Abstract

Detection, identification, and characterization of natural and artificial chiral materials have found numerous applications in biochemistry, chemistry, drugs, medicine, and engineering. With the extensive use of optical polarimetric scatterometry, the relationships between the parameters related to optical activity (optical rotation and circular dichroism) and the Mueller matrix elements (which totally characterize scattered light) have been derived when the host medium for the chiral material is dissipative and nondissipative. It is shown that for the general case when optimum excitation is accounted for in the analysis, the relationship is given in terms of a complex pairing of specific quasi-off-diagonal elements of the Mueller matrix. This work provides a road map for experimentalists to determine the optimum excitation (angles of incidence and scatter), wavelength, mode of operation (reflection or transmission), and the specific Muller matrix elements that need to be measured.

© 2008 Optical Society of America

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References

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  1. L. Barron, Molecular Light Scattering and Optical Activity, 2nd ed. (Cambridge U. Press, 2004).
    [Crossref]
  2. A. Lakhtakia, Beltrami Fields in Chiral Media (World Scientific, 1994).
    [Crossref]
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    [Crossref]
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    [Crossref]
  5. E. Bahar, "Applications of Mueller matrix and near field measurements to detect and identify trace species in drugs and threat agents," Proc. SPIE 5993, 1-9 (2005).
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    [Crossref]
  8. A. Lakhtakia, V. K. Varadan, and V. V. Varadan, "The harmonic electromagetic fields in chiral media," Notes Phys. Series 335 (Springer-Verlag, 1989).
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    [Crossref]
  10. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Vittanen, Electromagetic Waves in Chiral and Bi-isotropic Media (Artech House, 1994).
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    [Crossref]
  12. R. Kubik and E. Bahar, "Measurements for a polarmetric optical bistatic scatterometer," Proceedings of the Combined Optical Microwave Earth and Atmospheric Sensing Conference (CO-MEAS '93) (IEEE, 1993), pp. 173-176.
    [Crossref]
  13. E. Bahar, R. Kubik, and D. Alexander, "Use of new polarimetric optical bistatic scatterometer to measure the transmission and reflection Mueller matrices for arbitrary incident and scatter directions," in Proceedings of the 1992 Scientific Conference on Obscuration and Aerosol Research (1993), pp. 61-75.
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    [Crossref] [PubMed]
  15. E. Bahar and N. Ianno, "Complex media characterized by chirality and negative refractive index—analysis and applications," J. Nanophotonics , 1, 013509 (2007).
    [Crossref]

2007 (3)

2005 (2)

P. Crittenden and E. Bahar, "A modal solution for reflection and transmission at a chiral-chiral interface," Can. J. Phys. 83, 1267-1290 (2005).
[Crossref]

E. Bahar, "Applications of Mueller matrix and near field measurements to detect and identify trace species in drugs and threat agents," Proc. SPIE 5993, 1-9 (2005).

1999 (1)

1993 (1)

1986 (1)

Appl. Opt. (2)

Can. J. Phys. (1)

P. Crittenden and E. Bahar, "A modal solution for reflection and transmission at a chiral-chiral interface," Can. J. Phys. 83, 1267-1290 (2005).
[Crossref]

J. Nanophotonics (1)

E. Bahar and N. Ianno, "Complex media characterized by chirality and negative refractive index—analysis and applications," J. Nanophotonics , 1, 013509 (2007).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

Other (8)

R. Kubik and E. Bahar, "Measurements for a polarmetric optical bistatic scatterometer," Proceedings of the Combined Optical Microwave Earth and Atmospheric Sensing Conference (CO-MEAS '93) (IEEE, 1993), pp. 173-176.
[Crossref]

E. Bahar, R. Kubik, and D. Alexander, "Use of new polarimetric optical bistatic scatterometer to measure the transmission and reflection Mueller matrices for arbitrary incident and scatter directions," in Proceedings of the 1992 Scientific Conference on Obscuration and Aerosol Research (1993), pp. 61-75.

E. Bahar, "Applications of Mueller matrix and near field measurements to detect and identify trace species in drugs and threat agents," Proc. SPIE 5993, 1-9 (2005).

L. Barron, Molecular Light Scattering and Optical Activity, 2nd ed. (Cambridge U. Press, 2004).
[Crossref]

A. Lakhtakia, Beltrami Fields in Chiral Media (World Scientific, 1994).
[Crossref]

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, "The harmonic electromagetic fields in chiral media," Notes Phys. Series 335 (Springer-Verlag, 1989).

W. Weiglhofer and A. Lakhtakia, Introduction to Complex Mediums for Optics and Electromagnetics (SPIE, 2003).
[Crossref]

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Vittanen, Electromagetic Waves in Chiral and Bi-isotropic Media (Artech House, 1994).

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Equations (35)

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D ¯ = ε ( E ¯ + β x E ¯ ) ,
B ¯ = μ ( H ¯ + β x H ¯ ) .
E ¯ ( z , t ) = 1 2 E o Re [ exp [ j ( ω t γ 1 z ) ] [ a ¯ x j a ¯ y ] + exp [ j ( ω t γ 2 z ) ] ] [ a ¯ x + a ¯ y ] = Re E ̂ ( z ) exp ( j ω t ) = 1 2 E o [ cos ( ω t γ 1 z ) a ¯ x + sin ( ω t γ 1 z ) a ¯ y + cos ( ω t γ 2 z ) a ¯ x sin ( ω t γ 2 z ) a ¯ y ] .
γ 1 = k ( 1 k β ) , γ 2 = k ( 1 + k β ) , k = ω μ ε .
E ¯ ( 0 , t ) = E 0 cos ( ω t ) a ¯ x .
E ¯ ( l , t ) = 1 2 E 0 Re { [ exp ( j γ 1 l ) + exp ( j γ 2 γ ) ] a ¯ x j [ exp ( j γ 1 l ) exp ( j γ 2 l ) ] a ¯ y } exp ( j ω t ) = Re E ̂ ( l ) exp ( j ω t ) .
E ̂ ( l ) = 1 2 E 0 exp [ j ( γ 1 + γ 2 ) l 2 ] { exp [ j ( γ 1 γ 2 ) l 2 ] + exp [ j ( γ 1 γ 2 ) l 2 ] } a ¯ x j { exp [ j ( γ 1 γ 2 ) l 2 ] exp [ j ( γ 1 γ 2 ) l 2 ] } a ¯ y = E 0 exp [ j ( γ 1 + γ 2 ) l 2 ] [ cos [ ( γ 1 γ 2 ) l 2 ] a ¯ x sin [ ( γ 1 γ 2 ) l 2 ] a ¯ y ] .
E ¯ ( l , t ) = E 0 cos [ ω t ( γ 1 + γ 2 ) l 2 ] [ cos [ ( γ 1 γ 2 ) l 2 ] a ¯ x sin [ ( γ 1 γ 2 ) l 2 ] a ¯ y ] .
OR = ( γ 1 γ 2 ) l 2 = γ 1 γ 2 β l .
n 1 = γ 1 k 0 = n 1 j n 1 n 2 = γ 2 k 0 = n 2 j n 2 .
1 2 E 0 { exp [ k 0 n 1 l ] exp [ j k 0 n 1 l ] [ a ¯ x j a ¯ y ] + exp [ k 0 n 2 l ] exp [ j k 0 n 2 l ] [ a ¯ x + j a ¯ y ] } .
OR = k 0 ( n 1 n 2 ) l 2 = Re ( γ 1 γ 2 ) l 2 = Re ( γ 1 γ 2 β l ) ,
E ¯ max = 1 2 E 0 exp [ k 0 n 1 l ] + exp [ k 0 n 2 l ] .
E ¯ min = 1 2 E 0 exp [ k 0 n 1 l ] exp [ k 0 n 2 l ] .
tan ψ = tanh k 0 ( n 1 n 2 ) l 2 .
ψ = CD = k 0 ( n 1 n 2 ) l 2 = Im ( γ 1 γ 2 ) l 2 = Im ( γ 1 γ 2 β l ) .
OR + j CD k 2 [ β + j β ] l ,
β = OR k 2 l β = CD k 2 l .
M = [ M T L M T R M B L M B R ] .
M T L = 1 2 [ R H H 2 + R V V 2 R H H 2 R V V 2 R H H 2 R V V 2 R H H 2 + R V V 2 ] = [ m 11 m 12 m 21 m 22 ] ,
M B R = [ Re [ R V V R H H * ] Im [ R V V R H H * ] Im [ R V V R H H * ] Re [ R V V R H H * ] ] = [ m 33 m 34 m 43 m 44 ] ,
M B L = [ Re [ ( R H H R V V ) R H V * ] Re [ ( R H H + R V V ) R H V * ] Im [ ( R H H + R V V ) R H V * ] Im [ ( R H H R V V ) R H V * ] ] = [ m 31 m 32 m 41 m 42 ] ,
M T R = [ Re [ ( R H H R V V ) R H V * ] Im [ ( R H H + R V V ) R H V * ] Re [ ( R H H + R V V ) R H V * ] Im [ ( R H H R V V ) R H V * ] ] = [ m 13 m 14 m 23 m 24 ] .
R V H = R H V = T V H = T H V ( Z 1 Z 0 ) = 1 2 j k β T 01 H H T 10 V V tan 2 θ 1 j k β f 2 .
T 01 H H T 10 V V = T 01 V V T 10 H H = 4 cos θ 0 cos θ 1 ( Y 0 cos θ 0 + Y 1 cos θ 1 ) ( Z 0 cos θ 0 + Z 1 cos θ 1 ) .
m 14 = m 41 = 2 Im R H V * k β T 01 H H T 10 V V tan 2 θ 1 k β f ,
m 23 = m 32 = 2 Re R H V * k β T 01 H H T 10 V V tan 2 θ 1 k β f .
OR k 2 β = k m 14 f ,
CD k 2 β = k m 23 f .
OR + j CD = k ( m 14 + j m 23 ) f .
m 23 + j m 41 = m 32 + j m 14 = ( R H H + R V V ) R H V * = 1 2 ( R H H + R V V ) j ( k β f ) * ,
m 13 + j m 42 = m 31 + j m 24 = ( R H H R V V ) R H V * = 1 2 ( R H H R V V ) j ( k β f ) * .
( OR + j CD ) k 2 β = k 2 ( β + j β ) .
OR + j CD = 2 k ( m 41 + j m 23 ) ( R H H + R V V ) * f ,
OR + j CD = 2 k ( m 24 + j m 13 ) ( R H H R V V ) * f .

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