Abstract

This paper reports on time-domain modeling of an optical switch based on the parity–time (PT) symmetric Bragg grating. The switching response is triggered by suddenly switching on the gain in the Bragg grating to create a PT-symmetric Bragg grating. Transient and dynamic behaviors of the PT Bragg gratings are analyzed using the time-domain numerical transmission line modeling method including a simple gain saturation model. The on/off ratio and the switching time of the PT Bragg grating optical switch are analyzed in terms of the level of gain introduced in the system and the operating frequency. The paper also discusses the effect the gain saturation has on the operation of the PT-symmetric Bragg gratings.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
    [CrossRef]
  2. 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]
  3. K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Beam dynamics in PT symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008).
    [CrossRef]
  4. 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]
  5. J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A 45, 1–15 (2012).
    [CrossRef]
  6. T. Kottos, “Broken symmetry makes light works,” Nat. Phys. 6, 166–167 (2010).
    [CrossRef]
  7. H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodoulides, “Unidirectional nonlinear PT-symmetric optical structures,” Phys. Rev. A 82, 043803 (2010).
    [CrossRef]
  8. A. A. Sukhorukov, Z. Xu, and Y. S. Kivshar, “Nonlinear suppression of time reversals in PT-symmetric optical couplers,” Phys. Rev. A 82, 043818 (2010).
    [CrossRef]
  9. 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]
  10. C. M. Bender, S. Boettcher, and P. N. Meisinger, “PT-symmetric quantum mechanics,” J. Math. Phys. 40, 2201–2229 (1999).
    [CrossRef]
  11. S. Nixon, L. Ge, and J. Yang, “Stability analysis for soliton in PT-symmetric optical lattices,” Phys. Rev. A 85, 023822 (2012).
    [CrossRef]
  12. M. Kulishov, J. M. Laniel, N. Belanger, J. Azana, and D. V. Plant, “Nonreciprocal waveguide Bragg gratings,” Opt. Express 13, 3068–3078 (2005).
  13. M. Greenberg and M. Orenstein, “Unidirectional complex grating assisted couplers,” Opt. Express 12, 4013–4018 (2004).
    [CrossRef]
  14. M. Greenberg and M. Orenstein, “Optical unidirectional devices by complex spatial single sideband perturbation,” IEEE J. Quantum Electron. 41, 1013–1023 (2005).
    [CrossRef]
  15. R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32, 2632–2634 (2007).
    [CrossRef]
  16. L. Chen, R. Li, N. Yang, and L. Li, “Optical modes in PT-symmetric double channel waveguides,” in Proceedings of the Romanian Academy, Series A (2012), Vol. X, pp. 1–10.
  17. C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmertry in optics,” Nat. Phys. 6, 192–195 (2010).
    [CrossRef]
  18. A. Melloni, M. Chinello, and M. Martinelli, “All-optical switching in phase shifted fibre Bragg grating,” IEEE Photon. Technol. Lett. 12, 42–44 (2000).
    [CrossRef]
  19. Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
    [CrossRef]
  20. A. Majumdar, M. Bajcsy, D. Englund, and J. Vuckovic, “All optical switching with a single quantum dot strongly coupled to a photonic crystal cavity,” IEEE J. Sel. Top. Quantum Electron. 18, 1812–1817 (2012).
    [CrossRef]
  21. A. Mostafazadeh, “Invisibility and PT-symmetry,” arXiv:1206.0116 (2012).
  22. A. Mostafazadeh, “Spectral singularities of complex scattering potentials and infinite reflection and transmission coefficients at real energies,” Phys. Rev. Lett. 102, 220402 (2009).
    [CrossRef]
  23. J. Čtyroký, V. Kuzmiak, and S. Eyderman, “Waveguide structures with antisymmetric gain/loss profile,” Opt. Express 18, 21585–21593 (2010).
    [CrossRef]
  24. A. E. Siegman, Lasers (University Science Books, 1986).
  25. W. J. R. Hoefer, “The transmission-line matrix method—theory and applications,” IEEE Trans. Microw. Theory Tech. 33, 882–893 (1985).
    [CrossRef]
  26. C. Christopoulos, The Transmission Line Modeling Method: TLM (IEEE, 1995).
  27. M. Krumpholz, C. Huber, and P. Russer, “A field theoretical comparison of FDTD and TLM,” IEEE Trans. Microw. Theory Tech. 43, 1935–1950 (1995).
    [CrossRef]
  28. M. N. O. Sadiku, “A comparison of time-domain finite difference (FDTD) and transmission-line modeling (TLM) methods,” in Proceedings of the IEEE Southeastcon 2000 (IEEE, 2000), pp. 19–22.
  29. P. B. Johns, “On the relationship between TLM and finite-difference methods for Maxwell’s equation,” IEEE Trans. Microw. Theory Tech. 35, 60–61 (1987).
  30. R. E. Collin, Field Theory of Guided Waves, 2nd ed. (IEEE, 1991).
  31. D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
    [CrossRef]
  32. V. Janyani, A. Vukovic, J. D. Paul, P. Sewell, and T. M. Benson, “The development of TLM models for nonlinear optics,” IEEE Microw. Rev. 10, 35–42 (2004).
  33. J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material modes in TLM-part 3: material with nonlinear properties,” IEEE Trans. Antennas Propag. 50, 997–1004 (2002).
    [CrossRef]
  34. J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material model in TLM-part I: material with frequency-dependent properties,” IEEE Trans. Antennas Propag. 47, 1528–1534 (1999).
  35. K. Wörhoff, L. T. H. Hilderink, A. Driessen, and P. V. Lambeck, “Silicon oxynitride a versatile material for integrated optics applications,” J. Electrochem. Soc. 149, F85–F91 (2002).
    [CrossRef]
  36. S. Phang, A. Vukovic, H. Susanto, T. M. Benson, and P. Sewell, “Time domain modeling of all-optical switch based on PT-symmetric Bragg grating,” in Proceedings of the 29th Annual Review of Progress in Applied Computational Electromagnetics (ACES), Monterey, California, March20–28, 2013 (ACES, 2013), pp. 693–698.
  37. C. Larsen, D. Noordegraaf, P. M. W. Skovgaard, K. P. Hansen, K. E. Mattsson, and O. Bang, “Gain-switched CW fibre laser for improved supercontinuum generation in a PCF,” Opt. Express 19, 14883–14891 (2011).
    [CrossRef]

2013

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

2012

A. Majumdar, M. Bajcsy, D. Englund, and J. Vuckovic, “All optical switching with a single quantum dot strongly coupled to a photonic crystal cavity,” IEEE J. Sel. Top. Quantum Electron. 18, 1812–1817 (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]

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A 45, 1–15 (2012).
[CrossRef]

S. Nixon, L. Ge, and J. Yang, “Stability analysis for soliton in PT-symmetric optical lattices,” Phys. Rev. A 85, 023822 (2012).
[CrossRef]

2011

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]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (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]

C. Larsen, D. Noordegraaf, P. M. W. Skovgaard, K. P. Hansen, K. E. Mattsson, and O. Bang, “Gain-switched CW fibre laser for improved supercontinuum generation in a PCF,” Opt. Express 19, 14883–14891 (2011).
[CrossRef]

2010

J. Čtyroký, V. Kuzmiak, and S. Eyderman, “Waveguide structures with antisymmetric gain/loss profile,” Opt. Express 18, 21585–21593 (2010).
[CrossRef]

T. Kottos, “Broken symmetry makes light works,” Nat. Phys. 6, 166–167 (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]

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

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmertry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

2009

A. Mostafazadeh, “Spectral singularities of complex scattering potentials and infinite reflection and transmission coefficients at real energies,” Phys. Rev. Lett. 102, 220402 (2009).
[CrossRef]

2008

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[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]

2007

2005

M. Greenberg and M. Orenstein, “Optical unidirectional devices by complex spatial single sideband perturbation,” IEEE J. Quantum Electron. 41, 1013–1023 (2005).
[CrossRef]

M. Kulishov, J. M. Laniel, N. Belanger, J. Azana, and D. V. Plant, “Nonreciprocal waveguide Bragg gratings,” Opt. Express 13, 3068–3078 (2005).

2004

M. Greenberg and M. Orenstein, “Unidirectional complex grating assisted couplers,” Opt. Express 12, 4013–4018 (2004).
[CrossRef]

V. Janyani, A. Vukovic, J. D. Paul, P. Sewell, and T. M. Benson, “The development of TLM models for nonlinear optics,” IEEE Microw. Rev. 10, 35–42 (2004).

2002

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material modes in TLM-part 3: material with nonlinear properties,” IEEE Trans. Antennas Propag. 50, 997–1004 (2002).
[CrossRef]

K. Wörhoff, L. T. H. Hilderink, A. Driessen, and P. V. Lambeck, “Silicon oxynitride a versatile material for integrated optics applications,” J. Electrochem. Soc. 149, F85–F91 (2002).
[CrossRef]

2000

A. Melloni, M. Chinello, and M. Martinelli, “All-optical switching in phase shifted fibre Bragg grating,” IEEE Photon. Technol. Lett. 12, 42–44 (2000).
[CrossRef]

1999

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

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material model in TLM-part I: material with frequency-dependent properties,” IEEE Trans. Antennas Propag. 47, 1528–1534 (1999).

1995

M. Krumpholz, C. Huber, and P. Russer, “A field theoretical comparison of FDTD and TLM,” IEEE Trans. Microw. Theory Tech. 43, 1935–1950 (1995).
[CrossRef]

1987

P. B. Johns, “On the relationship between TLM and finite-difference methods for Maxwell’s equation,” IEEE Trans. Microw. Theory Tech. 35, 60–61 (1987).

1985

W. J. R. Hoefer, “The transmission-line matrix method—theory and applications,” IEEE Trans. Microw. Theory Tech. 33, 882–893 (1985).
[CrossRef]

Azana, J.

Baet, R.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

Bajcsy, M.

A. Majumdar, M. Bajcsy, D. Englund, and J. Vuckovic, “All optical switching with a single quantum dot strongly coupled to a photonic crystal cavity,” IEEE J. Sel. Top. Quantum Electron. 18, 1812–1817 (2012).
[CrossRef]

Bang, O.

Belanger, N.

Bender, C. M.

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

Benson, T. M.

V. Janyani, A. Vukovic, J. D. Paul, P. Sewell, and T. M. Benson, “The development of TLM models for nonlinear optics,” IEEE Microw. Rev. 10, 35–42 (2004).

S. Phang, A. Vukovic, H. Susanto, T. M. Benson, and P. Sewell, “Time domain modeling of all-optical switch based on PT-symmetric Bragg grating,” in Proceedings of the 29th Annual Review of Progress in Applied Computational Electromagnetics (ACES), Monterey, California, March20–28, 2013 (ACES, 2013), pp. 693–698.

Bersch, C.

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]

Boettcher, S.

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

Cao, H.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Chen, L.

L. Chen, R. Li, N. Yang, and L. Li, “Optical modes in PT-symmetric double channel waveguides,” in Proceedings of the Romanian Academy, Series A (2012), Vol. X, pp. 1–10.

Chinello, M.

A. Melloni, M. Chinello, and M. Martinelli, “All-optical switching in phase shifted fibre Bragg grating,” IEEE Photon. Technol. Lett. 12, 42–44 (2000).
[CrossRef]

Chong, Y. D.

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]

Christodoulides, D. N.

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]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (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. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmertry 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]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32, 2632–2634 (2007).
[CrossRef]

Christopoulos, C.

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material modes in TLM-part 3: material with nonlinear properties,” IEEE Trans. Antennas Propag. 50, 997–1004 (2002).
[CrossRef]

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material model in TLM-part I: material with frequency-dependent properties,” IEEE Trans. Antennas Propag. 47, 1528–1534 (1999).

C. Christopoulos, The Transmission Line Modeling Method: TLM (IEEE, 1995).

Collin, R. E.

R. E. Collin, Field Theory of Guided Waves, 2nd ed. (IEEE, 1991).

Ctyroký, J.

Doerr, C. R.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

Driessen, A.

K. Wörhoff, L. T. H. Hilderink, A. Driessen, and P. V. Lambeck, “Silicon oxynitride a versatile material for integrated optics applications,” J. Electrochem. Soc. 149, F85–F91 (2002).
[CrossRef]

Eich, M.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

Eichelkraut, T.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

El-Ganainy, R.

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. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmertry 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]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32, 2632–2634 (2007).
[CrossRef]

Ellis, F. M.

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A 45, 1–15 (2012).
[CrossRef]

Englund, D.

A. Majumdar, M. Bajcsy, D. Englund, and J. Vuckovic, “All optical switching with a single quantum dot strongly coupled to a photonic crystal cavity,” IEEE J. Sel. Top. Quantum Electron. 18, 1812–1817 (2012).
[CrossRef]

Eyderman, S.

Fan, S.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

Freude, W.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

Ge, L.

S. Nixon, L. Ge, and J. Yang, “Stability analysis for soliton in PT-symmetric optical lattices,” Phys. Rev. A 85, 023822 (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]

Green, W. M. J.

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[CrossRef]

Greenberg, M.

M. Greenberg and M. Orenstein, “Optical unidirectional devices by complex spatial single sideband perturbation,” IEEE J. Quantum Electron. 41, 1013–1023 (2005).
[CrossRef]

M. Greenberg and M. Orenstein, “Unidirectional complex grating assisted couplers,” Opt. Express 12, 4013–4018 (2004).
[CrossRef]

Hansen, K. P.

Hilderink, L. T. H.

K. Wörhoff, L. T. H. Hilderink, A. Driessen, and P. V. Lambeck, “Silicon oxynitride a versatile material for integrated optics applications,” J. Electrochem. Soc. 149, F85–F91 (2002).
[CrossRef]

Hoefer, W. J. R.

W. J. R. Hoefer, “The transmission-line matrix method—theory and applications,” IEEE Trans. Microw. Theory Tech. 33, 882–893 (1985).
[CrossRef]

Huber, C.

M. Krumpholz, C. Huber, and P. Russer, “A field theoretical comparison of FDTD and TLM,” IEEE Trans. Microw. Theory Tech. 43, 1935–1950 (1995).
[CrossRef]

Jalas, D.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

Janyani, V.

V. Janyani, A. Vukovic, J. D. Paul, P. Sewell, and T. M. Benson, “The development of TLM models for nonlinear optics,” IEEE Microw. Rev. 10, 35–42 (2004).

Joannopoulos, J. D.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

Johns, P. B.

P. B. Johns, “On the relationship between TLM and finite-difference methods for Maxwell’s equation,” IEEE Trans. Microw. Theory Tech. 35, 60–61 (1987).

Kip, D.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmertry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Kivshar, Y. S.

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

Kottos, T.

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A 45, 1–15 (2012).
[CrossRef]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

T. Kottos, “Broken symmetry makes light works,” Nat. Phys. 6, 166–167 (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]

Krumpholz, M.

M. Krumpholz, C. Huber, and P. Russer, “A field theoretical comparison of FDTD and TLM,” IEEE Trans. Microw. Theory Tech. 43, 1935–1950 (1995).
[CrossRef]

Kulishov, M.

Kuzmiak, V.

Lambeck, P. V.

K. Wörhoff, L. T. H. Hilderink, A. Driessen, and P. V. Lambeck, “Silicon oxynitride a versatile material for integrated optics applications,” J. Electrochem. Soc. 149, F85–F91 (2002).
[CrossRef]

Laniel, J. M.

Larsen, C.

Lee, J. M.

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A 45, 1–15 (2012).
[CrossRef]

Li, L.

L. Chen, R. Li, N. Yang, and L. Li, “Optical modes in PT-symmetric double channel waveguides,” in Proceedings of the Romanian Academy, Series A (2012), Vol. X, pp. 1–10.

Li, R.

L. Chen, R. Li, N. Yang, and L. Li, “Optical modes in PT-symmetric double channel waveguides,” in Proceedings of the Romanian Academy, Series A (2012), Vol. X, pp. 1–10.

Lin, Z.

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A 45, 1–15 (2012).
[CrossRef]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[CrossRef]

Majumdar, A.

A. Majumdar, M. Bajcsy, D. Englund, and J. Vuckovic, “All optical switching with a single quantum dot strongly coupled to a photonic crystal cavity,” IEEE J. Sel. Top. Quantum Electron. 18, 1812–1817 (2012).
[CrossRef]

Makris, K. G.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmertry 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]

R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32, 2632–2634 (2007).
[CrossRef]

Martinelli, M.

A. Melloni, M. Chinello, and M. Martinelli, “All-optical switching in phase shifted fibre Bragg grating,” IEEE Photon. Technol. Lett. 12, 42–44 (2000).
[CrossRef]

Mattsson, K. E.

Meisinger, P. N.

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

Melloni, A.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

A. Melloni, M. Chinello, and M. Martinelli, “All-optical switching in phase shifted fibre Bragg grating,” IEEE Photon. Technol. Lett. 12, 42–44 (2000).
[CrossRef]

Miri, M. A.

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]

Moravvej-Farshi, M. K.

Mostafazadeh, A.

A. Mostafazadeh, “Spectral singularities of complex scattering potentials and infinite reflection and transmission coefficients at real energies,” Phys. Rev. Lett. 102, 220402 (2009).
[CrossRef]

A. Mostafazadeh, “Invisibility and PT-symmetry,” arXiv:1206.0116 (2012).

Musslimani, Z. H.

Nazari, F.

Nazari, M.

Nixon, S.

S. Nixon, L. Ge, and J. Yang, “Stability analysis for soliton in PT-symmetric optical lattices,” Phys. Rev. A 85, 023822 (2012).
[CrossRef]

Noordegraaf, D.

Onishchukov, G.

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]

Orenstein, M.

M. Greenberg and M. Orenstein, “Optical unidirectional devices by complex spatial single sideband perturbation,” IEEE J. Quantum Electron. 41, 1013–1023 (2005).
[CrossRef]

M. Greenberg and M. Orenstein, “Unidirectional complex grating assisted couplers,” Opt. Express 12, 4013–4018 (2004).
[CrossRef]

Paul, J.

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material modes in TLM-part 3: material with nonlinear properties,” IEEE Trans. Antennas Propag. 50, 997–1004 (2002).
[CrossRef]

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material model in TLM-part I: material with frequency-dependent properties,” IEEE Trans. Antennas Propag. 47, 1528–1534 (1999).

Paul, J. D.

V. Janyani, A. Vukovic, J. D. Paul, P. Sewell, and T. M. Benson, “The development of TLM models for nonlinear optics,” IEEE Microw. Rev. 10, 35–42 (2004).

Peschel, U.

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]

Petrov, A.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

Phang, S.

S. Phang, A. Vukovic, H. Susanto, T. M. Benson, and P. Sewell, “Time domain modeling of all-optical switch based on PT-symmetric Bragg grating,” in Proceedings of the 29th Annual Review of Progress in Applied Computational Electromagnetics (ACES), Monterey, California, March20–28, 2013 (ACES, 2013), pp. 693–698.

Plant, D. V.

Popovic, M.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

Ramezani, H.

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A 45, 1–15 (2012).
[CrossRef]

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (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]

Regensburger, A.

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]

Renner, H.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

Russer, P.

M. Krumpholz, C. Huber, and P. Russer, “A field theoretical comparison of FDTD and TLM,” IEEE Trans. Microw. Theory Tech. 43, 1935–1950 (1995).
[CrossRef]

Rüter, C. E.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmertry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Sadiku, M. N. O.

M. N. O. Sadiku, “A comparison of time-domain finite difference (FDTD) and transmission-line modeling (TLM) methods,” in Proceedings of the IEEE Southeastcon 2000 (IEEE, 2000), pp. 19–22.

Schindler, J.

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A 45, 1–15 (2012).
[CrossRef]

Segev, M.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmertry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Sewell, P.

V. Janyani, A. Vukovic, J. D. Paul, P. Sewell, and T. M. Benson, “The development of TLM models for nonlinear optics,” IEEE Microw. Rev. 10, 35–42 (2004).

S. Phang, A. Vukovic, H. Susanto, T. M. Benson, and P. Sewell, “Time domain modeling of all-optical switch based on PT-symmetric Bragg grating,” in Proceedings of the 29th Annual Review of Progress in Applied Computational Electromagnetics (ACES), Monterey, California, March20–28, 2013 (ACES, 2013), pp. 693–698.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Skovgaard, P. M. W.

Stone, A. D.

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]

Sukhorukov, A. A.

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

Susanto, H.

S. Phang, A. Vukovic, H. Susanto, T. M. Benson, and P. Sewell, “Time domain modeling of all-optical switch based on PT-symmetric Bragg grating,” in Proceedings of the 29th Annual Review of Progress in Applied Computational Electromagnetics (ACES), Monterey, California, March20–28, 2013 (ACES, 2013), pp. 693–698.

Thomas, D. W. P.

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material modes in TLM-part 3: material with nonlinear properties,” IEEE Trans. Antennas Propag. 50, 997–1004 (2002).
[CrossRef]

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material model in TLM-part I: material with frequency-dependent properties,” IEEE Trans. Antennas Propag. 47, 1528–1534 (1999).

Vanwolleghem, M.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

Vlasov, Y.

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[CrossRef]

Vuckovic, J.

A. Majumdar, M. Bajcsy, D. Englund, and J. Vuckovic, “All optical switching with a single quantum dot strongly coupled to a photonic crystal cavity,” IEEE J. Sel. Top. Quantum Electron. 18, 1812–1817 (2012).
[CrossRef]

Vukovic, A.

V. Janyani, A. Vukovic, J. D. Paul, P. Sewell, and T. M. Benson, “The development of TLM models for nonlinear optics,” IEEE Microw. Rev. 10, 35–42 (2004).

S. Phang, A. Vukovic, H. Susanto, T. M. Benson, and P. Sewell, “Time domain modeling of all-optical switch based on PT-symmetric Bragg grating,” in Proceedings of the 29th Annual Review of Progress in Applied Computational Electromagnetics (ACES), Monterey, California, March20–28, 2013 (ACES, 2013), pp. 693–698.

Wörhoff, K.

K. Wörhoff, L. T. H. Hilderink, A. Driessen, and P. V. Lambeck, “Silicon oxynitride a versatile material for integrated optics applications,” J. Electrochem. Soc. 149, F85–F91 (2002).
[CrossRef]

Xia, F.

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[CrossRef]

Xu, Z.

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

Yang, J.

S. Nixon, L. Ge, and J. Yang, “Stability analysis for soliton in PT-symmetric optical lattices,” Phys. Rev. A 85, 023822 (2012).
[CrossRef]

Yang, N.

L. Chen, R. Li, N. Yang, and L. Li, “Optical modes in PT-symmetric double channel waveguides,” in Proceedings of the Romanian Academy, Series A (2012), Vol. X, pp. 1–10.

Yu, Z.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

IEEE J. Quantum Electron.

M. Greenberg and M. Orenstein, “Optical unidirectional devices by complex spatial single sideband perturbation,” IEEE J. Quantum Electron. 41, 1013–1023 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

A. Majumdar, M. Bajcsy, D. Englund, and J. Vuckovic, “All optical switching with a single quantum dot strongly coupled to a photonic crystal cavity,” IEEE J. Sel. Top. Quantum Electron. 18, 1812–1817 (2012).
[CrossRef]

IEEE Microw. Rev.

V. Janyani, A. Vukovic, J. D. Paul, P. Sewell, and T. M. Benson, “The development of TLM models for nonlinear optics,” IEEE Microw. Rev. 10, 35–42 (2004).

IEEE Photon. Technol. Lett.

A. Melloni, M. Chinello, and M. Martinelli, “All-optical switching in phase shifted fibre Bragg grating,” IEEE Photon. Technol. Lett. 12, 42–44 (2000).
[CrossRef]

IEEE Trans. Antennas Propag.

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material modes in TLM-part 3: material with nonlinear properties,” IEEE Trans. Antennas Propag. 50, 997–1004 (2002).
[CrossRef]

J. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material model in TLM-part I: material with frequency-dependent properties,” IEEE Trans. Antennas Propag. 47, 1528–1534 (1999).

IEEE Trans. Microw. Theory Tech.

M. Krumpholz, C. Huber, and P. Russer, “A field theoretical comparison of FDTD and TLM,” IEEE Trans. Microw. Theory Tech. 43, 1935–1950 (1995).
[CrossRef]

P. B. Johns, “On the relationship between TLM and finite-difference methods for Maxwell’s equation,” IEEE Trans. Microw. Theory Tech. 35, 60–61 (1987).

W. J. R. Hoefer, “The transmission-line matrix method—theory and applications,” IEEE Trans. Microw. Theory Tech. 33, 882–893 (1985).
[CrossRef]

J. Electrochem. Soc.

K. Wörhoff, L. T. H. Hilderink, A. Driessen, and P. V. Lambeck, “Silicon oxynitride a versatile material for integrated optics applications,” J. Electrochem. Soc. 149, F85–F91 (2002).
[CrossRef]

J. Math. Phys.

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

J. Phys. A

J. Schindler, Z. Lin, J. M. Lee, H. Ramezani, F. M. Ellis, and T. Kottos, “PT-symmetric electronics,” J. Phys. A 45, 1–15 (2012).
[CrossRef]

Nat. Photonics

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2, 242–246 (2008).
[CrossRef]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baet, M. Popovic, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is—and what is not an optical isolator,” Nat. Photonics 7, 579–582 (2013).
[CrossRef]

Nat. Phys.

T. Kottos, “Broken symmetry makes light works,” Nat. Phys. 6, 166–167 (2010).
[CrossRef]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmertry in optics,” Nat. Phys. 6, 192–195 (2010).
[CrossRef]

Nature

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]

Opt. Express

Opt. Lett.

Phys. Rev. A

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

S. Nixon, L. Ge, and J. Yang, “Stability analysis for soliton in PT-symmetric optical lattices,” Phys. Rev. A 85, 023822 (2012).
[CrossRef]

Phys. Rev. Lett.

Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, “Unidirectional invisibility induced by PT-symmetric periodic structures,” Phys. Rev. Lett. 106, 213901 (2011).
[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]

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. Mostafazadeh, “Spectral singularities of complex scattering potentials and infinite reflection and transmission coefficients at real energies,” Phys. Rev. Lett. 102, 220402 (2009).
[CrossRef]

Other

A. Mostafazadeh, “Invisibility and PT-symmetry,” arXiv:1206.0116 (2012).

A. E. Siegman, Lasers (University Science Books, 1986).

C. Christopoulos, The Transmission Line Modeling Method: TLM (IEEE, 1995).

S. Phang, A. Vukovic, H. Susanto, T. M. Benson, and P. Sewell, “Time domain modeling of all-optical switch based on PT-symmetric Bragg grating,” in Proceedings of the 29th Annual Review of Progress in Applied Computational Electromagnetics (ACES), Monterey, California, March20–28, 2013 (ACES, 2013), pp. 693–698.

R. E. Collin, Field Theory of Guided Waves, 2nd ed. (IEEE, 1991).

M. N. O. Sadiku, “A comparison of time-domain finite difference (FDTD) and transmission-line modeling (TLM) methods,” in Proceedings of the IEEE Southeastcon 2000 (IEEE, 2000), pp. 19–22.

L. Chen, R. Li, N. Yang, and L. Li, “Optical modes in PT-symmetric double channel waveguides,” in Proceedings of the Romanian Academy, Series A (2012), Vol. X, pp. 1–10.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1.
Fig. 1.

Schematic presentation of (a) the PT Bragg grating and (b) the refractive index profile for one period of the grating.

Fig. 2.
Fig. 2.

Single segment of 1D TLM meshing.

Fig. 3.
Fig. 3.

Comparison of the TLM and T-matrix results for the transmitted power from left (TL) and right (TR), power reflected from the left (ΓL), and power reflected from the right (ΓR) at the Bragg frequency fB as a function of the gain/loss parameter nI in a structure of 150 number of periods, nR=1.55 and ΔnR=0.01 for 2 different amplitudes of the input of CW signal (a) Em=0.002Esat and (b) Em=0.2Esat.

Fig. 4.
Fig. 4.

Saturation point as a function of saturation order k for three different CW input amplitudes.

Fig. 5.
Fig. 5.

Plot of the spectra of the (a) power transmitted for left (TL), (b) power reflected for left (ΓL), (c) power transmitted for right (TR), and (d) power reflected from the right (ΓR) obtained using the TLM method for different values of gain/loss parameter nI and maximum input signal amplitude Em in a 150 periods grating with nR=1.55 and ΔnR=0.01.

Fig. 6.
Fig. 6.

Time-domain response of the PT Bragg grating showing transmitted signal for (a) nI=0.0025, (b) nI=0.01, and (c) nI=0.013. The inset of Figs. 5(a) and 5(b) show the time-domain responses of the input signal to the PT Bragg grating. The inset of Fig. 5(c) shows an enlarged view of the temporal signal from 4.5 to 4.52 ps of TLM with and without the gain saturation model.

Fig. 7.
Fig. 7.

(a)–(d) Time-domain response and (e)–(h) frequency-domain response of a PT Bragg grating with an instantaneous switching of gain to nI=0.01 at a time of t=3ps. Excitation is a CW signal at the Bragg frequency fB. (a) Normalized transmitted TL and (b) reflected ΓL signal amplitude envelope for the incidence from the left. (c) Transmitted TR and (d) reflected ΓR signal amplitude envelope for the incidence from the right. Frequency response of (e) TL, (f) ΓL, (g) TR, and (h) ΓR signals with (solid line) and without (dashed line) switching. All the frequency-domain values are normalized to the frequency-domain value of the incident signal.

Fig. 8.
Fig. 8.

Switching time and on/off transmittance ratio as a function of frequency detuning from the Bragg frequency.

Fig. 9.
Fig. 9.

Switching time and on/off transmittance ratio as a function of gain/loss parameter nI.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

ΔC=ϵ0Re(n^21)Δx,
G=2ωBRe(n^)Im(n^)Δx,
G=G01+(EEsat)2k,

Metrics