums Of Pure Mueller Matricesmentioning

confidence: 99%

“…First of all, recalling that M is a pure Mueller matrix whenever T has one positive and three zero eigenvalues, the ratio of the second largest to the largest positive eigenvalue of T may be viewed as a measure for the degree to which a sum of pure Mueller matrices is pure [Cloude (1989[Cloude ( , 1992a, Anderson and Barakat (1994)]. Secondly, since a complex Hermitian matrix can be diagonalized by a unitary matrix whose columns form an orthonormal basis of its eigenvectors, one can write any sum of pure Mueller matrices as a sum of four pure Mueller matrices.…”

Section: A2 Relationships For Sums Of Pure Mueller Matricesmentioning

confidence: 99%

See 1 more Smart Citation

Fast computation of two-level circulant preconditioners

2006

View full text Add to dashboard Cite

In this paper we present an algorithm for the construction of the superoptimal circulant\ud preconditioner for a two-level Toeplitz linear system. The algorithm is fast, in the sense that it operates in FFT time. Numerical results are given to assess its performance when applied\ud to the solution of two-level Toeplitz systems by the conjugate gradient method, compared with the Strang and optimal circulant preconditioners

show abstract

“…Unfortunately, all practical systems are subject to noise, thus restricting the accuracy with which parameters of interest can be determined or the reliability of conclusions drawn. For example, searches for polarization signatures of quantum gravity in the cosmic background require highprecision polarimetric measurements [8], whilst error rates in wireless communications and polarimetric classification can be compromised by poor measurement accuracy [9,10]. Despite the growing prominence of polarization-based systems, no definition of resolution in a polarization domain exists in the literature, hence system capabilities cannot be easily assessed and compared.…”

Section: Introductionmentioning

confidence: 99%

Information and resolution in electromagnetic optical systems

Foreman

Török

2010

Phys. Rev. A

View full text Add to dashboard Cite

Quantitative analysis can play a vital role in a number of polarization-based optical systems, yet to date no definition regarding resolution in the polarization domain exists. By adopting a stochastic framework, a suitable metric is developed in this article, allowing a number of polarimetric systems to be assessed and compared. In so doing, the performance dependencies of polarization-based systems are demonstrated and fundamental trends are identified.

show abstract

Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix

Cited by 121 publications

References 10 publications

Physical Bounds to the Entropy-Depolarization Relation in Random Light Scattering

Physical Bounds to the Entropy-Depolarization Relation in Random Light Scattering

Fast computation of two-level circulant preconditioners

Information and resolution in electromagnetic optical systems

Contact Info

Product

Resources

About