Light depolarization by inhomogeneous linear birefringent media

The purpose of the article is to provide rigorous analysis of light depolarization by inhomogeneous linear birefringent media in single scattering case. The object under investigation is a lossless anisotropic crystalline slab with surface inhomogeneity. For the analysis we use the Mueller matrix...

Повний опис

Збережено в:

Бібліографічні деталі
Дата:	2009
Автори:	Savenkov, S.N., Oberemok, Y.A., Yakubchak, V.V., Aulin, Y.V., Barchuk, О.I.
Формат:	Стаття
Мова:	English
Опубліковано:	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 2009
Назва видання:	Semiconductor Physics Quantum Electronics & Optoelectronics
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/118607
Теги:	Додати тег Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:	Light depolarization by inhomogeneous linear birefringent media / S.N. Savenkov, Y.A. Oberemok, V.V. Yakubchak, Y.V. Aulin, О.I. Barchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 1. — С. 86-90. — Бібліогр.: 10 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine

id	irk-123456789-118607
record_format	dspace
spelling	irk-123456789-1186072017-05-31T03:06:29Z Light depolarization by inhomogeneous linear birefringent media Savenkov, S.N. Oberemok, Y.A. Yakubchak, V.V. Aulin, Y.V. Barchuk, О.I. The purpose of the article is to provide rigorous analysis of light depolarization by inhomogeneous linear birefringent media in single scattering case. The object under investigation is a lossless anisotropic crystalline slab with surface inhomogeneity. For the analysis we use the Mueller matrix model of such class of media derived in [1], Cloude’s coherency matrix method and known single value depolarization metrics. Sample calculations are given for calcite CaCO₃, paratellurite TeO₂ and lithium niobate LiNbO₃. 2009 Article Light depolarization by inhomogeneous linear birefringent media / S.N. Savenkov, Y.A. Oberemok, V.V. Yakubchak, Y.V. Aulin, О.I. Barchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 1. — С. 86-90. — Бібліогр.: 10 назв. — англ. 1560-8034 PACS 42.25.Dd, 42.25.Ja, 42.81.-i http://dspace.nbuv.gov.ua/handle/123456789/118607 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	The purpose of the article is to provide rigorous analysis of light depolarization by inhomogeneous linear birefringent media in single scattering case. The object under investigation is a lossless anisotropic crystalline slab with surface inhomogeneity. For the analysis we use the Mueller matrix model of such class of media derived in [1], Cloude’s coherency matrix method and known single value depolarization metrics. Sample calculations are given for calcite CaCO₃, paratellurite TeO₂ and lithium niobate LiNbO₃.
format	Article
author	Savenkov, S.N. Oberemok, Y.A. Yakubchak, V.V. Aulin, Y.V. Barchuk, О.I.
spellingShingle	Savenkov, S.N. Oberemok, Y.A. Yakubchak, V.V. Aulin, Y.V. Barchuk, О.I. Light depolarization by inhomogeneous linear birefringent media Semiconductor Physics Quantum Electronics & Optoelectronics
author_facet	Savenkov, S.N. Oberemok, Y.A. Yakubchak, V.V. Aulin, Y.V. Barchuk, О.I.
author_sort	Savenkov, S.N.
title	Light depolarization by inhomogeneous linear birefringent media
title_short	Light depolarization by inhomogeneous linear birefringent media
title_full	Light depolarization by inhomogeneous linear birefringent media
title_fullStr	Light depolarization by inhomogeneous linear birefringent media
title_full_unstemmed	Light depolarization by inhomogeneous linear birefringent media
title_sort	light depolarization by inhomogeneous linear birefringent media
publisher	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
publishDate	2009
url	http://dspace.nbuv.gov.ua/handle/123456789/118607
citation_txt	Light depolarization by inhomogeneous linear birefringent media / S.N. Savenkov, Y.A. Oberemok, V.V. Yakubchak, Y.V. Aulin, О.I. Barchuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 1. — С. 86-90. — Бібліогр.: 10 назв. — англ.
series	Semiconductor Physics Quantum Electronics & Optoelectronics
work_keys_str_mv	AT savenkovsn lightdepolarizationbyinhomogeneouslinearbirefringentmedia AT oberemokya lightdepolarizationbyinhomogeneouslinearbirefringentmedia AT yakubchakvv lightdepolarizationbyinhomogeneouslinearbirefringentmedia AT aulinyv lightdepolarizationbyinhomogeneouslinearbirefringentmedia AT barchukoi lightdepolarizationbyinhomogeneouslinearbirefringentmedia
first_indexed	2025-07-08T14:18:46Z
last_indexed	2025-07-08T14:18:46Z
_version_	1837088718728462336
fulltext	Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 1. P. 86-90. © 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 86 PACS 42.25.Dd, 42.25.Ja, 42.81.-i Light depolarization by inhomogeneous linear birefringent media S.N. Savenkov, Y.A. Oberemok, V.V. Yakubchak, Y.V. Aulin, О.I. Barchuk Taras Shevchenko Kyiv National University, Radiophysics Department, 5 build., 2, Acad. Glushkov ave., 03127 Kyiv, Ukraine, phone: (380-44)526-04-83; e-mail: sns@univ.kiev.ua Abstract. The purpose of the article is to provide rigorous analysis of light depolarization by inhomogeneous linear birefringent media in single scattering case. The object under investigation is a lossless anisotropic crystalline slab with surface inhomogeneity. For the analysis we use the Mueller matrix model of such class of media derived in [1], Cloude’s coherency matrix method and known single value depolarization metrics. Sample calculations are given for calcite CaCO3, paratellurite TeO2 and lithium niobate LiNbO3. Keywords: light scattering, depolarization, Mueller matrix, birefringence, Cloude’s coherency matrix, entropy. Manuscript received 09.12.08; accepted for publication 18.12.08; published online 02.03.09. 1. Introduction When the polarization state of the light is characterized by means of the Stokes parameters, the transformation matrix is known as the Mueller matrix [2, 3]. From the properties of the Mueller matrix, one can draw insightful information about the underlying system. The exploitation of light polarization properties has a wide range of applications in a variety of fields, namely photonics technology [2, 3], astrophysics [4], biological and ecological optics [5] where scattering is linked to polarization state transformation and occurrence of depolarization. Depolarization is the result of decorrelation of the phases and amplitudes of the light electric vector and selective absorption of polarization states [2]. As shown earlier [1], the Mueller matrix of anisotropic lossless crystalline slab with surface inhomogeneity (roughness) in the eigen coordinate system has the following form: , )(00 )(00 00 00 21122112 21122112 22112211 22112211 ⎟⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎝ ⎛ Φ+ΦΦ−Φ− Φ−ΦΦ+Φ Φ+ΦΦ−Φ Φ−ΦΦ+Φ = i i M (1) where ( ) , 2 ρ 1 1exp 1 2 ρexp1 2 2222 2 ⎟⎟ ⎟ ⎠ ⎞ ⎪⎭ ⎪ ⎬ ⎫ ⎪⎩ ⎪ ⎨ ⎧ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ +σ − +σ η + ⎜ ⎜ ⎝ ⎛ + ⎪⎭ ⎪ ⎬ ⎫ ⎪⎩ ⎪ ⎨ ⎧ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛−η−Φ=Φ z wk ww z wk xyxy xy xy brf xyxy (2,a) ( ) ( )( )2exp 222 eoheo brf xy nnkhnnik −σ−−=Φ , (2.b) ( ) 2124241 kdzdw += , (2.c) ( )( )11222 −−σ=σ eohxy nnk , (2.d) ( )2exp1 xyxy σ−−=η , (2.e) λπ= 2k is a wavenumber; h is the thickness of a crystalline slab; eon , denotes refractive indexes of medium associated with its linear eigenpolarizations, and d is the beam radius. After performing normalization, we get: ⎟⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ψψ− ψψ = )cos()sin(00 )sin()cos(00 001 001 bb bb a a M , (3) where ( ) ( )22112211 Φ+ΦΦ−Φ=a , (4) ( )2211122 Φ+ΦΦ=b , (5) ( )brf 12arg Φ=ψ . (6) To describe depolarization, it has been introduced several the so-called “single value depolarization metrics”. In this paper, we use only those of them which do not need scanning the polarization states of input light for characterization of medium depolarization ability. First single value metrics is the depolarization index DI introduced in [6]: Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 1. P. 86-90. © 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 87 11 2 1 2 11 4 1, 2 3 mmmDI ji ij ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −= ∑ = . (7) where ijm are Mueller matrix elements in the eigen coordinate system. The depolarization index lies within the range 10 ≤≤ DI . Boundary values of DI associate with the case of unpolarized and totally polarized output light, respectively. The Q -metrics is [7]: [ ] [ ] [ ]2 224 1 2 1 4 1 2 2 1 3 D DDImmQ j j j i ij + − == ∑∑ = = = , (8) where 2 14 2 13 2 12 mmmD ++= is the diattenuation parameter and 10 ≤≤ D . The bound on the Q -metric is 30 ≤≤ Q . In this case, 0=Q corresponds to totally depolarizing medium; 10 << Q − to partially depolarizing medium; 31 <≤ Q represents a partially depolarizing medium if, in addition, 10 << DI , otherwise, represents non- depolarizing diattenuating medium; 3=Q is for non- depolarizing non-diattenuating medium. One more singlular value depolarization metric that we use below is entropy. The entropy S was introduced in Cloude’s coherency matrix method [8, 9], which is as follows. The coherence matrix J (with elements ijJ ) is derived from the corresponding Mueller matrix as: ( )4433221111 41 mmmmJ +++= ( )4224311313 41 imimmmJ −++= ( )4334211221 41 imimmmJ −++= ( )4132231423 41 immmimJ −++= ( )4224311331 41 imimmmJ +−+= ( )4433221133 41 mmmmJ −+−= ( )4132231441 41 mimimmJ +−+= ( )4334211243 41 mmimimJ +++−= ( )4334211212 41 imimmmJ +−+= (9) ( )4132231414 41 mimimmJ ++−= ( )4433221122 41 mmmmJ −−+= ( )4224311324 41 mmimimJ +++−= ( )4132231432 41 immmimJ +++−= ( )4334211234 41 mmimimJ ++−= ( )4224311342 41 mmimimJ ++−= ( )4433221144 41 mmmmJ +−−= . Thus, J depends linearly on M . It can be seen that the coherence matrix J is positive semidefinite Hermitian and, hence, has always four real eigenvalues. The eigenvalues of the coherence matrix, iλ , can be combined to form a quantity that is a measure of depolarization in the studied medium. This quantity is called entropy and is defined as: ∑ ∑∑ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ λλ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ λλ−= N i j jiN j jiS 1 log . (10) When eigenvalues iλ of the coherence matrix J are given, we have for the initial Mueller matrix: qq D q q Dq TMMM ⇔λ=∑ = ; 4 1 , (11) here q DM are the Mueller-Jones matrices obtained from the Jones matrices [2]. The Jones matrix, T (with elements ijt ), in turn, is obtained in the following manner: ,4,1,, ,, )( 2 )( 1 )( 22 )( 4 )( 3 )( 21 )( 4 )( 3 )( 12 )( 2 )( 1 )( 11 =τ−τ=τ+τ= τ−τ=τ+τ= qtit itt qqqqqq qqqqqq (12) where ( ) ( )Tqq 4321τ ττττ= is q -th eigenvector of the coherence matrix J . Thus, the Cloude coherency matrix method is, in essence, an additive matrix model of the depolarizing Mueller matrix, and represents the initial depolarizing Mueller matrix as a weighted convex sum of four Mueller-Jones matrices. If three of the eigenvalues of J vanish, then the initial matrix M is a deterministic Mueller-Jones matrix. If all four eigenvalues of J are not equal to zero and, at that, 5.0≤S , then the Mueller-Jones matrix, which corresponds to the maximal eigenvalue, is the dominant type of deterministic polarization transformation of the studied medium. So, this method gives the possibility to study the anisotropy properties of depolarizing media. In this work, we investigate the features of light depolarization by inhomogeneous anisotropic media described by the Mueller matrix Eq. (3) using the singular value depolarization metrics presented above. 2. Simulation results and discussion 2.1. Cloude’s coherency matrix analysis Cloude’s coherency matrix corresponding to the Mueller matrix Eq. (3) has generally the form: ( ) ( ) ( ) ( ) ⎟⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ψ−ψ+ ψ−ψ+ = 0000 0000 00)cos(1)sin( 00)sin()cos(1 2 1 bbia biab T . (13) The eigenvalues of the coherency matrix T Eq. (3): ⎟ ⎠ ⎞⎜ ⎝ ⎛ +++−⇒λ 2222 1100 2 1 babai . (14) Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 1. P. 86-90. © 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 88 0.00 0.10 0.20 0.30 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 LiNbO3 TeO2 CaCO3 S σh, µm DI Fig. 1. Dependence of the entropy S on depolarization index DI and inhomogeneity σh. The deterministic Mueller matrices in Cloude decomposition Eq. (11): ( )11111 −−= diagM , (15) ( )11112 −−= diagM , (16) ⎟⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ψ−ψ− ψψ− − − ψ+ = )cos()sin(00 )sin()cos(00 00 00 )sin( 2 223 bb bb ra ar ba M , (17) ( ) ⎟⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ψψ ψ−ψψ+ ψ+ = )cos()sin(00 )sin()cos(00 00 00 )sin( )cos(2 224 bb bb ra ar ba brM , (18) where: 22 bar += . It can be shown that in order for Mueller matrix Eq. (3) to be physical, a following condition should be satisfied: 122 ≤+ ba . The analysis of 3M and 4M using 4-component model [10] leads us to the conclusion that these matrices are the matrices of sequence of a linear phase plate with birefringence value Ψ and partial polarizer with the linear dichroism value P . ⎟⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ψψ− ψψ = )cos()sin(00 )sin()cos(00 0010 0001 LinPhM , (19) ⎟⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎝ ⎛ +− −+ = P P PP PP LinAmp 2000 0200 0011 0011 M , (20) then . )cos(2)sin(200 )sin(2)cos(200 0011 0011 /. ⎟⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ψψ− ψψ +− −+ = = PP PP PP PP LinAmpLinPh MM (21) For 3M we obtain: , 2000 0200 0011 0011 )cos()sin(00 )sin()cos(00 0010 0001 3 3 33 33 33 33 33 ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ +− −+ × × ⎟⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎝ ⎛ δδ− δδ = P P PP PP CM (22) where ψ=δ3 , ar arP + − =3 , ( ) )(sin )()cos( 2223 ψ+ +ψ− = ba arbrC . Using the same method for 4M : , 2000 0200 0011 0011 )cos()sin(00 )sin()cos(00 0010 0001 4 4 44 44 44 44 44 ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ +− −+ × × ⎟⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜⎜ ⎜ ⎜ ⎜ ⎝ ⎛ δδ− δδ = P P PP PP CM (23) where ψ−=δ4 , ar arP − + =4 , ( ) )(sin )()cos( 2224 ψ+ −ψ+ = ba arbrC . 2.2. Singlular value depolarization metrics The expressions of depolarization index, polarization entropy and Q -metric for the Mueller matrix Eq. (3) has been determined according to [6-9] as follows: polarization entropy [ ])1()1( 4 )1()1(log 2 1 rr rrS −+ −+−= , (24) depolarization index ( )( ) 3112 2 −+= rDI , (25) Q -metric ( )22 121 abQ ++= . (26) Corresponding dependences ( ),( hDIS σ , ),( hQS σ , ),( baS , ),( baQ ) for the following crystals: calcite CaCO3, paratellurite TeO2 and lithium niobate LiNbO3 have been calculated and presented in (Figs 1 to 4). Fig. 1 presents the dependences of entropy S and depolarization index DI (with projections on corresponding reference planes) on the value of inhomogeneity hσ . It can be seen that the minimum Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 1. P. 86-90. © 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 89 0.00 0.10 0.20 0.30 1.0 1.5 2.0 2.5 3.0 0.0 0.1 0.2 0.3 0.4 LiNbO3 TeO2 CaCO3 S σh, µm Q Fig. 2. Dependence of the entropy S on Q-metric and inhomogeneity σh. value of depolarization index and the maximum value of entropy are various for different crystals. This, as it will be illustrated below, is determined by the values of refractive indexes of crystals. Fig. 2 shows that the maximum value of 3max =Q is observed at 0=σh for all the crystals, i.e., in the case when the Mueller matrix Eq. (3) corresponds to an ordinary linear birefringent plate. The minimum value is equal for all the crystals as well as for 1min =Q , which corresponds to the case of partially depolarizing medium. From Figs 3 and 4, one can see that the minimum value of Q -metric and maximum value of entropy S are reached at different values of a for different crystals, Figs 3b and 4b. This is determined by the values of refractive indexes of the crystals. Indeed, in case of large inhomogeneity ( ∞→σh ), we have: 2 2 2 1 2 2 2 1 2 2 1 1 )1()1( )1()1( ξ+ ξ− = −+− −−− =∞→σ nn nna h , (27) 0=∞→σh b , (28) where ξ is of the form: ( ) ( )11 21 −−=ξ nn . (29) Thus, the entropy S for this case is ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ξ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ξ+ −= ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ξ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ξ+ ∞→σ 22 11 1 2 1 1 24 11 1 1 1log h S . (30) Corresponding numerical values of ξ , ∞→σh a , ∞→σh S and value of inhomogeneity hσ when in matrix Eq. (3) 0=b , i.e. when the case of large inhomogeneity takes place, are presented in the table. Table. Numerical values of ξ , ∞→σh a , ∞→σh S and hσ for the case of large inhomogeneity. 1n 2n ξ ∞→σh a ∞→σh S hσ , mµ LiNbO3 2.208 2.300 0.93 0.07 0.498 2.896 TeO2 2.259 2.411 0.89 0.11 0.495 1.753 CaCO3 1.489 1.655 0.75 0.28 0.470 1.605 It needs to note that ∞→σh S in Eq. (30) is equal 5.0 when 1=ξ . This means that 21 nn = in this case and, thus, ∞→σh S for matrix Eq. (3) can never be equal to 5.0 . LiNbO3 TeO2 CaCO3 S a 0.0 0.1 0.2 0.3 0.0 0.3 0.6 0.9 1.2 0.0 0.2 0.4 LiNbO3 TeO2 CaCO3 S a b b Fig. 3. Dependence of the entropy S , Eq. (24), as a function of a and b . Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 1. P. 86-90. © 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 90 Q LiNbO3 TeO2 CaCO3 a 0.0 0.1 0.2 0.3 0.0 0.3 0.6 0.9 1.2 1.0 1.5 2.0 2.5 3.0 LiNbO3 TeO2 CaCO3 b Q a b Fig. 4. Dependence of the Q -metric, Eq. (26), as a function of a and b . Dependences from Figs 3b and 4b for calcite, paratellurite and lithium niobate are presented in Figs 3a and 4a by white lines. Surfaces in Figs 3a and 4a determine all the possible values of Q -metric and entropy S as functions of a and b for the media described by the Mueller matrix model Eq. (3). 3. Conclusions In summary, we have studied depolarization of light by inhomogeneous anisotropic lossless crystalline medium in the single scattering case. We describe this medium with the depolarization index DI , Q -metric and the polarization entropy S that is added by the medium to the scattered field. These quantities provide insights into the particular depolarization mechanisms of the various media. It has been shown that the polarization entropy of scattering medium in the case of large inhomogeneity differs from its maximal possible value for the class of depolarizing media with only two non-zero coherency matrix eigenvalues 5.0max =S . References 1. S.N. Savenkov, R.S. Muttiah, K.E. Yushtin, S.A. Volchkov, Mueller matrix model of inhomo- geneous, linear, birefringent medium: single scattering case // Journal of Quantitative Spectros- copy & Radiative Transfer 106, p. 475-486 (2007). 2. Ch. Brosseau, Fundamentals of Polarized Light. A Statistical Optics Approach. New York, North- Holland Publishing Company, p. 406, 1998. 3. P. Huard, Polarization of Light. New York, Wiley, p. 320, 1997. 4. A.A. Kokhanovsky, Light Scattering Media Optics: Problems and Solutions. Chichester, Praxis Publishing, p. 403, 2001. 5. S.N. Savenkov, Scattering (Mueller) matrices and experimental determination of matrix elements, Chap. 4, In: From Laboratory Spectroscopy to Remotely Sensed Spectra of Terrestrial Ecosystems, Eds. R.S. Muttiah. Kluwer Academic Publishers, Dordrecht, The Netherlands, p. 85-107, 2002. 6. J.J. Gil, E. Bernabeu, Depolarization and polarization indexes of an optical system // Opt. Acta 33, p. 185-189 (1986). 7. R. Espinosa-Luna, E. Bernabeu, On the Q(M) depolarization metric // Opt. Communs 277, p. 256- 258 (2007). 8. S.R. Cloude, Group theory and polarization algebra // Optik (Stuttgart) 7, p. 26-36 (1986). 9. S.R. Cloude, E. Pottier, Concept of polarization entropy in optical scattering // Opt. Eng. 34, p. 1599-1610 (1995) 10. S.N. Savenkov, V.V. Marienko, E.A. Oberemok, O.I. Sydoruk, Generalized matrix equivalence theorem for polarization theory // Phys. Rev. E 74, 056607 (2006).

Light depolarization by inhomogeneous linear birefringent media

Репозитарії

Схожі ресурси