Abstract

We present a traveling-wave large-signal simulation of the spatiotemporal dynamics of two-section distributed feedback lasers, emphasizing the self-pulsation phenomenon. For index-coupled lasers, self-pulsation is a result of the interaction of two modes, each spatially confined primarily to one section. For partially gain-coupled lasers, self-pulsation is a result of the interaction of two modes, one that is spatially confined primarily to one section and another that belongs to both sections. The self-pulsation frequency-tuning range and the modulation index of partially gain-coupled lasers are found to be substantially larger than those of index-coupled lasers. Experimentally, self-pulsation with a frequency-tuning range from 20 to 60 GHz in two-section partially gain-coupled distributed-feedback lasers has been characterized in the electrical domain. The noise of self-pulsation was reduced experimentally by optical feedback.

© 1999 Optical Society of America

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References

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  1. R. Schatz, “Longitudinal spatial instability in symmetric semiconductor lasers due to spatial hole burning,” IEEE J. Quantum Electron. 28, 1443–1449 (1992).
    [CrossRef]
  2. G. Pham and G.-H. Duan, “Self-pulsation in two-section DFB semiconductor laser and its synchronization to an external signal,” IEEE J. Quantum Electron. 24, 1000–1008 (1998).
    [CrossRef]
  3. M. Mohrle, U. Feiste, J. Hoerer, R. Molt, and B. Sartorius, “Gigahertz self-pulsation in 1.55-μm wavelength multisection DFB lasers,” IEEE Photon. Technol. Lett. 14, 976–979 (1992).
    [CrossRef]
  4. B. Sartorius, M. Mohrle, and U. Feiste, “12–64 GHz continuous frequency tuning in self-pulsating 1.55-μm multiquantum-well DFB lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 535–538 (1995).
    [CrossRef]
  5. X. Wang, M. Al-Mumin, W. Mao, S. A. Pappert, J. Hong, and G. Li, “Optical generation of microwave/millimeter wave signals using two-section gain-coupled DFB lasers,” IEEE Photon. Technol. Lett. (to be published).
  6. B. Sartorius, C. Bornholdt, O. Brox, H. J. Ehrke, D. Hoffmann, R. Ludwig, and M. Mohrle, “Bit rate flexible all-optical clock recovery,” in Digest of Optical Fiber Communication Conference (OFC) (Optical Society of America, Washington, D.C., 1999), pp. 24–26.
  7. P. E. Barnsley, H. J. Wickes, G. E. Wickens, and D. M. Spirit, “All-optical clock recovery from 5 Gb/s RZ data using a self-pulsating 1.56 μm laser diode,” IEEE Photon. Technol. Lett. 3, 942–945 (1991).
    [CrossRef]
  8. R.-P. Braun, G. Grosskopf, D. Rohde, and F. Schmidt, “Low-phase noise millimeter-wave generation at 64 GHz and data transmission using optical sideband injection locking,” IEEE Photon. Technol. Lett. 10, 728–730 (1998).
    [CrossRef]
  9. H. Wenzel, U. Bandelow, H.-J. Wunsche, and J. Rehberg, “Mechanisms of fast self pulsations in two-section DFB lasers,” IEEE J. Quantum Electron. 32, 69–78 (1996).
    [CrossRef]
  10. M. Liu, Principles and Applications of Optical Communications (Irwin, Chicago, Ill., 1996), p. 640.
  11. C. F. Tssang, D. D. Marcenac, J. E. Caroll, and L. M. Zhang, “Comparison between power matrix model and time domain model in modeling large signal responses of DFB lasers,” IEE Proc. Optoelectron. 141, 89–96 (1994).
    [CrossRef]
  12. G. P. Li, T. Makino, R. Moore, N. Puetz, K.-W. Leong, and H. Lu, “Partly gain-coupled 1.55 μm strained-layer multiquantum-well DFB lasers,” IEEE J. Quantum Electron. 29, 1736–1742 (1993).
    [CrossRef]
  13. C. K. Sun, R. J. Orazi, S. A. Pappert, and W. K. Burns, “A photonic-link millimeter-wave mixer using cascaded optical modulators and harmonic carrier generation,” IEEE Photon. Technol. Lett. 8, 1166–1168 (1996).
    [CrossRef]
  14. S. Yao and L. Maleki, “Converting light into spectrally pure microwave oscillation,” Opt. Lett. 21, 483–485 (1996).
    [CrossRef] [PubMed]
  15. E. A. Swanson and S. R. Chinn, “40-GHz pulse train generation using soliton compression of a Mach–Zehnder modulator output,” IEEE Photon. Technol. Lett. 7, 114–116 (1995).
    [CrossRef]

1998 (2)

G. Pham and G.-H. Duan, “Self-pulsation in two-section DFB semiconductor laser and its synchronization to an external signal,” IEEE J. Quantum Electron. 24, 1000–1008 (1998).
[CrossRef]

R.-P. Braun, G. Grosskopf, D. Rohde, and F. Schmidt, “Low-phase noise millimeter-wave generation at 64 GHz and data transmission using optical sideband injection locking,” IEEE Photon. Technol. Lett. 10, 728–730 (1998).
[CrossRef]

1996 (3)

H. Wenzel, U. Bandelow, H.-J. Wunsche, and J. Rehberg, “Mechanisms of fast self pulsations in two-section DFB lasers,” IEEE J. Quantum Electron. 32, 69–78 (1996).
[CrossRef]

C. K. Sun, R. J. Orazi, S. A. Pappert, and W. K. Burns, “A photonic-link millimeter-wave mixer using cascaded optical modulators and harmonic carrier generation,” IEEE Photon. Technol. Lett. 8, 1166–1168 (1996).
[CrossRef]

S. Yao and L. Maleki, “Converting light into spectrally pure microwave oscillation,” Opt. Lett. 21, 483–485 (1996).
[CrossRef] [PubMed]

1995 (2)

E. A. Swanson and S. R. Chinn, “40-GHz pulse train generation using soliton compression of a Mach–Zehnder modulator output,” IEEE Photon. Technol. Lett. 7, 114–116 (1995).
[CrossRef]

B. Sartorius, M. Mohrle, and U. Feiste, “12–64 GHz continuous frequency tuning in self-pulsating 1.55-μm multiquantum-well DFB lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 535–538 (1995).
[CrossRef]

1994 (1)

C. F. Tssang, D. D. Marcenac, J. E. Caroll, and L. M. Zhang, “Comparison between power matrix model and time domain model in modeling large signal responses of DFB lasers,” IEE Proc. Optoelectron. 141, 89–96 (1994).
[CrossRef]

1993 (1)

G. P. Li, T. Makino, R. Moore, N. Puetz, K.-W. Leong, and H. Lu, “Partly gain-coupled 1.55 μm strained-layer multiquantum-well DFB lasers,” IEEE J. Quantum Electron. 29, 1736–1742 (1993).
[CrossRef]

1992 (2)

M. Mohrle, U. Feiste, J. Hoerer, R. Molt, and B. Sartorius, “Gigahertz self-pulsation in 1.55-μm wavelength multisection DFB lasers,” IEEE Photon. Technol. Lett. 14, 976–979 (1992).
[CrossRef]

R. Schatz, “Longitudinal spatial instability in symmetric semiconductor lasers due to spatial hole burning,” IEEE J. Quantum Electron. 28, 1443–1449 (1992).
[CrossRef]

1991 (1)

P. E. Barnsley, H. J. Wickes, G. E. Wickens, and D. M. Spirit, “All-optical clock recovery from 5 Gb/s RZ data using a self-pulsating 1.56 μm laser diode,” IEEE Photon. Technol. Lett. 3, 942–945 (1991).
[CrossRef]

Bandelow, U.

H. Wenzel, U. Bandelow, H.-J. Wunsche, and J. Rehberg, “Mechanisms of fast self pulsations in two-section DFB lasers,” IEEE J. Quantum Electron. 32, 69–78 (1996).
[CrossRef]

Barnsley, P. E.

P. E. Barnsley, H. J. Wickes, G. E. Wickens, and D. M. Spirit, “All-optical clock recovery from 5 Gb/s RZ data using a self-pulsating 1.56 μm laser diode,” IEEE Photon. Technol. Lett. 3, 942–945 (1991).
[CrossRef]

Braun, R.-P.

R.-P. Braun, G. Grosskopf, D. Rohde, and F. Schmidt, “Low-phase noise millimeter-wave generation at 64 GHz and data transmission using optical sideband injection locking,” IEEE Photon. Technol. Lett. 10, 728–730 (1998).
[CrossRef]

Burns, W. K.

C. K. Sun, R. J. Orazi, S. A. Pappert, and W. K. Burns, “A photonic-link millimeter-wave mixer using cascaded optical modulators and harmonic carrier generation,” IEEE Photon. Technol. Lett. 8, 1166–1168 (1996).
[CrossRef]

Caroll, J. E.

C. F. Tssang, D. D. Marcenac, J. E. Caroll, and L. M. Zhang, “Comparison between power matrix model and time domain model in modeling large signal responses of DFB lasers,” IEE Proc. Optoelectron. 141, 89–96 (1994).
[CrossRef]

Chinn, S. R.

E. A. Swanson and S. R. Chinn, “40-GHz pulse train generation using soliton compression of a Mach–Zehnder modulator output,” IEEE Photon. Technol. Lett. 7, 114–116 (1995).
[CrossRef]

Duan, G.-H.

G. Pham and G.-H. Duan, “Self-pulsation in two-section DFB semiconductor laser and its synchronization to an external signal,” IEEE J. Quantum Electron. 24, 1000–1008 (1998).
[CrossRef]

Feiste, U.

B. Sartorius, M. Mohrle, and U. Feiste, “12–64 GHz continuous frequency tuning in self-pulsating 1.55-μm multiquantum-well DFB lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 535–538 (1995).
[CrossRef]

M. Mohrle, U. Feiste, J. Hoerer, R. Molt, and B. Sartorius, “Gigahertz self-pulsation in 1.55-μm wavelength multisection DFB lasers,” IEEE Photon. Technol. Lett. 14, 976–979 (1992).
[CrossRef]

Grosskopf, G.

R.-P. Braun, G. Grosskopf, D. Rohde, and F. Schmidt, “Low-phase noise millimeter-wave generation at 64 GHz and data transmission using optical sideband injection locking,” IEEE Photon. Technol. Lett. 10, 728–730 (1998).
[CrossRef]

Hoerer, J.

M. Mohrle, U. Feiste, J. Hoerer, R. Molt, and B. Sartorius, “Gigahertz self-pulsation in 1.55-μm wavelength multisection DFB lasers,” IEEE Photon. Technol. Lett. 14, 976–979 (1992).
[CrossRef]

Leong, K.-W.

G. P. Li, T. Makino, R. Moore, N. Puetz, K.-W. Leong, and H. Lu, “Partly gain-coupled 1.55 μm strained-layer multiquantum-well DFB lasers,” IEEE J. Quantum Electron. 29, 1736–1742 (1993).
[CrossRef]

Li, G. P.

G. P. Li, T. Makino, R. Moore, N. Puetz, K.-W. Leong, and H. Lu, “Partly gain-coupled 1.55 μm strained-layer multiquantum-well DFB lasers,” IEEE J. Quantum Electron. 29, 1736–1742 (1993).
[CrossRef]

Lu, H.

G. P. Li, T. Makino, R. Moore, N. Puetz, K.-W. Leong, and H. Lu, “Partly gain-coupled 1.55 μm strained-layer multiquantum-well DFB lasers,” IEEE J. Quantum Electron. 29, 1736–1742 (1993).
[CrossRef]

Makino, T.

G. P. Li, T. Makino, R. Moore, N. Puetz, K.-W. Leong, and H. Lu, “Partly gain-coupled 1.55 μm strained-layer multiquantum-well DFB lasers,” IEEE J. Quantum Electron. 29, 1736–1742 (1993).
[CrossRef]

Maleki, L.

Marcenac, D. D.

C. F. Tssang, D. D. Marcenac, J. E. Caroll, and L. M. Zhang, “Comparison between power matrix model and time domain model in modeling large signal responses of DFB lasers,” IEE Proc. Optoelectron. 141, 89–96 (1994).
[CrossRef]

Mohrle, M.

B. Sartorius, M. Mohrle, and U. Feiste, “12–64 GHz continuous frequency tuning in self-pulsating 1.55-μm multiquantum-well DFB lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 535–538 (1995).
[CrossRef]

M. Mohrle, U. Feiste, J. Hoerer, R. Molt, and B. Sartorius, “Gigahertz self-pulsation in 1.55-μm wavelength multisection DFB lasers,” IEEE Photon. Technol. Lett. 14, 976–979 (1992).
[CrossRef]

Molt, R.

M. Mohrle, U. Feiste, J. Hoerer, R. Molt, and B. Sartorius, “Gigahertz self-pulsation in 1.55-μm wavelength multisection DFB lasers,” IEEE Photon. Technol. Lett. 14, 976–979 (1992).
[CrossRef]

Moore, R.

G. P. Li, T. Makino, R. Moore, N. Puetz, K.-W. Leong, and H. Lu, “Partly gain-coupled 1.55 μm strained-layer multiquantum-well DFB lasers,” IEEE J. Quantum Electron. 29, 1736–1742 (1993).
[CrossRef]

Orazi, R. J.

C. K. Sun, R. J. Orazi, S. A. Pappert, and W. K. Burns, “A photonic-link millimeter-wave mixer using cascaded optical modulators and harmonic carrier generation,” IEEE Photon. Technol. Lett. 8, 1166–1168 (1996).
[CrossRef]

Pappert, S. A.

C. K. Sun, R. J. Orazi, S. A. Pappert, and W. K. Burns, “A photonic-link millimeter-wave mixer using cascaded optical modulators and harmonic carrier generation,” IEEE Photon. Technol. Lett. 8, 1166–1168 (1996).
[CrossRef]

Pham, G.

G. Pham and G.-H. Duan, “Self-pulsation in two-section DFB semiconductor laser and its synchronization to an external signal,” IEEE J. Quantum Electron. 24, 1000–1008 (1998).
[CrossRef]

Puetz, N.

G. P. Li, T. Makino, R. Moore, N. Puetz, K.-W. Leong, and H. Lu, “Partly gain-coupled 1.55 μm strained-layer multiquantum-well DFB lasers,” IEEE J. Quantum Electron. 29, 1736–1742 (1993).
[CrossRef]

Rehberg, J.

H. Wenzel, U. Bandelow, H.-J. Wunsche, and J. Rehberg, “Mechanisms of fast self pulsations in two-section DFB lasers,” IEEE J. Quantum Electron. 32, 69–78 (1996).
[CrossRef]

Rohde, D.

R.-P. Braun, G. Grosskopf, D. Rohde, and F. Schmidt, “Low-phase noise millimeter-wave generation at 64 GHz and data transmission using optical sideband injection locking,” IEEE Photon. Technol. Lett. 10, 728–730 (1998).
[CrossRef]

Sartorius, B.

B. Sartorius, M. Mohrle, and U. Feiste, “12–64 GHz continuous frequency tuning in self-pulsating 1.55-μm multiquantum-well DFB lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 535–538 (1995).
[CrossRef]

M. Mohrle, U. Feiste, J. Hoerer, R. Molt, and B. Sartorius, “Gigahertz self-pulsation in 1.55-μm wavelength multisection DFB lasers,” IEEE Photon. Technol. Lett. 14, 976–979 (1992).
[CrossRef]

Schatz, R.

R. Schatz, “Longitudinal spatial instability in symmetric semiconductor lasers due to spatial hole burning,” IEEE J. Quantum Electron. 28, 1443–1449 (1992).
[CrossRef]

Schmidt, F.

R.-P. Braun, G. Grosskopf, D. Rohde, and F. Schmidt, “Low-phase noise millimeter-wave generation at 64 GHz and data transmission using optical sideband injection locking,” IEEE Photon. Technol. Lett. 10, 728–730 (1998).
[CrossRef]

Spirit, D. M.

P. E. Barnsley, H. J. Wickes, G. E. Wickens, and D. M. Spirit, “All-optical clock recovery from 5 Gb/s RZ data using a self-pulsating 1.56 μm laser diode,” IEEE Photon. Technol. Lett. 3, 942–945 (1991).
[CrossRef]

Sun, C. K.

C. K. Sun, R. J. Orazi, S. A. Pappert, and W. K. Burns, “A photonic-link millimeter-wave mixer using cascaded optical modulators and harmonic carrier generation,” IEEE Photon. Technol. Lett. 8, 1166–1168 (1996).
[CrossRef]

Swanson, E. A.

E. A. Swanson and S. R. Chinn, “40-GHz pulse train generation using soliton compression of a Mach–Zehnder modulator output,” IEEE Photon. Technol. Lett. 7, 114–116 (1995).
[CrossRef]

Tssang, C. F.

C. F. Tssang, D. D. Marcenac, J. E. Caroll, and L. M. Zhang, “Comparison between power matrix model and time domain model in modeling large signal responses of DFB lasers,” IEE Proc. Optoelectron. 141, 89–96 (1994).
[CrossRef]

Wenzel, H.

H. Wenzel, U. Bandelow, H.-J. Wunsche, and J. Rehberg, “Mechanisms of fast self pulsations in two-section DFB lasers,” IEEE J. Quantum Electron. 32, 69–78 (1996).
[CrossRef]

Wickens, G. E.

P. E. Barnsley, H. J. Wickes, G. E. Wickens, and D. M. Spirit, “All-optical clock recovery from 5 Gb/s RZ data using a self-pulsating 1.56 μm laser diode,” IEEE Photon. Technol. Lett. 3, 942–945 (1991).
[CrossRef]

Wickes, H. J.

P. E. Barnsley, H. J. Wickes, G. E. Wickens, and D. M. Spirit, “All-optical clock recovery from 5 Gb/s RZ data using a self-pulsating 1.56 μm laser diode,” IEEE Photon. Technol. Lett. 3, 942–945 (1991).
[CrossRef]

Wunsche, H.-J.

H. Wenzel, U. Bandelow, H.-J. Wunsche, and J. Rehberg, “Mechanisms of fast self pulsations in two-section DFB lasers,” IEEE J. Quantum Electron. 32, 69–78 (1996).
[CrossRef]

Yao, S.

Zhang, L. M.

C. F. Tssang, D. D. Marcenac, J. E. Caroll, and L. M. Zhang, “Comparison between power matrix model and time domain model in modeling large signal responses of DFB lasers,” IEE Proc. Optoelectron. 141, 89–96 (1994).
[CrossRef]

IEE Proc. Optoelectron. (1)

C. F. Tssang, D. D. Marcenac, J. E. Caroll, and L. M. Zhang, “Comparison between power matrix model and time domain model in modeling large signal responses of DFB lasers,” IEE Proc. Optoelectron. 141, 89–96 (1994).
[CrossRef]

IEEE J. Quantum Electron. (4)

G. P. Li, T. Makino, R. Moore, N. Puetz, K.-W. Leong, and H. Lu, “Partly gain-coupled 1.55 μm strained-layer multiquantum-well DFB lasers,” IEEE J. Quantum Electron. 29, 1736–1742 (1993).
[CrossRef]

R. Schatz, “Longitudinal spatial instability in symmetric semiconductor lasers due to spatial hole burning,” IEEE J. Quantum Electron. 28, 1443–1449 (1992).
[CrossRef]

G. Pham and G.-H. Duan, “Self-pulsation in two-section DFB semiconductor laser and its synchronization to an external signal,” IEEE J. Quantum Electron. 24, 1000–1008 (1998).
[CrossRef]

H. Wenzel, U. Bandelow, H.-J. Wunsche, and J. Rehberg, “Mechanisms of fast self pulsations in two-section DFB lasers,” IEEE J. Quantum Electron. 32, 69–78 (1996).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

B. Sartorius, M. Mohrle, and U. Feiste, “12–64 GHz continuous frequency tuning in self-pulsating 1.55-μm multiquantum-well DFB lasers,” IEEE J. Sel. Top. Quantum Electron. 1, 535–538 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (5)

M. Mohrle, U. Feiste, J. Hoerer, R. Molt, and B. Sartorius, “Gigahertz self-pulsation in 1.55-μm wavelength multisection DFB lasers,” IEEE Photon. Technol. Lett. 14, 976–979 (1992).
[CrossRef]

P. E. Barnsley, H. J. Wickes, G. E. Wickens, and D. M. Spirit, “All-optical clock recovery from 5 Gb/s RZ data using a self-pulsating 1.56 μm laser diode,” IEEE Photon. Technol. Lett. 3, 942–945 (1991).
[CrossRef]

R.-P. Braun, G. Grosskopf, D. Rohde, and F. Schmidt, “Low-phase noise millimeter-wave generation at 64 GHz and data transmission using optical sideband injection locking,” IEEE Photon. Technol. Lett. 10, 728–730 (1998).
[CrossRef]

C. K. Sun, R. J. Orazi, S. A. Pappert, and W. K. Burns, “A photonic-link millimeter-wave mixer using cascaded optical modulators and harmonic carrier generation,” IEEE Photon. Technol. Lett. 8, 1166–1168 (1996).
[CrossRef]

E. A. Swanson and S. R. Chinn, “40-GHz pulse train generation using soliton compression of a Mach–Zehnder modulator output,” IEEE Photon. Technol. Lett. 7, 114–116 (1995).
[CrossRef]

Opt. Lett. (1)

Other (3)

M. Liu, Principles and Applications of Optical Communications (Irwin, Chicago, Ill., 1996), p. 640.

X. Wang, M. Al-Mumin, W. Mao, S. A. Pappert, J. Hong, and G. Li, “Optical generation of microwave/millimeter wave signals using two-section gain-coupled DFB lasers,” IEEE Photon. Technol. Lett. (to be published).

B. Sartorius, C. Bornholdt, O. Brox, H. J. Ehrke, D. Hoffmann, R. Ludwig, and M. Mohrle, “Bit rate flexible all-optical clock recovery,” in Digest of Optical Fiber Communication Conference (OFC) (Optical Society of America, Washington, D.C., 1999), pp. 24–26.

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Figures (12)

Fig. 1
Fig. 1

Schematic of the two-section DFB laser.

Fig. 2
Fig. 2

Turn-on transient of the output power at the left-hand facet for (a) an index-coupled laser (κ=100 cm-1), (b) a gain-coupled laser with a loss grating (κ=99.504+i9.9504cm-1), and (c) a gain-coupled laser with a gain grating DFB laser. Other parameters are given in Table 1. The same parameters are used for Figs. 37 below.

Fig. 3
Fig. 3

Spatiotemporal dynamics of the total power (on a logarithmic scale) inside the laser cavity. The power variation in the two sections is (a) out of phase for the index-coupled laser and (b) in phase for the gain-coupled laser.

Fig. 4
Fig. 4

Turn-on transient at z=-la (top) and the spatial distribution at t=2 ns (bottom) of the carrier number density for (a) the index-coupled and (b) the gain-coupled DFB lasers.

Fig. 5
Fig. 5

(a) Spectrum of the electric field of the laser output at the left-hand facet and the spatial distributions of the two modes for (b) the forward and (c) the backward waves for the index-coupled DFB laser.

Fig. 6
Fig. 6

(a) Spectrum of the electric field of the laser output at the left facet and the spatial distributions of the two modes for (b) the forward and (c) the backward waves for the gain-coupled DFB laser.

Fig. 7
Fig. 7

(a) Frequency-tuning characteristics and (b) modulation index of self-pulsation as functions of the detuning difference for both the index-coupled (filled triangles) and the gain-coupled (filled diamonds) lasers.

Fig. 8
Fig. 8

Reflectivity spectra of individual sections of (a) the two-section index and (b) the gain-coupled DFB lasers. Arrows indicate the modes that are responsible for the generation of the self-pulsation.

Fig. 9
Fig. 9

Schematic of the experimental setup: LD, laser diode; TE, thermal electric; EDFA, erbium-doped fiber amplifier; AMP’s, amplifiers; MZM, integrated Mach–Zehnder intensity modulator.

Fig. 10
Fig. 10

rf spectra of the continuously tunable self-pulsation signals from 24 to 61 GHz on the optical carrier.

Fig. 11
Fig. 11

Optical spectra corresponding to Fig. 10.

Fig. 12
Fig. 12

rf spectra of the self-pulsation signal at ∼22.3 GHz (a) with and (b) without optical feedback. Side peaks are due to unwanted optical feedback.

Tables (2)

Tables Icon

Table 1 Parameter Values for Simulation of Two-Section Index- and Complex-Coupled DFB Lasers

Tables Icon

Table 2 Parameter Values for the Reflectivity Spectra Shown in Fig. 8

Equations (12)

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

Fsz+1νsFst=12[Gs(Ns)+κgs fs-Γs]×Fs+iκsBs exp(-2iΔβsz),
Bsz-1νsBst=-12[Gs(Ns)+κgs fs-Γs]×Bs-iκsFs exp(2iΔβsz),
fs=Re2  FsBs*dz(FsFs*+BsBs*)dz,
Nst=IsqVs-Nsτs-[Gs(Ns)+κgsfs](|Fs|2+|Bs|2),
Fa(-la, t)exp(-jβala)=r1Ba(-la, t)exp(jβala),
Bb(lb, t)exp(-jβblb)=r2Fb(lb, t)exp(jβblb),
F(t, z)z+1νF(t, z)t=D(t, z).
F(t, z)t=F(t+Δt, z)-F(t, z)Δt
F(t, z)z=F(t, z+Δz)-F(t, z)Δz.
FtzΔt+FztΔz=F(t+Δt, z+Δz)-F(t, z).
1ΔzFzΔz+ΔzνFt=Fz+1νFt=1Δz[F(t+Δt, z+Δz)-F(t, z)].
F(t+Δt, z+Δz)-F(t, z)=ΔzD(t, z).

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