Depolarization and Polarization Indices of an Optical System

Gil, José J.; Bernabéu, Eusebio

doi:10.1080/713821924

Cited by 228 publications

(146 citation statements)

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“…In this case ψ λ (k) = T λλ0 (k, k 0 ) and the statistical distribution of the M µν 's can be numerically calculated accordingly to Eqs. (2)(3). In this way we have calculated the ensemble-averaged polariza-tion entropy E M and depolarization index D M of the medium, as functions of N for the case in which the angular aperture of the detector is so small that W ij (k) ≃ δ ij .…”

Section: Curvementioning

confidence: 99%

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

Aiello

Woerdman

2005

Phys. Rev. Lett.

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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 .

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Section: Curvementioning

confidence: 99%

“…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.…”

mentioning

confidence: 99%

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

Aiello

Woerdman

2005

Phys. Rev. Lett.

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“…The value for D ranges from 0 (nondepolarizing) to 1 (perfectly depolarizing). 11,12 Calculation of the anisotropy coefficients (α, β, and γ) from experimental MMSE data free of depolarization is very simple and straightforward. 13 Nondepolarizing MMSE data are retrieved using known mathematical decomposition techniques.…”

Section: Design Of Experimentsmentioning

confidence: 99%

Metrology for block copolymer directed self-assembly structures using Mueller matrix-based scatterometry

Dixit

Kamineni

Farrell

et al. 2015

J. Micro/Nanolith. MEMS MOEMS

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Abstract. Patterning based on directed self-assembly (DSA) of block copolymer (BCP) has been demonstrated to be a cost-effective manufacturing technique for advanced sub-20-nm structures. This paper describes the application of Mueller matrix spectroscopic ellipsometry (MMSE) based scatterometry to optically characterize polystyrene-b-polymethylmethacrylate patterns and Si fins fabricated with DSA. A regression-based (inverseproblem) approach is used to calculate the line-width, line-shape, sidewall-angle, and thickness of the DSA structures. In addition, anisotropy and depolarization calculations are used to determine the sensitivity of MMSE to DSA pattern defectivity. As pattern order decreases, the mean squared error value increases, depolarization value increases, and anisotropy value decreases. These specific trends are used in the current work as a method to judge the degree of alignment of the DSA patterns across the wafer. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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“…The DI as a single number metric for characterizing the depolarization of a Muller matrix was proposed in [26]. It is defined as…”

Section: Depolarization Indexmentioning

confidence: 99%

“…[24] using an optical path of 4.5 km. Gil and Bernabeu [25,26] introduced the depolarization index (DI), which features a well-defined and useful geometric meaning in the configuration space of the Mueller matrix. Two single-number metrics for the depolarization of samples were differentiated by Chipman [27].…”

Section: Introductionmentioning

confidence: 99%

Polarization Characteristics of a Partially Coherent Gaussian Schell-Model Beam in Slant Atmospheric Turbulence

Li¹,

Wu²,

Wang³

2011

PIER

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Abstract-On the basis of the extended Huygens-Fresnel principle, the cross-spectral density matrix (CSDM) of partially coherent Gaussian Schell-model (GSM) beams in the slant atmospheric turbulence is derived. Given that the light emitted from a transmitter is elliptically polarized light, the degree of polarization (DoP) of the partially coherent GSM beams is represented by Stokes parameters expressed by the elements of the CSDM. The expressions of the orientation angle, polarized light intensity in the major axis are derived and the numerical results are presented. Depolarization theory is studied using a Mueller matrix and the depolarization index (DI) is obtained to describe the depolarized state of the partially coherent GSM beams propagating in the slant atmospheric turbulence. Results show that the DOP and DI of the beam tend to their initial value in the long-range propagation.

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Depolarization and Polarization Indices of an Optical System

Cited by 228 publications

References 2 publications

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

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

Metrology for block copolymer directed self-assembly structures using Mueller matrix-based scatterometry

Polarization Characteristics of a Partially Coherent Gaussian Schell-Model Beam in Slant Atmospheric Turbulence

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