Abstract

Coaxial optical subwavelength elements support helical modes Lm with different topological indexes m. Here we propose to couple the two bright L±1 modes with the dark one L0 via a parity-time (PT) symmetric perturbation. We show that the cascading coupled configuration is similar to a three-level atomic system, and supports a special hybridized mode Lc via a classic analog of coherent-population-trapping effect. Resonant frequency of Lc is independent of the PT-symmetric perturbation. Populations in L±1 can be manipulated by tuning the PT-symmetric perturbation, and no population is trapped in L0. Since the L±1 modes are associated with optical waves of opposite circular polarizations, the polarization of transmitted wave is independent of the polarization of incidence but solely determined by the PT-symmetric perturbation. Such an effect can be utilized to manipulate the polarization state of light. Numerical simulation in a well-designed coaxial metamaterial verifies our analysis.

© 2017 Optical Society of America

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References

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  44. F. Yang, Z. Fang, Z. Pan, Q. Ye, H. Cai, and R. Qu, “Orthogonal polarization mode coupling for pure twisted polarization maintaining fiber Bragg gratings,” Opt. Express 20(27), 28839–28845 (2012).
    [Crossref] [PubMed]
  45. G. D. Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92(1), 011106 (2008).
    [Crossref]
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    [Crossref]
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    [Crossref]

2017 (1)

A. K. Jahromi, S. Shabahang, H. E. Kondakci, S. Orsila, P. Melanen, and A. F. Abouraddy, “Transparent perfect mirror,” ACS Photonics 4(5), 1026–1032 (2017).
[Crossref]

2016 (4)

H. Hodaei, M. A. Miri, A. U. Hassan, W. E. Hayenga, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Single mode lasing in transversely multi-moded PT-symmetric microring resonators,” Laser Photonics Rev. 10(3), 494–499 (2016).
[Crossref]

F. J. Shu, C. L. Zou, X. B. Zou, and L. Yang, “Chiral symmetry breaking in a microring optical cavity by engineered dissipation,” Phys. Rev. A 94(1), 013848 (2016).
[Crossref]

K. H. Kim, M. S. Hwang, H. R. Kim, J. H. Choi, Y. S. No, and H. G. Park, “Direct observation of exceptional points in coupled photonic-crystal lasers with asymmetric optical gains,” Nat. Commun. 7, 13893 (2016).
[Crossref] [PubMed]

A. K. Jahromi and A. F. Abouraddy, “Observation of Poynting’s vector reversal in an active photonic cavity,” Optica 3(11), 1194–1200 (2016).
[Crossref]

2015 (4)

B. He, S. B. Yan, J. Wang, and M. Xiao, “Quantum noise effects with Kerr-nonlinearity enhancement in coupled gain-loss waveguides,” Phys. Rev. A 91(5), 053832 (2015).
[Crossref]

F. Cardano and L. Marrucci, “Spin-orbit photonics,” Nat. Photonics 9(12), 776–778 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodriguez-Fortuno, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

Q. Guo, W. Gao, J. Chen, Y. Liu, and S. Zhang, “Line degeneracy and strong spin-orbit coupling of light with bulk bianisotropic metamaterials,” Phys. Rev. Lett. 115(6), 067402 (2015).
[Crossref] [PubMed]

2014 (8)

M. H. Teimourpour, R. El-Ganainy, A. Eisfeld, A. Szameit, and D. N. Christodoulides, “Light transport in PT-invariant photonic structures with hidden symmetries,” Phys. Rev. A 90(5), 053817 (2014).
[Crossref]

B. Peng, S. K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref] [PubMed]

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schoberl, H. E. Tureci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
[Crossref] [PubMed]

H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
[Crossref] [PubMed]

L. Feng, Z. J. Wong, R. M. Ma, Y. Wang, and X. Zhang, “Single-mode laser by parity-time symmetry breaking,” Science 346(6212), 972–975 (2014).
[Crossref] [PubMed]

L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, “Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators,” Nat. Photon. 8(7), 524–529 (2014).
[Crossref]

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[Crossref]

M. Yang, L. T. Wu, T. J. Guo, R. P. Guo, H. X. Cui, X. W. Cao, and J. Chen, “Study on photonic angular momentum states in coaxial magneto-optical waveguides,” J. Appl. Phys. 116(15), 153104 (2014).
[Crossref]

2013 (3)

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 (2013).
[Crossref]

Q. H. Guo, M. Kang, T. F. Li, H. X. Cui, and J. Chen, “Slow light from sharp dispersion by exciting dark photonic angular momentum states,” Opt. Lett. 38(3), 250–252 (2013).
[Crossref] [PubMed]

Q. H. Guo, M. Yang, T. F. Li, T. J. Guo, H. X. Cui, M. Kang, and J. Chen, “Circular polarizer via selective excitation of photonic angular momentum states in metamaterials,” Appl. Phys. Lett. 102(21), 211906 (2013).
[Crossref]

2012 (4)

M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482(7384), 204–207 (2012).
[Crossref] [PubMed]

N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012).
[Crossref] [PubMed]

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]

F. Yang, Z. Fang, Z. Pan, Q. Ye, H. Cai, and R. Qu, “Orthogonal polarization mode coupling for pure twisted polarization maintaining fiber Bragg gratings,” Opt. Express 20(27), 28839–28845 (2012).
[Crossref] [PubMed]

2011 (5)

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[Crossref] [PubMed]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Advances in Optics and Photonics 3(2), 161–204 (2011).
[Crossref]

Y. M. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev. 40(5), 2494–2507 (2011).
[Crossref] [PubMed]

S. Zhang, H. Wei, K. Bao, U. Hakanson, N. J. Halas, P. Nordlander, and H. Xu, “Chiral surface plasmon polaritons on metallic nanowires,” Phys. Rev. Lett. 107(9), 096801 (2011).
[Crossref] [PubMed]

J. Wang, K. H. Fung, H. Y. Dong, and N. X. Fang, “Zeeman splitting of photonic angular momentum states in a gyromagnetic cylinder,” Phys. Rev. B 84(23), 235122 (2011).
[Crossref]

2010 (4)

J. B. Khurgin, “Slow light in various media: a tutorial,” Advances in Optics and Photonics 2(3), 287–318 (2010).
[Crossref]

Z. Ruan and S. Fan, “Superscattering of light from subwavelength nanostructures,” Phys. Rev. Lett. 105(1), 013901 (2010).
[Crossref] [PubMed]

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]

2009 (2)

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, 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, “Quantum-optical analogies using photonic structures,” Laser and Photon. Rev. 3(3), 243–261 (2009).
[Crossref]

2008 (3)

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]

S. Klaiman, U. Gunther, and N. Moiseyev, “Visualization of branch points in PT-symmetric waveguides,” Phys. Rev. Lett. 101(8), 080402 (2008).
[Crossref] [PubMed]

G. D. Valle, M. Ornigotti, T. T. Fernandez, P. Laporta, S. Longhi, A. Coppa, and V. Foglietti, “Adiabatic light transfer via dressed states in optical waveguide arrays,” Appl. Phys. Lett. 92(1), 011106 (2008).
[Crossref]

2007 (3)

F. I. Baida, “Enhanced transmission through subwavelength metallic coaxial apertures by excitation of the TEM mode,” Appl. Phys. B 89, (2) 145–149 (2007).
[Crossref]

F. J. García de Abajo, “Colloquium: light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1289 (2007).
[Crossref]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).
[Crossref] [PubMed]

2006 (1)

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: role of the plasmonic modes,” Phys. Rev. B 74(20), 205419 (2006).
[Crossref]

2005 (2)

W. J. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced infrared transmission through subwavelength coaxial metallic arrays,” Phys. Rev. Lett. 94(3), 033902 (2005).
[Crossref] [PubMed]

M. J. Lockyear, A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, “Microwave transmission through a single subwavelength annular aperture in a metal plate,” Phys. Rev. Lett. 94(19), 193902 (2005).
[Crossref] [PubMed]

1999 (1)

J. A. Porto, F. J. García-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83(14), 2845–2848 (1999).
[Crossref]

1998 (1)

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

Abouraddy, A. F.

A. K. Jahromi, S. Shabahang, H. E. Kondakci, S. Orsila, P. Melanen, and A. F. Abouraddy, “Transparent perfect mirror,” ACS Photonics 4(5), 1026–1032 (2017).
[Crossref]

A. K. Jahromi and A. F. Abouraddy, “Observation of Poynting’s vector reversal in an active photonic cavity,” Optica 3(11), 1194–1200 (2016).
[Crossref]

Aimez, V.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, 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]

Almeida, V. R.

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 (2013).
[Crossref]

Baida, F. I.

F. I. Baida, “Enhanced transmission through subwavelength metallic coaxial apertures by excitation of the TEM mode,” Appl. Phys. B 89, (2) 145–149 (2007).
[Crossref]

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: role of the plasmonic modes,” Phys. Rev. B 74(20), 205419 (2006).
[Crossref]

Bao, K.

S. Zhang, H. Wei, K. Bao, U. Hakanson, N. J. Halas, P. Nordlander, and H. Xu, “Chiral surface plasmon polaritons on metallic nanowires,” Phys. Rev. Lett. 107(9), 096801 (2011).
[Crossref] [PubMed]

Belkhir, A.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: role of the plasmonic modes,” Phys. Rev. B 74(20), 205419 (2006).
[Crossref]

Bender, C. M.

B. Peng, S. K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346(6207), 328–332 (2014).
[Crossref] [PubMed]

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10(5), 394–398 (2014).
[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).
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H. Hodaei, M. A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, “Parity-time-symmetric microring lasers,” Science 346(6212), 975–978 (2014).
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Figures (5)

Fig. 1
Fig. 1 (a) In a coaxial element the optical eigenmodes are helical modes Lm with different topological indexes m. (b) The modes L±1 and L0 can be cascadingly coupled with each other by a P T -symmetric grating in the form of Δε = εA exp(−) + εB exp(+), which renders nonreciprocal back and forth transitions among L±1 and L0. (c) The hybridized mode can be detected by measuring the spectra of optical transmission and the associated polarization state of field.
Fig. 2
Fig. 2 (a) Spectra of eigenfrequencies versus B, when ω0 = 0.90ω1 and A = 0.08 ω 1 2 . At the exceptional point of A B = ( ω 1 2 ω 0 2 ) 2 / 8 the ω+ and ω modes coalescence. Below this value the phase is broken, and the eigenfrequencies are complex. (b) Variations of the magnitude of c±1 and c0 versus B for the coherent-trapped helical mode (ωc = ω1).
Fig. 3
Fig. 3 COMSOL simulation results on the variation of EOT spectra versus εB in the P T -symmetric metamaterial shown in Fig. 1(c). Parameters are r1 = 0.5mm, r2 = 0.7mm, h = 0.6mm, εd = 12, a = 2.5mm, and εA = 1. The branch ωc is the coherent trapped mode Lc within our interest.
Fig. 4
Fig. 4 (a) EOT spectra when εA = εB = 1, and the distribution of field intensity at (b) ω = 66.8 GHz, (c) ωc = 76.6 GHz, and (d) ω+ = 78.4 GHz, respectively. Plots (c) and (d) share the same colormap.
Fig. 5
Fig. 5 Variation of the polarization state S3 of transmitted field versus εB on the ωc branch. Red dots are these from COMSOL simulation and the blue solid line is given by Eq. (16).

Equations (16)

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ε ( θ ) = ε d + Δ ε = ε d + ε A e j θ + ε B e + j θ ,
1 ε 0 μ 0 ε d × × E = ( 1 + ε A ε d e j θ + ε B ε d e + j θ ) 2 E t 2 .
E P T = [ c + 1 e + 1 ( r , z ) e j θ + c 0 e 0 ( r , z ) + c 1 e 1 ( r , z ) e + j θ ] e j ω t ,
ω 1 2 c + 1 = ω 2 c + 1 + ω 2 ε A ε d κ c 0 ,
ω 0 2 c 0 = ω 2 c 0 + ω 2 ε A ε d κ c 1 + ω 2 ε B ε d κ * c + 1 ,
ω 1 2 c 1 = ω 2 c 1 + ω 2 ε B ε d κ * c 0 ,
κ = 2 π h / 2 h / 2 r 1 r 2 r e + 1 * e 0 d r d z
[ ω 1 2 A 0 B ω 0 2 A 0 B ω 1 2 ] [ c + 1 c 0 c 1 ] = ω 2 [ c + 1 c 0 c 1 ] ,
A = ε A ε d ω ¯ 2 κ ,
B = ε B ε d ω ¯ 2 κ * .
ω ± 2 = ω 1 2 + ω 0 2 2 ± ( ω 1 2 ω 0 2 2 ) 2 + 2 A B .
ω c = ω 1 .
c + 1 = ε A ε A 2 + ε B 2 ,
c 0 = 0 ,
c 1 = ε B ε A 2 + ε B 2 .
S 3 = ε A 2 ε B 2 ε A 2 + ε B 2 .

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