Abstract

The lateral shifts of the wave reflected and transmitted from PT-symmetric one-dimensional multilayer-structures are investigated near the coherent-perfect-absorption (CPA)-laser point and the exceptional points. We predict that at the CPA-Laser point, the reflections from both sides and transmission as well as the related shifts are all very large, reaching their negative (or positive) maxima. Moreover, we show that although the reflections are direction-dependent in the PT-symmetric multilayer-structure, the related lateral shifts have same behaviors from both sides. Additionally, one may realize the reversal of the lateral shift through the suitable adjustment of the incident angle and the layer numbers. Numerical simulations for Gaussian incident beams are performed, and reasonable agreement between the theoretical results and numerical simulations is found.

© 2017 Optical Society of America

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References

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    [Crossref]

2016 (3)

O. Shramkova and G. Tsironis, “Scattering properties of PT-symmetric layered periodic structures,” J. Opt. 18(10), 105101 (2016).
[Crossref]

Y. L. Ziauddin, Y. L. Chuang, S. Qamar, and R. K. Lee, “Goos-Hänchen shift of partially coherent light fields in epsilon-near-zero metamaterials,” Sci. Rep. 6(1), 26504 (2016).
[Crossref] [PubMed]

B. Zhu, R. Lü, and S. Chen, “PT-symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model,” Phys. Rev. A 93(3), 032129 (2016).
[Crossref]

2015 (2)

Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015).
[Crossref] [PubMed]

Y. C. Ziauddin and R. K. Lee, “Giant Goos-Hänchen shift using PT symmetry,” Phys. Rev. A 92(1), 013815 (2015).
[Crossref]

2014 (5)

Y. C. Lee, M. H. Hsieh, S. T. Flammia, and R.-K. Lee, “Local PT Symmetry Violates The No-Signaling Principle,” Phys. Rev. Lett. 112(13), 130404 (2014).
[Crossref] [PubMed]

S. Savoia, G. Castaldi, V. Galdi, A. Alu, and N. Engheta, “Tunneling of obliquely incident waves through PT-symmetric epsilon-near-zero bilayers,” Phys. Rev. B 89(8), 085105 (2014).
[Crossref]

R. Fleury, D. L. Sounas, and A. Alù, “Negative refraction and planar focusing based on parity-time symmetric metasurfaces,” Phys. Rev. Lett. 113(2), 023903 (2014).
[Crossref] [PubMed]

L. Feng, X. Zhu, S. Yang, H. Zhu, P. Zhang, X. Yin, Y. Wang, and X. Zhang, “Demonstration of a large-scale optical exceptional point structure,” Opt. Express 22(2), 1760–1767 (2014).
[Crossref] [PubMed]

X. F. Zhu, Y. G. Peng, and D. G. Zhao, “Anisotropic reflection oscillation in periodic multilayer structures of parity-time symmetry,” Opt. Express 22(15), 18401–18411 (2014).
[Crossref] [PubMed]

2013 (2)

X. Zhu, L. Feng, P. Zhang, X. Yin, and X. Zhang, “One-way invisible cloak using parity-time symmetric transformation optics,” Opt. Lett. 38(15), 2821–2824 (2013).
[Crossref] [PubMed]

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. 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 (2013).
[Crossref] [PubMed]

2012 (1)

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

2011 (3)

Y. D. Chong, L. Ge, and A. D. Stone, “PT-symmetry breaking and laser-absorber modes in optical scattering systems,” Phys. Rev. Lett. 106(9), 093902 (2011).
[Crossref] [PubMed]

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]

S. Longhi, G. Della Valle, and K. Staliunas, “Goos-Hänchen shift in complex crystals,” Phys. Rev. A 84(4), 042119 (2011).
[Crossref]

2010 (4)

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81(6), 063807 (2010).
[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
[Crossref]

D. Gao and L. Gao, “Goos–Hänchen shift of the reflection from nonlinear nanocomposites with electric field tunability,” Appl. Phys. Lett. 97(4), 041903 (2010).
[Crossref]

2009 (1)

2008 (1)

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]

2007 (1)

C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70(6), 947–1018 (2007).
[Crossref]

2006 (2)

2004 (2)

D. Felbacq and R. Smaâli, “BLOCH modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals,” Phys. Rev. Lett. 92(19), 193902 (2004).
[Crossref] [PubMed]

W. Li-Gang, L. Nian-Hua, L. Qiang, and Z. Shi-Yao, “Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016601 (2004).
[Crossref] [PubMed]

2003 (1)

2002 (3)

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89(27), 270401 (2002).
[Crossref] [PubMed]

A. Mostafazadeh, “Pseudo-Hermiticity versus PT symmetry: the necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian,” J. Math. Phys. 43(1), 205–214 (2002).
[Crossref]

H. M. Lai and S. W. Chan, “Large and negative Goos-Hänchen shift near the Brewster dip on reflection from weakly absorbing media,” Opt. Lett. 27(9), 680–682 (2002).
[Crossref] [PubMed]

2001 (1)

Z. Ahmed, “Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential,” Phys. Lett. A 282(6), 343–348 (2001).
[Crossref]

1999 (1)

C. M. Bender, G. V. Dunne, and P. N. Meisinger, “Complex periodic potentials with real band spectra,” Phys. Lett. A 252(6), 272–276 (1999).
[Crossref]

1998 (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]

B. M. Jost, A. A. R. Al-Rashed, and B. E. Saleh, “Observation of the Goos-Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81(11), 2233–2235 (1998).
[Crossref]

1997 (1)

P. Balcou and L. Dutriaux, “Dual optical tunneling times in frustrated total internal reflection,” Phys. Rev. Lett. 78(5), 851–854 (1997).
[Crossref]

1993 (1)

E. Pfleghaar, A. Marseille, and A. Weis, “Quantitative investigation of the effect of resonant absorbers on the Goos-Hänchen shift,” Phys. Rev. Lett. 70(15), 2281–2284 (1993).
[Crossref] [PubMed]

1985 (1)

1983 (1)

J. L. Birman, D. N. Pattanayak, and A. Puri, “Prediction of a resonance-enhanced laser-beam displacement at total internal reflection in semiconductors,” Phys. Rev. Lett. 50(21), 1664–1667 (1983).
[Crossref]

1977 (1)

J. Cowan and B. Aničin, “Longitudinal and transverse displacements of a bounded microwave beam at total internal reflection,” J. Opt. Soc. Am. A 67(10), 1307–1314 (1977).
[Crossref]

1964 (1)

R. H. Renard, “Total reflection: a new evaluation of the Goos–Hänchen shift,” J. Opt. Soc. Am. A 54(10), 1190–1197 (1964).
[Crossref]

1948 (1)

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437(1‐2), 87–102 (1948).
[Crossref]

1947 (1)

F. Goos and H. Hänchen, “A new and fundamental experiment on total reflection,” Ann. Phys. 1(7-8), 333–346 (1947).
[Crossref]

Ahmed, Z.

Z. Ahmed, “Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential,” Phys. Lett. A 282(6), 343–348 (2001).
[Crossref]

Almeida, V. R.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. 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 (2013).
[Crossref] [PubMed]

Al-Rashed, A. A. R.

B. M. Jost, A. A. R. Al-Rashed, and B. E. Saleh, “Observation of the Goos-Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81(11), 2233–2235 (1998).
[Crossref]

Alu, A.

S. Savoia, G. Castaldi, V. Galdi, A. Alu, and N. Engheta, “Tunneling of obliquely incident waves through PT-symmetric epsilon-near-zero bilayers,” Phys. Rev. B 89(8), 085105 (2014).
[Crossref]

Alù, A.

R. Fleury, D. L. Sounas, and A. Alù, “Negative refraction and planar focusing based on parity-time symmetric metasurfaces,” Phys. Rev. Lett. 113(2), 023903 (2014).
[Crossref] [PubMed]

Anicin, B.

J. Cowan and B. Aničin, “Longitudinal and transverse displacements of a bounded microwave beam at total internal reflection,” J. Opt. Soc. Am. A 67(10), 1307–1314 (1977).
[Crossref]

Artmann, K.

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437(1‐2), 87–102 (1948).
[Crossref]

Balcou, P.

P. Balcou and L. Dutriaux, “Dual optical tunneling times in frustrated total internal reflection,” Phys. Rev. Lett. 78(5), 851–854 (1997).
[Crossref]

Bender, C. M.

C. M. Bender, “Making sense of non-Hermitian Hamiltonians,” Rep. Prog. Phys. 70(6), 947–1018 (2007).
[Crossref]

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89(27), 270401 (2002).
[Crossref] [PubMed]

C. M. Bender, G. V. Dunne, and P. N. Meisinger, “Complex periodic potentials with real band spectra,” Phys. Lett. A 252(6), 272–276 (1999).
[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]

Bersch, C.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

Birman, J. L.

J. L. Birman, D. N. Pattanayak, and A. Puri, “Prediction of a resonance-enhanced laser-beam displacement at total internal reflection in semiconductors,” Phys. Rev. Lett. 50(21), 1664–1667 (1983).
[Crossref]

Boettcher, S.

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett. 80(24), 5243–5246 (1998).
[Crossref]

Brody, D. C.

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89(27), 270401 (2002).
[Crossref] [PubMed]

Cao, H.

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]

Castaldi, G.

S. Savoia, G. Castaldi, V. Galdi, A. Alu, and N. Engheta, “Tunneling of obliquely incident waves through PT-symmetric epsilon-near-zero bilayers,” Phys. Rev. B 89(8), 085105 (2014).
[Crossref]

Chan, C. T.

Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015).
[Crossref] [PubMed]

Chan, S. W.

Chen, H.

Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015).
[Crossref] [PubMed]

Chen, S.

B. Zhu, R. Lü, and S. Chen, “PT-symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model,” Phys. Rev. A 93(3), 032129 (2016).
[Crossref]

Chen, Y. F.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. 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 (2013).
[Crossref] [PubMed]

Chong, Y. D.

Y. D. Chong, L. Ge, and A. D. Stone, “PT-symmetry breaking and laser-absorber modes in optical scattering systems,” Phys. Rev. Lett. 106(9), 093902 (2011).
[Crossref] [PubMed]

Christodoulides, D. N.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

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]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81(6), 063807 (2010).
[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (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]

Chuang, Y. L.

Y. L. Ziauddin, Y. L. Chuang, S. Qamar, and R. K. Lee, “Goos-Hänchen shift of partially coherent light fields in epsilon-near-zero metamaterials,” Sci. Rep. 6(1), 26504 (2016).
[Crossref] [PubMed]

Cowan, J.

J. Cowan and B. Aničin, “Longitudinal and transverse displacements of a bounded microwave beam at total internal reflection,” J. Opt. Soc. Am. A 67(10), 1307–1314 (1977).
[Crossref]

Della Valle, G.

S. Longhi, G. Della Valle, and K. Staliunas, “Goos-Hänchen shift in complex crystals,” Phys. Rev. A 84(4), 042119 (2011).
[Crossref]

Dunne, G. V.

C. M. Bender, G. V. Dunne, and P. N. Meisinger, “Complex periodic potentials with real band spectra,” Phys. Lett. A 252(6), 272–276 (1999).
[Crossref]

Dutriaux, L.

P. Balcou and L. Dutriaux, “Dual optical tunneling times in frustrated total internal reflection,” Phys. Rev. Lett. 78(5), 851–854 (1997).
[Crossref]

Eichelkraut, T.

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]

El-Ganainy, R.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81(6), 063807 (2010).
[Crossref]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (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]

Engheta, N.

S. Savoia, G. Castaldi, V. Galdi, A. Alu, and N. Engheta, “Tunneling of obliquely incident waves through PT-symmetric epsilon-near-zero bilayers,” Phys. Rev. B 89(8), 085105 (2014).
[Crossref]

Fegadolli, W. S.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. 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 (2013).
[Crossref] [PubMed]

Felbacq, D.

D. Felbacq and R. Smaâli, “BLOCH modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals,” Phys. Rev. Lett. 92(19), 193902 (2004).
[Crossref] [PubMed]

D. Felbacq, A. Moreau, and R. Smaâli, “Goos-Hänchen effect in the gaps of photonic crystals,” Opt. Lett. 28(18), 1633–1635 (2003).
[Crossref] [PubMed]

Feng, L.

Flammia, S. T.

Y. C. Lee, M. H. Hsieh, S. T. Flammia, and R.-K. Lee, “Local PT Symmetry Violates The No-Signaling Principle,” Phys. Rev. Lett. 112(13), 130404 (2014).
[Crossref] [PubMed]

Fleury, R.

R. Fleury, D. L. Sounas, and A. Alù, “Negative refraction and planar focusing based on parity-time symmetric metasurfaces,” Phys. Rev. Lett. 113(2), 023903 (2014).
[Crossref] [PubMed]

Galdi, V.

S. Savoia, G. Castaldi, V. Galdi, A. Alu, and N. Engheta, “Tunneling of obliquely incident waves through PT-symmetric epsilon-near-zero bilayers,” Phys. Rev. B 89(8), 085105 (2014).
[Crossref]

Gao, D.

D. Gao and L. Gao, “Goos–Hänchen shift of the reflection from nonlinear nanocomposites with electric field tunability,” Appl. Phys. Lett. 97(4), 041903 (2010).
[Crossref]

Gao, L.

D. Gao and L. Gao, “Goos–Hänchen shift of the reflection from nonlinear nanocomposites with electric field tunability,” Appl. Phys. Lett. 97(4), 041903 (2010).
[Crossref]

B. Zhao and L. Gao, “Temperature-dependent Goos-Hänchen shift on the interface of metal/dielectric composites,” Opt. Express 17(24), 21433–21441 (2009).
[Crossref] [PubMed]

Ge, L.

Y. D. Chong, L. Ge, and A. D. Stone, “PT-symmetry breaking and laser-absorber modes in optical scattering systems,” Phys. Rev. Lett. 106(9), 093902 (2011).
[Crossref] [PubMed]

Goos, F.

F. Goos and H. Hänchen, “A new and fundamental experiment on total reflection,” Ann. Phys. 1(7-8), 333–346 (1947).
[Crossref]

Hänchen, H.

F. Goos and H. Hänchen, “A new and fundamental experiment on total reflection,” Ann. Phys. 1(7-8), 333–346 (1947).
[Crossref]

He, J.

He, S.

Hsieh, M. H.

Y. C. Lee, M. H. Hsieh, S. T. Flammia, and R.-K. Lee, “Local PT Symmetry Violates The No-Signaling Principle,” Phys. Rev. Lett. 112(13), 130404 (2014).
[Crossref] [PubMed]

Jones, H. F.

C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89(27), 270401 (2002).
[Crossref] [PubMed]

Jost, B. M.

B. M. Jost, A. A. R. Al-Rashed, and B. E. Saleh, “Observation of the Goos-Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81(11), 2233–2235 (1998).
[Crossref]

Kip, D.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Kottos, T.

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]

Lai, H. M.

Lee, R. K.

Y. L. Ziauddin, Y. L. Chuang, S. Qamar, and R. K. Lee, “Goos-Hänchen shift of partially coherent light fields in epsilon-near-zero metamaterials,” Sci. Rep. 6(1), 26504 (2016).
[Crossref] [PubMed]

Y. C. Ziauddin and R. K. Lee, “Giant Goos-Hänchen shift using PT symmetry,” Phys. Rev. A 92(1), 013815 (2015).
[Crossref]

Lee, R.-K.

Y. C. Lee, M. H. Hsieh, S. T. Flammia, and R.-K. Lee, “Local PT Symmetry Violates The No-Signaling Principle,” Phys. Rev. Lett. 112(13), 130404 (2014).
[Crossref] [PubMed]

Lee, Y. C.

Y. C. Lee, M. H. Hsieh, S. T. Flammia, and R.-K. Lee, “Local PT Symmetry Violates The No-Signaling Principle,” Phys. Rev. Lett. 112(13), 130404 (2014).
[Crossref] [PubMed]

Li-Gang, W.

W. Li-Gang, L. Nian-Hua, L. Qiang, and Z. Shi-Yao, “Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016601 (2004).
[Crossref] [PubMed]

Lin, Z.

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]

Longhi, S.

S. Longhi, G. Della Valle, and K. Staliunas, “Goos-Hänchen shift in complex crystals,” Phys. Rev. A 84(4), 042119 (2011).
[Crossref]

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
[Crossref]

Lu, M. H.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. 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 (2013).
[Crossref] [PubMed]

Lü, R.

B. Zhu, R. Lü, and S. Chen, “PT-symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model,” Phys. Rev. A 93(3), 032129 (2016).
[Crossref]

Makris, K. G.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81(6), 063807 (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]

Marseille, A.

E. Pfleghaar, A. Marseille, and A. Weis, “Quantitative investigation of the effect of resonant absorbers on the Goos-Hänchen shift,” Phys. Rev. Lett. 70(15), 2281–2284 (1993).
[Crossref] [PubMed]

Meisinger, P. N.

C. M. Bender, G. V. Dunne, and P. N. Meisinger, “Complex periodic potentials with real band spectra,” Phys. Lett. A 252(6), 272–276 (1999).
[Crossref]

Miri, M. A.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

Moreau, A.

Mostafazadeh, A.

A. Mostafazadeh, “Pseudo-Hermiticity versus PT symmetry: the necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian,” J. Math. Phys. 43(1), 205–214 (2002).
[Crossref]

Musslimani, Z. H.

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81(6), 063807 (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]

Nian-Hua, L.

W. Li-Gang, L. Nian-Hua, L. Qiang, and Z. Shi-Yao, “Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016601 (2004).
[Crossref] [PubMed]

Oliveira, J. E.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. 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 (2013).
[Crossref] [PubMed]

Onishchukov, G.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

Pattanayak, D. N.

J. L. Birman, D. N. Pattanayak, and A. Puri, “Prediction of a resonance-enhanced laser-beam displacement at total internal reflection in semiconductors,” Phys. Rev. Lett. 50(21), 1664–1667 (1983).
[Crossref]

Peng, Y. G.

Peschel, U.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

Pfleghaar, E.

E. Pfleghaar, A. Marseille, and A. Weis, “Quantitative investigation of the effect of resonant absorbers on the Goos-Hänchen shift,” Phys. Rev. Lett. 70(15), 2281–2284 (1993).
[Crossref] [PubMed]

Puri, A.

J. L. Birman, D. N. Pattanayak, and A. Puri, “Prediction of a resonance-enhanced laser-beam displacement at total internal reflection in semiconductors,” Phys. Rev. Lett. 50(21), 1664–1667 (1983).
[Crossref]

Qamar, S.

Y. L. Ziauddin, Y. L. Chuang, S. Qamar, and R. K. Lee, “Goos-Hänchen shift of partially coherent light fields in epsilon-near-zero metamaterials,” Sci. Rep. 6(1), 26504 (2016).
[Crossref] [PubMed]

Qiang, L.

W. Li-Gang, L. Nian-Hua, L. Qiang, and Z. Shi-Yao, “Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016601 (2004).
[Crossref] [PubMed]

Ramezani, H.

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]

Regensburger, A.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

Renard, R. H.

R. H. Renard, “Total reflection: a new evaluation of the Goos–Hänchen shift,” J. Opt. Soc. Am. A 54(10), 1190–1197 (1964).
[Crossref]

Riesz, R.

Rüter, C. E.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Saleh, B. E.

B. M. Jost, A. A. R. Al-Rashed, and B. E. Saleh, “Observation of the Goos-Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81(11), 2233–2235 (1998).
[Crossref]

Savoia, S.

S. Savoia, G. Castaldi, V. Galdi, A. Alu, and N. Engheta, “Tunneling of obliquely incident waves through PT-symmetric epsilon-near-zero bilayers,” Phys. Rev. B 89(8), 085105 (2014).
[Crossref]

Scherer, A.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. 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 (2013).
[Crossref] [PubMed]

Segev, M.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Shi-Yao, Z.

W. Li-Gang, L. Nian-Hua, L. Qiang, and Z. Shi-Yao, “Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016601 (2004).
[Crossref] [PubMed]

Shramkova, O.

O. Shramkova and G. Tsironis, “Scattering properties of PT-symmetric layered periodic structures,” J. Opt. 18(10), 105101 (2016).
[Crossref]

Simon, R.

Smaâli, R.

D. Felbacq and R. Smaâli, “BLOCH modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals,” Phys. Rev. Lett. 92(19), 193902 (2004).
[Crossref] [PubMed]

D. Felbacq, A. Moreau, and R. Smaâli, “Goos-Hänchen effect in the gaps of photonic crystals,” Opt. Lett. 28(18), 1633–1635 (2003).
[Crossref] [PubMed]

Sounas, D. L.

R. Fleury, D. L. Sounas, and A. Alù, “Negative refraction and planar focusing based on parity-time symmetric metasurfaces,” Phys. Rev. Lett. 113(2), 023903 (2014).
[Crossref] [PubMed]

Staliunas, K.

S. Longhi, G. Della Valle, and K. Staliunas, “Goos-Hänchen shift in complex crystals,” Phys. Rev. A 84(4), 042119 (2011).
[Crossref]

Stone, A. D.

Y. D. Chong, L. Ge, and A. D. Stone, “PT-symmetry breaking and laser-absorber modes in optical scattering systems,” Phys. Rev. Lett. 106(9), 093902 (2011).
[Crossref] [PubMed]

Tsironis, G.

O. Shramkova and G. Tsironis, “Scattering properties of PT-symmetric layered periodic structures,” J. Opt. 18(10), 105101 (2016).
[Crossref]

Wang, L. G.

Wang, Y.

Weis, A.

E. Pfleghaar, A. Marseille, and A. Weis, “Quantitative investigation of the effect of resonant absorbers on the Goos-Hänchen shift,” Phys. Rev. Lett. 70(15), 2281–2284 (1993).
[Crossref] [PubMed]

Xu, Y.

Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015).
[Crossref] [PubMed]

Xu, Y. L.

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. 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 (2013).
[Crossref] [PubMed]

Yang, S.

Yi, J.

Yin, X.

Zhang, P.

Zhang, X.

Zhao, B.

Zhao, D. G.

Zhu, B.

B. Zhu, R. Lü, and S. Chen, “PT-symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model,” Phys. Rev. A 93(3), 032129 (2016).
[Crossref]

Zhu, H.

Zhu, S. Y.

Zhu, X.

Zhu, X. F.

Ziauddin, Y. C.

Y. C. Ziauddin and R. K. Lee, “Giant Goos-Hänchen shift using PT symmetry,” Phys. Rev. A 92(1), 013815 (2015).
[Crossref]

Ziauddin, Y. L.

Y. L. Ziauddin, Y. L. Chuang, S. Qamar, and R. K. Lee, “Goos-Hänchen shift of partially coherent light fields in epsilon-near-zero metamaterials,” Sci. Rep. 6(1), 26504 (2016).
[Crossref] [PubMed]

Ann. Phys. (2)

F. Goos and H. Hänchen, “A new and fundamental experiment on total reflection,” Ann. Phys. 1(7-8), 333–346 (1947).
[Crossref]

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. 437(1‐2), 87–102 (1948).
[Crossref]

Appl. Phys. Lett. (1)

D. Gao and L. Gao, “Goos–Hänchen shift of the reflection from nonlinear nanocomposites with electric field tunability,” Appl. Phys. Lett. 97(4), 041903 (2010).
[Crossref]

J. Math. Phys. (1)

A. Mostafazadeh, “Pseudo-Hermiticity versus PT symmetry: the necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian,” J. Math. Phys. 43(1), 205–214 (2002).
[Crossref]

J. Opt. (1)

O. Shramkova and G. Tsironis, “Scattering properties of PT-symmetric layered periodic structures,” J. Opt. 18(10), 105101 (2016).
[Crossref]

J. Opt. Soc. Am. A (3)

R. H. Renard, “Total reflection: a new evaluation of the Goos–Hänchen shift,” J. Opt. Soc. Am. A 54(10), 1190–1197 (1964).
[Crossref]

J. Cowan and B. Aničin, “Longitudinal and transverse displacements of a bounded microwave beam at total internal reflection,” J. Opt. Soc. Am. A 67(10), 1307–1314 (1977).
[Crossref]

R. Riesz and R. Simon, “Reflection of a Gaussian beam from a dielectric slab,” J. Opt. Soc. Am. A 2(11), 1809–1817 (1985).
[Crossref]

Nat. Mater. (1)

L. Feng, Y. L. Xu, W. S. Fegadolli, M. H. Lu, J. E. 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 (2013).
[Crossref] [PubMed]

Nat. Phys. (1)

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Nature (1)

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (4)

Phys. Lett. A (2)

C. M. Bender, G. V. Dunne, and P. N. Meisinger, “Complex periodic potentials with real band spectra,” Phys. Lett. A 252(6), 272–276 (1999).
[Crossref]

Z. Ahmed, “Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential,” Phys. Lett. A 282(6), 343–348 (2001).
[Crossref]

Phys. Rev. A (5)

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81(6), 063807 (2010).
[Crossref]

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
[Crossref]

S. Longhi, G. Della Valle, and K. Staliunas, “Goos-Hänchen shift in complex crystals,” Phys. Rev. A 84(4), 042119 (2011).
[Crossref]

Y. C. Ziauddin and R. K. Lee, “Giant Goos-Hänchen shift using PT symmetry,” Phys. Rev. A 92(1), 013815 (2015).
[Crossref]

B. Zhu, R. Lü, and S. Chen, “PT-symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model,” Phys. Rev. A 93(3), 032129 (2016).
[Crossref]

Phys. Rev. B (1)

S. Savoia, G. Castaldi, V. Galdi, A. Alu, and N. Engheta, “Tunneling of obliquely incident waves through PT-symmetric epsilon-near-zero bilayers,” Phys. Rev. B 89(8), 085105 (2014).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

W. Li-Gang, L. Nian-Hua, L. Qiang, and Z. Shi-Yao, “Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016601 (2004).
[Crossref] [PubMed]

Phys. Rev. Lett. (12)

D. Felbacq and R. Smaâli, “BLOCH modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals,” Phys. Rev. Lett. 92(19), 193902 (2004).
[Crossref] [PubMed]

E. Pfleghaar, A. Marseille, and A. Weis, “Quantitative investigation of the effect of resonant absorbers on the Goos-Hänchen shift,” Phys. Rev. Lett. 70(15), 2281–2284 (1993).
[Crossref] [PubMed]

P. Balcou and L. Dutriaux, “Dual optical tunneling times in frustrated total internal reflection,” Phys. Rev. Lett. 78(5), 851–854 (1997).
[Crossref]

B. M. Jost, A. A. R. Al-Rashed, and B. E. Saleh, “Observation of the Goos-Hänchen effect in a phase-conjugate mirror,” Phys. Rev. Lett. 81(11), 2233–2235 (1998).
[Crossref]

J. L. Birman, D. N. Pattanayak, and A. Puri, “Prediction of a resonance-enhanced laser-beam displacement at total internal reflection in semiconductors,” Phys. Rev. Lett. 50(21), 1664–1667 (1983).
[Crossref]

R. Fleury, D. L. Sounas, and A. Alù, “Negative refraction and planar focusing based on parity-time symmetric metasurfaces,” Phys. Rev. Lett. 113(2), 023903 (2014).
[Crossref] [PubMed]

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]

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, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89(27), 270401 (2002).
[Crossref] [PubMed]

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]

Y. C. Lee, M. H. Hsieh, S. T. Flammia, and R.-K. Lee, “Local PT Symmetry Violates The No-Signaling Principle,” Phys. Rev. Lett. 112(13), 130404 (2014).
[Crossref] [PubMed]

Y. D. Chong, L. Ge, and A. D. Stone, “PT-symmetry breaking and laser-absorber modes in optical scattering systems,” Phys. Rev. Lett. 106(9), 093902 (2011).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

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[Crossref]

Sci. Rep. (2)

Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5, 8681 (2015).
[Crossref] [PubMed]

Y. L. Ziauddin, Y. L. Chuang, S. Qamar, and R. K. Lee, “Goos-Hänchen shift of partially coherent light fields in epsilon-near-zero metamaterials,” Sci. Rep. 6(1), 26504 (2016).
[Crossref] [PubMed]

Other (1)

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Figures (9)

Fig. 1
Fig. 1 (a) Geometry of the light beam propagating through a periodic multilayer-structure with complex-conjugate permittivities in linear homogeneous medium, and (b) schematic diagram of the model for S-matrix.
Fig. 2
Fig. 2 (a) Reflectivity/transmissivity and (b) the related shifts for the PT bilayer-structure (N = 1) as a function of the frequency, for the thickness of each slab L = 125 u m , the incident angle θ 0 = 5 d e g , the permittivities ε 1 = 0.1 0.1 i and ε 2 = 0.1 + 0.1 i . The insert in Fig. 2(b) shows the phases of reflectivity/transmissivity as a function of incident angle θ 0 at the CPA-Laser point.
Fig. 3
Fig. 3 (a) Reflectivity from left side and (b) the lateral shifts as a function of the frequency for different incident angles. Other parameters are L = 125 u m , ε 1 = 0.1 0.1 i , ε 2 = 0.1 + 0.1 i .
Fig. 4
Fig. 4 Reflectivity from left side and the related lateral shifts for (a, b) N = 5 and (c, d) N = 10 as a function of the frequency. Other parameters are the same as those in Fig. 2.
Fig. 5
Fig. 5 (a) Eigenvalues of the S matrix, (b) Reflectivity/transmissivity and (c) phases of reflection coefficients as a function of the frequency, for L = 125 u m , θ 0 = 5 d e g , ε 1 = 0.0001 0.001 i and ε 2 = 0.0001 + 0.001 i .
Fig. 6
Fig. 6 Reflectivity and the related shifts from left (blue solid line) and right (red dashed line) sides for (a, d)N = 1 (b, e)N = 45 and (c, f) N = 90 as a function of the frequency. Other parameters are the same as those in Fig. 5.
Fig. 7
Fig. 7 Dependence of the lateral shift of reflection from left on the stack periodicity N for ω = 3 × 10 13 s 1 . Other parameters are the same as those in Fig. 6.
Fig. 8
Fig. 8 (a,b) Reflectivity/transmissivity and (c) the related shifts for the PT bilayer-structure (N = 1) as a function of the incident angle, for L = 125 u m , ω = 1.49 × 10 13 s 1 , ε 1 = 0.1 0.1 i and ε 2 = 0.1 + 0.1 i .
Fig. 9
Fig. 9 Magnetic field amplitude distribution of all the calculated apace and in the surface of reflection and transmission for (a, b) θ0 = 2deg, ω = 1.452 × 10 13 s 1 , (c, d) θ0 = 5deg, ω = 1.493 × 10 13 s 1 , with ε 1 = 0.1 0.1 i and ε 2 = 0.1 + 0.1 i , and (e, f) θ0 = 5deg, ω = 1.493 × 10 13 s 1 , with ε 1 = 0.1 + 0.1 i and ε 2 = 0.1 0.1 i .

Equations (8)

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2 H ( x , z ) ε j μ j 2 z + ( k 0 2 k x 2 ε j μ j ) H ( x , z ) = 0 ,
H 0 ( x , z ) = e i ω t + i k 0 x x { H f e i k 0 z z + H b e i k 0 z z , z < N L H f + e i k 0 z z + H b + e i k 0 z z , z > N L
( H f + H b + ) = Q ( H f H b ) = ( c 2 k z ω ε 2 μ 2 c 2 k z ω ε 2 μ 2 1 1 ) 1 M ( c 2 k z ω ε 1 μ 1 c 2 k z ω ε 1 μ 1 1 1 ) ( H f H b ) ,
m j = ( cos ( k j z L ) i ω ε j μ j c 2 k j z sin ( k j z L ) i c 2 k j z ω ε j μ j sin ( k j z L ) cos ( k j z L ) ) , ( j = 1 , 2 )
Δ r , t = d φ r , t d k 0 x ,
Δ r , t = λ 2 π cos ( θ 0 ) d φ r , t d θ 0 .
( H b H f + ) = S ( H b + H f ) = ( t R r L r R t L ) ( H b + H f ) .
λ 1 , λ 2 = t ± r L r R 2 .

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