Unidirectional invisibility in a two-layer non-PT-symmetric slab |
Optics Express, Vol. 22, Issue 16, pp. 19440-19447 (2014)
http://dx.doi.org/10.1364/OE.22.019440
Acrobat PDF (568 KB)
Abstract
Recently, unidirectional invisibility has been demonstrated in parity-time (PT) symmetric periodic structures and has attracted great attention. Nevertheless, fabrication of a complex periodic structure may not be practically easy. In this paper, a simple two-layer non-PT-symmetric slab structure is proposed to realize unidirectional invisibility. We numerically show that in such conventional structure consisting of two slabs with different real parts of refractive indices, unidirectional invisibility can be achieved as proper imaginary parts of refractive indices and thicknesses of the slabs are satisfied. Moreover, the unidirectional invisibility can be converted to unidirectional reflection when the imaginary parts of the refractive indices are tuned to their odd symmetric forms.
© 2014 Optical Society of America
1. Introduction
1. S. Longhi and G. Della Valle, “Photonic realization of PT-symmetric quantum field theories,” Phys. Rev. A 85(1), 012112 (2012). [CrossRef]
2. C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998). [CrossRef]
3. C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70(6), 947–1018 (2007). [CrossRef]
4. N. Hatano and D. R. Nelson, “Localization transitions in non-Hermitian quantum mechanics,” Phys. Rev. Lett. 77(3), 570–573 (1996). [CrossRef] [PubMed]
5. O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103(3), 030402 (2009). [CrossRef] [PubMed]
6. M. Hiller, T. Kottos, and A. Ossipov, “Bifurcations in resonance widths of an open Bose-Hubbard dimer,” Phys. Rev. A 73(6), 063625 (2006). [CrossRef]
7. R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32(17), 2632–2634 (2007). [CrossRef] [PubMed]
9. O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Optical structures with local PT-symmetry,” J. Phys. A 43(26), 265305 (2010). [CrossRef]
10. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100(10), 103904 (2008). [CrossRef] [PubMed]
11. M. C. Zheng, D. N. Christodoulides, R. Fleischmann, and T. Kottos, “PT optical lattices and universality in beam dynamics,” Phys. Rev. A 82(1), 010103 (2010). [CrossRef]
12. A. Guo, G. J. Salamo, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103(9), 093902 (2009). [CrossRef] [PubMed]
10. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100(10), 103904 (2008). [CrossRef] [PubMed]
13. S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010). [CrossRef]
14. Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106(21), 213901 (2011). [CrossRef] [PubMed]
15. L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2012). [CrossRef] [PubMed]
2. Design and theory
16. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999). [CrossRef] [PubMed]
17. Y. Shen and G. P. Wang, “Gain-assisted time delay of plasmons in coupled metal ring resonator waveguides,” Opt. Express 17(15), 12807–12812 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-15-12807. [CrossRef] [PubMed]
3. Simulation and discussion
19. C. C. Baker, J. Heikenfeld, Z. Yu, and A. J. Steckl, “Optical amplification and electroluminescence at 1.54 μm in Er-doped zinc silicate germanate on silicon,” Appl. Phys. Lett. 84(9), 1462–1464 (2004). [CrossRef]
17. Y. Shen and G. P. Wang, “Gain-assisted time delay of plasmons in coupled metal ring resonator waveguides,” Opt. Express 17(15), 12807–12812 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-15-12807. [CrossRef] [PubMed]
21. Y. Shen and G. P. Wang, “Optical bistability in metal gap waveguide nanocavities,” Opt. Express 16(12), 8421–8426 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-12-8421. [CrossRef] [PubMed]
4. Conclusion
Acknowledgments
References and links
1. | S. Longhi and G. Della Valle, “Photonic realization of PT-symmetric quantum field theories,” Phys. Rev. A 85(1), 012112 (2012). [CrossRef] |
2. | C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998). [CrossRef] |
3. | C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70(6), 947–1018 (2007). [CrossRef] |
4. | N. Hatano and D. R. Nelson, “Localization transitions in non-Hermitian quantum mechanics,” Phys. Rev. Lett. 77(3), 570–573 (1996). [CrossRef] [PubMed] |
5. | O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103(3), 030402 (2009). [CrossRef] [PubMed] |
6. | M. Hiller, T. Kottos, and A. Ossipov, “Bifurcations in resonance widths of an open Bose-Hubbard dimer,” Phys. Rev. A 73(6), 063625 (2006). [CrossRef] |
7. | R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32(17), 2632–2634 (2007). [CrossRef] [PubMed] |
8. | S. Longhi, “Bloch oscillations in complex crystals with PT symmetry,” Phys. Rev. Lett. 103(12), 123601 (2009). [CrossRef] [PubMed] |
9. | O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Optical structures with local PT-symmetry,” J. Phys. A 43(26), 265305 (2010). [CrossRef] |
10. | K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100(10), 103904 (2008). [CrossRef] [PubMed] |
11. | M. C. Zheng, D. N. Christodoulides, R. Fleischmann, and T. Kottos, “PT optical lattices and universality in beam dynamics,” Phys. Rev. A 82(1), 010103 (2010). [CrossRef] |
12. | A. Guo, G. J. Salamo, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103(9), 093902 (2009). [CrossRef] [PubMed] |
13. | S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010). [CrossRef] |
14. | Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106(21), 213901 (2011). [CrossRef] [PubMed] |
15. | L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater. 12(2), 108–113 (2012). [CrossRef] [PubMed] |
16. | A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999). [CrossRef] [PubMed] |
17. | Y. Shen and G. P. Wang, “Gain-assisted time delay of plasmons in coupled metal ring resonator waveguides,” Opt. Express 17(15), 12807–12812 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-15-12807. [CrossRef] [PubMed] |
18. | E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985). |
19. | C. C. Baker, J. Heikenfeld, Z. Yu, and A. J. Steckl, “Optical amplification and electroluminescence at 1.54 μm in Er-doped zinc silicate germanate on silicon,” Appl. Phys. Lett. 84(9), 1462–1464 (2004). [CrossRef] |
20. | K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. AP-14, 302–307 (1966). |
21. | Y. Shen and G. P. Wang, “Optical bistability in metal gap waveguide nanocavities,” Opt. Express 16(12), 8421–8426 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-12-8421. [CrossRef] [PubMed] |
OCIS Codes
(230.7400) Optical devices : Waveguides, slab
(310.6860) Thin films : Thin films, optical properties
(290.5839) Scattering : Scattering, invisibility
ToC Category:
Thin Films
History
Original Manuscript: April 29, 2014
Revised Manuscript: July 16, 2014
Manuscript Accepted: July 17, 2014
Published: August 4, 2014
Citation
Yun Shen, Xiao Hua Deng, and Lin Chen, "Unidirectional invisibility in a two-layer non-PT-symmetric slab," Opt. Express 22, 19440-19447 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-16-19440
Sort: Year | Journal | Reset
References
- S. Longhi and G. Della Valle, “Photonic realization of PT-symmetric quantum field theories,” Phys. Rev. A85(1), 012112 (2012). [CrossRef]
- C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett.80(24), 5243–5246 (1998). [CrossRef]
- C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys.70(6), 947–1018 (2007). [CrossRef]
- N. Hatano and D. R. Nelson, “Localization transitions in non-Hermitian quantum mechanics,” Phys. Rev. Lett.77(3), 570–573 (1996). [CrossRef] [PubMed]
- O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett.103(3), 030402 (2009). [CrossRef] [PubMed]
- M. Hiller, T. Kottos, and A. Ossipov, “Bifurcations in resonance widths of an open Bose-Hubbard dimer,” Phys. Rev. A73(6), 063625 (2006). [CrossRef]
- R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett.32(17), 2632–2634 (2007). [CrossRef] [PubMed]
- S. Longhi, “Bloch oscillations in complex crystals with PT symmetry,” Phys. Rev. Lett.103(12), 123601 (2009). [CrossRef] [PubMed]
- O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Optical structures with local PT-symmetry,” J. Phys. A43(26), 265305 (2010). [CrossRef]
- K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett.100(10), 103904 (2008). [CrossRef] [PubMed]
- M. C. Zheng, D. N. Christodoulides, R. Fleischmann, and T. Kottos, “PT optical lattices and universality in beam dynamics,” Phys. Rev. A82(1), 010103 (2010). [CrossRef]
- A. Guo, G. J. Salamo, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of PT-symmetry breaking in complex optical potentials,” Phys. Rev. Lett.103(9), 093902 (2009). [CrossRef] [PubMed]
- S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A82(3), 031801 (2010). [CrossRef]
- Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett.106(21), 213901 (2011). [CrossRef] [PubMed]
- L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. B. Oliveira, V. R. Almeida, Y. F. Chen, and A. Scherer, “Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies,” Nat. Mater.12(2), 108–113 (2012). [CrossRef] [PubMed]
- A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett.24(11), 711–713 (1999). [CrossRef] [PubMed]
- Y. Shen and G. P. Wang, “Gain-assisted time delay of plasmons in coupled metal ring resonator waveguides,” Opt. Express17(15), 12807–12812 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-15-12807 . [CrossRef] [PubMed]
- E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
- C. C. Baker, J. Heikenfeld, Z. Yu, and A. J. Steckl, “Optical amplification and electroluminescence at 1.54 μm in Er-doped zinc silicate germanate on silicon,” Appl. Phys. Lett.84(9), 1462–1464 (2004). [CrossRef]
- K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag.AP-14, 302–307 (1966).
- Y. Shen and G. P. Wang, “Optical bistability in metal gap waveguide nanocavities,” Opt. Express16(12), 8421–8426 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-12-8421 . [CrossRef] [PubMed]
Cited By |
Alert me when this paper is cited |
OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.
« Previous Article | Next Article »
OSA is a member of CrossRef.