Abstract

We analyze the performance of distributed-feedback lasers with special grating structures. These grating structures consist of subgratings with different lengths (that are integer multiples of a reference length) and∕or different phase shifts (that are also integer multiples of a reference phase shift). These grating structures can provide transmission peaks with high quality factors, which may be useful for distributed-feedback lasers. To assess the usefulness of these devices, threshold and steady-state analysis are performed for a few selected examples. A given design example is shown to provide a low threshold without major variations in photon density along the device.

© 2007 Optical Society of America

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References

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  1. A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1997).
  2. H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
    [CrossRef]
  3. H. Ghafouri-Shiraz and B. Lo, "Structural dependence of three-phase-shift distributed feedback semiconductor laser diodes at threshold using the transfer matrix method (TMM)," Semicond. Sci. Technol. 8, 1126-1132 (1994).
    [CrossRef]
  4. S. Ogita, Y. Kotaki, M. Hatsuta, Y. Kuwara, and H. Ishikawa, "Long cavity multiple-phase shift distributed feedback laser diode for linewidth narrowing," J. Lightwave Technol. 8, 1596-1603 (1990).
    [CrossRef]
  5. J. E. A. Whiteaway, B. Garret, G. H. B. Thompson, A. J. Collar, C. J. Armstead, and M. J. Fice, "The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures," IEEE J. Quantum Electron. 28, 1272-1293 (1992).
    [CrossRef]
  6. H. T. Hattori, V. M. Schneider, and O. Lisboa, "Cantor set fiber Bragg grating," J. Opt. Soc. Am. A 17, 1583-1587 (2000).
    [CrossRef]
  7. C. L. Barbosa, R. M. Cazo, and H. T. Hattori, "Grating structures with symmetric fractionally organized gaps," Microwave Opt. Technol. Lett. 31, 223-229 (2001).
    [CrossRef]
  8. B. S. K. Lo and H. Ghafouri-Shiraz, "Spectral characteristics of distributed feedback laser diodes with distributed coupling coefficient," J. Lightwave Technol. 13, 200-212 (1995).
    [CrossRef]
  9. H. Ghafouri-Shiraz, Distributed Feedback Laser Diodes and Optical Tunable Filters (Wiley, 2003).
    [CrossRef]
  10. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
    [CrossRef]
  11. P. Correc, "Coupling efficiency for a trapezoidal grating," IEEE J. Quantum Electron. 24, 8-10 (1988).
    [CrossRef]
  12. L. D. Westbrook, "Measurement of dg/dN and dn/dN and their dependence on photon energy in λ = 1.5 μm InGaAsP laser diodes," IEE Proc.: Optoelectron. 133, 135-143 (1985).
  13. J. D. Faires and R. Burden, Numerical Methods (ITP, 1998).
  14. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

2001 (1)

C. L. Barbosa, R. M. Cazo, and H. T. Hattori, "Grating structures with symmetric fractionally organized gaps," Microwave Opt. Technol. Lett. 31, 223-229 (2001).
[CrossRef]

2000 (1)

1999 (1)

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

1995 (1)

B. S. K. Lo and H. Ghafouri-Shiraz, "Spectral characteristics of distributed feedback laser diodes with distributed coupling coefficient," J. Lightwave Technol. 13, 200-212 (1995).
[CrossRef]

1994 (1)

H. Ghafouri-Shiraz and B. Lo, "Structural dependence of three-phase-shift distributed feedback semiconductor laser diodes at threshold using the transfer matrix method (TMM)," Semicond. Sci. Technol. 8, 1126-1132 (1994).
[CrossRef]

1992 (1)

J. E. A. Whiteaway, B. Garret, G. H. B. Thompson, A. J. Collar, C. J. Armstead, and M. J. Fice, "The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures," IEEE J. Quantum Electron. 28, 1272-1293 (1992).
[CrossRef]

1990 (1)

S. Ogita, Y. Kotaki, M. Hatsuta, Y. Kuwara, and H. Ishikawa, "Long cavity multiple-phase shift distributed feedback laser diode for linewidth narrowing," J. Lightwave Technol. 8, 1596-1603 (1990).
[CrossRef]

1988 (1)

P. Correc, "Coupling efficiency for a trapezoidal grating," IEEE J. Quantum Electron. 24, 8-10 (1988).
[CrossRef]

1987 (1)

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

1985 (1)

L. D. Westbrook, "Measurement of dg/dN and dn/dN and their dependence on photon energy in λ = 1.5 μm InGaAsP laser diodes," IEE Proc.: Optoelectron. 133, 135-143 (1985).

Armstead, C. J.

J. E. A. Whiteaway, B. Garret, G. H. B. Thompson, A. J. Collar, C. J. Armstead, and M. J. Fice, "The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures," IEEE J. Quantum Electron. 28, 1272-1293 (1992).
[CrossRef]

Barbosa, C. L.

C. L. Barbosa, R. M. Cazo, and H. T. Hattori, "Grating structures with symmetric fractionally organized gaps," Microwave Opt. Technol. Lett. 31, 223-229 (2001).
[CrossRef]

Burden, R.

J. D. Faires and R. Burden, Numerical Methods (ITP, 1998).

Cazo, R. M.

C. L. Barbosa, R. M. Cazo, and H. T. Hattori, "Grating structures with symmetric fractionally organized gaps," Microwave Opt. Technol. Lett. 31, 223-229 (2001).
[CrossRef]

Coldren, L. A.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

Collar, A. J.

J. E. A. Whiteaway, B. Garret, G. H. B. Thompson, A. J. Collar, C. J. Armstead, and M. J. Fice, "The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures," IEEE J. Quantum Electron. 28, 1272-1293 (1992).
[CrossRef]

Correc, P.

P. Correc, "Coupling efficiency for a trapezoidal grating," IEEE J. Quantum Electron. 24, 8-10 (1988).
[CrossRef]

Corzine, S. W.

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

Faires, J. D.

J. D. Faires and R. Burden, Numerical Methods (ITP, 1998).

Fan, S.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Fice, M. J.

J. E. A. Whiteaway, B. Garret, G. H. B. Thompson, A. J. Collar, C. J. Armstead, and M. J. Fice, "The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures," IEEE J. Quantum Electron. 28, 1272-1293 (1992).
[CrossRef]

Garret, B.

J. E. A. Whiteaway, B. Garret, G. H. B. Thompson, A. J. Collar, C. J. Armstead, and M. J. Fice, "The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures," IEEE J. Quantum Electron. 28, 1272-1293 (1992).
[CrossRef]

Ghafouri-Shiraz, H.

B. S. K. Lo and H. Ghafouri-Shiraz, "Spectral characteristics of distributed feedback laser diodes with distributed coupling coefficient," J. Lightwave Technol. 13, 200-212 (1995).
[CrossRef]

H. Ghafouri-Shiraz and B. Lo, "Structural dependence of three-phase-shift distributed feedback semiconductor laser diodes at threshold using the transfer matrix method (TMM)," Semicond. Sci. Technol. 8, 1126-1132 (1994).
[CrossRef]

H. Ghafouri-Shiraz, Distributed Feedback Laser Diodes and Optical Tunable Filters (Wiley, 2003).
[CrossRef]

Hatsuta, M.

S. Ogita, Y. Kotaki, M. Hatsuta, Y. Kuwara, and H. Ishikawa, "Long cavity multiple-phase shift distributed feedback laser diode for linewidth narrowing," J. Lightwave Technol. 8, 1596-1603 (1990).
[CrossRef]

Hattori, H. T.

C. L. Barbosa, R. M. Cazo, and H. T. Hattori, "Grating structures with symmetric fractionally organized gaps," Microwave Opt. Technol. Lett. 31, 223-229 (2001).
[CrossRef]

H. T. Hattori, V. M. Schneider, and O. Lisboa, "Cantor set fiber Bragg grating," J. Opt. Soc. Am. A 17, 1583-1587 (2000).
[CrossRef]

Imai, H.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

Ishikawa, H.

S. Ogita, Y. Kotaki, M. Hatsuta, Y. Kuwara, and H. Ishikawa, "Long cavity multiple-phase shift distributed feedback laser diode for linewidth narrowing," J. Lightwave Technol. 8, 1596-1603 (1990).
[CrossRef]

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Johnson, S. G.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Kolodziejski, L. A.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Kotaki, Y.

S. Ogita, Y. Kotaki, M. Hatsuta, Y. Kuwara, and H. Ishikawa, "Long cavity multiple-phase shift distributed feedback laser diode for linewidth narrowing," J. Lightwave Technol. 8, 1596-1603 (1990).
[CrossRef]

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

Kuwara, Y.

S. Ogita, Y. Kotaki, M. Hatsuta, Y. Kuwara, and H. Ishikawa, "Long cavity multiple-phase shift distributed feedback laser diode for linewidth narrowing," J. Lightwave Technol. 8, 1596-1603 (1990).
[CrossRef]

Lisboa, O.

Lo, B.

H. Ghafouri-Shiraz and B. Lo, "Structural dependence of three-phase-shift distributed feedback semiconductor laser diodes at threshold using the transfer matrix method (TMM)," Semicond. Sci. Technol. 8, 1126-1132 (1994).
[CrossRef]

Lo, B. S. K.

B. S. K. Lo and H. Ghafouri-Shiraz, "Spectral characteristics of distributed feedback laser diodes with distributed coupling coefficient," J. Lightwave Technol. 13, 200-212 (1995).
[CrossRef]

Ogita, S.

S. Ogita, Y. Kotaki, M. Hatsuta, Y. Kuwara, and H. Ishikawa, "Long cavity multiple-phase shift distributed feedback laser diode for linewidth narrowing," J. Lightwave Technol. 8, 1596-1603 (1990).
[CrossRef]

Schneider, V. M.

Soda, H.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

Sudo, H.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

Thompson, G. H. B.

J. E. A. Whiteaway, B. Garret, G. H. B. Thompson, A. J. Collar, C. J. Armstead, and M. J. Fice, "The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures," IEEE J. Quantum Electron. 28, 1272-1293 (1992).
[CrossRef]

Villeneuve, P. R.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Westbrook, L. D.

L. D. Westbrook, "Measurement of dg/dN and dn/dN and their dependence on photon energy in λ = 1.5 μm InGaAsP laser diodes," IEE Proc.: Optoelectron. 133, 135-143 (1985).

Whiteaway, J. E. A.

J. E. A. Whiteaway, B. Garret, G. H. B. Thompson, A. J. Collar, C. J. Armstead, and M. J. Fice, "The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures," IEEE J. Quantum Electron. 28, 1272-1293 (1992).
[CrossRef]

Yamakoshi, S.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1997).

IEEE J. Quantum Electron. (3)

H. Soda, Y. Kotaki, H. Sudo, H. Ishikawa, S. Yamakoshi, and H. Imai, "Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers," IEEE J. Quantum Electron. 23, 804-814 (1987).
[CrossRef]

J. E. A. Whiteaway, B. Garret, G. H. B. Thompson, A. J. Collar, C. J. Armstead, and M. J. Fice, "The static and dynamic characteristics of single and multiple phase-shifted DFB laser structures," IEEE J. Quantum Electron. 28, 1272-1293 (1992).
[CrossRef]

P. Correc, "Coupling efficiency for a trapezoidal grating," IEEE J. Quantum Electron. 24, 8-10 (1988).
[CrossRef]

J. Lightwave Technol. (2)

B. S. K. Lo and H. Ghafouri-Shiraz, "Spectral characteristics of distributed feedback laser diodes with distributed coupling coefficient," J. Lightwave Technol. 13, 200-212 (1995).
[CrossRef]

S. Ogita, Y. Kotaki, M. Hatsuta, Y. Kuwara, and H. Ishikawa, "Long cavity multiple-phase shift distributed feedback laser diode for linewidth narrowing," J. Lightwave Technol. 8, 1596-1603 (1990).
[CrossRef]

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

Microwave Opt. Technol. Lett. (1)

C. L. Barbosa, R. M. Cazo, and H. T. Hattori, "Grating structures with symmetric fractionally organized gaps," Microwave Opt. Technol. Lett. 31, 223-229 (2001).
[CrossRef]

Optoelectron. (1)

L. D. Westbrook, "Measurement of dg/dN and dn/dN and their dependence on photon energy in λ = 1.5 μm InGaAsP laser diodes," IEE Proc.: Optoelectron. 133, 135-143 (1985).

Phys. Rev. B (1)

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999).
[CrossRef]

Semicond. Sci. Technol. (1)

H. Ghafouri-Shiraz and B. Lo, "Structural dependence of three-phase-shift distributed feedback semiconductor laser diodes at threshold using the transfer matrix method (TMM)," Semicond. Sci. Technol. 8, 1126-1132 (1994).
[CrossRef]

Other (4)

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1997).

H. Ghafouri-Shiraz, Distributed Feedback Laser Diodes and Optical Tunable Filters (Wiley, 2003).
[CrossRef]

J. D. Faires and R. Burden, Numerical Methods (ITP, 1998).

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

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Figures (6)

Fig. 1
Fig. 1

Schematic of a three phase-shifted distributed feedback laser.

Fig. 2
Fig. 2

Normalized threshold gain ( αnL at the threshold level) as a function of the wavelength displacement (λλB) . (a) Dashed curve is for a uniform grating, while the other curves are for θ1=θ2=θ3=π/2 . The dashed curve with circular markers is for L1=L2=L3=L4=2Lref , the solid curve with square markers is for L1=3L2=3L3=L4=3Lref , and the solid curve is for 3L1=L2=L3=3L4=3Lref . (b) In this case, θ1=θ2=θ3=2π/3 . The solid curve is for L1=L2=L3=L4=2Lref , the solid curve with square markers is for L1=3L2=3L3=L4=3Lref , and the dashed curve is for 3L1=L2=L3=3L4=3Lref , with Lref=L/8 .

Fig. 3
Fig. 3

Normalized threshold gain curves for (a) 2θ1=θ2=2θ3=2π/3 and (b) 3θ1=θ2=3θ3=3π/2 . The solid curves are for L1=L2=L3=L4=2Lref , while the dotted curves are for L1=3L2=3L3=L4=3Lref , with Lref=L/8 .

Fig. 4
Fig. 4

(a) Photon density and (b) carrier concentration for different DFB structures at I=40 mA . The curve without markers is for a uniform grating at λ=1550.5  nm , the curve with square markers is for θ1=θ2=θ3=2π/3 and L1=L2=L3=L4=2Lref at λ=1549.9  nm , and the curve with circular markers is for 2θ1=θ2=2θ3=2π/3 and L1=L2=L3=L4=2Lref at λ=1550.35  nm .

Fig. 5
Fig. 5

(a) Emitted power (right facet) as a function of the injection current. The curve without markers is for a uniform grating at λ=1550.5  nm , the curve with square markers is for θ1=θ2=θ3=2π/3 and L1=L2=L3=L4=2Lref at λ=1549.9  nm , and the curve with circular markers is for 2θ1=θ2=2θ3=2π/3 and L1=L2=L3=L4=2Lref at λ=1550.35  nm . (b) Spectral bandwidth (Δvsp) for the DFB structure with 2θ1=θ2=2θ3=2π/3 and L1=L2=L3=L4=2Lref as a function of the injected current.

Fig. 6
Fig. 6

Effects of the facet field reflectivity in a DFB structure with 2θ1=θ2=2θ3=2π/3 and L1=L2=L3=L4=2Lref . (a) Threshold current as a function of the facet field reflectivity and (b) emitted power at I=40  mA as a function of the facet field reflectivity.

Equations (21)

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

[Ei(zn+1)Er(zn+1)]=[r11nr21nr12nr22n][Ei(zn)Er(zn)],
r11n=(Gnρn2Gn1)exp[jβo(zn+1zn)]1ρn2,
r12n=ρn(GnGn1)exp(jΩn)exp[jβo(zn+1+zn)]1ρn2,
r21n=ρn(GnGn1)exp(jΩn)exp[jβo(zn+1+zn)]1ρn2,
r22n=(ρn2GnGn1)exp[jβo(zn+1zn)]1ρn2,
Gn=exp[γn(zn+1zn)],
ρn=jκcαnjδn+κc,
γn2=(αnjδn)2+κc2,
αn=Γgαloss2,
δn=2πneffλ2πngr(λλB)λλBπΛ.
g=Ao(NNt),
[Ei(zm+)Er(zm+)]=[exp(jθm)00exp(jθm)][Ei(zm)Er(zm)],
y22=0.
Ith=qVηi[NthτA+BNth2+CNth3],
ηiIqV=NτA+BN2+CN3+vgrgS1+εS,
S=2εon(z)ngrλhcco2[|Ei(z)|2+|Er(z)|2].
Pleft=t1wΓvgrhcλS(z=0),
Pright=t1wΓvgrhcλS(z=L),
Δvsp=Rsp4πPnum(1+αeff2),
Rsp=4Λ2nspvgrλ20Lgn|E2(z)|dz0Ln|E2(z)|2dz|y12y22/ω|2,
Pnum=t1wΓ0LS(z)dz,

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