Abstract

At a free-space-chiral interface, the complete modal expansion of the electromagnetic fields consists of the radiation fields and lateral waves, associated with branch cut integrals as well as guided surface waves associated with the poles of the like- and cross-polarized elements of the reflection matrix. The cross-polarized surface waves, considered here in detail, are proportional to the chiral measure and contain the footprints of the optical activity of the material. Explicit expressions are desired for the residue contributions at the poles of the cross-polarized reflection coefficients in terms of the optical activity. Thus, measurements of the ratio of the cross- to like- polarized surface waves, which can be excited by electric or magnetic dipoles near the interface, can be used to identify the optically active materials.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Lakhtakia, Beltrami Fields in Chiral Media (World Scientific, 1994).
    [CrossRef]
  2. L. Barron, Molecular Light Scattering and Optical Activity, 2nd ed. (Cambridge University, 2004).
    [CrossRef]
  3. J. Lenker, “Optical properties of isotropic chiral media,” Pure Appl. Opt. 5, 417–443 (1996).
    [CrossRef]
  4. E. Bahar, “Characterizations of natural and artificial optical activity by the Mueller matrices for oblique incidence, total internal reflection, and Brewster angle,” J. Opt. Soc. Am. B 25, 1294–1302 (2008).
    [CrossRef]
  5. E. Bahar, “Road maps for the use of Mueller matrix measurements to detect and identify biological materials through their optical activity: potential applications in biomedicine, biochemistry, security, and industry,” J. Opt. Soc. Am. B 26, 364–370.
    [CrossRef]
  6. E. Bahar, “Detection and identification of optical activity using polarimetry—applications to biophotonics, biomedicine and biochemistry,” J. Biophotonics 1, doi:10.1002/jbi0.200810021, 230–237 (2008).
    [CrossRef]
  7. 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]
  8. E. Bahar, “Reflection and transmission matrices at a free-space-chiral interface based on the invariant constitutive relations for gyrotropic media and the Drude–Born–Federov constitutive relations,” J. Opt. Soc. Am. A 26, 1834–1838(2009).
    [CrossRef]
  9. L. M. Brekhovskikh, Waves in Layered Media (Academic, 1960).
  10. A. Banos, Dipole Radiation in the Presence of a Conducting Half-Space, (Pergamon, 1966).
  11. E. Bahar, “Generalized Fourier transforms for stratified media,” Can. J. Phys. 50, 3123–3131 (1972).
    [CrossRef]
  12. P. Crittenden, “Electromagnetic sensing of chiral materials,” Ph.D. Thesis, (University of Nebraska—Lincoln, Lincoln, Nebraska, 2002).
  13. 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]
  14. M. Silverman, “Reflection and refraction at the surface of a chiral medium: comparison of gyrotropic constitutive relations invariant and noninvariant under a duality transformation,” J. Opt. Soc. Am. A 3, 830–837 (1986).
    [CrossRef]
  15. M. Silverman, Waves and Grains (Princeton University, 1998).
  16. E. Bahar, “Total transmission of incident plane waves that satisfy the Brewster conditions at a free-space-chiral interface,” J. Opt. Soc. Am. A 27, 2055–2060 (2010).
    [CrossRef]
  17. M. Born and E. Wolf, Principles of Optics, 4th ed.(Pergamon, 1970).
  18. M. Silverman, N. Ritche, G. Cushman, and B. Fisher, “Experimental configurations using optical phase modulation to measure chiral asymmetries in light,” J. Opt. Soc. Am. A 5, 1854–1862.
  19. M. Silverman and T. Black, “Experimental method to detect chiral asymmetry in specular light scattering from a naturally optically active medium,” Phys. Lett. A 126, 171–176(1987).
    [CrossRef]
  20. E. Bahar, “Optimum electromagnetic wave excitation of complex media characterized by positive or negative refractive indices and by chiral properties,” J. Opt. Soc. Am. B 24, 2807–2812 (2007).
    [CrossRef]
  21. A. Carrieri, J. Bottinger, D. Owens, and E. Roese, “Differential absorption Mueller matrix spectroscopy and the infrared detection of crystalline organics,” Appl. Opt. 37, 6550–6557(1998).
    [CrossRef]
  22. A. Carrieri, “Neural network pattern recognition by means of differential absorption Mueller matrix spectroscopy,” Appl. Opt. 38, 3759–3766 (1999).
    [CrossRef]
  23. E. Bahar and R. Kubik, “Description of versatile optical polarimetric scatterometer that measures all 16 elements of the Mueller matrix for reflection and transmission: application to measurements of scatter cross sections, ellipsometric parameters, optical activity and the complex chiral parameter,” Opt. Eng. 47, 093603 (2008).
    [CrossRef]

2010 (1)

2009 (1)

2008 (3)

E. Bahar, “Characterizations of natural and artificial optical activity by the Mueller matrices for oblique incidence, total internal reflection, and Brewster angle,” J. Opt. Soc. Am. B 25, 1294–1302 (2008).
[CrossRef]

E. Bahar, “Detection and identification of optical activity using polarimetry—applications to biophotonics, biomedicine and biochemistry,” J. Biophotonics 1, doi:10.1002/jbi0.200810021, 230–237 (2008).
[CrossRef]

E. Bahar and R. Kubik, “Description of versatile optical polarimetric scatterometer that measures all 16 elements of the Mueller matrix for reflection and transmission: application to measurements of scatter cross sections, ellipsometric parameters, optical activity and the complex chiral parameter,” Opt. Eng. 47, 093603 (2008).
[CrossRef]

2007 (2)

2005 (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]

1999 (1)

1998 (1)

1996 (1)

J. Lenker, “Optical properties of isotropic chiral media,” Pure Appl. Opt. 5, 417–443 (1996).
[CrossRef]

1987 (1)

M. Silverman and T. Black, “Experimental method to detect chiral asymmetry in specular light scattering from a naturally optically active medium,” Phys. Lett. A 126, 171–176(1987).
[CrossRef]

1986 (1)

1972 (1)

E. Bahar, “Generalized Fourier transforms for stratified media,” Can. J. Phys. 50, 3123–3131 (1972).
[CrossRef]

Bahar, E.

E. Bahar, “Total transmission of incident plane waves that satisfy the Brewster conditions at a free-space-chiral interface,” J. Opt. Soc. Am. A 27, 2055–2060 (2010).
[CrossRef]

E. Bahar, “Reflection and transmission matrices at a free-space-chiral interface based on the invariant constitutive relations for gyrotropic media and the Drude–Born–Federov constitutive relations,” J. Opt. Soc. Am. A 26, 1834–1838(2009).
[CrossRef]

E. Bahar, “Detection and identification of optical activity using polarimetry—applications to biophotonics, biomedicine and biochemistry,” J. Biophotonics 1, doi:10.1002/jbi0.200810021, 230–237 (2008).
[CrossRef]

E. Bahar, “Characterizations of natural and artificial optical activity by the Mueller matrices for oblique incidence, total internal reflection, and Brewster angle,” J. Opt. Soc. Am. B 25, 1294–1302 (2008).
[CrossRef]

E. Bahar and R. Kubik, “Description of versatile optical polarimetric scatterometer that measures all 16 elements of the Mueller matrix for reflection and transmission: application to measurements of scatter cross sections, ellipsometric parameters, optical activity and the complex chiral parameter,” Opt. Eng. 47, 093603 (2008).
[CrossRef]

E. Bahar, “Optimum electromagnetic wave excitation of complex media characterized by positive or negative refractive indices and by chiral properties,” J. Opt. Soc. Am. B 24, 2807–2812 (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]

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, “Generalized Fourier transforms for stratified media,” Can. J. Phys. 50, 3123–3131 (1972).
[CrossRef]

E. Bahar, “Road maps for the use of Mueller matrix measurements to detect and identify biological materials through their optical activity: potential applications in biomedicine, biochemistry, security, and industry,” J. Opt. Soc. Am. B 26, 364–370.
[CrossRef]

Banos, A.

A. Banos, Dipole Radiation in the Presence of a Conducting Half-Space, (Pergamon, 1966).

Barron, L.

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

Black, T.

M. Silverman and T. Black, “Experimental method to detect chiral asymmetry in specular light scattering from a naturally optically active medium,” Phys. Lett. A 126, 171–176(1987).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 4th ed.(Pergamon, 1970).

Bottinger, J.

Brekhovskikh, L. M.

L. M. Brekhovskikh, Waves in Layered Media (Academic, 1960).

Carrieri, A.

Crittenden, P.

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]

P. Crittenden, “Electromagnetic sensing of chiral materials,” Ph.D. Thesis, (University of Nebraska—Lincoln, Lincoln, Nebraska, 2002).

Cushman, G.

M. Silverman, N. Ritche, G. Cushman, and B. Fisher, “Experimental configurations using optical phase modulation to measure chiral asymmetries in light,” J. Opt. Soc. Am. A 5, 1854–1862.

Fisher, B.

M. Silverman, N. Ritche, G. Cushman, and B. Fisher, “Experimental configurations using optical phase modulation to measure chiral asymmetries in light,” J. Opt. Soc. Am. A 5, 1854–1862.

Kubik, R.

E. Bahar and R. Kubik, “Description of versatile optical polarimetric scatterometer that measures all 16 elements of the Mueller matrix for reflection and transmission: application to measurements of scatter cross sections, ellipsometric parameters, optical activity and the complex chiral parameter,” Opt. Eng. 47, 093603 (2008).
[CrossRef]

Lakhtakia, A.

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

Lenker, J.

J. Lenker, “Optical properties of isotropic chiral media,” Pure Appl. Opt. 5, 417–443 (1996).
[CrossRef]

Owens, D.

Ritche, N.

M. Silverman, N. Ritche, G. Cushman, and B. Fisher, “Experimental configurations using optical phase modulation to measure chiral asymmetries in light,” J. Opt. Soc. Am. A 5, 1854–1862.

Roese, E.

Silverman, M.

M. Silverman and T. Black, “Experimental method to detect chiral asymmetry in specular light scattering from a naturally optically active medium,” Phys. Lett. A 126, 171–176(1987).
[CrossRef]

M. Silverman, “Reflection and refraction at the surface of a chiral medium: comparison of gyrotropic constitutive relations invariant and noninvariant under a duality transformation,” J. Opt. Soc. Am. A 3, 830–837 (1986).
[CrossRef]

M. Silverman, Waves and Grains (Princeton University, 1998).

M. Silverman, N. Ritche, G. Cushman, and B. Fisher, “Experimental configurations using optical phase modulation to measure chiral asymmetries in light,” J. Opt. Soc. Am. A 5, 1854–1862.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 4th ed.(Pergamon, 1970).

Appl. Opt. (2)

Can. J. Phys. (2)

E. Bahar, “Generalized Fourier transforms for stratified media,” Can. J. Phys. 50, 3123–3131 (1972).
[CrossRef]

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. Biophotonics (1)

E. Bahar, “Detection and identification of optical activity using polarimetry—applications to biophotonics, biomedicine and biochemistry,” J. Biophotonics 1, doi:10.1002/jbi0.200810021, 230–237 (2008).
[CrossRef]

J. Opt. Soc. Am. A (4)

J. Opt. Soc. Am. B (4)

Opt. Eng. (1)

E. Bahar and R. Kubik, “Description of versatile optical polarimetric scatterometer that measures all 16 elements of the Mueller matrix for reflection and transmission: application to measurements of scatter cross sections, ellipsometric parameters, optical activity and the complex chiral parameter,” Opt. Eng. 47, 093603 (2008).
[CrossRef]

Phys. Lett. A (1)

M. Silverman and T. Black, “Experimental method to detect chiral asymmetry in specular light scattering from a naturally optically active medium,” Phys. Lett. A 126, 171–176(1987).
[CrossRef]

Pure Appl. Opt. (1)

J. Lenker, “Optical properties of isotropic chiral media,” Pure Appl. Opt. 5, 417–443 (1996).
[CrossRef]

Other (7)

M. Born and E. Wolf, Principles of Optics, 4th ed.(Pergamon, 1970).

M. Silverman, Waves and Grains (Princeton University, 1998).

P. Crittenden, “Electromagnetic sensing of chiral materials,” Ph.D. Thesis, (University of Nebraska—Lincoln, Lincoln, Nebraska, 2002).

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

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

L. M. Brekhovskikh, Waves in Layered Media (Academic, 1960).

A. Banos, Dipole Radiation in the Presence of a Conducting Half-Space, (Pergamon, 1966).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Schematic of surface (guided) waves.

Fig. 2
Fig. 2

Block diagram for the specularly reflected linearly polarized waves.

Fig. 3
Fig. 3

Block diagram for the surface waves associated with the residues of R L at its poles at q = q P , ( P = V , H ) .

Equations (36)

Equations on this page are rendered with MathJax. Learn more.

E r L = P 1 L R L P 0 L E i L .
E i L = ( E i V E i H ) and E r L = ( E r V E r H )
P m L = ( exp ( j k 0 L m ) 0 0 exp ( j k 0 L m ) ) m = 0 , 1 ,
R L = ( R V V R V H R H V R H H ) .
E r L = P 1 P P S P R S L P 0 P E i L .
P S P = ( e j q V L L 0 0 e j q H L L ) .
u 0 P = ( k 0 2 ( q P ) 2 ) 1 / 2 , P = V , H .
E r s L = P 1 P P S P R s L P 0 P E i s L .
R s L = 2 π i R es ( R V V R V H R H V R H H ) / k 0 .
R L = ( R V V R V H R H V R H H ) .
R 0 V V = u 0 ε 1 u 1 ε 0 u 0 ε 1 + u 1 ε 0 = R 1 V V and R 0 H H = u 0 μ 1 u 1 μ 0 u 0 μ 1 + u 1 μ 0 = R 1 H H .
u 0 = ( k 0 2 q 2 ) 1 / 2 and u 1 = ( k 1 2 q 2 ) 1 / 2 .
R 0 V H = R 0 H V = 1 2 j k 1 β 1 T 01 H H T 10 V V tan 2 θ 1 1 2 j k 1 β 1 F .
T 10 V V = 1 + R 0 V V = 2 u 0 ε 1 u 0 ε 1 + u 1 ε 0 and T 01 H H = 1 + R 1 H H = 2 u 1 μ 0 u 0 μ 1 + u 1 μ 1 .
F = T 01 H H T 10 V V tan 2 θ 1 = T 01 V V T 10 H H tan 2 θ 1 = 4 ε 0 μ 1 u 1 u 0 ( q 2 / u 1 2 ) [ u 0 ε 1 + u 1 ε 0 ] [ u 0 μ 1 + u 1 μ 0 ] .
q V = [ 1 ( ε 0 μ 1 μ 0 ε 1 ) ] 1 2 k 0 k 1 [ k 0 2 ( ε 0 μ 1 μ 0 ε 1 ) k 1 2 ] 1 2 = k 1 [ ζ r 2 1 ] 1 2 [ 1 ε r 2 ] 1 2
q H = [ 1 ( μ 0 ε 1 ε 0 μ 1 ) ] 1 2 k 0 k 1 [ k 0 2 ( μ 0 ε 1 ε 0 μ 1 ) k 1 2 ] 1 2 = k 1 [ η r 2 1 ] 1 2 [ 1 μ r 2 ] 1 2
R es ( R 0 V V ) = 2 u 0 ε 1 d d q ( u 0 ε 1 + u 1 ε 0 ) | q = q V .
d u 0 d q = d d q ( k 0 2 q 2 ) 1 2 = q u 0 .
d u 1 d q = q u 1 .
R es ( R 0 V V ) = 2 u 0 ε 1 q ( ε 1 u 0 + ε 0 u 1 ) q = q V .
R es ( R 0 V V ) = 2 u 0 2 q V [ 1 ( ε 0 ε 1 ) 2 ] .
R es ( R 0 H H ) = 2 u 0 2 q H [ 1 ( μ 0 μ 1 ) 2 ] .
F = 4 u 0 u 1 ε 1 μ 0 ( q / u 1 ) z ( u 0 ε 1 + u 1 ε 0 ) ( u 0 μ 1 + u 1 μ 0 ) ,
R es F = 4 u 0 u 1 ε 1 μ 0 ( q / u 1 ) 2 ( ε 1 d u 0 d q + ε 0 d u 1 d q ) ( u 0 μ 1 + u 1 μ 0 ) | q V 4 u 0 u 1 ε 1 μ 0 ( q / u 1 ) 2 ( u 0 ε 1 + μ 0 ε 0 ) ( μ 1 d u 0 d q + μ 0 d u 1 d q ) | q H = 4 u 0 u 1 ε 1 μ 0 ( q / u 1 ) 2 q ( ε 1 u 0 + ε 0 u 1 ) u 1 μ 0 ( 1 + ε 0 μ 1 ε 1 μ 0 ) | q V + 4 u 0 u 1 ε 1 μ 0 ( q / u 1 ) 2 q ε 1 u 0 ( 1 ε 0 μ 1 ε 1 μ 0 ) ( μ 1 u 0 + μ 0 u 1 ) | q H = 4 [ 1 η r 2 ] { q V [ ε r 2 1 ] + q H [ 1 μ r 2 ] } ,
R es R D V H = j 2 k 1 β 1 R es F = 2 j k 1 β 1 ( 1 η r ) [ q V [ ε r 2 1 ] + q H [ 1 μ r 2 ] ] .
u 0 P = { k 0 2 ( q P ) 2 } 1 / 2 = j { ( q P ) 2 k 0 2 } 1 / 2 .
P S P = ( e [ j q V | x x | ] 0 0 e [ j q H | x x | ] ) .
P 0 P = ( e [ { ( q V ) 2 k 0 2 } 1 / 2 y ] 0 0 e [ { ( q H ) 2 k 0 2 } 1 / 2 y ] ) ,
P 1 P = ( e [ { ( q P ) 2 k 0 2 } 1 / 2 y ] 0 0 e [ { ( q H ) 2 k 0 2 } 1 / 2 y ] ) .
E = E V L e j k L L + E V P e j q V L .
j k L ( 1 + j ) k 0 ( σ 1 2 ω ε 1 ) 1 / 2 and q V k 0 .
ν P c = 1 μ 0 ε 0 ,
ν s = c 2 ω ε L σ 1 < c .
P C R 01 C P C R 01 C = I .
O R + j C D = k 1 2 β 1 .

Metrics