D. A. Zezyulin and V. V. Konotop, “Nonlinear modes in the harmonic PT-symmetric potential,” Phys. Rev. A 85, 043840(2012).

[CrossRef]

F. Nazari, M. Nazari, and M. K. Moravvej-Farshi, “A 2×2 spatial optical switch based on PT-symmetry,” Opt. Lett. 36, 4368–4370 (2011).

[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]

Z. Lu and Z. Zhang, “Defect solitons in parity-time symmetric superlattices,” Opt. Express 19, 11457–11462 (2011).

[CrossRef]

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83, 041805 (2011).

[CrossRef]

A. A. Sukhorukov, Z. Xu, and Y. S. Kivshar, “Nonlinearsuppression of time-reversals in PT-symmetric optical couplers,” Phys. Rev. A 82, 043818 (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]

C. E. Ruter, 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, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010).

[CrossRef]

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).

[CrossRef]

M. Ebnali-Heidari, M. K. Moravvej-Farshi, and A. Zarifkar, “Swing effect of spatial solitons propagating through Gaussian and triangular waveguides,” Appl. Opt. 48, 5005–5014 (2009).

[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, 103904 (2008).

[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).

[CrossRef]

A. Suryanto and E. van Groesen, “Self-splitting of multisoliton bound states in planar Kerr waveguides,” Opt. Commun. 258, 264–274 (2006).

[CrossRef]

A. Ruschhaupt, F. Delgado, and J. G. Muga, “Physical realization of PT-symmetric potential scattering in a planar slab waveguide,” J. Phys. A 38, 171–176 (2005).

[CrossRef]

C. M. Bender, S. Bottcher, and P. N. Meisinger, “PT-symmetric quantum mechanics,” J. Math. Phys. 40, 2201–2229 (1999).

[CrossRef]

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

[CrossRef]

F. Garzia, C. Sibilia, and M. Bertolotti, “Swing effect of spatial soliton,” Opt. Commun. 139, 193–198 (1997).

[CrossRef]

L. Lefort and A. Barthelemy, “All-optical demultiplexing of a signal using collision and waveguiding of spatial solitons,” IEEE Photon. Technol. Lett. 9, 1364–1366 (1997).

[CrossRef]

A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light beam propagation at nonlinear interfaces. I. Equivalent particle theory for a single interface,” Phys. Rev. A 39, 1809(1989).

[CrossRef]

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83, 041805 (2011).

[CrossRef]

A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light beam propagation at nonlinear interfaces. I. Equivalent particle theory for a single interface,” Phys. Rev. A 39, 1809(1989).

[CrossRef]

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

[CrossRef]

L. Lefort and A. Barthelemy, “All-optical demultiplexing of a signal using collision and waveguiding of spatial solitons,” IEEE Photon. Technol. Lett. 9, 1364–1366 (1997).

[CrossRef]

C. M. Bender, S. Bottcher, and P. N. Meisinger, “PT-symmetric quantum mechanics,” J. Math. Phys. 40, 2201–2229 (1999).

[CrossRef]

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

[CrossRef]

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).

[CrossRef]

F. Garzia, C. Sibilia, and M. Bertolotti, “New phase modulation technique based on spatial soliton switching,” J. Lightwave Technol. 19, 1036–1042 (2001).

[CrossRef]

F. Garzia, C. Sibilia, and M. Bertolotti, “Swing effect of spatial soliton,” Opt. Commun. 139, 193–198 (1997).

[CrossRef]

C. M. Bender, S. Bottcher, and P. N. Meisinger, “PT-symmetric quantum mechanics,” J. Math. Phys. 40, 2201–2229 (1999).

[CrossRef]

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

[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]

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

[CrossRef]

C. E. Ruter, 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, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 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, 103904 (2008).

[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).

[CrossRef]

A. Ruschhaupt, F. Delgado, and J. G. Muga, “Physical realization of PT-symmetric potential scattering in a planar slab waveguide,” J. Phys. A 38, 171–176 (2005).

[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]

C. E. Ruter, 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, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010).

[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).

[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, 103904 (2008).

[CrossRef]

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).

[CrossRef]

F. Garzia, C. Sibilia, and M. Bertolotti, “New phase modulation technique based on spatial soliton switching,” J. Lightwave Technol. 19, 1036–1042 (2001).

[CrossRef]

F. Garzia, C. Sibilia, and M. Bertolotti, “Swing effect of spatial soliton,” Opt. Commun. 139, 193–198 (1997).

[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]

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83, 041805 (2011).

[CrossRef]

T. Kato, Perturbation Theory for Linear Operators (Springer Verlag, 1966).

C. E. Ruter, 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. A. Sukhorukov, Z. Xu, and Y. S. Kivshar, “Nonlinearsuppression of time-reversals in PT-symmetric optical couplers,” Phys. Rev. A 82, 043818 (2010).

[CrossRef]

D. A. Zezyulin and V. V. Konotop, “Nonlinear modes in the harmonic PT-symmetric potential,” Phys. Rev. A 85, 043840(2012).

[CrossRef]

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83, 041805 (2011).

[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]

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).

[CrossRef]

L. Lefort and A. Barthelemy, “All-optical demultiplexing of a signal using collision and waveguiding of spatial solitons,” IEEE Photon. Technol. Lett. 9, 1364–1366 (1997).

[CrossRef]

C. E. Ruter, 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, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 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, 103904 (2008).

[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).

[CrossRef]

C. M. Bender, S. Bottcher, and P. N. Meisinger, “PT-symmetric quantum mechanics,” J. Math. Phys. 40, 2201–2229 (1999).

[CrossRef]

A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light beam propagation at nonlinear interfaces. I. Equivalent particle theory for a single interface,” Phys. Rev. A 39, 1809(1989).

[CrossRef]

F. Nazari, M. Nazari, and M. K. Moravvej-Farshi, “A 2×2 spatial optical switch based on PT-symmetry,” Opt. Lett. 36, 4368–4370 (2011).

[CrossRef]

M. Ebnali-Heidari, M. K. Moravvej-Farshi, and A. Zarifkar, “Swing effect of spatial solitons propagating through Gaussian and triangular waveguides,” Appl. Opt. 48, 5005–5014 (2009).

[CrossRef]

M. Ebnali-Heidary, M. K. Moravvej-Farshi, and A. Zarifkar, “Multichannel wavelength conversion using fourth-order soliton decay,” J. Lightwave Technol. 25, 2571–2578(2007).

[CrossRef]

A. Ruschhaupt, F. Delgado, and J. G. Muga, “Physical realization of PT-symmetric potential scattering in a planar slab waveguide,” J. Phys. A 38, 171–176 (2005).

[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 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, 103904 (2008).

[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).

[CrossRef]

A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light beam propagation at nonlinear interfaces. I. Equivalent particle theory for a single interface,” Phys. Rev. A 39, 1809(1989).

[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. Ruschhaupt, F. Delgado, and J. G. Muga, “Physical realization of PT-symmetric potential scattering in a planar slab waveguide,” J. Phys. A 38, 171–176 (2005).

[CrossRef]

C. E. Ruter, 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]

C. E. Ruter, 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]

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).

[CrossRef]

F. Garzia, C. Sibilia, and M. Bertolotti, “New phase modulation technique based on spatial soliton switching,” J. Lightwave Technol. 19, 1036–1042 (2001).

[CrossRef]

F. Garzia, C. Sibilia, and M. Bertolotti, “Swing effect of spatial soliton,” Opt. Commun. 139, 193–198 (1997).

[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]

A. A. Sukhorukov, Z. Xu, and Y. S. Kivshar, “Nonlinearsuppression of time-reversals in PT-symmetric optical couplers,” Phys. Rev. A 82, 043818 (2010).

[CrossRef]

A. Suryanto and E. van Groesen, “Self-splitting of multisoliton bound states in planar Kerr waveguides,” Opt. Commun. 258, 264–274 (2006).

[CrossRef]

A. Suryanto and E. van Groesen, “Self-splitting of multisoliton bound states in planar Kerr waveguides,” Opt. Commun. 258, 264–274 (2006).

[CrossRef]

A. A. Sukhorukov, Z. Xu, and Y. S. Kivshar, “Nonlinearsuppression of time-reversals in PT-symmetric optical couplers,” Phys. Rev. A 82, 043818 (2010).

[CrossRef]

M. Ebnali-Heidari, M. K. Moravvej-Farshi, and A. Zarifkar, “Swing effect of spatial solitons propagating through Gaussian and triangular waveguides,” Appl. Opt. 48, 5005–5014 (2009).

[CrossRef]

M. Ebnali-Heidary, M. K. Moravvej-Farshi, and A. Zarifkar, “Multichannel wavelength conversion using fourth-order soliton decay,” J. Lightwave Technol. 25, 2571–2578(2007).

[CrossRef]

D. A. Zezyulin and V. V. Konotop, “Nonlinear modes in the harmonic PT-symmetric potential,” Phys. Rev. A 85, 043840(2012).

[CrossRef]

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83, 041805 (2011).

[CrossRef]

L. Lefort and A. Barthelemy, “All-optical demultiplexing of a signal using collision and waveguiding of spatial solitons,” IEEE Photon. Technol. Lett. 9, 1364–1366 (1997).

[CrossRef]

M. Ebnali-Heidary, M. K. Moravvej-Farshi, and A. Zarifkar, “Multichannel wavelength conversion using fourth-order soliton decay,” J. Lightwave Technol. 25, 2571–2578(2007).

[CrossRef]

F. Garzia, C. Sibilia, and M. Bertolotti, “New phase modulation technique based on spatial soliton switching,” J. Lightwave Technol. 19, 1036–1042 (2001).

[CrossRef]

C. M. Bender, S. Bottcher, and P. N. Meisinger, “PT-symmetric quantum mechanics,” J. Math. Phys. 40, 2201–2229 (1999).

[CrossRef]

A. Ruschhaupt, F. Delgado, and J. G. Muga, “Physical realization of PT-symmetric potential scattering in a planar slab waveguide,” J. Phys. A 38, 171–176 (2005).

[CrossRef]

C. E. Ruter, 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. Suryanto and E. van Groesen, “Self-splitting of multisoliton bound states in planar Kerr waveguides,” Opt. Commun. 258, 264–274 (2006).

[CrossRef]

F. Garzia, C. Sibilia, and M. Bertolotti, “Swing effect of spatial soliton,” Opt. Commun. 139, 193–198 (1997).

[CrossRef]

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

[CrossRef]

F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in PT-symmetric nonlinear lattices,” Phys. Rev. A 83, 041805 (2011).

[CrossRef]

D. A. Zezyulin and V. V. Konotop, “Nonlinear modes in the harmonic PT-symmetric potential,” Phys. Rev. A 85, 043840(2012).

[CrossRef]

A. B. Aceves, J. V. Moloney, and A. C. Newell, “Theory of light beam propagation at nonlinear interfaces. I. Equivalent particle theory for a single interface,” Phys. Rev. A 39, 1809(1989).

[CrossRef]

A. A. Sukhorukov, Z. Xu, and Y. S. Kivshar, “Nonlinearsuppression of time-reversals in PT-symmetric optical couplers,” Phys. Rev. A 82, 043818 (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, D. N. Christodoulides, and Z. H. Musslimani, “PT-symmetric optical lattices,” Phys. Rev. A 81, 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, 103904 (2008).

[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in PT periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008).

[CrossRef]

O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, “Exponentially fragile PT symmetry in lattices with localized eigenmodes,” Phys. Rev. Lett. 103, 030402 (2009).

[CrossRef]

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

[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]

T. Kato, Perturbation Theory for Linear Operators (Springer Verlag, 1966).