N. Bender, S. Factor, J.D. Bodyfelt, H. Ramezani, D. N. Christodoulides, F. Ellis, and T. Kottos, “Observation of asymmetric transport in structures with active nonlinearities,” Phys. Rev. Lett. 110, 234101 (2013).

[Crossref]

L. Fan, J. Wang, L.T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).

[Crossref]

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

[Crossref]
[PubMed]

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A -Math and Theor. 45, 444029 (2012).

[Crossref]

H. Ramezani, J. Schindler, F.M. Ellis, U. Günther, and T. Kottos, “Bypassing the bandwidth theorem with PT symmetry,” Phys. Rev. A 85, 062122 (2012).

[Crossref]

Z. Lin, J. Schindler, F.M. Ellis, and T. Kottos, “Experimental observation of the dual behavior of PT-symmetric scattering,” Phys. Rev. A 85, 050101 (2012).

[Crossref]

B-B Li, Y-F Xiao, C-L Zou, X-F Jiang, Y-C Liu, F-W Sun, Y Li, and Q Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators”, Applied Phys. Lett. 100, 021108 (2012).

[Crossref]

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

[Crossref]
[PubMed]

A. E. Miroshnichenko, B.A. Malomed, and Y.S. Kivshar, “Nonlinearly PT-symmetric systems: spontaneous symmetry breaking and transmission resonances,” Phys. Rev. A 84, 012123 (2011).

[Crossref]

M.S. Kang, A. Butsch, and P.S.J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics 5, 549–553 (2011).

[Crossref]

S. Lepri and G. Casati, “Asymmetric wave propagation in nonlinear systems,” Phys. Rev. Lett. 106, 164101 (2011).

[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, 192–195 (2010).

[Crossref]

A. E. Miroshnichenko, S. Flach, and Y.S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).

[Crossref]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Unidirectional nonlinear PT-symmetric optical structures,” Phys. Rev. A 82, 043803 (2010).

[Crossref]

Y-F Xiao, M. Li, Y-C Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).

[Crossref]

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

[Crossref]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).

[Crossref]

K. G. Makris, R. El-Ganainy, and D.N. Christodoulides, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).

[Crossref]
[PubMed]

C. M. Bender, “Making sense of non-hermitian hamiltonians,” Rep. Prog. Phys. 70, 947–1018 (2007).

[Crossref]

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98, 213904 (2007).

[Crossref]
[PubMed]

J. Ctyroky, I. Richter, and V. Sinor, “Dual resonance in a waveguide-coupled ring microresonator,” Optic. Quantum Electron. 38, 781–797 (2006).

[Crossref]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).

[Crossref]
[PubMed]

K. Srinivasan, M. Borselli, O. Painter, A. Stintz, and S. Krishna, “Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots,” Opt. Express 14, 1094–1105 (2006).

[Crossref]
[PubMed]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).

[Crossref]

K. J. Vahala, “Optical microcavities,” Nature (London) 424, 839–846 (2003).

[Crossref]

K. Gallo and G. Assanto, “All-optical diode based on second-harmonic generation in an asymmetric waveguide,” JOSA B 16, 267–269 (1999).

[Crossref]

M. Scalora, J.P. Dowling, C.M. Bowden, and M.J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).

[Crossref]

K. Gallo and G. Assanto, “All-optical diode based on second-harmonic generation in an asymmetric waveguide,” JOSA B 16, 267–269 (1999).

[Crossref]

C. M. Bender, “Making sense of non-hermitian hamiltonians,” Rep. Prog. Phys. 70, 947–1018 (2007).

[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, “Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities,” arXiv:1308.4564 (2013).

N. Bender, S. Factor, J.D. Bodyfelt, H. Ramezani, D. N. Christodoulides, F. Ellis, and T. Kottos, “Observation of asymmetric transport in structures with active nonlinearities,” Phys. Rev. Lett. 110, 234101 (2013).

[Crossref]

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

[Crossref]
[PubMed]

M. Scalora, J.P. Dowling, C.M. Bowden, and M.J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).

[Crossref]

N. Bender, S. Factor, J.D. Bodyfelt, H. Ramezani, D. N. Christodoulides, F. Ellis, and T. Kottos, “Observation of asymmetric transport in structures with active nonlinearities,” Phys. Rev. Lett. 110, 234101 (2013).

[Crossref]

M. Scalora, J.P. Dowling, C.M. Bowden, and M.J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).

[Crossref]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).

[Crossref]

M.S. Kang, A. Butsch, and P.S.J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics 5, 549–553 (2011).

[Crossref]

S. Lepri and G. Casati, “Asymmetric wave propagation in nonlinear systems,” Phys. Rev. Lett. 106, 164101 (2011).

[Crossref]
[PubMed]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).

[Crossref]

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

[Crossref]
[PubMed]

N. Bender, S. Factor, J.D. Bodyfelt, H. Ramezani, D. N. Christodoulides, F. Ellis, and T. Kottos, “Observation of asymmetric transport in structures with active nonlinearities,” Phys. Rev. Lett. 110, 234101 (2013).

[Crossref]

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

[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, 192–195 (2010).

[Crossref]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Unidirectional nonlinear PT-symmetric optical structures,” Phys. Rev. A 82, 043803 (2010).

[Crossref]

K. G. Makris, R. El-Ganainy, and D.N. Christodoulides, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).

[Crossref]
[PubMed]

J. Ctyroky, I. Richter, and V. Sinor, “Dual resonance in a waveguide-coupled ring microresonator,” Optic. Quantum Electron. 38, 781–797 (2006).

[Crossref]

M. Scalora, J.P. Dowling, C.M. Bowden, and M.J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).

[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, 192–195 (2010).

[Crossref]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Unidirectional nonlinear PT-symmetric optical structures,” Phys. Rev. A 82, 043803 (2010).

[Crossref]

K. G. Makris, R. El-Ganainy, and D.N. Christodoulides, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).

[Crossref]
[PubMed]

N. Bender, S. Factor, J.D. Bodyfelt, H. Ramezani, D. N. Christodoulides, F. Ellis, and T. Kottos, “Observation of asymmetric transport in structures with active nonlinearities,” Phys. Rev. Lett. 110, 234101 (2013).

[Crossref]

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A -Math and Theor. 45, 444029 (2012).

[Crossref]

H. Ramezani, J. Schindler, F.M. Ellis, U. Günther, and T. Kottos, “Bypassing the bandwidth theorem with PT symmetry,” Phys. Rev. A 85, 062122 (2012).

[Crossref]

Z. Lin, J. Schindler, F.M. Ellis, and T. Kottos, “Experimental observation of the dual behavior of PT-symmetric scattering,” Phys. Rev. A 85, 050101 (2012).

[Crossref]

N. Bender, S. Factor, J.D. Bodyfelt, H. Ramezani, D. N. Christodoulides, F. Ellis, and T. Kottos, “Observation of asymmetric transport in structures with active nonlinearities,” Phys. Rev. Lett. 110, 234101 (2013).

[Crossref]

L. Fan, J. Wang, L.T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).

[Crossref]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).

[Crossref]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).

[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, “Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities,” arXiv:1308.4564 (2013).

A. E. Miroshnichenko, S. Flach, and Y.S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).

[Crossref]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).

[Crossref]

K. Gallo and G. Assanto, “All-optical diode based on second-harmonic generation in an asymmetric waveguide,” JOSA B 16, 267–269 (1999).

[Crossref]

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

[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, “Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities,” arXiv:1308.4564 (2013).

B-B Li, Y-F Xiao, C-L Zou, X-F Jiang, Y-C Liu, F-W Sun, Y Li, and Q Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators”, Applied Phys. Lett. 100, 021108 (2012).

[Crossref]

Y-F Xiao, M. Li, Y-C Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).

[Crossref]

H. Ramezani, J. Schindler, F.M. Ellis, U. Günther, and T. Kottos, “Bypassing the bandwidth theorem with PT symmetry,” Phys. Rev. A 85, 062122 (2012).

[Crossref]

B-B Li, Y-F Xiao, C-L Zou, X-F Jiang, Y-C Liu, F-W Sun, Y Li, and Q Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators”, Applied Phys. Lett. 100, 021108 (2012).

[Crossref]

M.S. Kang, A. Butsch, and P.S.J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics 5, 549–553 (2011).

[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, 192–195 (2010).

[Crossref]

A. E. Miroshnichenko, B.A. Malomed, and Y.S. Kivshar, “Nonlinearly PT-symmetric systems: spontaneous symmetry breaking and transmission resonances,” Phys. Rev. A 84, 012123 (2011).

[Crossref]

A. E. Miroshnichenko, S. Flach, and Y.S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).

[Crossref]

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98, 213904 (2007).

[Crossref]
[PubMed]

N. Bender, S. Factor, J.D. Bodyfelt, H. Ramezani, D. N. Christodoulides, F. Ellis, and T. Kottos, “Observation of asymmetric transport in structures with active nonlinearities,” Phys. Rev. Lett. 110, 234101 (2013).

[Crossref]

Z. Lin, J. Schindler, F.M. Ellis, and T. Kottos, “Experimental observation of the dual behavior of PT-symmetric scattering,” Phys. Rev. A 85, 050101 (2012).

[Crossref]

H. Ramezani, J. Schindler, F.M. Ellis, U. Günther, and T. Kottos, “Bypassing the bandwidth theorem with PT symmetry,” Phys. Rev. A 85, 062122 (2012).

[Crossref]

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A -Math and Theor. 45, 444029 (2012).

[Crossref]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Unidirectional nonlinear PT-symmetric optical structures,” Phys. Rev. A 82, 043803 (2010).

[Crossref]

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A -Math and Theor. 45, 444029 (2012).

[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, “Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities,” arXiv:1308.4564 (2013).

S. Lepri and G. Casati, “Asymmetric wave propagation in nonlinear systems,” Phys. Rev. Lett. 106, 164101 (2011).

[Crossref]
[PubMed]

B-B Li, Y-F Xiao, C-L Zou, X-F Jiang, Y-C Liu, F-W Sun, Y Li, and Q Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators”, Applied Phys. Lett. 100, 021108 (2012).

[Crossref]

Y-F Xiao, M. Li, Y-C Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).

[Crossref]

B-B Li, Y-F Xiao, C-L Zou, X-F Jiang, Y-C Liu, F-W Sun, Y Li, and Q Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators”, Applied Phys. Lett. 100, 021108 (2012).

[Crossref]

Y-F Xiao, M. Li, Y-C Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).

[Crossref]

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A -Math and Theor. 45, 444029 (2012).

[Crossref]

Z. Lin, J. Schindler, F.M. Ellis, and T. Kottos, “Experimental observation of the dual behavior of PT-symmetric scattering,” Phys. Rev. A 85, 050101 (2012).

[Crossref]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).

[Crossref]
[PubMed]

B-B Li, Y-F Xiao, C-L Zou, X-F Jiang, Y-C Liu, F-W Sun, Y Li, and Q Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators”, Applied Phys. Lett. 100, 021108 (2012).

[Crossref]

Y-F Xiao, M. Li, Y-C Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).

[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, “Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities,” arXiv:1308.4564 (2013).

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82, 031801 (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, 192–195 (2010).

[Crossref]

K. G. Makris, R. El-Ganainy, and D.N. Christodoulides, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).

[Crossref]
[PubMed]

A. E. Miroshnichenko, B.A. Malomed, and Y.S. Kivshar, “Nonlinearly PT-symmetric systems: spontaneous symmetry breaking and transmission resonances,” Phys. Rev. A 84, 012123 (2011).

[Crossref]

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

[Crossref]
[PubMed]

A. E. Miroshnichenko, B.A. Malomed, and Y.S. Kivshar, “Nonlinearly PT-symmetric systems: spontaneous symmetry breaking and transmission resonances,” Phys. Rev. A 84, 012123 (2011).

[Crossref]

A. E. Miroshnichenko, S. Flach, and Y.S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).

[Crossref]

Y. Xu and A. E. Miroshnichenko, “Reconfigurable nonreciprocity with nonlinear Fano diode,” eprint arXiv:1311.2533 (2013).

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities,” arXiv:1308.4564 (2013).

L. Fan, J. Wang, L.T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).

[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, “Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities,” arXiv:1308.4564 (2013).

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

[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, “Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities,” arXiv:1308.4564 (2013).

B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities,” arXiv:1308.4564 (2013).

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

[Crossref]
[PubMed]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).

[Crossref]
[PubMed]

L. Fan, J. Wang, L.T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).

[Crossref]

N. Bender, S. Factor, J.D. Bodyfelt, H. Ramezani, D. N. Christodoulides, F. Ellis, and T. Kottos, “Observation of asymmetric transport in structures with active nonlinearities,” Phys. Rev. Lett. 110, 234101 (2013).

[Crossref]

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A -Math and Theor. 45, 444029 (2012).

[Crossref]

H. Ramezani, J. Schindler, F.M. Ellis, U. Günther, and T. Kottos, “Bypassing the bandwidth theorem with PT symmetry,” Phys. Rev. A 85, 062122 (2012).

[Crossref]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Unidirectional nonlinear PT-symmetric optical structures,” Phys. Rev. A 82, 043803 (2010).

[Crossref]

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

[Crossref]
[PubMed]

J. Ctyroky, I. Richter, and V. Sinor, “Dual resonance in a waveguide-coupled ring microresonator,” Optic. Quantum Electron. 38, 781–797 (2006).

[Crossref]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).

[Crossref]

M.S. Kang, A. Butsch, and P.S.J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics 5, 549–553 (2011).

[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, 192–195 (2010).

[Crossref]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).

[Crossref]
[PubMed]

M. Scalora, J.P. Dowling, C.M. Bowden, and M.J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).

[Crossref]

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A -Math and Theor. 45, 444029 (2012).

[Crossref]

H. Ramezani, J. Schindler, F.M. Ellis, U. Günther, and T. Kottos, “Bypassing the bandwidth theorem with PT symmetry,” Phys. Rev. A 85, 062122 (2012).

[Crossref]

Z. Lin, J. Schindler, F.M. Ellis, and T. Kottos, “Experimental observation of the dual behavior of PT-symmetric scattering,” Phys. Rev. A 85, 050101 (2012).

[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, 192–195 (2010).

[Crossref]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).

[Crossref]
[PubMed]

L. Fan, J. Wang, L.T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).

[Crossref]

J. Ctyroky, I. Richter, and V. Sinor, “Dual resonance in a waveguide-coupled ring microresonator,” Optic. Quantum Electron. 38, 781–797 (2006).

[Crossref]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).

[Crossref]

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

[Crossref]
[PubMed]

B-B Li, Y-F Xiao, C-L Zou, X-F Jiang, Y-C Liu, F-W Sun, Y Li, and Q Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators”, Applied Phys. Lett. 100, 021108 (2012).

[Crossref]

Y-F Xiao, M. Li, Y-C Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).

[Crossref]

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98, 213904 (2007).

[Crossref]
[PubMed]

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98, 213904 (2007).

[Crossref]
[PubMed]

K. J. Vahala, “Optical microcavities,” Nature (London) 424, 839–846 (2003).

[Crossref]

L. Fan, J. Wang, L.T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).

[Crossref]

L. Fan, J. Wang, L.T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).

[Crossref]

L. Fan, J. Wang, L.T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).

[Crossref]

B-B Li, Y-F Xiao, C-L Zou, X-F Jiang, Y-C Liu, F-W Sun, Y Li, and Q Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators”, Applied Phys. Lett. 100, 021108 (2012).

[Crossref]

Y-F Xiao, M. Li, Y-C Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).

[Crossref]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).

[Crossref]
[PubMed]

Y. Xu and A. E. Miroshnichenko, “Reconfigurable nonreciprocity with nonlinear Fano diode,” eprint arXiv:1311.2533 (2013).

L. Fan, J. Wang, L.T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).

[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, “Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities,” arXiv:1308.4564 (2013).

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).

[Crossref]

B-B Li, Y-F Xiao, C-L Zou, X-F Jiang, Y-C Liu, F-W Sun, Y Li, and Q Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators”, Applied Phys. Lett. 100, 021108 (2012).

[Crossref]

B-B Li, Y-F Xiao, C-L Zou, X-F Jiang, Y-C Liu, F-W Sun, Y Li, and Q Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators”, Applied Phys. Lett. 100, 021108 (2012).

[Crossref]

M. Scalora, J.P. Dowling, C.M. Bowden, and M.J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).

[Crossref]

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A -Math and Theor. 45, 444029 (2012).

[Crossref]

K. Gallo and G. Assanto, “All-optical diode based on second-harmonic generation in an asymmetric waveguide,” JOSA B 16, 267–269 (1999).

[Crossref]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3, 91–94 (2009).

[Crossref]

M.S. Kang, A. Butsch, and P.S.J. Russell, “Reconfigurable light-driven opto-acoustic isolators in photonic crystal fibre,” Nat. Photonics 5, 549–553 (2011).

[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, 192–195 (2010).

[Crossref]

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

[Crossref]
[PubMed]

K. J. Vahala, “Optical microcavities,” Nature (London) 424, 839–846 (2003).

[Crossref]

J. Ctyroky, I. Richter, and V. Sinor, “Dual resonance in a waveguide-coupled ring microresonator,” Optic. Quantum Electron. 38, 781–797 (2006).

[Crossref]

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

[Crossref]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Unidirectional nonlinear PT-symmetric optical structures,” Phys. Rev. A 82, 043803 (2010).

[Crossref]

H. Ramezani, J. Schindler, F.M. Ellis, U. Günther, and T. Kottos, “Bypassing the bandwidth theorem with PT symmetry,” Phys. Rev. A 85, 062122 (2012).

[Crossref]

Z. Lin, J. Schindler, F.M. Ellis, and T. Kottos, “Experimental observation of the dual behavior of PT-symmetric scattering,” Phys. Rev. A 85, 050101 (2012).

[Crossref]

Y-F Xiao, M. Li, Y-C Liu, Y. Li, X. Sun, and Q. Gong, “Asymmetric Fano resonance analysis in indirectly coupled microresonators,” Phys. Rev. A 82, 065804 (2010).

[Crossref]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69, 063804 (2004).

[Crossref]

A. E. Miroshnichenko, B.A. Malomed, and Y.S. Kivshar, “Nonlinearly PT-symmetric systems: spontaneous symmetry breaking and transmission resonances,” Phys. Rev. A 84, 012123 (2011).

[Crossref]

Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. 96, 123901 (2006).

[Crossref]
[PubMed]

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency,” Phys. Rev. Lett. 98, 213904 (2007).

[Crossref]
[PubMed]

K. G. Makris, R. El-Ganainy, and D.N. Christodoulides, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).

[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, 093902 (2011).

[Crossref]
[PubMed]

S. Lepri and G. Casati, “Asymmetric wave propagation in nonlinear systems,” Phys. Rev. Lett. 106, 164101 (2011).

[Crossref]
[PubMed]

N. Bender, S. Factor, J.D. Bodyfelt, H. Ramezani, D. N. Christodoulides, F. Ellis, and T. Kottos, “Observation of asymmetric transport in structures with active nonlinearities,” Phys. Rev. Lett. 110, 234101 (2013).

[Crossref]

C. M. Bender, “Making sense of non-hermitian hamiltonians,” Rep. Prog. Phys. 70, 947–1018 (2007).

[Crossref]

A. E. Miroshnichenko, S. Flach, and Y.S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).

[Crossref]

L. Fan, J. Wang, L.T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).

[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, “Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities,” arXiv:1308.4564 (2013).

Y. Xu and A. E. Miroshnichenko, “Reconfigurable nonreciprocity with nonlinear Fano diode,” eprint arXiv:1311.2533 (2013).

The 𝒫𝒯-symmetric phase transition can be also achieved by manipulating the coupling strength between the gain an loss elements while keeping the balanced gain and loss parameter constant. Specifically it can be shown that decreasing the coupling strength is equivalent to increasing the gain and loss parameter.