Abstract

We investigate the effects of spatial chirp of the built-in grating on the spectral range and switching power of all-optical switching in active semiconductor periodic structures. We show that a total linear variation in the grating period of as little as 0.24% nearly triples the spectral range of low-power switching. Moreover, the upward-switching power at the onset of bistability is lowered by two orders of magnitude, to a value below 10 nW for typical device-parameter values. These improvements occur for optical signals tuned to the long-wavelength side of the stop band and propagating in the direction of increasing grating period. We also predict the existence of multiple bistable hystereses in devices with large amounts of spatial chirp.

© 1998 Optical Society of America

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References

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  1. G. P. Agrawal, Ed., Semiconductor Lasers: Past, Present, and Future, (AIP Press, New York, 1995).
  2. M. J. Adams and R. J. Wyatt, “Optical Bistability in distributed feedback semiconductor laser amplifiers,” IEE Proc., Pt. J 134, 35–40 (1987).
  3. K. Otsuka and S. Kobayashi, “Optical Bistability and Nonlinear Resonance in a Resonant-Type Semiconductor Laser Amplifier,” Electron. Lett. 19, 262–263 (1983).
    [Crossref]
  4. R. P. Webb, “Error-rate measurements on an all-optically regenerated signal,” Opt. Quantum Electron. 19, S57–S60 (1987).
    [Crossref]
  5. N. Ogasawara and R. Ito, “Static and Dynamic Properties of Nonlinear Semiconductor Lasers Amplifiers,” Jpn. J. Appl. Phys. 25, 739–742 (1986).
    [Crossref]
  6. W. F. Sharfin and M. Dagenais, “High Contrast, 1.3 μm optical AND gate with gain,” Appl. Phys. Lett. 48, 1510–1512 (1986).
    [Crossref]
  7. Z. Pan and M. Dagenais “Bistable Diode Laser Amplifiers as Narrow Bandwidth High-Gain Filter for Use in Wavelength Division Demultiplexing,” IEEE Photon. Tech. Lett. 4, 1054–1057 (1992).
    [Crossref]
  8. H. J. Westlake, M. J. Adams, and M. J. O’Mahony, “Measurement of Optical Bistability in an InGaAsP Laser Amplifier at 1.5 μm,” Electron. Lett. 21, 992–993 (1985).
    [Crossref]
  9. W. F. Sharfin and M. Dagenais, “Femtojoule optical switching in nonlinear semiconductor laser amplifiers,” Appl. Phys. Lett. 48, 321–322 (1986).
    [Crossref]
  10. K. Tada and Y. Nakano, “Semiconductor Photonic Integrated Devices,” Electron. Commun. Japan 77, 238–249 (1994).
  11. M. J. Adams, H. J. Westlake, and M. J. O’Mahony, “Optical Bistability in 1.55 μm Semiconductor Laser Amplifiers,” in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, Ed. (Springer, Berlin, 1986).
  12. G. Assanto and R. Zanoni, “Almost-Periodic Nonlinear Distributed Feedback Gratings,” Opt. Acta 34, 89–101 (1987).
  13. G. Assanto, R. Zanoni, and G. I. Stegeman, “Effects of Taper in Nonlinear Distributed Feedback Gratings,” J. Mod. Opt. 35, 871–883 (1988).
    [Crossref]
  14. 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]
  15. J. Liu, C. Liao, S. Liu, and W. Xu, “The dynamics of direction-dependent switching in nonlinear chirped gratings,” Opt. Commun. 130, 295–301 (1996).
    [Crossref]
  16. S. Radic, N. George, and G. P. Agrawal, “Generalized distributed feedback design: amplification, filtering and switching,” SPIE Proc. 2399, 37–48 (1995).
    [Crossref]
  17. D. N. Maywar and G. P. Agrawal, “Transfer-Matrix Analysis of Optical Bistability in DFB Semiconductor Laser Amplifiers with Nonuniform Gratings,” IEEE J. Quantum Electron. 33, 2029–2037 (1997).
    [Crossref]
  18. M. Yamada and K. Sakuda, “Adjustable gain and bandwidth light amplifiers in terms of distributed-feedback structures,” J. Opt. Soc. Am. A 4, 69–76 (1987).
    [Crossref]

1997 (1)

D. N. Maywar and G. P. Agrawal, “Transfer-Matrix Analysis of Optical Bistability in DFB Semiconductor Laser Amplifiers with Nonuniform Gratings,” IEEE J. Quantum Electron. 33, 2029–2037 (1997).
[Crossref]

1996 (1)

J. Liu, C. Liao, S. Liu, and W. Xu, “The dynamics of direction-dependent switching in nonlinear chirped gratings,” Opt. Commun. 130, 295–301 (1996).
[Crossref]

1995 (2)

S. Radic, N. George, and G. P. Agrawal, “Generalized distributed feedback design: amplification, filtering and switching,” SPIE Proc. 2399, 37–48 (1995).
[Crossref]

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]

1994 (1)

K. Tada and Y. Nakano, “Semiconductor Photonic Integrated Devices,” Electron. Commun. Japan 77, 238–249 (1994).

1992 (1)

Z. Pan and M. Dagenais “Bistable Diode Laser Amplifiers as Narrow Bandwidth High-Gain Filter for Use in Wavelength Division Demultiplexing,” IEEE Photon. Tech. Lett. 4, 1054–1057 (1992).
[Crossref]

1988 (1)

G. Assanto, R. Zanoni, and G. I. Stegeman, “Effects of Taper in Nonlinear Distributed Feedback Gratings,” J. Mod. Opt. 35, 871–883 (1988).
[Crossref]

1987 (4)

M. Yamada and K. Sakuda, “Adjustable gain and bandwidth light amplifiers in terms of distributed-feedback structures,” J. Opt. Soc. Am. A 4, 69–76 (1987).
[Crossref]

G. Assanto and R. Zanoni, “Almost-Periodic Nonlinear Distributed Feedback Gratings,” Opt. Acta 34, 89–101 (1987).

M. J. Adams and R. J. Wyatt, “Optical Bistability in distributed feedback semiconductor laser amplifiers,” IEE Proc., Pt. J 134, 35–40 (1987).

R. P. Webb, “Error-rate measurements on an all-optically regenerated signal,” Opt. Quantum Electron. 19, S57–S60 (1987).
[Crossref]

1986 (4)

N. Ogasawara and R. Ito, “Static and Dynamic Properties of Nonlinear Semiconductor Lasers Amplifiers,” Jpn. J. Appl. Phys. 25, 739–742 (1986).
[Crossref]

W. F. Sharfin and M. Dagenais, “High Contrast, 1.3 μm optical AND gate with gain,” Appl. Phys. Lett. 48, 1510–1512 (1986).
[Crossref]

M. J. Adams, H. J. Westlake, and M. J. O’Mahony, “Optical Bistability in 1.55 μm Semiconductor Laser Amplifiers,” in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, Ed. (Springer, Berlin, 1986).

W. F. Sharfin and M. Dagenais, “Femtojoule optical switching in nonlinear semiconductor laser amplifiers,” Appl. Phys. Lett. 48, 321–322 (1986).
[Crossref]

1985 (1)

H. J. Westlake, M. J. Adams, and M. J. O’Mahony, “Measurement of Optical Bistability in an InGaAsP Laser Amplifier at 1.5 μm,” Electron. Lett. 21, 992–993 (1985).
[Crossref]

1983 (1)

K. Otsuka and S. Kobayashi, “Optical Bistability and Nonlinear Resonance in a Resonant-Type Semiconductor Laser Amplifier,” Electron. Lett. 19, 262–263 (1983).
[Crossref]

Adams, M. J.

M. J. Adams and R. J. Wyatt, “Optical Bistability in distributed feedback semiconductor laser amplifiers,” IEE Proc., Pt. J 134, 35–40 (1987).

M. J. Adams, H. J. Westlake, and M. J. O’Mahony, “Optical Bistability in 1.55 μm Semiconductor Laser Amplifiers,” in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, Ed. (Springer, Berlin, 1986).

H. J. Westlake, M. J. Adams, and M. J. O’Mahony, “Measurement of Optical Bistability in an InGaAsP Laser Amplifier at 1.5 μm,” Electron. Lett. 21, 992–993 (1985).
[Crossref]

Agrawal, G. P.

D. N. Maywar and G. P. Agrawal, “Transfer-Matrix Analysis of Optical Bistability in DFB Semiconductor Laser Amplifiers with Nonuniform Gratings,” IEEE J. Quantum Electron. 33, 2029–2037 (1997).
[Crossref]

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]

S. Radic, N. George, and G. P. Agrawal, “Generalized distributed feedback design: amplification, filtering and switching,” SPIE Proc. 2399, 37–48 (1995).
[Crossref]

Assanto, G.

G. Assanto, R. Zanoni, and G. I. Stegeman, “Effects of Taper in Nonlinear Distributed Feedback Gratings,” J. Mod. Opt. 35, 871–883 (1988).
[Crossref]

G. Assanto and R. Zanoni, “Almost-Periodic Nonlinear Distributed Feedback Gratings,” Opt. Acta 34, 89–101 (1987).

Dagenais, M.

Z. Pan and M. Dagenais “Bistable Diode Laser Amplifiers as Narrow Bandwidth High-Gain Filter for Use in Wavelength Division Demultiplexing,” IEEE Photon. Tech. Lett. 4, 1054–1057 (1992).
[Crossref]

W. F. Sharfin and M. Dagenais, “High Contrast, 1.3 μm optical AND gate with gain,” Appl. Phys. Lett. 48, 1510–1512 (1986).
[Crossref]

W. F. Sharfin and M. Dagenais, “Femtojoule optical switching in nonlinear semiconductor laser amplifiers,” Appl. Phys. Lett. 48, 321–322 (1986).
[Crossref]

George, N.

S. Radic, N. George, and G. P. Agrawal, “Generalized distributed feedback design: amplification, filtering and switching,” SPIE Proc. 2399, 37–48 (1995).
[Crossref]

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]

Ito, R.

N. Ogasawara and R. Ito, “Static and Dynamic Properties of Nonlinear Semiconductor Lasers Amplifiers,” Jpn. J. Appl. Phys. 25, 739–742 (1986).
[Crossref]

Kobayashi, S.

K. Otsuka and S. Kobayashi, “Optical Bistability and Nonlinear Resonance in a Resonant-Type Semiconductor Laser Amplifier,” Electron. Lett. 19, 262–263 (1983).
[Crossref]

Liao, C.

J. Liu, C. Liao, S. Liu, and W. Xu, “The dynamics of direction-dependent switching in nonlinear chirped gratings,” Opt. Commun. 130, 295–301 (1996).
[Crossref]

Liu, J.

J. Liu, C. Liao, S. Liu, and W. Xu, “The dynamics of direction-dependent switching in nonlinear chirped gratings,” Opt. Commun. 130, 295–301 (1996).
[Crossref]

Liu, S.

J. Liu, C. Liao, S. Liu, and W. Xu, “The dynamics of direction-dependent switching in nonlinear chirped gratings,” Opt. Commun. 130, 295–301 (1996).
[Crossref]

Maywar, D. N.

D. N. Maywar and G. P. Agrawal, “Transfer-Matrix Analysis of Optical Bistability in DFB Semiconductor Laser Amplifiers with Nonuniform Gratings,” IEEE J. Quantum Electron. 33, 2029–2037 (1997).
[Crossref]

Nakano, Y.

K. Tada and Y. Nakano, “Semiconductor Photonic Integrated Devices,” Electron. Commun. Japan 77, 238–249 (1994).

O’Mahony, M. J.

M. J. Adams, H. J. Westlake, and M. J. O’Mahony, “Optical Bistability in 1.55 μm Semiconductor Laser Amplifiers,” in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, Ed. (Springer, Berlin, 1986).

H. J. Westlake, M. J. Adams, and M. J. O’Mahony, “Measurement of Optical Bistability in an InGaAsP Laser Amplifier at 1.5 μm,” Electron. Lett. 21, 992–993 (1985).
[Crossref]

Ogasawara, N.

N. Ogasawara and R. Ito, “Static and Dynamic Properties of Nonlinear Semiconductor Lasers Amplifiers,” Jpn. J. Appl. Phys. 25, 739–742 (1986).
[Crossref]

Otsuka, K.

K. Otsuka and S. Kobayashi, “Optical Bistability and Nonlinear Resonance in a Resonant-Type Semiconductor Laser Amplifier,” Electron. Lett. 19, 262–263 (1983).
[Crossref]

Pan, Z.

Z. Pan and M. Dagenais “Bistable Diode Laser Amplifiers as Narrow Bandwidth High-Gain Filter for Use in Wavelength Division Demultiplexing,” IEEE Photon. Tech. Lett. 4, 1054–1057 (1992).
[Crossref]

Radic, S.

S. Radic, N. George, and G. P. Agrawal, “Generalized distributed feedback design: amplification, filtering and switching,” SPIE Proc. 2399, 37–48 (1995).
[Crossref]

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]

Sakuda, K.

Sharfin, W. F.

W. F. Sharfin and M. Dagenais, “Femtojoule optical switching in nonlinear semiconductor laser amplifiers,” Appl. Phys. Lett. 48, 321–322 (1986).
[Crossref]

W. F. Sharfin and M. Dagenais, “High Contrast, 1.3 μm optical AND gate with gain,” Appl. Phys. Lett. 48, 1510–1512 (1986).
[Crossref]

Stegeman, G. I.

G. Assanto, R. Zanoni, and G. I. Stegeman, “Effects of Taper in Nonlinear Distributed Feedback Gratings,” J. Mod. Opt. 35, 871–883 (1988).
[Crossref]

Tada, K.

K. Tada and Y. Nakano, “Semiconductor Photonic Integrated Devices,” Electron. Commun. Japan 77, 238–249 (1994).

Webb, R. P.

R. P. Webb, “Error-rate measurements on an all-optically regenerated signal,” Opt. Quantum Electron. 19, S57–S60 (1987).
[Crossref]

Westlake, H. J.

M. J. Adams, H. J. Westlake, and M. J. O’Mahony, “Optical Bistability in 1.55 μm Semiconductor Laser Amplifiers,” in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, Ed. (Springer, Berlin, 1986).

H. J. Westlake, M. J. Adams, and M. J. O’Mahony, “Measurement of Optical Bistability in an InGaAsP Laser Amplifier at 1.5 μm,” Electron. Lett. 21, 992–993 (1985).
[Crossref]

Wyatt, R. J.

M. J. Adams and R. J. Wyatt, “Optical Bistability in distributed feedback semiconductor laser amplifiers,” IEE Proc., Pt. J 134, 35–40 (1987).

Xu, W.

J. Liu, C. Liao, S. Liu, and W. Xu, “The dynamics of direction-dependent switching in nonlinear chirped gratings,” Opt. Commun. 130, 295–301 (1996).
[Crossref]

Yamada, M.

Zanoni, R.

G. Assanto, R. Zanoni, and G. I. Stegeman, “Effects of Taper in Nonlinear Distributed Feedback Gratings,” J. Mod. Opt. 35, 871–883 (1988).
[Crossref]

G. Assanto and R. Zanoni, “Almost-Periodic Nonlinear Distributed Feedback Gratings,” Opt. Acta 34, 89–101 (1987).

Appl. Phys. Lett. (2)

W. F. Sharfin and M. Dagenais, “High Contrast, 1.3 μm optical AND gate with gain,” Appl. Phys. Lett. 48, 1510–1512 (1986).
[Crossref]

W. F. Sharfin and M. Dagenais, “Femtojoule optical switching in nonlinear semiconductor laser amplifiers,” Appl. Phys. Lett. 48, 321–322 (1986).
[Crossref]

Electron. Commun. Japan (1)

K. Tada and Y. Nakano, “Semiconductor Photonic Integrated Devices,” Electron. Commun. Japan 77, 238–249 (1994).

Electron. Lett. (2)

H. J. Westlake, M. J. Adams, and M. J. O’Mahony, “Measurement of Optical Bistability in an InGaAsP Laser Amplifier at 1.5 μm,” Electron. Lett. 21, 992–993 (1985).
[Crossref]

K. Otsuka and S. Kobayashi, “Optical Bistability and Nonlinear Resonance in a Resonant-Type Semiconductor Laser Amplifier,” Electron. Lett. 19, 262–263 (1983).
[Crossref]

IEE Proc., Pt. J (1)

M. J. Adams and R. J. Wyatt, “Optical Bistability in distributed feedback semiconductor laser amplifiers,” IEE Proc., Pt. J 134, 35–40 (1987).

IEEE J. Quantum Electron. (1)

D. N. Maywar and G. P. Agrawal, “Transfer-Matrix Analysis of Optical Bistability in DFB Semiconductor Laser Amplifiers with Nonuniform Gratings,” IEEE J. Quantum Electron. 33, 2029–2037 (1997).
[Crossref]

IEEE Photon. Tech. Lett. (1)

Z. Pan and M. Dagenais “Bistable Diode Laser Amplifiers as Narrow Bandwidth High-Gain Filter for Use in Wavelength Division Demultiplexing,” IEEE Photon. Tech. Lett. 4, 1054–1057 (1992).
[Crossref]

J. Mod. Opt. (1)

G. Assanto, R. Zanoni, and G. I. Stegeman, “Effects of Taper in Nonlinear Distributed Feedback Gratings,” J. Mod. Opt. 35, 871–883 (1988).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (1)

N. Ogasawara and R. Ito, “Static and Dynamic Properties of Nonlinear Semiconductor Lasers Amplifiers,” Jpn. J. Appl. Phys. 25, 739–742 (1986).
[Crossref]

Opt. Acta (1)

G. Assanto and R. Zanoni, “Almost-Periodic Nonlinear Distributed Feedback Gratings,” Opt. Acta 34, 89–101 (1987).

Opt. Commun. (1)

J. Liu, C. Liao, S. Liu, and W. Xu, “The dynamics of direction-dependent switching in nonlinear chirped gratings,” Opt. Commun. 130, 295–301 (1996).
[Crossref]

Opt. Quantum Electron. (1)

R. P. Webb, “Error-rate measurements on an all-optically regenerated signal,” Opt. Quantum Electron. 19, S57–S60 (1987).
[Crossref]

SPIE Proc. (1)

S. Radic, N. George, and G. P. Agrawal, “Generalized distributed feedback design: amplification, filtering and switching,” SPIE Proc. 2399, 37–48 (1995).
[Crossref]

Other (2)

M. J. Adams, H. J. Westlake, and M. J. O’Mahony, “Optical Bistability in 1.55 μm Semiconductor Laser Amplifiers,” in Optical Bistability III, H. M. Gibbs, P. Mandel, N. Peyghambarian, S. D. Smith, Ed. (Springer, Berlin, 1986).

G. P. Agrawal, Ed., Semiconductor Lasers: Past, Present, and Future, (AIP Press, New York, 1995).

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Figures (5)

Figure 1.
Figure 1.

(a) Schematic of an active semiconductor periodic structure. The grating is typically fabricated outside of the active region (shaded grey). (b) Small-signal transmittivity spectrum for the device driven to provide 30-dB amplification at the resonance peaks. The detuning parameter δ is given by Eq. (4).

Figure 2.
Figure 2.

(a) Bistable transmission for δL = 6.785 and Psat = 10 mW. Switching occurs between the stable branches, as indicated. (b) Upward- and downward- switching input powers plotted over the entire spectral range of switching.

Figure 3.
Figure 3.

(a) Schematic illustration of a DFB SOA with a linearly chirped grating, indicating the P–direction (C > 0) and N–direction (C < 0). (b) Small-signal transmittivity spectra for three chirped gratings for the case of 30-dB amplification.

Figure 4.
Figure 4.

Spectral range of bistable switching for optical signals incident in the (a) P–direction and (b) N–direction of a chirped-grating DFB SOA. The long-wavelength side of (b) for C = -10 exhibits the lowest switching power and the broadest spectral range of low-power switching.

Figure 5.
Figure 5.

(a) Double bistability. (b) Transmission through a DFB SOA with |C| = 15 driven at 98% of its lasing threshold.

Equations (6)

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

E ( x , y , z , t ) = Re { ϵ F ( x , y ) [ A ( z ) exp ( i β B z ) + B ( z ) exp ( i β B z ) ] exp ( iωt ) } ,
d A d z = [ i δ + g 0 2 ( 1 ) 1 + P ̅ α int 2 ] A + iκB ,
d B d z = [ i δ + g 0 2 ( 1 i α ) 1 + P ̅ α int 2 ] B + iκA .
δ = β 0 β B = 2 π n 0 λ 0 π Λ ,
P ̅ = E 2 σ P sat [ A ( z ) 2 + B ( z ) 2 ] Γσ P sat ,
β B ( z ) = β ̅ B + C L 2 ( z L 2 ) ,

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