Abstract

We experimentally and theoretically investigate the stability of a single-mode integrated filtered-feedback laser as a function of the electrically controlled feedback phase. We interpret the measurements in terms of feedback-induced dynamics, compare them with the results from a stability analysis model for conventional feedback, and find good qualitative agreement.

© 2012 OSA

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References

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  1. C. H. Henry, “Phase noise in semiconductor laser,” J. Lightwave Technol.4(3), 298–311 (1986).
    [CrossRef]
  2. S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H. J. Wünsche, and F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.69(1), 016206 (2004).
    [CrossRef] [PubMed]
  3. J. Zhao, P. J. Williams, M. K. Smit, and X. J. M. Leijtens, “ Monolithic integrated filtered-feedback multi-wavelength laser,” in Proc. Optical Fiber Communication Conf. (OFC 2012), Los Angeles, USA, Mar. 4–8, 2012, Paper OW1G.5.
  4. E. Kleijn, M. K. Smit, M. J. Wale, and X. J. M. Leijtens, “New two-port multimode interference reflectors,” in Proc. 16th Eur. Conf. Int. Opt. (ECIO ’12), Sitges-Barcelona, Spain, Apr.18–20, (2012).
  5. M. Yousefi and D. Lenstra, “Dynamical behavior of a semiconductor laser with filtered external optical feedback,” IEEE J. Quantum Electron.35(6), 970–976 (1999).
    [CrossRef]
  6. G. H. M. Van Tartwijk, “Semiconductor lasers with optical injection and feedback,” Thesis Amsterdam, 76–80&88–90 (1994); see also J. Quantum Semiclass. Opt. 7, 87–143 (1995).
  7. G. A. Acket, D. Lenstra, B. H. Verbeek, and A. J. Den Boef, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron.20(10), 1163–1169 (1984).
    [CrossRef]
  8. J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: Theory and Experiment,” IEEE J. Quantum Electron.28(1), 93–108 (1992).
    [CrossRef]
  9. S. H. Strogatz, Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, (Perseus Books, Addison-Wesley Publishing, 1994).
  10. D. Lenstra, B. H. Verbeek, and A. J. Den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron.21(6), 674–679 (1985).
    [CrossRef]
  11. G. Liu, X. Jin, and S. L. Chuang, “Measurement of inewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett.13(5), 430–432 (2001).
    [CrossRef]
  12. I. Petitbon, P. Gallion, G. Debarge, and C. Chabran, “Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser,” IEEE J. Quantum Electron.24(2), 148–154 (1988).
    [CrossRef]

2004

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H. J. Wünsche, and F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.69(1), 016206 (2004).
[CrossRef] [PubMed]

2001

G. Liu, X. Jin, and S. L. Chuang, “Measurement of inewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett.13(5), 430–432 (2001).
[CrossRef]

1999

M. Yousefi and D. Lenstra, “Dynamical behavior of a semiconductor laser with filtered external optical feedback,” IEEE J. Quantum Electron.35(6), 970–976 (1999).
[CrossRef]

1992

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: Theory and Experiment,” IEEE J. Quantum Electron.28(1), 93–108 (1992).
[CrossRef]

1988

I. Petitbon, P. Gallion, G. Debarge, and C. Chabran, “Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser,” IEEE J. Quantum Electron.24(2), 148–154 (1988).
[CrossRef]

1986

C. H. Henry, “Phase noise in semiconductor laser,” J. Lightwave Technol.4(3), 298–311 (1986).
[CrossRef]

1985

D. Lenstra, B. H. Verbeek, and A. J. Den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron.21(6), 674–679 (1985).
[CrossRef]

1984

G. A. Acket, D. Lenstra, B. H. Verbeek, and A. J. Den Boef, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron.20(10), 1163–1169 (1984).
[CrossRef]

Acket, G. A.

G. A. Acket, D. Lenstra, B. H. Verbeek, and A. J. Den Boef, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron.20(10), 1163–1169 (1984).
[CrossRef]

Bauer, S.

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H. J. Wünsche, and F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.69(1), 016206 (2004).
[CrossRef] [PubMed]

Brox, O.

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H. J. Wünsche, and F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.69(1), 016206 (2004).
[CrossRef] [PubMed]

Chabran, C.

I. Petitbon, P. Gallion, G. Debarge, and C. Chabran, “Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser,” IEEE J. Quantum Electron.24(2), 148–154 (1988).
[CrossRef]

Chuang, S. L.

G. Liu, X. Jin, and S. L. Chuang, “Measurement of inewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett.13(5), 430–432 (2001).
[CrossRef]

Debarge, G.

I. Petitbon, P. Gallion, G. Debarge, and C. Chabran, “Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser,” IEEE J. Quantum Electron.24(2), 148–154 (1988).
[CrossRef]

Den Boef, A. J.

D. Lenstra, B. H. Verbeek, and A. J. Den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron.21(6), 674–679 (1985).
[CrossRef]

G. A. Acket, D. Lenstra, B. H. Verbeek, and A. J. Den Boef, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron.20(10), 1163–1169 (1984).
[CrossRef]

Gallion, P.

I. Petitbon, P. Gallion, G. Debarge, and C. Chabran, “Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser,” IEEE J. Quantum Electron.24(2), 148–154 (1988).
[CrossRef]

Henneberger, F.

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H. J. Wünsche, and F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.69(1), 016206 (2004).
[CrossRef] [PubMed]

Henry, C. H.

C. H. Henry, “Phase noise in semiconductor laser,” J. Lightwave Technol.4(3), 298–311 (1986).
[CrossRef]

Jin, X.

G. Liu, X. Jin, and S. L. Chuang, “Measurement of inewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett.13(5), 430–432 (2001).
[CrossRef]

Kreissl, J.

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H. J. Wünsche, and F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.69(1), 016206 (2004).
[CrossRef] [PubMed]

Lenstra, D.

M. Yousefi and D. Lenstra, “Dynamical behavior of a semiconductor laser with filtered external optical feedback,” IEEE J. Quantum Electron.35(6), 970–976 (1999).
[CrossRef]

D. Lenstra, B. H. Verbeek, and A. J. Den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron.21(6), 674–679 (1985).
[CrossRef]

G. A. Acket, D. Lenstra, B. H. Verbeek, and A. J. Den Boef, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron.20(10), 1163–1169 (1984).
[CrossRef]

Liu, G.

G. Liu, X. Jin, and S. L. Chuang, “Measurement of inewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett.13(5), 430–432 (2001).
[CrossRef]

Mark, J.

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: Theory and Experiment,” IEEE J. Quantum Electron.28(1), 93–108 (1992).
[CrossRef]

Mork, J.

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: Theory and Experiment,” IEEE J. Quantum Electron.28(1), 93–108 (1992).
[CrossRef]

Petitbon, I.

I. Petitbon, P. Gallion, G. Debarge, and C. Chabran, “Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser,” IEEE J. Quantum Electron.24(2), 148–154 (1988).
[CrossRef]

Radziunas, M.

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H. J. Wünsche, and F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.69(1), 016206 (2004).
[CrossRef] [PubMed]

Sartorius, B.

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H. J. Wünsche, and F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.69(1), 016206 (2004).
[CrossRef] [PubMed]

Sieber, J.

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H. J. Wünsche, and F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.69(1), 016206 (2004).
[CrossRef] [PubMed]

Tromborg, B.

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: Theory and Experiment,” IEEE J. Quantum Electron.28(1), 93–108 (1992).
[CrossRef]

Verbeek, B. H.

D. Lenstra, B. H. Verbeek, and A. J. Den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron.21(6), 674–679 (1985).
[CrossRef]

G. A. Acket, D. Lenstra, B. H. Verbeek, and A. J. Den Boef, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron.20(10), 1163–1169 (1984).
[CrossRef]

Wünsche, H. J.

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H. J. Wünsche, and F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.69(1), 016206 (2004).
[CrossRef] [PubMed]

Yousefi, M.

M. Yousefi and D. Lenstra, “Dynamical behavior of a semiconductor laser with filtered external optical feedback,” IEEE J. Quantum Electron.35(6), 970–976 (1999).
[CrossRef]

IEEE J. Quantum Electron.

M. Yousefi and D. Lenstra, “Dynamical behavior of a semiconductor laser with filtered external optical feedback,” IEEE J. Quantum Electron.35(6), 970–976 (1999).
[CrossRef]

G. A. Acket, D. Lenstra, B. H. Verbeek, and A. J. Den Boef, “The influence of feedback intensity on longitudinal mode properties and optical noise in index-guided semiconductor lasers,” IEEE J. Quantum Electron.20(10), 1163–1169 (1984).
[CrossRef]

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: Theory and Experiment,” IEEE J. Quantum Electron.28(1), 93–108 (1992).
[CrossRef]

D. Lenstra, B. H. Verbeek, and A. J. Den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron.21(6), 674–679 (1985).
[CrossRef]

I. Petitbon, P. Gallion, G. Debarge, and C. Chabran, “Locking bandwidth and relaxation oscillations of an injection-locked semiconductor laser,” IEEE J. Quantum Electron.24(2), 148–154 (1988).
[CrossRef]

IEEE Photon. Technol. Lett.

G. Liu, X. Jin, and S. L. Chuang, “Measurement of inewidth enhancement factor of semiconductor lasers using an injection-locking technique,” IEEE Photon. Technol. Lett.13(5), 430–432 (2001).
[CrossRef]

J. Lightwave Technol.

C. H. Henry, “Phase noise in semiconductor laser,” J. Lightwave Technol.4(3), 298–311 (1986).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

S. Bauer, O. Brox, J. Kreissl, B. Sartorius, M. Radziunas, J. Sieber, H. J. Wünsche, and F. Henneberger, “Nonlinear dynamics of semiconductor lasers with active optical feedback,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.69(1), 016206 (2004).
[CrossRef] [PubMed]

Other

J. Zhao, P. J. Williams, M. K. Smit, and X. J. M. Leijtens, “ Monolithic integrated filtered-feedback multi-wavelength laser,” in Proc. Optical Fiber Communication Conf. (OFC 2012), Los Angeles, USA, Mar. 4–8, 2012, Paper OW1G.5.

E. Kleijn, M. K. Smit, M. J. Wale, and X. J. M. Leijtens, “New two-port multimode interference reflectors,” in Proc. 16th Eur. Conf. Int. Opt. (ECIO ’12), Sitges-Barcelona, Spain, Apr.18–20, (2012).

S. H. Strogatz, Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, (Perseus Books, Addison-Wesley Publishing, 1994).

G. H. M. Van Tartwijk, “Semiconductor lasers with optical injection and feedback,” Thesis Amsterdam, 76–80&88–90 (1994); see also J. Quantum Semiclass. Opt. 7, 87–143 (1995).

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic of the device and (b) Microscopy photograph of the realized device. The chip dimensions are approximately 2 × 2.5 mm.

Fig. 2
Fig. 2

Schematic of one channel: a FP laser and the external cavity with phase shifter inside; On the bottom, sketches of spectra feature are shown: FP modes (left) and the AWG passband (right).

Fig. 3
Fig. 3

The measurement setup. Ipump is the laser injection current, and Iphase is the current on the phase shifter to tune the feedback phase; TEC denotes the temperature controller; ISO is an optical isolator. After the 50/50 coupler, one of the two branches of light is fed to a 50 GHz photodiode, amplified by a low noise amplifier (LNA) and measured with an electrical spectrum analyzer, while the other branch connects to an optical spectrum analyzer.

Fig. 4
Fig. 4

Intensity noise (dashed lines) and optical spectral (solid lines) from the ESA and OSA, respectively, for different feedback phase tuning 0°, 90°, 150°, 180°, 210°.

Fig. 5
Fig. 5

(a) Measured map of laser stability versus phase shifter current with different injection current. The dark region is the unstable region and the bright region is the stable region. (b) Theoretical stability diagram for a single-mode laser vs. pump strength p (vertical) and feedback phase (horizontal), with p defined as p=(J J thr )/ J thr . Color white denotes stable operation; black denotes unstable. Parameters are: feedback rate 5× 10 9 s 1 ; feedback delay time 7× 10 11 s and α=2.6 ; the injection-current-induced frequency shift of the solitary laser is −0.6 GHz/mA. The most left column gives the relaxation oscillation frequency in GHz.

Fig. 6
Fig. 6

Injection locking measurement setup. DUT is the device under test. See the text for other details.

Fig. 7
Fig. 7

Frequency locking range dependence on injected power. FP laser is under injection current of 35 mA at 18 °C.

Equations (11)

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

P ˙ =ξNP+2γ P(t)P(tτ) cos[ϕ(t)ϕ(tτ)+ ω 0 τ];
ϕ ˙ = 1 2 αξNγ P(tτ) P(t) sin[ϕ(t)ϕ(tτ)+ ω 0 τ],
N ˙ =( 1 T 1 +ξP)N Γ 0 (P P 0 ).
γ= r ext (1 r 2 ) τ in r
P 0 = J J thr Γ 0
P= P s ;N= N s ;ϕ=Δ ω s t
Δ ω s =γ 1+ α 2 sin(arctanα+ ω 0 τ+Δ ω s τ),
N s = 2γ ξ cos( ω 0 τ+Δ ω s τ),
P s = P 0 N s Γ 0 T 1 1+ ξ N s Γ 0 .
ν R = 1 2π ξ(J J thr )
ϕ=Δ ω s t+δϕ;N= N s +δN;P= P s +δP.

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