Abstract

We present a new scattering matrix formalism for the modeling of electromagnetic wave propagation in stratified media. It is computationally efficient and stable and is well suited to the layer geometry that is characteristic of stratified materials. It is applied successfully to the modeling of total attenuated reflection in nematic liquid crystals with beyond-critical-angle incidence when the conventional transfer matrix methods normally fail.

© 1988 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap. 1, Sec. 1.6.
  2. J. Lekner, M. C. Dorf, “Matrix methods for the calculation of reflection amplitudes,” J. Opt. Soc. Am. A 4, 2092–2095 (1987).
    [CrossRef]
  3. D. W. Berreman, “Optics in stratified and anisotropic media: 4 × 4-matrix formulation,” J. Opt. Soc. Am. 62, 502–510 (1972).
    [CrossRef]
  4. S. Teitler, B. W. Henvis, “Refraction in stratified, anisotropic media,” J. Opt. Soc. Am. 60, 830–834 (1970).
    [CrossRef]
  5. K. R. Welford, J. R. Sambles, M. G. Clark, “Guided modes and surface plasmon-polaritons observed with a nematic liquid crystal using attenuated total reflection,” Liq. Crys. 2, 91–105 (1987).
    [CrossRef]
  6. K. R. Welford, J. R. Sambles, “Detection of surface director reorientation in a nematic liquid crystal,” Appl. Phys. Lett. 50, 871–873 (1987).
    [CrossRef]
  7. E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), Chap. 6, Sec. 6.
  8. P. Maksym, “Some aspects of RHEED theory,” in Thin Film Growth Techniques for Low Dimensional Structures, NATO Advance Research Workshop, Sussex, England, 1986 (Plenum, New York, 1987).

1987 (3)

J. Lekner, M. C. Dorf, “Matrix methods for the calculation of reflection amplitudes,” J. Opt. Soc. Am. A 4, 2092–2095 (1987).
[CrossRef]

K. R. Welford, J. R. Sambles, M. G. Clark, “Guided modes and surface plasmon-polaritons observed with a nematic liquid crystal using attenuated total reflection,” Liq. Crys. 2, 91–105 (1987).
[CrossRef]

K. R. Welford, J. R. Sambles, “Detection of surface director reorientation in a nematic liquid crystal,” Appl. Phys. Lett. 50, 871–873 (1987).
[CrossRef]

1972 (1)

1970 (1)

Berreman, D. W.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap. 1, Sec. 1.6.

Clark, M. G.

K. R. Welford, J. R. Sambles, M. G. Clark, “Guided modes and surface plasmon-polaritons observed with a nematic liquid crystal using attenuated total reflection,” Liq. Crys. 2, 91–105 (1987).
[CrossRef]

Dorf, M. C.

Henvis, B. W.

Lekner, J.

Maksym, P.

P. Maksym, “Some aspects of RHEED theory,” in Thin Film Growth Techniques for Low Dimensional Structures, NATO Advance Research Workshop, Sussex, England, 1986 (Plenum, New York, 1987).

Merzbacher, E.

E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), Chap. 6, Sec. 6.

Sambles, J. R.

K. R. Welford, J. R. Sambles, “Detection of surface director reorientation in a nematic liquid crystal,” Appl. Phys. Lett. 50, 871–873 (1987).
[CrossRef]

K. R. Welford, J. R. Sambles, M. G. Clark, “Guided modes and surface plasmon-polaritons observed with a nematic liquid crystal using attenuated total reflection,” Liq. Crys. 2, 91–105 (1987).
[CrossRef]

Teitler, S.

Welford, K. R.

K. R. Welford, J. R. Sambles, M. G. Clark, “Guided modes and surface plasmon-polaritons observed with a nematic liquid crystal using attenuated total reflection,” Liq. Crys. 2, 91–105 (1987).
[CrossRef]

K. R. Welford, J. R. Sambles, “Detection of surface director reorientation in a nematic liquid crystal,” Appl. Phys. Lett. 50, 871–873 (1987).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap. 1, Sec. 1.6.

Appl. Phys. Lett. (1)

K. R. Welford, J. R. Sambles, “Detection of surface director reorientation in a nematic liquid crystal,” Appl. Phys. Lett. 50, 871–873 (1987).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Liq. Crys. (1)

K. R. Welford, J. R. Sambles, M. G. Clark, “Guided modes and surface plasmon-polaritons observed with a nematic liquid crystal using attenuated total reflection,” Liq. Crys. 2, 91–105 (1987).
[CrossRef]

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1964), Chap. 1, Sec. 1.6.

E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), Chap. 6, Sec. 6.

P. Maksym, “Some aspects of RHEED theory,” in Thin Film Growth Techniques for Low Dimensional Structures, NATO Advance Research Workshop, Sussex, England, 1986 (Plenum, New York, 1987).

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

Reflection coefficients and P-polarized radiation calculated by using (a) the scattering matrix formalism and (b) the transfer matrix formalism.

Fig. 2
Fig. 2

Transmission coefficients for P-polarized radiation calculated by using (a) the scattering matrix formalism and (b) the transfer matrix formalism.

Fig. 3
Fig. 3

Reflection coefficient for P-polarized radiation calculated by using the scattering matrix formalism fitted with experimental data.

Equations (11)

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

[ a n b 0 ] = S ( 0 , n ) [ a 0 b n ] ,
[ a n b n ] = I ( n + 1 ) [ a n + 1 b n + 1 ] .
[ a n + 1 b 0 ] = S ( 0 , n + 1 ) [ a 0 b n + 1 ] ,
S 11 ( 0 , n + 1 ) = ( I 11 S 12 I 21 ) 1 S 11 , S 12 ( 0 , n + 1 ) = ( I 11 S 12 I 21 ) 1 ( S 12 I 22 I 12 ) , S 21 ( 0 , n + 1 ) = S 22 I 21 S 11 ( 0 , n + 1 ) + S 21 , S 22 ( 0 , n + 1 ) = S 22 I 21 S 12 ( 0 , n + 1 ) + S 22 I 22 .
A = [ A 11 A 12 A 21 A 22 ] ,
T ( 0 , n + 1 ) = I ( n + 1 ) 1 I ( n ) 1 I ( 3 ) 1 I ( 2 ) 1 I ( 1 ) 1 ,
[ a n + 1 b n + 1 ] = T ( 0 , n + 1 ) [ a 0 b 0 ] ,
I = [ D 1 M 11 D 1 M 12 D 2 M 21 D 2 M 22 ] ,
[ a N b 0 ] = S ( 0 , N ) [ a 0 b N ] .
[ a N b n ] = S ( n , N ) [ a n b N ] .
a n = [ 1 S 12 ( 0 , n ) S 21 ( n , N ) ] 1 × [ S 11 ( 0 , n ) a 0 + S 12 ( 0 , n ) S 22 ( n , N ) b N ] , b n = [ 1 S 21 ( n , N ) S 12 ( 0 , n ) ] 1 × [ S 21 ( n , N ) S 11 ( 0 , n ) a 0 + S 22 ( n , N ) b N ] . ,

Metrics