Frontiers of Optoelectronics >
Singular PT-symmetry broken point with infinite transmittance and reflectance----a classical analytical demonstration
Received date: 29 Sep 2019
Accepted date: 18 Nov 2019
Published date: 15 Dec 2021
Copyright
To demonstrate the existence of singular parity-time symmetry (PT-symmetry) broken point in optics system, we designed a one-dimensional PT symmetric structure including N unit-cell with loss and gain materials in half. We performed an analytical deduction to obtain the transmittance and reflectance of the structure basing on Maxwell’s equations. We found that with the exact structure unit-cell number and the imaginary part of refraction index, the transmittance and reflectance are both close to infinite. Such strict condition is called the singular point in this study. At the singular point position, both the transmission and reflection are direction-independent. Away from the singular point, the transmittance and reflectance become finite. In light of classical wave optics, the single unit and total structure both become the resonance units. The infinite transmittance and reflectance result from the resonance matching of single unit and total structure. In light of quantum theory, the singular point corresponds to the single eigenvalue of electromagnetic scattering matrix. The infinite transmittance and reflectance mean a huge energy transformation from pumping source to light waves. Numerical calculation and software simulation both demonstrate the result.
Yingxin JIANG . Singular PT-symmetry broken point with infinite transmittance and reflectance----a classical analytical demonstration[J]. Frontiers of Optoelectronics, 2021 , 14(4) : 438 -444 . DOI: 10.1007/s12200-020-0969-3
1 |
Joannopoulos J D, Villeneuve P R, Fan S. Photonic crystals: putting new twist on light. Nature, 1997, 386(6621): 143–149
|
2 |
Knight J C, Broeng J, Birks T A, Russell P S J. Photonic band gap guidance in optical fibers. Science, 1998, 282(5393): 1476–1478
|
3 |
Barnes W L, Dereux A, Ebbesen T W. Surface plasmon subwavelength optics. Nature, 2003, 424(6950): 824–830
|
4 |
Shelby R A, Smith D R, Schultz S. Experimental verification of a negative index of refraction. Science, 2001, 292(5514): 77–79
|
5 |
Marani R, D’Orazio A, Petruzzelli V, Rodrigo S G, Martin-Moreno L, Garcia-Vidal F J, Bravo-Abad J. Gain-assisted extraordinary optical transmission through periodic arrays of subwavelength apertures. New Journal of Physics, 2012, 14(1): 013020
|
6 |
Feng L, Xu Y L, Fegadolli W S, Lu M H, Oliveira J E, Almeida V R, Chen Y F, Scherer A. Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies. Nature Materials, 2013, 12(2): 108–113
|
7 |
Rüter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M, Kip D. Observation of parity–time symmetry in optics. Nature Physics, 2010, 6(3): 192–195
|
8 |
Mostafazadeh A. Spectral singularities of complex scattering potentials and infinite reflection and transmission coefficients at real energies. Physical Review Letters, 2009, 102(22): 220402
|
9 |
Guo A, Salamo G J, Duchesne D, Morandotti R, Volatier-Ravat M, Aimez V, Siviloglou G A, Christodoulides D N. Observation of PT-symmetry breaking in complex optical potentials. Physical Review Letters, 2009, 103(9): 093902
|
10 |
Longhi S. PT-symmetric laser absorber. Physical Review A, 2010, 82(3): 031801
|
11 |
Chong Y D, Ge L, Stone A D. PT-symmetry breaking and laser-absorber modes in optical scattering systems. Physical Review Letters, 2011, 106(9): 093902
|
12 |
Ge L, Chong Y D, Rotter S, Tureci H E, Stone A D. Unconventional modes in lasers with spatially varying gain and loss. Physical Review A, 2011, 84(2): 023820
|
13 |
Nazari F, Nazari M, Moravvej-Farshi M K. A 2×2 spatial optical switch based on PT-symmetry. Optics Letters, 2011, 36(22): 4368–4370
|
14 |
Bender N, Factor S, Bodyfelt J D, Ramezani H, Christodoulides D N, Ellis F M, Kottos T. Observation of asymmetric transport in structures with active nonlinearities. Physical Review Letters, 2013, 110(23): 234101
|
15 |
Nazari F, Bender N, Ramezani H, Moravvej-Farshi M K, Christodoulides D N, Kottos T. Optical isolation via PT-symmetric nonlinear Fano resonances. Optics Express, 2014, 22(8): 9574–9584
|
16 |
Peng B, Özdemir S K, Lei F, Monifi F, Gianfreda M, Long G L, Fan S H, Nori F, Bender C M, Yang L. Parity-time-symmetric whispering-gallery microcavities. Nature Physics, 2014, 10(5): 394–398
|
17 |
Lin Z, Ramezani H, Eichelkraut T, Kottos T, Cao H, Christodoulides D N. Unidirectional invisibility induced by PT-symmetric periodic structures. Physical Review Letters, 2011, 106(21): 213901
|
18 |
Longhi S. Invisibility in PT-symmetric complex crystals. Journal of Physics A, Mathematical and Theoretical, 2011, 44(48): 485302
|
19 |
Zhu X F, Peng Y G, Zhao D G. Anisotropic reflection oscillation in periodic multilayer structures of parity-time symmetry. Optics Express, 2014, 22(15): 18401–18411
|
20 |
Ding S, Wang G P. Extraordinary reflection and transmission with direction dependent wavelength selectivity based on parity-time-symmetric multilayers. Journal of Applied Physics, 2015, 117(2): 023104
|
21 |
Born M, Wolf E. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Elsevier, Cambridge University, 1997
|
22 |
Ge L, Chong Y D, Stone A D. Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures. Physical Review A, 2012, 85(2): 023802
|
23 |
Schomerus H. Quantum noise and self-sustained radiation of PT-symmetric systems. Physical Review Letters, 2010, 104(23): 233601
|
/
〈 | 〉 |