Abstract

We discuss experimental results that demonstrate all-optical switching and pulse-routing functionality, at 1.55 μm, of nonlinear multiple-quantum-well waveguides equipped with a Bragg grating. Basing on the nonlinear Time-Domain Beam Propagation Method, the switching behavior has been theoretically investigated using a model, developed as part of this work.

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  1. H. G. Winful, J. H. Marburger, and E. Garmire, "Theory of bistability in nonlinear distributed feedback structures," Appl. Phys. Lett. 35, 379-381 (1979).
    [CrossRef]
  2. W. Chen, and D. L. Mills, "Gap solitons and the nonlinear optical response of superlattices," Phys. Rev. Lett. 58, 160-163 (1987).
    [CrossRef] [PubMed]
  3. G. Assanto, and G. I. Stegeman, "Optical bistability in nonlocally nonlinear periodic structures," Appl. Phys. Lett. 56, 2285-2287 (1990).
    [CrossRef]
  4. C. M. de Sterke, and J. E. Sipe, "Switching dynamics of finite periodic nonlinear media: A numerical study," Phys. Rev. A 42, 2858-2869 (1990).
    [CrossRef] [PubMed]
  5. H. G. Winful, R. Zamir, and S. Feldman, "Modulation instability in nonlinear periodic structures: Implications for gap solitons," Appl. Phys. Lett. 58, 1001-1003 (1991).
    [CrossRef]
  6. J. He, and M. Cada, "Optical bistability in semiconductor periodic structures," IEEE J. Quantum Electron. 27, 1182-1188 (1991).
    [CrossRef]
  7. G. P. Bava, F. Castelli, P. Debernardi, L. A. Lugiato, "Optical bistability in a multiple quantum well structure with Fabry-Perot and distributed feedback resonators," Phys. Rev. A 45, 5180-5192 (1992).
    [CrossRef] [PubMed]
  8. C. M. de Sterke and J. E. Sipe, "Gap solitons" in Progress in Optics XXXIII, E. Wolf, ed. (Elsevier, Amsterdam, 1994), Chap. III.
  9. B. Acklin, M. Cada, J. He, M. -A. Dupertuis, "Bistable switching in a nonlinear Bragg reflector," Appl. Phys. Lett. 63, 2177-2179 (1993).
    [CrossRef]
  10. C. Coriasso, D. Campi, C. Cacciatore, L. Faustini, C. Rigo, and A. Stano, "Butterfly bistability in an InGaAs/InP multiple-quantum well waveguide with distributed feedback," Appl. Phys. Lett. 67, 585-587 (1995).
    [CrossRef]
  11. J. E. Ehrlich, G. Assanto, and G. I. Stegeman, "All-optical tuning of waveguide nonlinear distributed feedback gratings," Appl. Phys. Lett. 56, 602-604 (1990).
    [CrossRef]
  12. 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]
  13. S. La Rochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, "All-optical switching of grating transmission using cross-phase modulation in optical fibers," Electron. Lett. 26, 1459-1460 (1990).
    [CrossRef]
  14. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, "Bragg grating solitons," Phys. Rev. Lett. 76, 1627-1630 (1996).
    [CrossRef] [PubMed]
  15. 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 (1998).
    [CrossRef]
  16. C. Coriasso, D. Campi, C. Cacciatore, L. Faustini, C. Rigo, and A. Stano, "All-optical switching and pulse routing in a distributed-feedback waveguide device", Opt. Lett. 23, 183-185 (1998).
    [CrossRef]
  17. G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953-970 (1988).
    [CrossRef]
  18. C. Rigo, L. Gastaldi, D. Campi, L. Faustini, C. Coriasso, C. Cacciatore, and D. Soldani, "Multiple quantum well compressive strained heterostructures for low driving power all-optical waveguide devices," J. Crystal Growth 188, 317-322 (1998).
    [CrossRef]
  19. D. Campi, and G. Col?, "Greens-function approach to the optical nonlinearities in semiconductors and quantum-confined structures," Phys. Rev. B 54, R8365-R8368 (1996).
    [CrossRef]
  20. D. Campi, G. Col?, and M. Vallone, "Formulation of the optical response in semiconductors and quantum-confined structures," Phys. Rev. B 57, 4681-4686 (1998).
    [CrossRef]
  21. D. Campi, and C. Coriasso, "Optical nonlinearities in multiple-quantum wells: Generalized Elliott formula," Phys. Rev. B 51, 10719-10728 (1995).
    [CrossRef]
  22. C. Cacciatore, L. Faustini, G. Leo, C. Coriasso, D. Campi, A. Stano, and C. Rigo, "Dynamics of nonlinear optical properties in InxGa1-xAs/InP quantum-well waveguides," Phys Rev. B 55, R4883-R4886 (1997).
    [CrossRef]
  23. P. -L Liu, Q. Zhao, and F. -S. Choa, "Slow-Wave Finite-Difference Beam Propagation Method," IEEE Photon. Technol. Lett. 7, 890-892 (1995).
    [CrossRef]
  24. Y. Chung, and N. Dagli, "An assessment of Finite Difference Beam Propagation Method," IEEE J. Quantum Electron. 26, 1335-1339 (1990).
    [CrossRef]
  25. W. H. Press, B. P. Flannery, S. A. Teucolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing. (Cambridge Univ., New York, 1986), pp. 40-41.

Other (25)

H. G. Winful, J. H. Marburger, and E. Garmire, "Theory of bistability in nonlinear distributed feedback structures," Appl. Phys. Lett. 35, 379-381 (1979).
[CrossRef]

W. Chen, and D. L. Mills, "Gap solitons and the nonlinear optical response of superlattices," Phys. Rev. Lett. 58, 160-163 (1987).
[CrossRef] [PubMed]

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

C. M. de Sterke, and J. E. Sipe, "Switching dynamics of finite periodic nonlinear media: A numerical study," Phys. Rev. A 42, 2858-2869 (1990).
[CrossRef] [PubMed]

H. G. Winful, R. Zamir, and S. Feldman, "Modulation instability in nonlinear periodic structures: Implications for gap solitons," Appl. Phys. Lett. 58, 1001-1003 (1991).
[CrossRef]

J. He, and M. Cada, "Optical bistability in semiconductor periodic structures," IEEE J. Quantum Electron. 27, 1182-1188 (1991).
[CrossRef]

G. P. Bava, F. Castelli, P. Debernardi, L. A. Lugiato, "Optical bistability in a multiple quantum well structure with Fabry-Perot and distributed feedback resonators," Phys. Rev. A 45, 5180-5192 (1992).
[CrossRef] [PubMed]

C. M. de Sterke and J. E. Sipe, "Gap solitons" in Progress in Optics XXXIII, E. Wolf, ed. (Elsevier, Amsterdam, 1994), Chap. III.

B. Acklin, M. Cada, J. He, M. -A. Dupertuis, "Bistable switching in a nonlinear Bragg reflector," Appl. Phys. Lett. 63, 2177-2179 (1993).
[CrossRef]

C. Coriasso, D. Campi, C. Cacciatore, L. Faustini, C. Rigo, and A. Stano, "Butterfly bistability in an InGaAs/InP multiple-quantum well waveguide with distributed feedback," Appl. Phys. Lett. 67, 585-587 (1995).
[CrossRef]

J. E. Ehrlich, G. Assanto, and G. I. Stegeman, "All-optical tuning of waveguide nonlinear distributed feedback gratings," Appl. Phys. Lett. 56, 602-604 (1990).
[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]

S. La Rochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, "All-optical switching of grating transmission using cross-phase modulation in optical fibers," Electron. Lett. 26, 1459-1460 (1990).
[CrossRef]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, "Bragg grating solitons," Phys. Rev. Lett. 76, 1627-1630 (1996).
[CrossRef] [PubMed]

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 (1998).
[CrossRef]

C. Coriasso, D. Campi, C. Cacciatore, L. Faustini, C. Rigo, and A. Stano, "All-optical switching and pulse routing in a distributed-feedback waveguide device", Opt. Lett. 23, 183-185 (1998).
[CrossRef]

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953-970 (1988).
[CrossRef]

C. Rigo, L. Gastaldi, D. Campi, L. Faustini, C. Coriasso, C. Cacciatore, and D. Soldani, "Multiple quantum well compressive strained heterostructures for low driving power all-optical waveguide devices," J. Crystal Growth 188, 317-322 (1998).
[CrossRef]

D. Campi, and G. Col?, "Greens-function approach to the optical nonlinearities in semiconductors and quantum-confined structures," Phys. Rev. B 54, R8365-R8368 (1996).
[CrossRef]

D. Campi, G. Col?, and M. Vallone, "Formulation of the optical response in semiconductors and quantum-confined structures," Phys. Rev. B 57, 4681-4686 (1998).
[CrossRef]

D. Campi, and C. Coriasso, "Optical nonlinearities in multiple-quantum wells: Generalized Elliott formula," Phys. Rev. B 51, 10719-10728 (1995).
[CrossRef]

C. Cacciatore, L. Faustini, G. Leo, C. Coriasso, D. Campi, A. Stano, and C. Rigo, "Dynamics of nonlinear optical properties in InxGa1-xAs/InP quantum-well waveguides," Phys Rev. B 55, R4883-R4886 (1997).
[CrossRef]

P. -L Liu, Q. Zhao, and F. -S. Choa, "Slow-Wave Finite-Difference Beam Propagation Method," IEEE Photon. Technol. Lett. 7, 890-892 (1995).
[CrossRef]

Y. Chung, and N. Dagli, "An assessment of Finite Difference Beam Propagation Method," IEEE J. Quantum Electron. 26, 1335-1339 (1990).
[CrossRef]

W. H. Press, B. P. Flannery, S. A. Teucolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing. (Cambridge Univ., New York, 1986), pp. 40-41.

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Figures (8)

Fig. 1.
Fig. 1.

Device structure.

Fig. 2.
Fig. 2.

Optical properties of the MQW material, calculated according to Ref. [21]: a) Linear spectrum of the real part of the refractive index. b) Linear spectrum of the imaginary part of the refractive index. c) Spectral changes of the real part of the refractive index at different carrier densities, ranging from 108 to 5×1011 cm-2. d) Same as c) but for the imaginary part of the refractive index. The orange dashed lines indicate the wavelength of the 1st exciton resonance, while the red dashed lines indicate the Bragg wavelength of the grating, around that the device is operated.

Fig. 3.
Fig. 3.

Spectral features of the grating. a) Transmittance curve in the linear (blue solid line) and nonlinear (red dashed line) regime. b) Reflectance curve in the linear (blue solid line) and nonlinear (red dashed line) regime. These curves were calculated using the coupled-mode theory and taking into account the material dispersion. The nonlinear regime corresponds to a carrier density of 1011 cm-2. The black arrows indicate the position of the linear Bragg wavelength and the vertical black dashed lines indicate the width of the photonic band gap [8].

Fig. 4.
Fig. 4.

Transient changes of the cw probe beam induced by a 10-ps pump pulse tuned at 1544 nm. a) Transmittance variation observed at the transmission port, by tuning the probe beam either at the Bragg wavelength, λB , or 5 nm below λB . b) Reflectance variation observed at the reflection port , by tuning the probe beam either at the λB or 5 nm below λB . τ and E refer to the recovery time and to pump-pulse energy, respectively.

Fig. 5.
Fig. 5.

Pulse routing experiment: a) Injected pump (control) pulses. b) Injected probe (signal) pulses. c) Transmitted probe (signal) pulses, having a wavelength detuned by 5 nm from the Bragg wavelength. d) Transmitted probe (signal) pulses, tuned to the Bragg wavelength.

Fig. 5.
Fig. 5.

Propagation of the pump pulse calculated using the TD-BPM. The pump wavelength is detuned by 10 nm from the Bragg wavelength.

Fig. 6.
Fig. 6.

Propagation of the probe pulse, tuned within the grating stop-band (λ=λB +1nm), calculated using the TD-BPM. a) Linear (without pump). b) Nonlinear (with pump).

Fig. 7.
Fig. 7.

Propagation of the probe pulse, tuned at one edge of the grating stop-band (λ=λB -2nm), calculated using the TD-BPM. a) Linear (without pump). b) Nonlinear (with pump).

Equations (11)

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2 E z 2 n o 2 2 E c 2 t 2 = 0
t Ψ = i 2 ω ( c 2 n 2 2 z 2 + ω 2 ) Ψ
c 1 Ψ j 1 , k + 1 + c 2 Ψ j , k + 1 + c 1 Ψ j + 1 , k + 1 = c 1 * Ψ j 1 , k + c 3 Ψ j , k + c 1 * Ψ j + 1 , k
z j = z min + j Δ z , j = 0,1 , , z max z min Δ z
t k = t min + k Δ t , k = 0,1 , , t max t min Δt
c 1 = i ω Δ t
c 2 = 2 i ω Δ t + ( 2 π λ Δ z ) 2 ( 4 + i ω Δ t ) · n 2
c 3 = 2 i ω Δ t + ( 2 π λ Δ z ) 2 ( 4 i ω Δ t ) · n 2
Ψ j , 0 = exp [ ( z z 0 c n j , 0 σ t ) 2 ] exp ( i 2 π λ n j , o z )
d N 3 D d t = N 3 D τ + d p d t
N j , k + l = ( 1 Δ t τ ) N j , k + 1 ħ J o L w σ Im ( n j , k 2 ) Ψ j , k 2 j ε j , 0 Ψ j , 0 2 Δ z Δ t

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