Abstract

Chirped pulse scheme is shown to be highly effective to attain large tunable time shifts via slow and fast light for an ultra-short pulse through a semiconductor optical amplifier (SOA). We show for the first time that advance can be turned into delay by simply reversing the sign of the chirp. A large continuously tunable advance-bandwidth product (ABP) of 4.7 and delay-bandwidth product (DBP) of 4.0 are achieved for a negatively and positively chirped pulse in the same device, respectively. We show that the tunable time shift is a direct result of self-phase modulation (SPM). Theoretical simulation agrees well with experimental results. Further, our simulation results show that by proper optimization of the SOA and chirper design, a large continuously tunable DBP of 55 can be achieved.

© 2009 Optical Society of America

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References

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  1. C. J. Chang-Hasnain, P. C. Ku, J. Kim and S. L. Chuang, "Variable Optical Buffer using Slow Light in Semiconductor Nanostructures," Proc. of the IEEE 91, 1884-1897 (2003).
    [CrossRef]
  2. R. W. Boyd and D. J. Gauthier, "Slow and Fast Light," Prog. Opt. 43, 497-530 (2002).
    [CrossRef]
  3. F. Ohman, K. Yvind and J. Mork, "Slow Light in a Semiconductor Waveguide for True-Time Delay Applications in Microwave Photonics," IEEE Photon. Techol. Lett. 19, 1145-1147 (2007).
    [CrossRef]
  4. L. V. Hau, S. E. Harris, Z. Dutton and C. H. Behroozi, " Light speed reduction to 17 meters per second in an ultracold atomic gas," Nature 397, 594-598 (1999).
    [CrossRef]
  5. M. S. Bigelow, N. N. Lepeshkin and R. W. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200-202 (2003).
    [CrossRef] [PubMed]
  6. R. M. Camacho, M. V. Pack and J. Howell, "Wide-bandwidth, Tunable, Multiple-pulse-width optical delays using slow light in cesium vapor," Phys. Rev. Lett. 98, 153601 (2007).
    [CrossRef] [PubMed]
  7. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schqeinsberg, D. J. Gautheir, R. W. Boyd and A. L. Gaeta, "Tunable all-optical delays via brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
    [CrossRef] [PubMed]
  8. T. Baba, "Toward photonic crystal optical buffer," CLEO/QELS, San Jose, CA, CWH1 (2008).
  9. S. Sarkar, Y. Guo and H. Wang, "Tunable optical delay via carrier induced exciton dephasing in semiconductor quantum wells," Opt. Express 14, 2845-2850 (2006).
    [CrossRef] [PubMed]
  10. M. V. Poel, J. Mørk and J. M. Hvam, "Controllable delay of ultrashort pulses in a quantum dot optical amplifier," Opt. Express 13, 8032-8037 (2005).
    [CrossRef] [PubMed]
  11. F. G. Sedgwick, B. Pesala, J. Y. Lin, W. S. Ko, X. Zhao and C. J. Chang-Hasnain, "THz-bandwidth tunable slow light in semiconductor optical amplifiers," Opt. Express 15, 747-753 (2007).
    [CrossRef] [PubMed]
  12. F. G. Sedgwick, B. Pesala, A. V. Uskov and C. J. Chang-Hasnain, "Chirp-enhanced fast light in semiconductor optical amplifiers," Opt. Express 15, 17631-17638 (2007).
    [CrossRef] [PubMed]
  13. G. P. Agrawal and A. Olsson, "Self-Phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE J. Quantuim Electron. 25, (1989).
    [CrossRef]
  14. E. B. Treacy, "Optical pulse compression with diffraction gratings," IEEE J. Quantum. Electron. 5, (1969).
    [CrossRef]
  15. A. V. Uskov, J. Mork and J. Mark, "Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning," IEEE J. Quantum. Electron. 30, 1769-1781 (1994).
    [CrossRef]
  16. N. Storkfelt, B. Mikkelsen, D. S. Olesen, M. Yamaguchi and K. E. Stubkjaer, "Measurement of carrier lifetime and linewidth enhancement factor for 1.5-um ridge-waveguide laser amplifier," IEEE Photon. Technol. Lett. 3, 632-634 (1991).
    [CrossRef]
  17. R. F. Brenot, O. Pommereau, O. L. Gouezigou, J. Landreau, F. Poingt, L. L. Gouezigou, B. Rousseau, F. Lelarge, F. Martin and G.H. Duan, "Experimental study of the impact of optical confinement on saturation effects in SOA," Optical Fiber Communication Conference OFC/NFOEC OME50 (2005).
  18. S. Shunji, T. Yamanaka, W. Lui and K. Yokoyama, "Theoretical analysis of differential gain of 1.55 um InGaAsP/InP compressive-strained multiple-quantum-well lasers," J. Appl. Phys. 75, 1299-1303 (1994).
    [CrossRef]
  19. B. Pesala, F. G. Sedgwick, A. V. Uskov and C. J. Chang-Hasnain, "Ultra-high bandwidth electrically tunable fast and slow light in semiconductor optical amplifiers", J. Opt. Soc. Am. B 25, C46-C54 (2008).
    [CrossRef]

2008 (1)

2007 (4)

F. G. Sedgwick, B. Pesala, J. Y. Lin, W. S. Ko, X. Zhao and C. J. Chang-Hasnain, "THz-bandwidth tunable slow light in semiconductor optical amplifiers," Opt. Express 15, 747-753 (2007).
[CrossRef] [PubMed]

F. G. Sedgwick, B. Pesala, A. V. Uskov and C. J. Chang-Hasnain, "Chirp-enhanced fast light in semiconductor optical amplifiers," Opt. Express 15, 17631-17638 (2007).
[CrossRef] [PubMed]

F. Ohman, K. Yvind and J. Mork, "Slow Light in a Semiconductor Waveguide for True-Time Delay Applications in Microwave Photonics," IEEE Photon. Techol. Lett. 19, 1145-1147 (2007).
[CrossRef]

R. M. Camacho, M. V. Pack and J. Howell, "Wide-bandwidth, Tunable, Multiple-pulse-width optical delays using slow light in cesium vapor," Phys. Rev. Lett. 98, 153601 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (2)

M. V. Poel, J. Mørk and J. M. Hvam, "Controllable delay of ultrashort pulses in a quantum dot optical amplifier," Opt. Express 13, 8032-8037 (2005).
[CrossRef] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schqeinsberg, D. J. Gautheir, R. W. Boyd and A. L. Gaeta, "Tunable all-optical delays via brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

2003 (2)

C. J. Chang-Hasnain, P. C. Ku, J. Kim and S. L. Chuang, "Variable Optical Buffer using Slow Light in Semiconductor Nanostructures," Proc. of the IEEE 91, 1884-1897 (2003).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin and R. W. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200-202 (2003).
[CrossRef] [PubMed]

2002 (1)

R. W. Boyd and D. J. Gauthier, "Slow and Fast Light," Prog. Opt. 43, 497-530 (2002).
[CrossRef]

1999 (1)

L. V. Hau, S. E. Harris, Z. Dutton and C. H. Behroozi, " Light speed reduction to 17 meters per second in an ultracold atomic gas," Nature 397, 594-598 (1999).
[CrossRef]

1994 (2)

A. V. Uskov, J. Mork and J. Mark, "Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning," IEEE J. Quantum. Electron. 30, 1769-1781 (1994).
[CrossRef]

S. Shunji, T. Yamanaka, W. Lui and K. Yokoyama, "Theoretical analysis of differential gain of 1.55 um InGaAsP/InP compressive-strained multiple-quantum-well lasers," J. Appl. Phys. 75, 1299-1303 (1994).
[CrossRef]

1991 (1)

N. Storkfelt, B. Mikkelsen, D. S. Olesen, M. Yamaguchi and K. E. Stubkjaer, "Measurement of carrier lifetime and linewidth enhancement factor for 1.5-um ridge-waveguide laser amplifier," IEEE Photon. Technol. Lett. 3, 632-634 (1991).
[CrossRef]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton and C. H. Behroozi, " Light speed reduction to 17 meters per second in an ultracold atomic gas," Nature 397, 594-598 (1999).
[CrossRef]

Bigelow, M. S.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schqeinsberg, D. J. Gautheir, R. W. Boyd and A. L. Gaeta, "Tunable all-optical delays via brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin and R. W. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200-202 (2003).
[CrossRef] [PubMed]

Boyd, R. W.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schqeinsberg, D. J. Gautheir, R. W. Boyd and A. L. Gaeta, "Tunable all-optical delays via brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin and R. W. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200-202 (2003).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, "Slow and Fast Light," Prog. Opt. 43, 497-530 (2002).
[CrossRef]

Camacho, R. M.

R. M. Camacho, M. V. Pack and J. Howell, "Wide-bandwidth, Tunable, Multiple-pulse-width optical delays using slow light in cesium vapor," Phys. Rev. Lett. 98, 153601 (2007).
[CrossRef] [PubMed]

Chang-Hasnain, C. J.

Chuang, S. L.

C. J. Chang-Hasnain, P. C. Ku, J. Kim and S. L. Chuang, "Variable Optical Buffer using Slow Light in Semiconductor Nanostructures," Proc. of the IEEE 91, 1884-1897 (2003).
[CrossRef]

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton and C. H. Behroozi, " Light speed reduction to 17 meters per second in an ultracold atomic gas," Nature 397, 594-598 (1999).
[CrossRef]

Gaeta, A. L.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schqeinsberg, D. J. Gautheir, R. W. Boyd and A. L. Gaeta, "Tunable all-optical delays via brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Gautheir, D. J.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schqeinsberg, D. J. Gautheir, R. W. Boyd and A. L. Gaeta, "Tunable all-optical delays via brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, "Slow and Fast Light," Prog. Opt. 43, 497-530 (2002).
[CrossRef]

Guo, Y.

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton and C. H. Behroozi, " Light speed reduction to 17 meters per second in an ultracold atomic gas," Nature 397, 594-598 (1999).
[CrossRef]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton and C. H. Behroozi, " Light speed reduction to 17 meters per second in an ultracold atomic gas," Nature 397, 594-598 (1999).
[CrossRef]

Howell, J.

R. M. Camacho, M. V. Pack and J. Howell, "Wide-bandwidth, Tunable, Multiple-pulse-width optical delays using slow light in cesium vapor," Phys. Rev. Lett. 98, 153601 (2007).
[CrossRef] [PubMed]

Hvam, J. M.

Kim, J.

C. J. Chang-Hasnain, P. C. Ku, J. Kim and S. L. Chuang, "Variable Optical Buffer using Slow Light in Semiconductor Nanostructures," Proc. of the IEEE 91, 1884-1897 (2003).
[CrossRef]

Ko, W. S.

Ku, P. C.

C. J. Chang-Hasnain, P. C. Ku, J. Kim and S. L. Chuang, "Variable Optical Buffer using Slow Light in Semiconductor Nanostructures," Proc. of the IEEE 91, 1884-1897 (2003).
[CrossRef]

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin and R. W. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200-202 (2003).
[CrossRef] [PubMed]

Lin, J. Y.

Lui, W.

S. Shunji, T. Yamanaka, W. Lui and K. Yokoyama, "Theoretical analysis of differential gain of 1.55 um InGaAsP/InP compressive-strained multiple-quantum-well lasers," J. Appl. Phys. 75, 1299-1303 (1994).
[CrossRef]

Mark, J.

A. V. Uskov, J. Mork and J. Mark, "Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning," IEEE J. Quantum. Electron. 30, 1769-1781 (1994).
[CrossRef]

Mikkelsen, B.

N. Storkfelt, B. Mikkelsen, D. S. Olesen, M. Yamaguchi and K. E. Stubkjaer, "Measurement of carrier lifetime and linewidth enhancement factor for 1.5-um ridge-waveguide laser amplifier," IEEE Photon. Technol. Lett. 3, 632-634 (1991).
[CrossRef]

Mork, J.

F. Ohman, K. Yvind and J. Mork, "Slow Light in a Semiconductor Waveguide for True-Time Delay Applications in Microwave Photonics," IEEE Photon. Techol. Lett. 19, 1145-1147 (2007).
[CrossRef]

A. V. Uskov, J. Mork and J. Mark, "Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning," IEEE J. Quantum. Electron. 30, 1769-1781 (1994).
[CrossRef]

Mørk, J.

Ohman, F.

F. Ohman, K. Yvind and J. Mork, "Slow Light in a Semiconductor Waveguide for True-Time Delay Applications in Microwave Photonics," IEEE Photon. Techol. Lett. 19, 1145-1147 (2007).
[CrossRef]

Okawachi, Y.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schqeinsberg, D. J. Gautheir, R. W. Boyd and A. L. Gaeta, "Tunable all-optical delays via brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Olesen, D. S.

N. Storkfelt, B. Mikkelsen, D. S. Olesen, M. Yamaguchi and K. E. Stubkjaer, "Measurement of carrier lifetime and linewidth enhancement factor for 1.5-um ridge-waveguide laser amplifier," IEEE Photon. Technol. Lett. 3, 632-634 (1991).
[CrossRef]

Pack, M. V.

R. M. Camacho, M. V. Pack and J. Howell, "Wide-bandwidth, Tunable, Multiple-pulse-width optical delays using slow light in cesium vapor," Phys. Rev. Lett. 98, 153601 (2007).
[CrossRef] [PubMed]

Pesala, B.

Poel, M. V.

Sarkar, S.

Schqeinsberg, A.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schqeinsberg, D. J. Gautheir, R. W. Boyd and A. L. Gaeta, "Tunable all-optical delays via brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Sedgwick, F. G.

Sharping, J. E.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schqeinsberg, D. J. Gautheir, R. W. Boyd and A. L. Gaeta, "Tunable all-optical delays via brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Shunji, S.

S. Shunji, T. Yamanaka, W. Lui and K. Yokoyama, "Theoretical analysis of differential gain of 1.55 um InGaAsP/InP compressive-strained multiple-quantum-well lasers," J. Appl. Phys. 75, 1299-1303 (1994).
[CrossRef]

Storkfelt, N.

N. Storkfelt, B. Mikkelsen, D. S. Olesen, M. Yamaguchi and K. E. Stubkjaer, "Measurement of carrier lifetime and linewidth enhancement factor for 1.5-um ridge-waveguide laser amplifier," IEEE Photon. Technol. Lett. 3, 632-634 (1991).
[CrossRef]

Stubkjaer, K. E.

N. Storkfelt, B. Mikkelsen, D. S. Olesen, M. Yamaguchi and K. E. Stubkjaer, "Measurement of carrier lifetime and linewidth enhancement factor for 1.5-um ridge-waveguide laser amplifier," IEEE Photon. Technol. Lett. 3, 632-634 (1991).
[CrossRef]

Uskov, A. V.

Wang, H.

Yamaguchi, M.

N. Storkfelt, B. Mikkelsen, D. S. Olesen, M. Yamaguchi and K. E. Stubkjaer, "Measurement of carrier lifetime and linewidth enhancement factor for 1.5-um ridge-waveguide laser amplifier," IEEE Photon. Technol. Lett. 3, 632-634 (1991).
[CrossRef]

Yamanaka, T.

S. Shunji, T. Yamanaka, W. Lui and K. Yokoyama, "Theoretical analysis of differential gain of 1.55 um InGaAsP/InP compressive-strained multiple-quantum-well lasers," J. Appl. Phys. 75, 1299-1303 (1994).
[CrossRef]

Yokoyama, K.

S. Shunji, T. Yamanaka, W. Lui and K. Yokoyama, "Theoretical analysis of differential gain of 1.55 um InGaAsP/InP compressive-strained multiple-quantum-well lasers," J. Appl. Phys. 75, 1299-1303 (1994).
[CrossRef]

Yvind, K.

F. Ohman, K. Yvind and J. Mork, "Slow Light in a Semiconductor Waveguide for True-Time Delay Applications in Microwave Photonics," IEEE Photon. Techol. Lett. 19, 1145-1147 (2007).
[CrossRef]

Zhao, X.

Zhu, Z.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schqeinsberg, D. J. Gautheir, R. W. Boyd and A. L. Gaeta, "Tunable all-optical delays via brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

IEEE J. Quantum. Electron. (1)

A. V. Uskov, J. Mork and J. Mark, "Wave mixing in semiconductor laser amplifiers due to carrier heating and spectral-hole burning," IEEE J. Quantum. Electron. 30, 1769-1781 (1994).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

N. Storkfelt, B. Mikkelsen, D. S. Olesen, M. Yamaguchi and K. E. Stubkjaer, "Measurement of carrier lifetime and linewidth enhancement factor for 1.5-um ridge-waveguide laser amplifier," IEEE Photon. Technol. Lett. 3, 632-634 (1991).
[CrossRef]

IEEE Photon. Techol. Lett. (1)

F. Ohman, K. Yvind and J. Mork, "Slow Light in a Semiconductor Waveguide for True-Time Delay Applications in Microwave Photonics," IEEE Photon. Techol. Lett. 19, 1145-1147 (2007).
[CrossRef]

J. Appl. Phys. (1)

S. Shunji, T. Yamanaka, W. Lui and K. Yokoyama, "Theoretical analysis of differential gain of 1.55 um InGaAsP/InP compressive-strained multiple-quantum-well lasers," J. Appl. Phys. 75, 1299-1303 (1994).
[CrossRef]

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

Nature (1)

L. V. Hau, S. E. Harris, Z. Dutton and C. H. Behroozi, " Light speed reduction to 17 meters per second in an ultracold atomic gas," Nature 397, 594-598 (1999).
[CrossRef]

Opt. Express (4)

Phys. Rev. Lett. (2)

R. M. Camacho, M. V. Pack and J. Howell, "Wide-bandwidth, Tunable, Multiple-pulse-width optical delays using slow light in cesium vapor," Phys. Rev. Lett. 98, 153601 (2007).
[CrossRef] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schqeinsberg, D. J. Gautheir, R. W. Boyd and A. L. Gaeta, "Tunable all-optical delays via brillouin slow light in an optical fiber," Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Proc. of the IEEE (1)

C. J. Chang-Hasnain, P. C. Ku, J. Kim and S. L. Chuang, "Variable Optical Buffer using Slow Light in Semiconductor Nanostructures," Proc. of the IEEE 91, 1884-1897 (2003).
[CrossRef]

Prog. Opt. (1)

R. W. Boyd and D. J. Gauthier, "Slow and Fast Light," Prog. Opt. 43, 497-530 (2002).
[CrossRef]

Science (1)

M. S. Bigelow, N. N. Lepeshkin and R. W. Boyd, "Superluminal and slow light propagation in a room-temperature solid," Science 301, 200-202 (2003).
[CrossRef] [PubMed]

Other (4)

T. Baba, "Toward photonic crystal optical buffer," CLEO/QELS, San Jose, CA, CWH1 (2008).

G. P. Agrawal and A. Olsson, "Self-Phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE J. Quantuim Electron. 25, (1989).
[CrossRef]

E. B. Treacy, "Optical pulse compression with diffraction gratings," IEEE J. Quantum. Electron. 5, (1969).
[CrossRef]

R. F. Brenot, O. Pommereau, O. L. Gouezigou, J. Landreau, F. Poingt, L. L. Gouezigou, B. Rousseau, F. Lelarge, F. Martin and G.H. Duan, "Experimental study of the impact of optical confinement on saturation effects in SOA," Optical Fiber Communication Conference OFC/NFOEC OME50 (2005).

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Figures (11)

Fig. 1.
Fig. 1.

Schematic of the chirped pulse scheme. An ultra-short pulse (370 fs) enters the chirper (stage 1) which stretches it to 16 ps and introduces a linear negative chirp on the pulse. The pulse then goes through the SOA (stage 2) and acquires additional non-linear chirp due to self-phase modulation. SPM induced chirp is much smaller in magnitude compared to the input chirp because the pulse is stretched in time to large values (370 fs to 16 ps) before entering the SOA. The compensator after the SOA (stage 3) removes the original chirp and compresses the pulse back close to its original width. However, additional chirp due to SOA translates to a large advance which can be controlled electrically by changing the SOA bias. By reversing the sign of the dispersion coefficient of both the chirpers, we obtain a large delay instead.

Fig. 2.
Fig. 2.

Experimental set-up to realize chirped-pulse scheme. Output from a mode-locked laser is split into two branches. One of the branches passes through a fixed delay line and acts as a reference. The signal branch goes through the chirper, SOA and compensator. The delay or advance of the pulses is measured by optical cross-correlation with the reference. An EDFA is used to boost the signal power for the second harmonic generation.

Fig. 3.
Fig. 3.

(a). Normalized cross-correlation traces for a negatively chirped pulse as the SOA gain is increased continuously by increasing the bias. A large ABP of 4.7 is observed as the gain is increased from transparency to maximum gain. (b) Normalized advance (advance/input pulse-width) or ABP and pulse broadening ((final pulsewidth - initial pulsewidth)/initial pulsewidth) are plotted as the linear gain is varied. Advance increases linearly with increasing gain as expected. Pulse broadening is less than 75% across the entire tuning range.

Fig. 4.
Fig. 4.

(a) Normalized cross-correlation traces for a positively chirped pulse as the SOA gain is increased continuously by increasing the bias. A large DBP of 4.0 is observed as the gain is increased from transparency to maximum gain. (b) Normalised delay (delay/input pulse-width) or DBP and pulse broadening ((final pulsewidth– initial pulsewidth)/initial pulsewidth) are plotted as the linear gain is varied. Delay increases linearly with increasing gain as expected. Pulse broadening is less than 80% across the entire tuning range.

Fig. 5.
Fig. 5.

Novel scheme based on cross-bar switches to combine the results of advance and delay. (a) In bar configuration (blue path), pulse experiences an advance with increasing current. (b) In cross configuration (red path), pulse experiences a delay with increasing current. A continuously tunable DBP of 8.7 can be achieved by switching between bar and cross configurations.

Fig. 6.
Fig. 6.

(a) Results of the simulation for a 370 fs input pulse negatively chirped to 16 ps. When SPM is absent (α = 0), the pulse doesn’t experience advance as the gain is increased (red curve). However, the presence of SPM (α = 3) results in a large advance as the linear gain is increased from transparency (0 dB) to maximum gain (30 dB). (b) Results of spectral filtering to reduce the pulse pedestal. When the low frequency components are cut-off (red curve), pulse pedestal is reduced significantly (solid blue curve).

Fig. 7.
Fig. 7.

Comparison of results of the simulation (dotted lines) with the experimental results (solid lines). Excellent match is achieved for a negatively chirped pulse (a) and a positively chirped pulse (b). A linewidth enhancement factor of 4 is used in the simulations.

Fig. 8.
Fig. 8.

Simulation results as the linewidth enhancement factor is increased from 4 to 7. a) A large ABP of 10.3 is observed for a negatively chirped pulse b) A large DBP of 10.2 is observed for a positively chirped pulse. Pulse broadening is large compared to the case of α = 4 because the linear chirpers employed in this scheme cannot exactly compensate for SOA induced chirp at all gain values. Using crossbar switches, a continuously tunable DBP of 20.5 can be achieved.

Fig. 9.
Fig. 9.

(a) Simulation results as the confinement factor is increased from 0.1 to 0.7. A linewidth enhancement factor of 5 is used in this simulation. Large ABP of 10.3 is achieved as the gain is increased from 0.5 to 9. A large confinement factor leads to efficient SPM which results in a large advance. (b) Simulation results as the differential gain is increased 5 times from 4.10-16 cm2 to 2.10-15 cm2. A confinement factor of 0.1 and linewidth enhancement factor of 5 is used in this simulation. Large ABP of 10.6 is achieved as the gain is increased from 0.5 to 9. Higher differential gain leads to large advance due to efficient SPM.

Fig. 10.
Fig. 10.

Simulation results as the linewidth enhanced factor and confinement factor are increased from 10 and 0.8 respectively. For a negatively chirped pulse a large ABP of 26.8 is achieved while for a positively chirped pulse

Fig. 11.
Fig. 11.

Comparison of simulation results for a 200 fs input pulse at a maximum linear gain of 30dB and for a linewidth enhancement factor of 7. In the first scenario (unchirped case), a transform limited pulse entering the SOA experiences an advance due to ultra-fast non-linear processes. A compensator is added after the SOA to leverage the non-linear chirp induced by ultra-fast processes. In this case, an ABP of 4.7 is observed. In the second scenario (chirped-pulse scheme), the same input pulse is chirped to 20 ps using an input chirper before entering the SOA. Compensator after the SOA helps in compressing the pulse back to its original width. In this case, the SPM induced chirp results in an ABP of 9.6 pulses compared to an ABP of 4.7 for unchirped case. Further, broadening in this case is only 40% compared to a broadening of 100% for unchirped case which clearly shows that chirping the pulse to large values before entering the SOA not only increases the advance but also results in less broadening.

Equations (3)

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P z = ( g α int ) P
∂ϕ z = 1 2 α g
g τ = g o g τ c g P E sat

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