## All-optical switching in distributed-feedback multiple-quantum-well waveguides

Optics Express, Vol. 3, Issue 11, pp. 454-464 (1998)

http://dx.doi.org/10.1364/OE.3.000454

Acrobat PDF (472 KB)

### 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.

© Optical Society of America

## 1. Introduction

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]

9. B. Acklin, M. Cada, J. He, and M. -A. Dupertuis, “Bistable switching in a nonlinear Bragg reflector,” Appl. Phys. Lett. **63**, 2177–2179 (1993). [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]

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]

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]

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]

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]

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]

## 2. Device

_{B}= 1.556μm. We chose counter-propagating coupling because it requires a short period grating, compatible with integrated-optics dimensions, and for the sake of simplicity, in fact it produces a transfer of energy between two opposite propagation directions of the same mode in the same single-mode waveguide.

19. D. Campi and G. Colì, “Green’s-function approach to the optical nonlinearities in semiconductors and quantum-confined structures,” Phys. Rev. B **54**, R8365–R8368 (1996). [CrossRef]

19. D. Campi and G. Colì, “Green’s-function approach to the optical nonlinearities in semiconductors and quantum-confined structures,” Phys. Rev. B **54**, R8365–R8368 (1996). [CrossRef]

20. D. Campi, G. Colì, 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]

*(*

**n***λ*,

*N*) =

*n*(

*λ*,

*N*)+

*ik*(

*λ*,

*N*) and it has been successfully used by us to interpret experiments on waveguided, nonlinear devices [10

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]

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]

_{1}-hh

_{1}in the case addressed here). In particular in this region the refractive variations,

*Δn*, are negative and strong enough to obtain all-optical switching, while the absorption variations,

*Δk*, are positive and have a significant impact on the device operation.

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]

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]

_{4}/H

_{2}RIE, which causes an increase of the recovery time to about 600 ps, and we are currently working to find alternative etching processes which preserve the fast material characteristics.

*κ*, which depends on the optical power fraction in the grating. The coupling coefficient can be adjusted by varying the distance between the grating and the core layer, the void fraction of the grating or its etching depth. In our structure the stop-band width is approximately 2 nm. When MQW core material is populated through the absorption of intense light pulses, its optical properties change and the device response is modified, see the dashed-line red curves in Fig. 3. In particular, as the real part of the refractive index is lowered, the grating spectral bands are shifted towards shorter wavelengths. The nonlinear absorption increase causes a reduction in the depth of these bands.

*λ*, lies within the (linear) grating stop-band can be either reflected in the linear regime or transmitted in the nonlinear regime. On the contrary, a weak signal pulse of wavelength

_{1}*λ*slightly detuned toward shorter wavelengths from the (linear) grating stop-band, can be either transmitted in the linear regime or reflected in the nonlinear regime. In this way, the cross-bar switching functionality for wavelengths

_{2}*λ*and

_{1}*λ*can be achieved. The nonlinear mechanism is thus a cross interaction between a strong optical control pulse and a weak optical signal pulse. It is basically different from the self-interaction mechanism experienced by a single intense pulse tuned in proximity of the grating stop-band, which is at the basis of Bragg grating soliton generation [14

_{2}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]

## 3. Experimental results

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]

**23**, 183–185 (1998). [CrossRef]

*control*) pulses, while the second curve represents the injected probe (

*signal*) pulses. In the third curve we show the transmitted probe pulses tuned 5 nm below the Bragg wavelength. The probe pulse coinciding with the pump pulse is switched off, in fact this it is routed from the transmission port to the reflection port, while pulses injected at later time are transmitted. In the last black curve we report the transmitted probe pulses tuned at the Bragg wavelength. The behavior here is opposite: the probe pulse coinciding with the pump pulse is routed to the transmission port, while the others are reflected. Evaluating the ratio between linearly- and nonlinearly-transmitted pulses, we could measure an on-off ratio of 10 dB for inhibited transmission and 12 dB for induced transmission respectively, limited by the electrical noise level in detection.

## 4. Modelling

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

*n*is the modal refractive index of the waveguide. Using the slow-wave approximation [23

_{o}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]

*ω*, equation (1) becomes

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

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

^{*}represents the complex conjugate, while the indexes

*j*and

*k*refer to the coordinate of the grid points

*z*, and

_{j}*t*, respectively. These define the computational window according to

_{k}*c*,

_{1}*c*, and

_{2}*c*, are

_{3}*λ*is the wavelength in vacuum. The algebraic system (3) can be solved using a standard numerical method for tridiagonal matrix inversion [25].

*σ*propagating in the forward direction.

_{t}*N*is the volume carrier density,

_{3D}*p*is the volume photon density and

*τ*is the carrier recombination time. Equation (7) can be solved within a finite-difference approach adopting the same computational window of the TD-BPM. Following this approach, equation (7) becomes

*ħ*is the reduced Planck constant,

*J*is the pulse energy,

_{o}*σ*is the waveguide-mode area, and

*L*is the well width. The algebraic equation (8) has to be solved jointly with the TD-BPM equation (3). Using the model here described, we simulated the all-optical switching functionality of our structure.

_{w}## 5. Conclusions

*λ*and

_{1}*λ*, accomplishing a cross-bar switching functionality on these two wavelengths: from reflect

_{2}*λ*/transmit

_{1}*λ*in the absence of the control pulse to transmit /

_{2}*λ*/reflect

_{1}*λ*in the presence of the control pulse. The on-off contrast ratio here reported is 10 dB or slightly more. This figure can be improved by increasing the coupling coefficient, and by improving the quality of the grating lithography process. One advantage of using passive nonlinear devices, over their active counterparts, is that electrical wiring and contact pads are eliminated, making the operation of the former class of devices intrinsically reliable. In addition, passive devices are more readily and easily integrated within monolithic or hybrid optical circuitry, making it possible to achieve more sophisticated functionality.

_{2}## Acknowledgements

## References and links

1. | H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. |

2. | W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. |

3. | G. Assanto and G. I. Stegeman, “Optical bistability in nonlocally nonlinear periodic structures,” Appl. Phys. Lett. |

4. | C. M. de Sterke and J. E. Sipe, “Switching dynamics of finite periodic nonlinear media: A numerical study,” Phys. Rev. A |

5. | H. G. Winful, R. Zamir, and S. Feldman, “Modulation instability in nonlinear periodic structures: Implications for ‘gap solitons’,” Appl. Phys. Lett. |

6. | J. He and M. Cada, “Optical bistability in semiconductor periodic structures,” IEEE J. Quantum Electron. |

7. | G. P. Bava, F. Castelli, P. Debernardi, and L. A. Lugiato, “Optical bistability in a multiple quantum well structure with Fabry-Perot and distributed feedback resonators,” Phys. Rev. A |

8. | C. M. de Sterke and J. E. Sipe, “Gap solitons” in |

9. | B. Acklin, M. Cada, J. He, and M. -A. Dupertuis, “Bistable switching in a nonlinear Bragg reflector,” Appl. Phys. Lett. |

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. |

11. | J. E. Ehrlich, G. Assanto, and G. I. Stegeman, “All-optical tuning of waveguide nonlinear distributed feedback gratings,” Appl. Phys. Lett. |

12. | N. D. Sankey, D. F. Prelewitz, and T. G. Brown, “All-optical switching in a nonlinear periodic-waveguide structure,” Appl. Phys. Lett. |

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. |

14. | B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. |

15. | B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B. |

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. |

17. | G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. |

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 |

19. | D. Campi and G. Colì, “Green’s-function approach to the optical nonlinearities in semiconductors and quantum-confined structures,” Phys. Rev. B |

20. | D. Campi, G. Colì, and M. Vallone, “Formulation of the optical response in semiconductors and quantum-confined structures,” Phys. Rev. B |

21. | D. Campi and C. Coriasso, “Optical nonlinearities in multiple-quantum wells: Generalized Elliott formula,” Phys. Rev. B |

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 |

23. | P. -L Liu, Q. Zhao, and F. -S. Choa, “Slow-Wave Finite-Difference Beam Propagation Method,” IEEE Photon. Technol. Lett. |

24. | Y. Chung and N. Dagli, “An assessment of Finite Difference Beam Propagation Method,” IEEE J. Quantum Electron. |

25. | W. H. Press, B. P. Flannery, S. A. Teucolsky, and W. T. Vetterling, |

**OCIS Codes**

(060.1810) Fiber optics and optical communications : Buffers, couplers, routers, switches, and multiplexers

(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW

(230.1150) Optical devices : All-optical devices

**ToC Category:**

Focus Issue: Bragg solitons and nonlinear optics of periodic structures

**History**

Original Manuscript: October 1, 1998

Published: November 23, 1998

**Citation**

Claudio Coriasso, Domenico Campi, Carmelo Cacciatroe, L. Faustini, S. Mautino, C. Rigo, and A. Stano, "All-optical switching in distributed-feedback muiltiple-quantum-well waveguides," Opt. Express **3**, 454-464 (1998)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-3-11-454

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### References

- 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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