Abstract

Optically active natural or artificial materials are characterized by their optical rotation and circular dichroism. The optical activity of materials is expressed here by the constitutive equations, through a complex chiral parameter. The characteristic equations of optically active materials are the right and left circularly polarized waves with different propagation coefficients. The optical rotation (OR) is associated with differences in the phase velocities, and circular dichroism (CD) is associated with differences in the attenuation constants. These properties can be used to detect and identify biological materials. Artificial materials that are optically active have novel applications. The OR and the CD are usually defined for waves that are normally incident upon chiral materials. At oblique incidence the reflected waves are depolarized. In this manuscript we present numerical simulations to identify pairs of Mueller matrix elements suitable for the measurement of OR and CD for waves obliquely incident upon optically active dissipative media. These simulations can also be used to determine the dependence of the Mueller matrix elements upon the angles of incidence, the permittivity and permeability of the host medium, and the wavelength. For a low-loss host medium, the measurements of OR and CD decouple. Total internal reflection and the Brewster angle are also considered for these optically active materials. These investigations have potential applications in biochemistry, medicine, defense, homeland security, and for the optimum excitation of metamaterial devices.

© 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]
  3. E. Bahar, “The relationships between optical rotation and circular dichroism and elements of the Mueller matrix for natural and artificial materials,” J. Opt. Soc. Am. B 29, 218-222 (2008).
    [CrossRef]
  4. E. Bahar, “Mueller matrices for waves reflected and transmitted through chiral materials, waveguide modal solutions and applications,” J. Opt. Soc. Am. B 24, 1610-1619 (2007).
    [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, 108 (2005).
  6. E. Bahar and N. Ianno, “Complex media characterized by chirality and negative refractive index, analysis and applications,” J. Nanophotonics 1, 013509 (2007).
    [CrossRef]
  7. J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1352-1355 (2004).
    [CrossRef]
  8. A. Lakhtakia, Beltrami Fields in Chiral Media (World Scientific, 1994), pp. 313-318.
  9. C. W. Qui, H. Y. Yao, S. Zouhdi, L. W. Li, and M. S. Liong, “On the constitutive relations of G-chiral media and the potential to realize negative-index media,” Microwave Opt. Technol. Lett. 48, 2534-2538 (2007).
    [CrossRef]
  10. E. Bahar, “Optimum electromagnetic wave excitations of complex media characterized by positive or negative refractive indices and by chiral properties,” J. Opt. Soc. Am. B 24, 2807-2813 (2007).
    [CrossRef]
  11. R. Kubik and E. Bahar, “Measurements from a polarimetric optical bistatic scatterometer,” in Proceedings of the IEEE Tepical Symposium on Combined Optical, Microwave, Earth, and Atmospheric Sensing (IEEE, 1993), pp. 173-176.
    [CrossRef]
  12. R. Kubik, E. Bahar, 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 (US Army, 1993), pp. 61-75.
  13. Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B 73, 113104-1-113104-4 (2006).
    [CrossRef]
  14. Q. Cheng and T. J. Cui, “Negative refractions and backward waves in biaxially anisotropic chiral media,” Opt. Express 14, 6322-6332 (2006).
    [CrossRef] [PubMed]
  15. G. Eleftheriades and K. Balmain, Negative Refraction Metamaterials, Fundamental Principles and Applications (IEEE, 2005).
    [CrossRef]

2008 (1)

E. Bahar, “The relationships between optical rotation and circular dichroism and elements of the Mueller matrix for natural and artificial materials,” J. Opt. Soc. Am. B 29, 218-222 (2008).
[CrossRef]

2007 (4)

E. Bahar, “Mueller matrices for waves reflected and transmitted through chiral materials, waveguide modal solutions and applications,” J. Opt. Soc. Am. B 24, 1610-1619 (2007).
[CrossRef]

E. Bahar, “Optimum electromagnetic wave excitations of complex media characterized by positive or negative refractive indices and by chiral properties,” J. Opt. Soc. Am. B 24, 2807-2813 (2007).
[CrossRef]

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

C. W. Qui, H. Y. Yao, S. Zouhdi, L. W. Li, and M. S. Liong, “On the constitutive relations of G-chiral media and the potential to realize negative-index media,” Microwave Opt. Technol. Lett. 48, 2534-2538 (2007).
[CrossRef]

2006 (2)

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B 73, 113104-1-113104-4 (2006).
[CrossRef]

Q. Cheng and T. J. Cui, “Negative refractions and backward waves in biaxially anisotropic chiral media,” Opt. Express 14, 6322-6332 (2006).
[CrossRef] [PubMed]

2005 (1)

E. Bahar, “Applications of Mueller matrix and near field measurements to detect and identify trace species in drugs and threat agents,” Proc. SPIE 5993, 108 (2005).

2004 (1)

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1352-1355 (2004).
[CrossRef]

Alexander, D.

R. Kubik, E. Bahar, 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 (US Army, 1993), pp. 61-75.

Bahar, E.

E. Bahar, “The relationships between optical rotation and circular dichroism and elements of the Mueller matrix for natural and artificial materials,” J. Opt. Soc. Am. B 29, 218-222 (2008).
[CrossRef]

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

E. Bahar, “Optimum electromagnetic wave excitations of complex media characterized by positive or negative refractive indices and by chiral properties,” J. Opt. Soc. Am. B 24, 2807-2813 (2007).
[CrossRef]

E. Bahar, “Mueller matrices for waves reflected and transmitted through chiral materials, waveguide modal solutions and applications,” J. Opt. Soc. Am. B 24, 1610-1619 (2007).
[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, 108 (2005).

R. Kubik and E. Bahar, “Measurements from a polarimetric optical bistatic scatterometer,” in Proceedings of the IEEE Tepical Symposium on Combined Optical, Microwave, Earth, and Atmospheric Sensing (IEEE, 1993), pp. 173-176.
[CrossRef]

R. Kubik, E. Bahar, 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 (US Army, 1993), pp. 61-75.

Balmain, K.

G. Eleftheriades and K. Balmain, Negative Refraction Metamaterials, Fundamental Principles and Applications (IEEE, 2005).
[CrossRef]

Barron, L.

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

Cheng, Q.

Q. Cheng and T. J. Cui, “Negative refractions and backward waves in biaxially anisotropic chiral media,” Opt. Express 14, 6322-6332 (2006).
[CrossRef] [PubMed]

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B 73, 113104-1-113104-4 (2006).
[CrossRef]

Cui, T. J.

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B 73, 113104-1-113104-4 (2006).
[CrossRef]

Q. Cheng and T. J. Cui, “Negative refractions and backward waves in biaxially anisotropic chiral media,” Opt. Express 14, 6322-6332 (2006).
[CrossRef] [PubMed]

Eleftheriades, G.

G. Eleftheriades and K. Balmain, Negative Refraction Metamaterials, Fundamental Principles and Applications (IEEE, 2005).
[CrossRef]

Ianno, N.

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

Kubik, R.

R. Kubik, E. Bahar, 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 (US Army, 1993), pp. 61-75.

R. Kubik and E. Bahar, “Measurements from a polarimetric optical bistatic scatterometer,” in Proceedings of the IEEE Tepical Symposium on Combined Optical, Microwave, Earth, and Atmospheric Sensing (IEEE, 1993), pp. 173-176.
[CrossRef]

Lakhtakia, A.

A. Lakhtakia, Beltrami Fields in Chiral Media (World Scientific, 1994), pp. 313-318.

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

Li, L. W.

C. W. Qui, H. Y. Yao, S. Zouhdi, L. W. Li, and M. S. Liong, “On the constitutive relations of G-chiral media and the potential to realize negative-index media,” Microwave Opt. Technol. Lett. 48, 2534-2538 (2007).
[CrossRef]

Liong, M. S.

C. W. Qui, H. Y. Yao, S. Zouhdi, L. W. Li, and M. S. Liong, “On the constitutive relations of G-chiral media and the potential to realize negative-index media,” Microwave Opt. Technol. Lett. 48, 2534-2538 (2007).
[CrossRef]

Pendry, J. B.

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1352-1355 (2004).
[CrossRef]

Qui, C. W.

C. W. Qui, H. Y. Yao, S. Zouhdi, L. W. Li, and M. S. Liong, “On the constitutive relations of G-chiral media and the potential to realize negative-index media,” Microwave Opt. Technol. Lett. 48, 2534-2538 (2007).
[CrossRef]

Yao, H. Y.

C. W. Qui, H. Y. Yao, S. Zouhdi, L. W. Li, and M. S. Liong, “On the constitutive relations of G-chiral media and the potential to realize negative-index media,” Microwave Opt. Technol. Lett. 48, 2534-2538 (2007).
[CrossRef]

Zouhdi, S.

C. W. Qui, H. Y. Yao, S. Zouhdi, L. W. Li, and M. S. Liong, “On the constitutive relations of G-chiral media and the potential to realize negative-index media,” Microwave Opt. Technol. Lett. 48, 2534-2538 (2007).
[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. B (3)

Microwave Opt. Technol. Lett. (1)

C. W. Qui, H. Y. Yao, S. Zouhdi, L. W. Li, and M. S. Liong, “On the constitutive relations of G-chiral media and the potential to realize negative-index media,” Microwave Opt. Technol. Lett. 48, 2534-2538 (2007).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

Q. Cheng and T. J. Cui, “Negative refractions in uniaxially anisotropic chiral media,” Phys. Rev. B 73, 113104-1-113104-4 (2006).
[CrossRef]

Proc. SPIE (1)

E. Bahar, “Applications of Mueller matrix and near field measurements to detect and identify trace species in drugs and threat agents,” Proc. SPIE 5993, 108 (2005).

Science (1)

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1352-1355 (2004).
[CrossRef]

Other (6)

A. Lakhtakia, Beltrami Fields in Chiral Media (World Scientific, 1994), pp. 313-318.

R. Kubik and E. Bahar, “Measurements from a polarimetric optical bistatic scatterometer,” in Proceedings of the IEEE Tepical Symposium on Combined Optical, Microwave, Earth, and Atmospheric Sensing (IEEE, 1993), pp. 173-176.
[CrossRef]

R. Kubik, E. Bahar, 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 (US Army, 1993), pp. 61-75.

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]

G. Eleftheriades and K. Balmain, Negative Refraction Metamaterials, Fundamental Principles and Applications (IEEE, 2005).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Plots of m 14 k 0 β as functions of the angle of incidence in free space.

Fig. 2
Fig. 2

Plots of m 24 k 0 β as functions of the angle of incidence in free space.

Fig. 3
Fig. 3

Plots of m 14 k 0 β as functions of the angle of incidence in free space.

Fig. 4
Fig. 4

Plots of m 23 k 0 β as functions of the angle of incidence in free space.

Fig. 5
Fig. 5

Plots of m 14 k 0 β and m 23 k 0 β as functions of the angle of incidence in free space.

Fig. 6
Fig. 6

Plots of R V H k 0 β and R V V as functions of the angle of incidence in free space.

Equations (28)

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D ¯ = ϵ ( E ¯ + β × E ¯ ) ,
B ¯ = μ ( H ¯ + β × H ¯ ) .
γ 1 = k ( 1 k β ) = k 0 ( n 1 j n 1 ) ,
γ 2 = k ( 1 + k β ) = k 0 ( n 2 j n 2 ) ,
k = ω μ ϵ = n k 0 = ( n j n ) k 0 , k 0 = ω μ 0 ϵ 0 .
E ̂ ( z ) = 1 2 E 0 { exp [ k 0 n 1 z ] exp [ j k 0 n 1 z ] [ a x j a ¯ y ] + exp [ k 0 n 2 z ] exp [ j k 0 n 2 z ] [ a ¯ x + j a ¯ y ] } .
E ¯ ( 0 , t ) = Re E ̂ e j ω t = E 0 cos ( ω t ) a ¯ x .
cos [ k 0 ( n 1 n 2 ) l 2 ] a ¯ x sin [ k 0 ( n 1 n 2 ) l 2 ] a ¯ y ,
E max = E 0 2 exp [ k 0 n 1 l ] + exp [ k 0 n 2 l ] .
{ sin [ k 0 ( n 1 n 2 ) l 2 ] a ¯ x + cos [ ( n 1 n 2 ) l 2 ] a ¯ y } ,
E min = E 0 2 exp [ k 0 ( n 1 l ) ] exp [ k 0 ( n 2 l ) ] .
OR + j CD = ( γ 1 γ 2 ) l 2 = Re ( γ 1 γ 2 ) l 2 + j Im ( γ 1 γ 2 ) l 2 = k 0 ( n 1 n 2 ) l 2 + j k 0 ( n 1 n 2 ) l 2 .
OR + j CD = k 2 β = k 0 2 ( n j n ) 2 ( β + j β ) .
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 .
Z 0 = ( μ 0 ϵ 0 ) 1 2 = Y 0 1 , Z = ( μ ϵ ) 1 2 = Y 1 ,
T 01 H H T 10 V V = 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 ) .
k 0 sin θ 0 = k 1 sin θ 1 = k 0 n sin θ 1 .
m 23 + j m 41 = m 32 + j m 14 = ( R H H + R V V ) R H V * = j ( R H H + R V V ) ( k β f ) * 2 ,
m 13 + j m 42 = m 31 + j m 24 = ( R H H R V V ) R H V * = j ( R H H R V V ) ( k β f ) * 2 .
OR + j CD = 2 k ( m 41 + j m 23 ) ( R H H + R V V ) * f = 2 k ( m 14 j m 32 ) ( R H H + R V V ) * f
OR + j CD = 2 k ( m 24 + j m 13 ) ( R H H R V V ) * f = 2 k ( m 42 j m 31 ) ( R H H R V V ) * f .
OR = k 2 β 2 k m 41 ( R H H + R V V ) f = 2 k m 24 ( R H H R V V ) f ,
CD = k 2 β 2 k m 23 ( R H H + R V V ) f = 2 k m 13 ( R H H R V V ) f .
OR + j CD = k 2 { ( m 14 + m 41 + m 24 + m 42 ) + j ( m 23 m 32 + m 13 m 31 ) } R H H * f
OR + j CD = k 2 { ( m 14 + m 41 m 24 m 42 ) + j ( m 23 m 32 m 13 + m 31 ) } R V V * f .
sin θ 1 = 1 n sin θ 0 c = 1 , cos θ 1 = 0 ,
sin θ 1 R < 1 and sin θ 1 L > 1 .
f = T 01 H H T 10 V V tan 2 θ 1 = 4 cos θ 0 cos θ 1 ( Z 0 cos θ 0 + Z 1 cos θ 1 ) ( Y 0 cos θ 0 + Y 1 cos θ 1 ) tan 2 θ 1 .

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