Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures

被引:387
作者
Ge, Li [1 ]
Chong, Y. D. [2 ]
Stone, A. D. [2 ]
机构
[1] Princeton Univ, Dept Elect Engn, Princeton, NJ 08544 USA
[2] Yale Univ, Dept Appl Phys, New Haven, CT 06520 USA
来源
PHYSICAL REVIEW A | 2012年 / 85卷 / 02期
关键词
Anisotropy; -; Resonance;
D O I
10.1103/PhysRevA.85.023802
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
We analyze the optical properties of one-dimensional PT-symmetric structures of arbitrary complexity. These structures violate normal unitarity (photon flux conservation) but are shown to satisfy generalized unitarity relations, which relate the elements of the scattering matrix and lead to a conservation relation in terms of the transmittance and (left and right) reflectances. One implication of this relation is that there exist anisotropic transmission resonances in PT-symmetric systems, frequencies at which there is unit transmission and zero reflection, but only for waves incident from a single side. The spatial profile of these transmission resonances is symmetric, and they can occur even at PT-symmetry-breaking points. The general conservation relations can be utilized as an experimental signature of the presence of PT symmetry and of PT-symmetry-breaking transitions. The uniqueness of PT-symmetry-breaking transitions of the scattering matrix is briefly discussed by comparing to the corresponding non-Hermitian Hamiltonians.
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页数:10
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共 29 条
[1]   Random-matrix theory of quantum transport [J].
Beenakker, CWJ .
REVIEWS OF MODERN PHYSICS, 1997, 69 (03) :731-808
[2]   Complex extension of quantum mechanics [J].
Bender, CM ;
Brody, DC ;
Jones, HF .
PHYSICAL REVIEW LETTERS, 2002, 89 (27)
[3]   Real spectra in non-Hermitian Hamiltonians having PT symmetry [J].
Bender, CM ;
Boettcher, S .
PHYSICAL REVIEW LETTERS, 1998, 80 (24) :5243-5246
[4]   PT-symmetric quantum mechanics [J].
Bender, CM ;
Boettcher, S ;
Meisinger, PN .
JOURNAL OF MATHEMATICAL PHYSICS, 1999, 40 (05) :2201-2229
[5]   Scattering in PT-symmetric quantum mechanics [J].
Cannata, Francesco ;
Dedonder, Jean-Pierre ;
Ventura, Alberto .
ANNALS OF PHYSICS, 2007, 322 (02) :397-433
[6]   PT-Symmetry Breaking and Laser-Absorber Modes in Optical Scattering Systems [J].
Chong, Y. D. ;
Ge, Li ;
Stone, A. Douglas .
PHYSICAL REVIEW LETTERS, 2011, 106 (09)
[7]   Coherent Perfect Absorbers: Time-Reversed Lasers [J].
Chong, Y. D. ;
Ge, Li ;
Cao, Hui ;
Stone, A. D. .
PHYSICAL REVIEW LETTERS, 2010, 105 (05)
[8]   Theory of coupled optical PT-symmetric structures [J].
El-Ganainy, R. ;
Makris, K. G. ;
Christodoulides, D. N. ;
Musslimani, Ziad H. .
OPTICS LETTERS, 2007, 32 (17) :2632-2634
[9]   Unconventional modes in lasers with spatially varying gain and loss [J].
Ge, Li ;
Chong, Y. D. ;
Rotter, S. ;
Tuereci, H. E. ;
Stone, A. D. .
PHYSICAL REVIEW A, 2011, 84 (02)
[10]   Observation of PT-Symmetry Breaking in Complex Optical Potentials [J].
Guo, A. ;
Salamo, G. J. ;
Duchesne, D. ;
Morandotti, R. ;
Volatier-Ravat, M. ;
Aimez, V. ;
Siviloglou, G. A. ;
Christodoulides, D. N. .
PHYSICAL REVIEW LETTERS, 2009, 103 (09)