Abstract

Using analytical modeling and detailed numerical simulations, we investigate the input-output transmission regimes in one-dimensional (1D) nonlinear photonic crystal including array defect layers. A coupled-mode system is derived from the Maxwell equations and analyzed for the stationary-transmission regime in the new proposed structure. Using the idea about introducing defect layers into 1D nonlinear photonic crystals, a new method for creating and controlling optical bistability is proposed. The periodic optical structures with array defect layers can be used as all optical switches between lower- and higher-transmissive states, whereas it possesses one jumping from a low-transmissive state to a transparent state.

© 2012 Optical Society of America

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  1. H. Wen, O. Kuzucu, T. Hou, M. Lipson, and A. Gaeta, “All-optical switching of a single resonance in silicon ring resonators,” Opt. Lett. 36, 1413–1415 (2011).
    [CrossRef]
  2. E. Heydaria, E. Mohajerani, and A. Shamsa, “All optical switching in azo-polymer planar waveguide,” Opt. Commun. 284, 1208–1212 (2011).
    [CrossRef]
  3. W. Zhang and S. Yu, “Bistable switching using an optical Tamm cavity with a Kerr medium,” Opt. Commun. 283, 2622–2626 (2010).
    [CrossRef]
  4. Y. Dumeige, C. Arnaud, and P. Feron, “Combining FDTD with coupled mode theories for bistability in micro-ring resonators,” Opt. Commun. 250, 376–383 (2005).
    [CrossRef]
  5. Z. G. Zang and W. X. Yang, “Theoretical and experimental investigation of all-optical switching based on cascaded LPFGs separated by an erbium-doped fiber,” J. Appl. Phys. 109, 103106–103110 (2011).
    [CrossRef]
  6. C. F. Li and Z. G. Zang, “Optical switching in a nonlinear-fiber connected long-period fiber grating pair,” Chin. Opt. Lett. 35, 1919–1923 (2008).
  7. Z. G. Zang and Y. J. Zhang, “Low-switching power (<45  mW) optical bistability based on optical nonlinearity of ytterbium-doped fiber with a fiber Bragg grating pair,” J. Mod. Opt. 59, 161–165 (2012).
    [CrossRef]
  8. Z. Zang, “Numerical analysis of optical bistability based on fiber Bragg grating cavity containing a high nonlinearity doped-fiber,” Opt. Commun. 285, 521–526 (2012).
    [CrossRef]
  9. N. G. R. Broderick, D. Taverner, and D. J. Richardson, “Nonlinear switching in fibre Bragg gratings,” Opt. Express 3, 447–453 (1998).
    [CrossRef]
  10. N. D. Sankey, D. F. Prelewitz, and T. G. Brown, “All‐optical switching in a nonlinear periodic‐waveguide structure,” Appl. Phys. Lett. 60, 1427–1429 (1992).
    [CrossRef]
  11. G. Assanto and G. I. Stegeman, “Optical bistability in nonlocally nonlinear periodic structures,” Appl. Phys. Lett. 56, 2285–2287 (1990).
    [CrossRef]
  12. J. He and H. E. Cada, “Optical bistability in semiconductor periodic structures,” IEEE J. Quantum Electron. 27, 1182–1188 (1991).
    [CrossRef]
  13. D. Pelinovsky, L. Brzozowski, and E. H. Sargent, “Transmission regimes of periodic nonlinear optical structures,” Phys. Rev. E 62, R4536–R4539 (2000).
    [CrossRef]
  14. D. Pelinovsky, L. Brzozowski, J. Sears, and E. H. Sargent, “Stable all-optical limiting in nonlinear periodic structures. I. Analysis,” J. Opt. Soc. Am. B 19, 43–53 (2002).
    [CrossRef]
  15. S. Radic, N. George, and G. P. Agrawal, “Theory of low-threshold optical switching in nonlinear phase-shifted periodic structures,” J. Opt. Soc. Am. B 12, 671–680(1995).
    [CrossRef]
  16. M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66, 2324–2326 (1995).
    [CrossRef]
  17. C. M. de Sterke and J. E. Sipe, “Gap solitons,” E. Wolf, ed., Progress in Optics 33, 203–260 (1994).
    [CrossRef]
  18. W. Samir, S. J. Garth, and C. Past, “Interplay of grating and nonlinearity in mode coupling,” J. Opt. Soc. Am. B 11, 64–71 (1994).
    [CrossRef]
  19. B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton pulse generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
    [CrossRef]
  20. B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B 14, 2980–2993 (1997).
    [CrossRef]
  21. T. Hattori, N. Tsurumachi, and H. Nakatsuka, “Analysis of optical nonlinearity by defect states in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 14, 348–355 (1997).
    [CrossRef]
  22. J. He and M. Cada, “Combined distributed feedback and Fabry Perot structures with a phase-matching layer for optical bistable devices,” Appl. Phys. Lett. 61, 2150–2152 (1992).
    [CrossRef]
  23. E. Lidorikis, K. Busch, Q. M. Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single non-linear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090–15099 (1997).
    [CrossRef]
  24. P. Hou, Y. Chen, J. Shi, M. Shen, and Q. Wang, “Optical bistability in one-dimensional photonic band gap structures with coupled nonlinear defects,” Opt. Commun. 273, 441–445 (2007).
    [CrossRef]
  25. R. Wang, J. Dong, and D. Y. Xing, “Dispersive optical bistability in onedimensional doped photonic band gap structures,” Phys. Rev. E 55, 6301 (1997).
    [CrossRef]
  26. R. P. Stanley, R. Houdre, U. Oesterle, M. Ilegems, and C. Weisbuch, “Impurity modes in one-dimensional periodic-systems: The transition from photonic band-gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
    [CrossRef]
  27. P. Tran, “Optical switching with a nonlinear photonic crystal: A numerical study,” Opt. Lett. 21, 1138–1140 (1996).
    [CrossRef]
  28. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
  29. D. Pelinovsky and E. H. Sargent, “Stable all-optical limiting in nonlinear periodic structures. II. Computations,” J. Opt. Soc. Am. B 19, 1873–1889 (2002).
    [CrossRef]

2012 (2)

Z. G. Zang and Y. J. Zhang, “Low-switching power (<45  mW) optical bistability based on optical nonlinearity of ytterbium-doped fiber with a fiber Bragg grating pair,” J. Mod. Opt. 59, 161–165 (2012).
[CrossRef]

Z. Zang, “Numerical analysis of optical bistability based on fiber Bragg grating cavity containing a high nonlinearity doped-fiber,” Opt. Commun. 285, 521–526 (2012).
[CrossRef]

2011 (3)

H. Wen, O. Kuzucu, T. Hou, M. Lipson, and A. Gaeta, “All-optical switching of a single resonance in silicon ring resonators,” Opt. Lett. 36, 1413–1415 (2011).
[CrossRef]

E. Heydaria, E. Mohajerani, and A. Shamsa, “All optical switching in azo-polymer planar waveguide,” Opt. Commun. 284, 1208–1212 (2011).
[CrossRef]

Z. G. Zang and W. X. Yang, “Theoretical and experimental investigation of all-optical switching based on cascaded LPFGs separated by an erbium-doped fiber,” J. Appl. Phys. 109, 103106–103110 (2011).
[CrossRef]

2010 (1)

W. Zhang and S. Yu, “Bistable switching using an optical Tamm cavity with a Kerr medium,” Opt. Commun. 283, 2622–2626 (2010).
[CrossRef]

2008 (1)

C. F. Li and Z. G. Zang, “Optical switching in a nonlinear-fiber connected long-period fiber grating pair,” Chin. Opt. Lett. 35, 1919–1923 (2008).

2007 (1)

P. Hou, Y. Chen, J. Shi, M. Shen, and Q. Wang, “Optical bistability in one-dimensional photonic band gap structures with coupled nonlinear defects,” Opt. Commun. 273, 441–445 (2007).
[CrossRef]

2005 (1)

Y. Dumeige, C. Arnaud, and P. Feron, “Combining FDTD with coupled mode theories for bistability in micro-ring resonators,” Opt. Commun. 250, 376–383 (2005).
[CrossRef]

2002 (2)

2000 (1)

D. Pelinovsky, L. Brzozowski, and E. H. Sargent, “Transmission regimes of periodic nonlinear optical structures,” Phys. Rev. E 62, R4536–R4539 (2000).
[CrossRef]

1998 (2)

N. G. R. Broderick, D. Taverner, and D. J. Richardson, “Nonlinear switching in fibre Bragg gratings,” Opt. Express 3, 447–453 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton pulse generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
[CrossRef]

1997 (4)

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B 14, 2980–2993 (1997).
[CrossRef]

T. Hattori, N. Tsurumachi, and H. Nakatsuka, “Analysis of optical nonlinearity by defect states in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 14, 348–355 (1997).
[CrossRef]

R. Wang, J. Dong, and D. Y. Xing, “Dispersive optical bistability in onedimensional doped photonic band gap structures,” Phys. Rev. E 55, 6301 (1997).
[CrossRef]

E. Lidorikis, K. Busch, Q. M. Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single non-linear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090–15099 (1997).
[CrossRef]

1996 (1)

1995 (2)

S. Radic, N. George, and G. P. Agrawal, “Theory of low-threshold optical switching in nonlinear phase-shifted periodic structures,” J. Opt. Soc. Am. B 12, 671–680(1995).
[CrossRef]

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66, 2324–2326 (1995).
[CrossRef]

1994 (2)

C. M. de Sterke and J. E. Sipe, “Gap solitons,” E. Wolf, ed., Progress in Optics 33, 203–260 (1994).
[CrossRef]

W. Samir, S. J. Garth, and C. Past, “Interplay of grating and nonlinearity in mode coupling,” J. Opt. Soc. Am. B 11, 64–71 (1994).
[CrossRef]

1993 (1)

R. P. Stanley, R. Houdre, U. Oesterle, M. Ilegems, and C. Weisbuch, “Impurity modes in one-dimensional periodic-systems: The transition from photonic band-gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef]

1992 (2)

J. He and M. Cada, “Combined distributed feedback and Fabry Perot structures with a phase-matching layer for optical bistable devices,” Appl. Phys. Lett. 61, 2150–2152 (1992).
[CrossRef]

N. D. Sankey, D. F. Prelewitz, and T. G. Brown, “All‐optical switching in a nonlinear periodic‐waveguide structure,” Appl. Phys. Lett. 60, 1427–1429 (1992).
[CrossRef]

1991 (1)

J. He and H. E. Cada, “Optical bistability in semiconductor periodic structures,” IEEE J. Quantum Electron. 27, 1182–1188 (1991).
[CrossRef]

1990 (1)

G. Assanto and G. I. Stegeman, “Optical bistability in nonlocally nonlinear periodic structures,” Appl. Phys. Lett. 56, 2285–2287 (1990).
[CrossRef]

Aceves, A. B.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton pulse generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
[CrossRef]

Agrawal, G. P.

Arnaud, C.

Y. Dumeige, C. Arnaud, and P. Feron, “Combining FDTD with coupled mode theories for bistability in micro-ring resonators,” Opt. Commun. 250, 376–383 (2005).
[CrossRef]

Assanto, G.

G. Assanto and G. I. Stegeman, “Optical bistability in nonlocally nonlinear periodic structures,” Appl. Phys. Lett. 56, 2285–2287 (1990).
[CrossRef]

Bloemer, M. J.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66, 2324–2326 (1995).
[CrossRef]

Bowden, C. M.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66, 2324–2326 (1995).
[CrossRef]

Broderick, N. G. R.

Brown, T. G.

N. D. Sankey, D. F. Prelewitz, and T. G. Brown, “All‐optical switching in a nonlinear periodic‐waveguide structure,” Appl. Phys. Lett. 60, 1427–1429 (1992).
[CrossRef]

Brzozowski, L.

D. Pelinovsky, L. Brzozowski, J. Sears, and E. H. Sargent, “Stable all-optical limiting in nonlinear periodic structures. I. Analysis,” J. Opt. Soc. Am. B 19, 43–53 (2002).
[CrossRef]

D. Pelinovsky, L. Brzozowski, and E. H. Sargent, “Transmission regimes of periodic nonlinear optical structures,” Phys. Rev. E 62, R4536–R4539 (2000).
[CrossRef]

Busch, K.

E. Lidorikis, K. Busch, Q. M. Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single non-linear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090–15099 (1997).
[CrossRef]

Cada, H. E.

J. He and H. E. Cada, “Optical bistability in semiconductor periodic structures,” IEEE J. Quantum Electron. 27, 1182–1188 (1991).
[CrossRef]

Cada, M.

J. He and M. Cada, “Combined distributed feedback and Fabry Perot structures with a phase-matching layer for optical bistable devices,” Appl. Phys. Lett. 61, 2150–2152 (1992).
[CrossRef]

Chan, C. T.

E. Lidorikis, K. Busch, Q. M. Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single non-linear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090–15099 (1997).
[CrossRef]

Chen, Y.

P. Hou, Y. Chen, J. Shi, M. Shen, and Q. Wang, “Optical bistability in one-dimensional photonic band gap structures with coupled nonlinear defects,” Opt. Commun. 273, 441–445 (2007).
[CrossRef]

de Sterke, C. M.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton pulse generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B 14, 2980–2993 (1997).
[CrossRef]

C. M. de Sterke and J. E. Sipe, “Gap solitons,” E. Wolf, ed., Progress in Optics 33, 203–260 (1994).
[CrossRef]

Dong, J.

R. Wang, J. Dong, and D. Y. Xing, “Dispersive optical bistability in onedimensional doped photonic band gap structures,” Phys. Rev. E 55, 6301 (1997).
[CrossRef]

Dowling, J. P.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66, 2324–2326 (1995).
[CrossRef]

Dumeige, Y.

Y. Dumeige, C. Arnaud, and P. Feron, “Combining FDTD with coupled mode theories for bistability in micro-ring resonators,” Opt. Commun. 250, 376–383 (2005).
[CrossRef]

Eggleton, B. J.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton pulse generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B 14, 2980–2993 (1997).
[CrossRef]

Feron, P.

Y. Dumeige, C. Arnaud, and P. Feron, “Combining FDTD with coupled mode theories for bistability in micro-ring resonators,” Opt. Commun. 250, 376–383 (2005).
[CrossRef]

Gaeta, A.

Garth, S. J.

George, N.

Hattori, T.

He, J.

J. He and M. Cada, “Combined distributed feedback and Fabry Perot structures with a phase-matching layer for optical bistable devices,” Appl. Phys. Lett. 61, 2150–2152 (1992).
[CrossRef]

J. He and H. E. Cada, “Optical bistability in semiconductor periodic structures,” IEEE J. Quantum Electron. 27, 1182–1188 (1991).
[CrossRef]

Heydaria, E.

E. Heydaria, E. Mohajerani, and A. Shamsa, “All optical switching in azo-polymer planar waveguide,” Opt. Commun. 284, 1208–1212 (2011).
[CrossRef]

Hou, P.

P. Hou, Y. Chen, J. Shi, M. Shen, and Q. Wang, “Optical bistability in one-dimensional photonic band gap structures with coupled nonlinear defects,” Opt. Commun. 273, 441–445 (2007).
[CrossRef]

Hou, T.

Houdre, R.

R. P. Stanley, R. Houdre, U. Oesterle, M. Ilegems, and C. Weisbuch, “Impurity modes in one-dimensional periodic-systems: The transition from photonic band-gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef]

Ilegems, M.

R. P. Stanley, R. Houdre, U. Oesterle, M. Ilegems, and C. Weisbuch, “Impurity modes in one-dimensional periodic-systems: The transition from photonic band-gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef]

Kuzucu, O.

Li, C. F.

C. F. Li and Z. G. Zang, “Optical switching in a nonlinear-fiber connected long-period fiber grating pair,” Chin. Opt. Lett. 35, 1919–1923 (2008).

Li, Q. M.

E. Lidorikis, K. Busch, Q. M. Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single non-linear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090–15099 (1997).
[CrossRef]

Lidorikis, E.

E. Lidorikis, K. Busch, Q. M. Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single non-linear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090–15099 (1997).
[CrossRef]

Lipson, M.

Mohajerani, E.

E. Heydaria, E. Mohajerani, and A. Shamsa, “All optical switching in azo-polymer planar waveguide,” Opt. Commun. 284, 1208–1212 (2011).
[CrossRef]

Nakatsuka, H.

Oesterle, U.

R. P. Stanley, R. Houdre, U. Oesterle, M. Ilegems, and C. Weisbuch, “Impurity modes in one-dimensional periodic-systems: The transition from photonic band-gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef]

Past, C.

Pelinovsky, D.

Prelewitz, D. F.

N. D. Sankey, D. F. Prelewitz, and T. G. Brown, “All‐optical switching in a nonlinear periodic‐waveguide structure,” Appl. Phys. Lett. 60, 1427–1429 (1992).
[CrossRef]

Radic, S.

Richardson, D. J.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

Samir, W.

Sankey, N. D.

N. D. Sankey, D. F. Prelewitz, and T. G. Brown, “All‐optical switching in a nonlinear periodic‐waveguide structure,” Appl. Phys. Lett. 60, 1427–1429 (1992).
[CrossRef]

Sargent, E. H.

Scalora, M.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66, 2324–2326 (1995).
[CrossRef]

Sears, J.

Shamsa, A.

E. Heydaria, E. Mohajerani, and A. Shamsa, “All optical switching in azo-polymer planar waveguide,” Opt. Commun. 284, 1208–1212 (2011).
[CrossRef]

Shen, M.

P. Hou, Y. Chen, J. Shi, M. Shen, and Q. Wang, “Optical bistability in one-dimensional photonic band gap structures with coupled nonlinear defects,” Opt. Commun. 273, 441–445 (2007).
[CrossRef]

Shi, J.

P. Hou, Y. Chen, J. Shi, M. Shen, and Q. Wang, “Optical bistability in one-dimensional photonic band gap structures with coupled nonlinear defects,” Opt. Commun. 273, 441–445 (2007).
[CrossRef]

Sipe, J. E.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton pulse generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
[CrossRef]

C. M. de Sterke and J. E. Sipe, “Gap solitons,” E. Wolf, ed., Progress in Optics 33, 203–260 (1994).
[CrossRef]

Slusher, R. E.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton pulse generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B 14, 2980–2993 (1997).
[CrossRef]

Soukoulis, C. M.

E. Lidorikis, K. Busch, Q. M. Li, C. T. Chan, and C. M. Soukoulis, “Optical nonlinear response of a single non-linear dielectric layer sandwiched between two linear dielectric structures,” Phys. Rev. B 56, 15090–15099 (1997).
[CrossRef]

Stanley, R. P.

R. P. Stanley, R. Houdre, U. Oesterle, M. Ilegems, and C. Weisbuch, “Impurity modes in one-dimensional periodic-systems: The transition from photonic band-gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef]

Stegeman, G. I.

G. Assanto and G. I. Stegeman, “Optical bistability in nonlocally nonlinear periodic structures,” Appl. Phys. Lett. 56, 2285–2287 (1990).
[CrossRef]

Strasser, T. A.

B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, “Modulational instability and multiple soliton pulse generation in apodized fiber gratings,” Opt. Commun. 149, 267–271 (1998).
[CrossRef]

Taverner, D.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).

Tocci, M. D.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, “Thin-film nonlinear optical diode,” Appl. Phys. Lett. 66, 2324–2326 (1995).
[CrossRef]

Tran, P.

Tsurumachi, N.

Wang, Q.

P. Hou, Y. Chen, J. Shi, M. Shen, and Q. Wang, “Optical bistability in one-dimensional photonic band gap structures with coupled nonlinear defects,” Opt. Commun. 273, 441–445 (2007).
[CrossRef]

Wang, R.

R. Wang, J. Dong, and D. Y. Xing, “Dispersive optical bistability in onedimensional doped photonic band gap structures,” Phys. Rev. E 55, 6301 (1997).
[CrossRef]

Weisbuch, C.

R. P. Stanley, R. Houdre, U. Oesterle, M. Ilegems, and C. Weisbuch, “Impurity modes in one-dimensional periodic-systems: The transition from photonic band-gaps to microcavities,” Phys. Rev. A 48, 2246–2250 (1993).
[CrossRef]

Wen, H.

Xing, D. Y.

R. Wang, J. Dong, and D. Y. Xing, “Dispersive optical bistability in onedimensional doped photonic band gap structures,” Phys. Rev. E 55, 6301 (1997).
[CrossRef]

Yang, W. X.

Z. G. Zang and W. X. Yang, “Theoretical and experimental investigation of all-optical switching based on cascaded LPFGs separated by an erbium-doped fiber,” J. Appl. Phys. 109, 103106–103110 (2011).
[CrossRef]

Yu, S.

W. Zhang and S. Yu, “Bistable switching using an optical Tamm cavity with a Kerr medium,” Opt. Commun. 283, 2622–2626 (2010).
[CrossRef]

Zang, Z.

Z. Zang, “Numerical analysis of optical bistability based on fiber Bragg grating cavity containing a high nonlinearity doped-fiber,” Opt. Commun. 285, 521–526 (2012).
[CrossRef]

Zang, Z. G.

Z. G. Zang and Y. J. Zhang, “Low-switching power (<45  mW) optical bistability based on optical nonlinearity of ytterbium-doped fiber with a fiber Bragg grating pair,” J. Mod. Opt. 59, 161–165 (2012).
[CrossRef]

Z. G. Zang and W. X. Yang, “Theoretical and experimental investigation of all-optical switching based on cascaded LPFGs separated by an erbium-doped fiber,” J. Appl. Phys. 109, 103106–103110 (2011).
[CrossRef]

C. F. Li and Z. G. Zang, “Optical switching in a nonlinear-fiber connected long-period fiber grating pair,” Chin. Opt. Lett. 35, 1919–1923 (2008).

Zhang, W.

W. Zhang and S. Yu, “Bistable switching using an optical Tamm cavity with a Kerr medium,” Opt. Commun. 283, 2622–2626 (2010).
[CrossRef]

Zhang, Y. J.

Z. G. Zang and Y. J. Zhang, “Low-switching power (<45  mW) optical bistability based on optical nonlinearity of ytterbium-doped fiber with a fiber Bragg grating pair,” J. Mod. Opt. 59, 161–165 (2012).
[CrossRef]

Appl. Phys. Lett. (4)

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Figures (9)

Fig. 1.
Fig. 1.

(a) The array of nonlinear defect layers embedded into a one-dimensional nonlinear periodic structure. (b) The profile of the linear refractive indices and Kerr coefficients of the optical device.

Fig. 2.
Fig. 2.

Typical result for the proposed photonic crystal without defect.

Fig. 3.
Fig. 3.

Typical result for the proposed photonic crystal with different number of defect layers in the in-phase-matching state (n0k=0.02). (a) Without any defect, (b) twin defects; (c) triplet defects, (d) quartet defects, (e) quintet defects; and (f) sextet defects.

Fig. 4.
Fig. 4.

Typical result for the proposed photonic crystal with different number of defect layers in the out-of-phase matching state (n0k=0.02), the effect of number of defects.

Fig. 5.
Fig. 5.

Typical result for the proposed photonic crystal with quintet defects in the out-of-phase matching state (n0k=0.02), the effect of distance between defects.

Fig. 6.
Fig. 6.

Typical result for the proposed photonic crystal with quintet defects in the in-phase-matching state (n0k=0.02), the effect of distance between defects.

Fig. 7.
Fig. 7.

Typical result for the proposed photonic crystal with quintet defects, the effect of position of defects.

Fig. 8.
Fig. 8.

Typical result for the proposed photonic crystal with quintet defects. (a) The effect of index Δ0 from perturbation in n0k=0.02. (b) The effect of index Δnl from perturbation in n0k=0.02. (c) The effect of index Δ0 from perturbation in n0k=0.02. (d) The effect of index Δnl from perturbation in n0k=0.02.

Fig. 9.
Fig. 9.

Typical result for the proposed photonic crystal with quartet defects (the effect of the length of optical device).

Equations (12)

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2Ez2n2(z,|E|2)c22Et2=0.
n2(z,|E|2)2Et22Etn2t+E2n2t2.
nperiodic(z,|E|2)=nln+2n0kcoskz+nnl|E|2+2n2k|E|2coskz,
nln=n01+n022,nnl=nnl1+nnl22,n0k=n01n02π,n2k=nnl1nnl2π.
n(z,|E|2)=nperiodic(z,|E|2)+Δl(z)+Δnl(z)|E|2.
Δl(z)=n=1NDΔ0exp[k2(zmnd)2],Δnl(z)=n=1NDΔnlexp[k2(zmnd)2],
n(z,|E|2)=nln+2n0kcoskz+nnl|E|2+2n2k|E|2coskz+n=1ND(Δ0+Δnl|E|2)exp[k2(zmnd)2].
Δ0=n0dn01,Δnl=nnldnnl1.
n2(z,|E|2)=nln2+2nln(2n0kcoskz+nnl|E|2+2n2k|E|2coskz)+n=1ND2nln(Δ0+Δnl|E|2)exp[k2(zmnd)2].
E(z,t)=A+(z,t)exp[i(k0zω0t)]+A(z,t)exp[i(k0z+ω0t)]+higher-order terms,
i(A+Z+A+T)+n0kA+Δ0A+n=1NDexp[π2(ZmnD)2]+(nnl+Δnln=1NDexp[π2(ZmnD)2])(|A+|2+2|A|2)A++n2k[(2|A+|2+|A|2)A+A+2A*]=0,i(AZAT)+n0kA++Δ0An=1NDexp[π2(ZmnD)2]+(nnl+Δnln=1NDexp[π2(ZmnD)2])(2|A+|2+|A|2)A++n2k[(|A+|2+2|A|2)A++A+*A2]=0,
|A+(Z)|2|A(Z)|2=IinIref=Iout.

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