Abstract

The expressions for the linear and cross-polarized reflection and transmission coefficients based on the invariant gyrotropic constitutive relations and the Drude–Born–Federov constitutive relations are compared. A physical interpretation for the first-order terms in the gyrotropic parameter and the chiral parameter is presented for normal and oblique angles of incidence. The analytical expressions for the linear cross-polarized or circular-like polarized reflection coefficients are proportional to the product of the gyrotropic measure, the tangent squared of the angle of refraction in the host medium, the round trip transmission coefficients for the horizontally and vertically polarized waves, and the polarization dependent reflection coefficients for a perfectly conducting mirror. These analytical results are consistent with the observed enhancement of the differential circular reflection for near-grazing incidence.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. P. Silverman, “Reflection and refraction at the surface of a chiral medium: comparison of gyrotropic constitutive relations invariant or noninvariant under a duality transformation,” J. Opt. Soc. Am. A 3, 830-837 (1986).
    [CrossRef]
  2. E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432-457 (1937).
    [CrossRef]
  3. M. P. Silverman and T. C. 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]
  4. M. P. Silverman, N. Ritchie, G. M. Cushman, and B. Fisher, “Experimental configurations using optical phase modulation to measure chiral asymmetries in light,” J. Opt. Soc. Am. A 5, 1854-1862 (1988).
    [CrossRef]
  5. M. P. Silverman, J. Badoz, and B. Briat, “Chiral reflection from a naturally optically active medium,” Opt. Lett. 17, 886-888 (1992).
    [CrossRef] [PubMed]
  6. M. P. Silverman, Waves and Grains (Princeton Univ. Press, 1998).
  7. P. E. Crittenden and E. Bahar, “A modal solution for reflection and transmission at a chiral-chiral interface,” Can. J. Phys. 83, 1267-1290 (2005).
    [CrossRef]
  8. E. Bahar, “Muller matrices for waves reflected and transmitted through chiral materials: waveguide modal solutions and applications,” J. Opt. Soc. Am. B 24, 1610-1619 (2007).
    [CrossRef]
  9. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon Press, 1970), pp. 100-108.
  10. E. Bahar, “Relationship between optical rotation and circular dichroism and elements of the Mueller matrix for natural and artificial chiral materials,” J. Opt. Soc. Am. B 25, 218-222 (2008).
    [CrossRef]
  11. 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, 2807-2813 (2007).
    [CrossRef]
  12. E. Bahar, “Characterization of natural and artificial optical activity by the Mueller matrix for oblique incidence, total internal reflection, and Brewster angle,” J. Opt. Soc. Am. B 25, 1294-1302 (2008).
    [CrossRef]
  13. 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 (2009).
    [CrossRef]

2009 (1)

2008 (2)

2007 (2)

2005 (1)

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

1992 (1)

1988 (1)

M. P. Silverman, N. Ritchie, G. M. Cushman, and B. Fisher, “Experimental configurations using optical phase modulation to measure chiral asymmetries in light,” J. Opt. Soc. Am. A 5, 1854-1862 (1988).
[CrossRef]

1987 (1)

M. P. Silverman and T. C. 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)

1937 (1)

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432-457 (1937).
[CrossRef]

Badoz, J.

Bahar, E.

Black, T. C.

M. P. Silverman and T. C. 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 Press, 1970), pp. 100-108.

Briat, B.

Condon, E. U.

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432-457 (1937).
[CrossRef]

Crittenden, P. E.

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

Cushman, G. M.

M. P. Silverman, N. Ritchie, G. M. Cushman, and B. Fisher, “Experimental configurations using optical phase modulation to measure chiral asymmetries in light,” J. Opt. Soc. Am. A 5, 1854-1862 (1988).
[CrossRef]

Fisher, B.

M. P. Silverman, N. Ritchie, G. M. Cushman, and B. Fisher, “Experimental configurations using optical phase modulation to measure chiral asymmetries in light,” J. Opt. Soc. Am. A 5, 1854-1862 (1988).
[CrossRef]

Ritchie, N.

M. P. Silverman, N. Ritchie, G. M. Cushman, and B. Fisher, “Experimental configurations using optical phase modulation to measure chiral asymmetries in light,” J. Opt. Soc. Am. A 5, 1854-1862 (1988).
[CrossRef]

Silverman, M. P.

M. P. Silverman, J. Badoz, and B. Briat, “Chiral reflection from a naturally optically active medium,” Opt. Lett. 17, 886-888 (1992).
[CrossRef] [PubMed]

M. P. Silverman, N. Ritchie, G. M. Cushman, and B. Fisher, “Experimental configurations using optical phase modulation to measure chiral asymmetries in light,” J. Opt. Soc. Am. A 5, 1854-1862 (1988).
[CrossRef]

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

M. P. Silverman, Waves and Grains (Princeton Univ. Press, 1998).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon Press, 1970), pp. 100-108.

Can. J. Phys. (1)

P. E. 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. Opt. Soc. Am. A (2)

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

M. P. Silverman, N. Ritchie, G. M. Cushman, and B. Fisher, “Experimental configurations using optical phase modulation to measure chiral asymmetries in light,” J. Opt. Soc. Am. A 5, 1854-1862 (1988).
[CrossRef]

J. Opt. Soc. Am. B (5)

Opt. Lett. (1)

Phys. Lett. A (1)

M. P. Silverman and T. C. 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]

Rev. Mod. Phys. (1)

E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys. 9, 432-457 (1937).
[CrossRef]

Other (2)

M. P. Silverman, Waves and Grains (Princeton Univ. Press, 1998).

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon Press, 1970), pp. 100-108.

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.


Equations (56)

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

D = ε E g H t ,
B = μ H + g E t ,
D = ε ( E + β x E ) ,
B = μ ( H + β x H ) ,
E ± ( r , t ) = E [ ( i β ± n ± ) a x + a y ± i ( α ± n ± ) a z ] exp [ i k ± r ] exp ( i ω t ) ,
H ± ( r , t ) = i Y E ± .
k ± = [ α ± a x + β ± a z ] = a ± k ± ,
α ± 2 + β ± 2 = n ± 2 = n 2 ( 1 ± f ) 2 = ( ε ± μ ± ) .
Re E ± × Re H ± = Re E ± × H ± * 2 = E 2 Re Y Re a ± exp [ 2 Im k ± r ] .
ε ± = ε ( 1 ± f ) , μ ± = μ ( 1 ± f ) ,
Y = ( ε μ ) 1 2 = ( ε ± μ ± ) 1 2 = Y ± ,   and n = ( μ ε ) 1 2 .
( D + D ) = ( ε + 0 0 ε ) ( E + E ) ,
( B + B ) = ( μ + 0 0 μ ) ( H + H ) .
E r L = ( E r H E r V ) = ( R H H R H V R V H R V V ) ( E i H E i V ) ( a 1 a 2 b 1 b 2 ) ( E i H E i V ) = R L L E i L .
E t c = [ E t + E ± ] = [ T + H T + V T H T V ] [ E i H E i V ] = [ A 1 + A 2 + A 1 A 2 ] [ E i H E i V ] = T C L E i L .
[ T H H T H V T V H T V V ] = A [ T + H T + V T H T V ] = [ 1 1 i i ] [ A 1 + A 2 + A 1 A 2 ] = [ A 1 + + A 1 A 2 + + A 2 i ( A 1 + A 1 ) i ( A 2 + A 2 ) ] .
A = [ 1 1 i i ]
E H = E [ 0 , 1 , 0 ] , E V = E [ cos φ , 0 , sin φ ] .
k = k 0 n ( sin φ , 0 , cos φ ) .
R L L = R 0 L L + f R 0 L L , T L L = T 0 L L + f T 0 L L .
R 0 L L = ( R H H 0 0 R V V ) , T 0 L L = ( T H H 0 0 T V V ) .
R 1 0 H H = Y 0 cos θ 0 Y cos φ Y 0 cos θ 0 + Y cos φ , R 1 0 V V = Z 0 cos θ 0 Z cos φ Z 0 cos θ 0 + Z cos φ .
T 10 H H = 2 Y 0 cos θ 0 Y 0 cos θ 0 + Y cos φ = 1 + R 1 0 H H ,
T 10 V V = 2 Z cos θ 0 Z 0 cos θ 0 + Z cos φ = [ 1 + R V V ] Z Z 0 .
f R 0 L L = ( 0 R H V R V H 0 ) = i f 2 T 01 H H T 10 V V tan 2 φ ( 0 1 1 0 ) .
T 01 H H T 10 V V = 4 cos θ 0 cos φ ( Z 0 cos θ 0 + Z cos φ ) ( Y 0 cos θ 0 + Y cos φ ) .
f T 0 L L = ( 0 T H V T V H 0 ) = i f 2 T 10 H H T 01 V V tan 2 φ ( 0 1 Z Z 0 0 ) .
T H V = R H V , T V H = Z Z 0 R V H .
( 1 + R V V ) Z Z 0 = T V V , R H V = T H V .
( 1 + R H H ) = T H H ,     Z Z 0 R V H = T V H .
R c = R 0 c + k β R 0 C , T C = T 0 C + k β T 0 C .
R 0 c = ( R R R R R L R L R R L L ) = 1 2 ( R V V + R H H R V V R H H R V V R H H R V V + R H H ) ,
T 0 c = [ T R R T R L T L R T L L ] = 1 2 [ T V V + T H H T V V T H H T V V T H H T V V + T H H ] ;
k β R 0 c = k β 2 T 01 H H T 10 V V tan 2 φ ( 1 0 0 1 ) ,
k β T 0 c = R R R ( Y 1 + Y 0 ) Y 0 [ 1 Y 1 Y 0 Y 1 + Y 0 Y 1 Y 0 Y 1 + Y 0 1 ] .
R c ( φ 0 = 0 ) = ( 0 R V V R V V 0 ) = Z 0 Z Z 0 + Z ( 0 1 1 0 ) ,
T c ( φ 0 = 0 ) = [ T V V 0 0 T V V ] = 2 Z Z 0 + Z ( 1 0 0 1 ) .
β = β + j β = k 2 [ OR + j CD ] l = f k .
DCR = Re { ( R V V + R H H ) * ( R L L R R R ) } | R V V | 2 + | R H H | 2 ,
R L L R R R = i ( R H V R V H ) = k β tan 2 φ T 01 H H T 10 V V .
R V V + 2 i R H V = R R R + R L R ,
R H H + 2 i R V H = R R R R L R .
R P Q = i k β 2 tan 2 φ T 01 P P R m Q Q T 10 Q Q ,
P Q , P , Q = V or H .
a 1 = [ x 2 1 2 ( z + + z ) ( q q 1 ) x z + z ] D ,
b 1 = i ( z + z ) x D ,
a 2 = i ( z z + ) x D ,
b 2 = [ x 2 + ( z + + z ) ( q q 1 ) x z + z ] D ,
A 1 + = ( z + q x ) x q D ,
A 1 = ( z + + q x ) x q D ,
A 2 + = i ( q z + x ) x q D ,
A 2 = i ( q z + + x ) x q D .
D = x 2 + 1 2 ( z + + z ) ( q + q 1 ) x + z + z ,
x = cos θ 0 ,
z ± = β ± n 2 ± = [ 1 ( sin θ 0 n ± ) 2 ] 1 2 ,
q = n μ 0 μ = Y Y 0 = Z 0 Z 1 .

Metrics