Universal shift of the Brewster angle and disorder-enhanced delocalization of p waves in stratified random media |
Optics Express, Vol. 19, Issue 21, pp. 20817-20826 (2011)
http://dx.doi.org/10.1364/OE.19.020817
Acrobat PDF (985 KB)
Abstract
We study theoretically the propagation and the Anderson localization of p-polarized electromagnetic waves incident obliquely on randomly stratified dielectric media with weak uncorrelated Gaussian disorder. Using the invariant imbedding method, we calculate the localization length and the disorder-averaged transmittance in a numerically precise manner. We find that the localization length takes an extremely large maximum value at some critical incident angle, which we call the generalized Brewster angle. The disorder-averaged transmittance also takes a maximum very close to one at the same incident angle. Even in the presence of an arbitrarily weak disorder, the generalized Brewster angle is found to be substantially different from the ordinary Brewster angle in uniform media. It is a rapidly increasing function of the average dielectric permittivity and approaches 90° when the average relative dielectric permittivity is slightly larger than two. We make a remarkable observation that the dependence of the generalized Brewster angle on the average dielectric permittivity is universal in the sense that it is independent of the strength of disorder. We also find, surprisingly, that when the average relative dielectric permittivity is less than one and the incident angle is larger than the generalized Brewster angle, both the localization length and the disorder-averaged transmittance increase substantially as the strength of disorder increases in a wide range of the disorder parameter. In other words, the Anderson localization of incident p waves can be weakened by disorder in a certain parameter regime.
© 2011 OSA
1. Introduction
1. J.-J. Greffet, “Theoretical model of the shift of the Brewster angle on a rough surface,” Opt. Lett. 17, 238–240 (1992). [CrossRef] [PubMed]
2. T. Kawanishi, “The shift of Brewster’s scattering angle,” Opt. Commun. 186, 251–258 (2000). [CrossRef]
3. P. A. Lee and T. V. Ramakrishnan, “Disordered electronic systems,” Rev. Mod. Phys. 57, 287–337 (1985). [CrossRef]
3. P. A. Lee and T. V. Ramakrishnan, “Disordered electronic systems,” Rev. Mod. Phys. 57, 287–337 (1985). [CrossRef]
6. F. Delyon, B. Simon, and B. Souillard, “From power-localized to extended states in a class of one-dimensional disordered systems,” Phys. Rev. Lett. 52, 2187–2189 (1984). [CrossRef]
9. J. Heinrichs, “Absence of localization in a disordered one-dimensional ring threaded by an Aharonov-Bohm flux,” J. Phys. Condens. Matter 21, 295701 (2009). [CrossRef] [PubMed]
10. J. E. Sipe, P. Sheng, B. S. White, and M. H. Cohen, “Brewster anomalies: a polarization-induced delocalization effect,” Phys. Rev. Lett. 60, 108–111 (1988). [CrossRef] [PubMed]
10. J. E. Sipe, P. Sheng, B. S. White, and M. H. Cohen, “Brewster anomalies: a polarization-induced delocalization effect,” Phys. Rev. Lett. 60, 108–111 (1988). [CrossRef] [PubMed]
17. D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light and Brewster anomalies in disordered superlattices containing a dispersive metamaterial,” Phys. Rev. B 82, 081105 (2010). [CrossRef]
18. R. Rammal and B. Doucot, “Invariant imbedding approach to localization. I. general framework and basic equations,” J. Phys. (Paris) 48, 509–526 (1987). [CrossRef]
22. K. Kim, D. K. Phung, F. Rotermund, and H. Lim, “Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses,” Opt. Express 16, 1150–1164 (2008). [CrossRef] [PubMed]
2. Wave equation
3. Invariant imbedding equations
18. R. Rammal and B. Doucot, “Invariant imbedding approach to localization. I. general framework and basic equations,” J. Phys. (Paris) 48, 509–526 (1987). [CrossRef]
4. Disorder-averaged transmittance and the localization length
24. K. Kim, “Reflection coefficient and localization length of waves in one-dimensional random media,” Phys. Rev. B 58, 6153–6160 (1998). [CrossRef]
24. K. Kim, “Reflection coefficient and localization length of waves in one-dimensional random media,” Phys. Rev. B 58, 6153–6160 (1998). [CrossRef]
10. J. E. Sipe, P. Sheng, B. S. White, and M. H. Cohen, “Brewster anomalies: a polarization-induced delocalization effect,” Phys. Rev. Lett. 60, 108–111 (1988). [CrossRef] [PubMed]
10. J. E. Sipe, P. Sheng, B. S. White, and M. H. Cohen, “Brewster anomalies: a polarization-induced delocalization effect,” Phys. Rev. Lett. 60, 108–111 (1988). [CrossRef] [PubMed]
5. Results
10. J. E. Sipe, P. Sheng, B. S. White, and M. H. Cohen, “Brewster anomalies: a polarization-induced delocalization effect,” Phys. Rev. Lett. 60, 108–111 (1988). [CrossRef] [PubMed]
6. Conclusion
Acknowledgments
References and links
1. | J.-J. Greffet, “Theoretical model of the shift of the Brewster angle on a rough surface,” Opt. Lett. 17, 238–240 (1992). [CrossRef] [PubMed] |
2. | T. Kawanishi, “The shift of Brewster’s scattering angle,” Opt. Commun. 186, 251–258 (2000). [CrossRef] |
3. | P. A. Lee and T. V. Ramakrishnan, “Disordered electronic systems,” Rev. Mod. Phys. 57, 287–337 (1985). [CrossRef] |
4. | I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988). |
5. | P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic Press, 1995). |
6. | F. Delyon, B. Simon, and B. Souillard, “From power-localized to extended states in a class of one-dimensional disordered systems,” Phys. Rev. Lett. 52, 2187–2189 (1984). [CrossRef] |
7. | N. Hatano and D. R. Nelson, “Localization transitions in non-Hermitian quantum mechanics,” Phys. Rev. Lett. 77, 570–573 (1996). [CrossRef] [PubMed] |
8. | F. A. B. F. de Moura and M. L. Lyra, “Delocalization in the 1D Anderson model with long-range correlated disorder,” Phys. Rev. Lett. 81, 3735–3738 (1998). [CrossRef] |
9. | J. Heinrichs, “Absence of localization in a disordered one-dimensional ring threaded by an Aharonov-Bohm flux,” J. Phys. Condens. Matter 21, 295701 (2009). [CrossRef] [PubMed] |
10. | J. E. Sipe, P. Sheng, B. S. White, and M. H. Cohen, “Brewster anomalies: a polarization-induced delocalization effect,” Phys. Rev. Lett. 60, 108–111 (1988). [CrossRef] [PubMed] |
11. | A. G. Aronov, V. M. Gasparian, and U. Gummich, “Transmission of waves throgh one-dimensional random layered systems,” J. Phys. Condens. Matter 3, 3023–3039 (1991). [CrossRef] |
12. | W. Kohler, G. Papanicolaou, M. Postel, and B. White, “Reflection of pulsed electromagnetic waves from a randomly stratified half-space,” J. Opt. Soc. Am. A 8, 1109–1125 (1991). [CrossRef] |
13. | A. Kondilis, “Combined effect of periodicity, disorder, and absorption on wave propagation through stratified media: an approximate analytical solution,” Phys. Rev. B 55, 14214–14221 (1997). [CrossRef] |
14. | W. Deng and Z.-Q. Zhang, “Amplification and localization behaviors of obliquely incident light in randomly layered media,” Phys. Rev. B 55, 14230–14235 (1997). [CrossRef] |
15. | X. Du, D. Zhang, X. Zhang, B. Feng, and D. Zhang, “Localization and delocalization of light under oblique incidence,” Phys. Rev. B 56, 28–31 (1997). [CrossRef] |
16. | K. Kim, F. Rotermund, D.-H. Lee, and H. Lim, “Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: random phase approximation,” Wave Random Complex 17, 43–53 (2007). [CrossRef] |
17. | D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light and Brewster anomalies in disordered superlattices containing a dispersive metamaterial,” Phys. Rev. B 82, 081105 (2010). [CrossRef] |
18. | R. Rammal and B. Doucot, “Invariant imbedding approach to localization. I. general framework and basic equations,” J. Phys. (Paris) 48, 509–526 (1987). [CrossRef] |
19. | V. I. Klyatskin, “The imbedding method in statistical boundary-value wave problems,” Prog. Opt. 33, 1–127 (1994). [CrossRef] |
20. | K. Kim, H. Lim, and D.-H. Lee, “Invariant imbedding equations for electromagnetic waves in stratified magnetic media: applications to one-dimensional photonic crystals,” J. Korean Phys. Soc. 39, L956–L960 (2001). |
21. | K. Kim, D.-H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” Europhys. Lett. 69, 207–213 (2005). [CrossRef] |
22. | K. Kim, D. K. Phung, F. Rotermund, and H. Lim, “Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses,” Opt. Express 16, 1150–1164 (2008). [CrossRef] [PubMed] |
23. | E. A. Novikov, “Functionals and the random-force method in turbulence theory,” Sov. Phys. JETP 20, 1290–1294 (1965). |
24. | K. Kim, “Reflection coefficient and localization length of waves in one-dimensional random media,” Phys. Rev. B 58, 6153–6160 (1998). [CrossRef] |
25. | V. Freilikher, M. Pustilnik, and I. Yurkevich, “Enhanced transmission through a disordered potential barrier,” Phys. Rev. B 53, 7413–7416 (1996). [CrossRef] |
26. | J. M. Luck, “Non-monotonic disorder-induced enhanced tunnelling,” J. Phys. A 37, 259–271 (2004). [CrossRef] |
27. | K. Kim, F. Rotermund, and H. Lim, “Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: exact calculation based on the invariant imbedding method,” Phys. Rev. B 77, 024203 (2008). [CrossRef] |
28. | J. Heinrichs, “Enhanced quantum tunnelling induced by disorder,” J. Phys. Condens. Matter 20, 395215 (2008). [CrossRef] |
OCIS Codes
(030.6600) Coherence and statistical optics : Statistical optics
(240.7040) Optics at surfaces : Tunneling
(260.5430) Physical optics : Polarization
(260.2710) Physical optics : Inhomogeneous optical media
ToC Category:
Physical Optics
History
Original Manuscript: July 28, 2011
Revised Manuscript: September 21, 2011
Manuscript Accepted: September 27, 2011
Published: October 4, 2011
Citation
Kwang Jin Lee and Kihong Kim, "Universal shift of the Brewster angle and disorder-enhanced delocalization of p waves in stratified random media," Opt. Express 19, 20817-20826 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-21-20817
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References
- J.-J. Greffet, “Theoretical model of the shift of the Brewster angle on a rough surface,” Opt. Lett.17, 238–240 (1992). [CrossRef] [PubMed]
- T. Kawanishi, “The shift of Brewster’s scattering angle,” Opt. Commun.186, 251–258 (2000). [CrossRef]
- P. A. Lee and T. V. Ramakrishnan, “Disordered electronic systems,” Rev. Mod. Phys.57, 287–337 (1985). [CrossRef]
- I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, 1988).
- P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena (Academic Press, 1995).
- F. Delyon, B. Simon, and B. Souillard, “From power-localized to extended states in a class of one-dimensional disordered systems,” Phys. Rev. Lett.52, 2187–2189 (1984). [CrossRef]
- N. Hatano and D. R. Nelson, “Localization transitions in non-Hermitian quantum mechanics,” Phys. Rev. Lett.77, 570–573 (1996). [CrossRef] [PubMed]
- F. A. B. F. de Moura and M. L. Lyra, “Delocalization in the 1D Anderson model with long-range correlated disorder,” Phys. Rev. Lett.81, 3735–3738 (1998). [CrossRef]
- J. Heinrichs, “Absence of localization in a disordered one-dimensional ring threaded by an Aharonov-Bohm flux,” J. Phys. Condens. Matter21, 295701 (2009). [CrossRef] [PubMed]
- J. E. Sipe, P. Sheng, B. S. White, and M. H. Cohen, “Brewster anomalies: a polarization-induced delocalization effect,” Phys. Rev. Lett.60, 108–111 (1988). [CrossRef] [PubMed]
- A. G. Aronov, V. M. Gasparian, and U. Gummich, “Transmission of waves throgh one-dimensional random layered systems,” J. Phys. Condens. Matter3, 3023–3039 (1991). [CrossRef]
- W. Kohler, G. Papanicolaou, M. Postel, and B. White, “Reflection of pulsed electromagnetic waves from a randomly stratified half-space,” J. Opt. Soc. Am. A8, 1109–1125 (1991). [CrossRef]
- A. Kondilis, “Combined effect of periodicity, disorder, and absorption on wave propagation through stratified media: an approximate analytical solution,” Phys. Rev. B55, 14214–14221 (1997). [CrossRef]
- W. Deng and Z.-Q. Zhang, “Amplification and localization behaviors of obliquely incident light in randomly layered media,” Phys. Rev. B55, 14230–14235 (1997). [CrossRef]
- X. Du, D. Zhang, X. Zhang, B. Feng, and D. Zhang, “Localization and delocalization of light under oblique incidence,” Phys. Rev. B56, 28–31 (1997). [CrossRef]
- K. Kim, F. Rotermund, D.-H. Lee, and H. Lim, “Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: random phase approximation,” Wave Random Complex17, 43–53 (2007). [CrossRef]
- D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light and Brewster anomalies in disordered superlattices containing a dispersive metamaterial,” Phys. Rev. B82, 081105 (2010). [CrossRef]
- R. Rammal and B. Doucot, “Invariant imbedding approach to localization. I. general framework and basic equations,” J. Phys. (Paris)48, 509–526 (1987). [CrossRef]
- V. I. Klyatskin, “The imbedding method in statistical boundary-value wave problems,” Prog. Opt.33, 1–127 (1994). [CrossRef]
- K. Kim, H. Lim, and D.-H. Lee, “Invariant imbedding equations for electromagnetic waves in stratified magnetic media: applications to one-dimensional photonic crystals,” J. Korean Phys. Soc.39, L956–L960 (2001).
- K. Kim, D.-H. Lee, and H. Lim, “Theory of the propagation of coupled waves in arbitrarily inhomogeneous stratified media,” Europhys. Lett.69, 207–213 (2005). [CrossRef]
- K. Kim, D. K. Phung, F. Rotermund, and H. Lim, “Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses,” Opt. Express16, 1150–1164 (2008). [CrossRef] [PubMed]
- E. A. Novikov, “Functionals and the random-force method in turbulence theory,” Sov. Phys. JETP20, 1290–1294 (1965).
- K. Kim, “Reflection coefficient and localization length of waves in one-dimensional random media,” Phys. Rev. B58, 6153–6160 (1998). [CrossRef]
- V. Freilikher, M. Pustilnik, and I. Yurkevich, “Enhanced transmission through a disordered potential barrier,” Phys. Rev. B53, 7413–7416 (1996). [CrossRef]
- J. M. Luck, “Non-monotonic disorder-induced enhanced tunnelling,” J. Phys. A37, 259–271 (2004). [CrossRef]
- K. Kim, F. Rotermund, and H. Lim, “Disorder-enhanced transmission of a quantum mechanical particle through a disordered tunneling barrier in one dimension: exact calculation based on the invariant imbedding method,” Phys. Rev. B77, 024203 (2008). [CrossRef]
- J. Heinrichs, “Enhanced quantum tunnelling induced by disorder,” J. Phys. Condens. Matter20, 395215 (2008). [CrossRef]
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