Abstract

As Part III of this series, this paper focuses on an above-threshold modal analysis which includes gain saturation effects in the surface-emitting chirped circular grating lasers. We derive an exact energy relation which states that, in steady state, the net power generated in the gain medium is equal to the sum of peripheral leakage power and vertical emission power. This relation is particularly useful in checking the accuracy of numerical mode solving. Numerical simulations demonstrate the dependence of required pump level on the vertical emission power and compare the laser threshold and energy conversion efficiency under uniform, Gaussian, and annular pump profiles. A larger overlap between the pump profile and modal intensity distribution leads to a lower threshold and a higher energy conversion efficiency. Finally the dependence of required pump level on device sizes offers us new design guidelines of these lasers for single-mode, high-efficiency, high-power applications.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback semiconductor lasers: an analysis," J. Appl. Phys. 68, 1435-1444 (1990).
    [CrossRef]
  2. C. Wu, M. Svilans, M. Fallahi, T. Makino, J. Glinski, C. Maritan, and C. Blaauw, "Optical pumped surface-emitting DFB GaInAsP/InP lasers with circular grating," Electron. Lett. 27, 1819-1821 (1991).
    [CrossRef]
  3. A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G.-L. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96, 3043-3049 (2004).
    [CrossRef]
  4. G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
    [CrossRef]
  5. Y. Chen, Z. Li, Z. Zhang, D. Psaltis, and A. Scherer, "Nanoimprinted circular grating distributed feedback dye laser," Appl. Phys. Lett. 91, 051109 (2007).
    [CrossRef]
  6. J. Scheuer and A. Yariv, "Coupled-waves approach to the design and analysis of Bragg and photonic crystal annular resonators," IEEE J. Quantum Electron. 39, 1555-1562 (2003).
    [CrossRef]
  7. X. K. Sun and A. Yariv, "Surface-emitting circular DFB, disk-, and ring- Bragg resonator lasers with chirped gratings: a unified theory and comparative study," Opt. Express 16, 9155-9164 (2008).
    [CrossRef] [PubMed]
  8. X. K. Sun and A. Yariv, "Surface-emitting circular DFB, disk-, and ring- Bragg resonator lasers with chirped gratings. II: nonuniform pumping and far-field patterns," Opt. Express 17, 1-6 (2009).
    [CrossRef] [PubMed]
  9. H. A. Haus, "Gain saturation in distributed feedback lasers," Appl. Opt. 14, 2650-2652 (1975).
    [CrossRef] [PubMed]
  10. K. J. Kasunic and M. Fallahi, "Gain satuation in circular-grating distributed-feedback semiconductor lasers," J. Opt. Soc. Am. B 14, 2147-2152 (1997).
    [CrossRef]
  11. A. M. Shams-Zadeh-Amiri, X. Li, and W. P. Huang, "Above-threshold analysis of second-order circular-grating DFB lasers," IEEE J. Quantum Electron. 36, 259-267 (2000).
    [CrossRef]
  12. T. Kossek and P. Szczepanski, "Nonlinear operation of a planar circular-grating DBR laser," IEEE J. Quantum Electron. 37, 742-751 (2001).
    [CrossRef]
  13. X. K. Sun and A. Yariv, "Modal properties and modal control in vertically emitting annular Bragg lasers," Opt. Express 15, 17323-17333 (2007).
    [CrossRef] [PubMed]

2009 (1)

2008 (1)

2007 (2)

X. K. Sun and A. Yariv, "Modal properties and modal control in vertically emitting annular Bragg lasers," Opt. Express 15, 17323-17333 (2007).
[CrossRef] [PubMed]

Y. Chen, Z. Li, Z. Zhang, D. Psaltis, and A. Scherer, "Nanoimprinted circular grating distributed feedback dye laser," Appl. Phys. Lett. 91, 051109 (2007).
[CrossRef]

2005 (1)

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

2004 (1)

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G.-L. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96, 3043-3049 (2004).
[CrossRef]

2003 (1)

J. Scheuer and A. Yariv, "Coupled-waves approach to the design and analysis of Bragg and photonic crystal annular resonators," IEEE J. Quantum Electron. 39, 1555-1562 (2003).
[CrossRef]

2001 (1)

T. Kossek and P. Szczepanski, "Nonlinear operation of a planar circular-grating DBR laser," IEEE J. Quantum Electron. 37, 742-751 (2001).
[CrossRef]

2000 (1)

A. M. Shams-Zadeh-Amiri, X. Li, and W. P. Huang, "Above-threshold analysis of second-order circular-grating DFB lasers," IEEE J. Quantum Electron. 36, 259-267 (2000).
[CrossRef]

1997 (1)

1991 (1)

C. Wu, M. Svilans, M. Fallahi, T. Makino, J. Glinski, C. Maritan, and C. Blaauw, "Optical pumped surface-emitting DFB GaInAsP/InP lasers with circular grating," Electron. Lett. 27, 1819-1821 (1991).
[CrossRef]

1990 (1)

T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback semiconductor lasers: an analysis," J. Appl. Phys. 68, 1435-1444 (1990).
[CrossRef]

1975 (1)

Bachtold, W.

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G.-L. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96, 3043-3049 (2004).
[CrossRef]

Barlow, G. F.

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

Bauer, C.

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G.-L. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96, 3043-3049 (2004).
[CrossRef]

Blaauw, C.

C. Wu, M. Svilans, M. Fallahi, T. Makino, J. Glinski, C. Maritan, and C. Blaauw, "Optical pumped surface-emitting DFB GaInAsP/InP lasers with circular grating," Electron. Lett. 27, 1819-1821 (1991).
[CrossRef]

Bona, G.-L.

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G.-L. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96, 3043-3049 (2004).
[CrossRef]

Carleton, A.

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

Chen, Y.

Y. Chen, Z. Li, Z. Zhang, D. Psaltis, and A. Scherer, "Nanoimprinted circular grating distributed feedback dye laser," Appl. Phys. Lett. 91, 051109 (2007).
[CrossRef]

Erdogan, T.

T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback semiconductor lasers: an analysis," J. Appl. Phys. 68, 1435-1444 (1990).
[CrossRef]

Erni, D.

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G.-L. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96, 3043-3049 (2004).
[CrossRef]

Fallahi, M.

K. J. Kasunic and M. Fallahi, "Gain satuation in circular-grating distributed-feedback semiconductor lasers," J. Opt. Soc. Am. B 14, 2147-2152 (1997).
[CrossRef]

C. Wu, M. Svilans, M. Fallahi, T. Makino, J. Glinski, C. Maritan, and C. Blaauw, "Optical pumped surface-emitting DFB GaInAsP/InP lasers with circular grating," Electron. Lett. 27, 1819-1821 (1991).
[CrossRef]

Glinski, J.

C. Wu, M. Svilans, M. Fallahi, T. Makino, J. Glinski, C. Maritan, and C. Blaauw, "Optical pumped surface-emitting DFB GaInAsP/InP lasers with circular grating," Electron. Lett. 27, 1819-1821 (1991).
[CrossRef]

Hall, D. G.

T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback semiconductor lasers: an analysis," J. Appl. Phys. 68, 1435-1444 (1990).
[CrossRef]

Haus, H. A.

Huang, W. P.

A. M. Shams-Zadeh-Amiri, X. Li, and W. P. Huang, "Above-threshold analysis of second-order circular-grating DFB lasers," IEEE J. Quantum Electron. 36, 259-267 (2000).
[CrossRef]

Jebali, A.

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G.-L. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96, 3043-3049 (2004).
[CrossRef]

Kasunic, K. J.

Kossek, T.

T. Kossek and P. Szczepanski, "Nonlinear operation of a planar circular-grating DBR laser," IEEE J. Quantum Electron. 37, 742-751 (2001).
[CrossRef]

Krauss, T. F.

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

Li, X.

A. M. Shams-Zadeh-Amiri, X. Li, and W. P. Huang, "Above-threshold analysis of second-order circular-grating DFB lasers," IEEE J. Quantum Electron. 36, 259-267 (2000).
[CrossRef]

Li, Z.

Y. Chen, Z. Li, Z. Zhang, D. Psaltis, and A. Scherer, "Nanoimprinted circular grating distributed feedback dye laser," Appl. Phys. Lett. 91, 051109 (2007).
[CrossRef]

Mahrt, R. F.

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G.-L. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96, 3043-3049 (2004).
[CrossRef]

Makino, T.

C. Wu, M. Svilans, M. Fallahi, T. Makino, J. Glinski, C. Maritan, and C. Blaauw, "Optical pumped surface-emitting DFB GaInAsP/InP lasers with circular grating," Electron. Lett. 27, 1819-1821 (1991).
[CrossRef]

Maritan, C.

C. Wu, M. Svilans, M. Fallahi, T. Makino, J. Glinski, C. Maritan, and C. Blaauw, "Optical pumped surface-emitting DFB GaInAsP/InP lasers with circular grating," Electron. Lett. 27, 1819-1821 (1991).
[CrossRef]

Moll, N.

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G.-L. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96, 3043-3049 (2004).
[CrossRef]

Psaltis, D.

Y. Chen, Z. Li, Z. Zhang, D. Psaltis, and A. Scherer, "Nanoimprinted circular grating distributed feedback dye laser," Appl. Phys. Lett. 91, 051109 (2007).
[CrossRef]

Samuel, I. D. W.

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

Scherer, A.

Y. Chen, Z. Li, Z. Zhang, D. Psaltis, and A. Scherer, "Nanoimprinted circular grating distributed feedback dye laser," Appl. Phys. Lett. 91, 051109 (2007).
[CrossRef]

Scheuer, J.

J. Scheuer and A. Yariv, "Coupled-waves approach to the design and analysis of Bragg and photonic crystal annular resonators," IEEE J. Quantum Electron. 39, 1555-1562 (2003).
[CrossRef]

Shams-Zadeh-Amiri, A. M.

A. M. Shams-Zadeh-Amiri, X. Li, and W. P. Huang, "Above-threshold analysis of second-order circular-grating DFB lasers," IEEE J. Quantum Electron. 36, 259-267 (2000).
[CrossRef]

Shore, K. A.

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

Sun, X. K.

Svilans, M.

C. Wu, M. Svilans, M. Fallahi, T. Makino, J. Glinski, C. Maritan, and C. Blaauw, "Optical pumped surface-emitting DFB GaInAsP/InP lasers with circular grating," Electron. Lett. 27, 1819-1821 (1991).
[CrossRef]

Szczepanski, P.

T. Kossek and P. Szczepanski, "Nonlinear operation of a planar circular-grating DBR laser," IEEE J. Quantum Electron. 37, 742-751 (2001).
[CrossRef]

Tahraouhi, A.

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

Turnbull, G. A.

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

Wu, C.

C. Wu, M. Svilans, M. Fallahi, T. Makino, J. Glinski, C. Maritan, and C. Blaauw, "Optical pumped surface-emitting DFB GaInAsP/InP lasers with circular grating," Electron. Lett. 27, 1819-1821 (1991).
[CrossRef]

Yariv, A.

Zhang, Z.

Y. Chen, Z. Li, Z. Zhang, D. Psaltis, and A. Scherer, "Nanoimprinted circular grating distributed feedback dye laser," Appl. Phys. Lett. 91, 051109 (2007).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

G. A. Turnbull, A. Carleton, A. Tahraouhi, T. F. Krauss, I. D. W. Samuel, G. F. Barlow, and K. A. Shore, "Effect of gain localization in circular-grating distributed feedback lasers," Appl. Phys. Lett. 87, 201101 (2005).
[CrossRef]

Y. Chen, Z. Li, Z. Zhang, D. Psaltis, and A. Scherer, "Nanoimprinted circular grating distributed feedback dye laser," Appl. Phys. Lett. 91, 051109 (2007).
[CrossRef]

Electron. Lett. (1)

C. Wu, M. Svilans, M. Fallahi, T. Makino, J. Glinski, C. Maritan, and C. Blaauw, "Optical pumped surface-emitting DFB GaInAsP/InP lasers with circular grating," Electron. Lett. 27, 1819-1821 (1991).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. Scheuer and A. Yariv, "Coupled-waves approach to the design and analysis of Bragg and photonic crystal annular resonators," IEEE J. Quantum Electron. 39, 1555-1562 (2003).
[CrossRef]

A. M. Shams-Zadeh-Amiri, X. Li, and W. P. Huang, "Above-threshold analysis of second-order circular-grating DFB lasers," IEEE J. Quantum Electron. 36, 259-267 (2000).
[CrossRef]

T. Kossek and P. Szczepanski, "Nonlinear operation of a planar circular-grating DBR laser," IEEE J. Quantum Electron. 37, 742-751 (2001).
[CrossRef]

J. Appl. Phys. (2)

T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback semiconductor lasers: an analysis," J. Appl. Phys. 68, 1435-1444 (1990).
[CrossRef]

A. Jebali, R. F. Mahrt, N. Moll, D. Erni, C. Bauer, G.-L. Bona, and W. Bachtold, "Lasing in organic circular grating structures," J. Appl. Phys. 96, 3043-3049 (2004).
[CrossRef]

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

Opt. Express (3)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

Surface-emitting chirped circular grating lasers: (a) circular DFB laser; (b) disk Bragg resonator laser; (c) ring Bragg resonator laser. Laser emission is coupled out of the resonator plane in vertical direction via the gratings.

Fig. 2.
Fig. 2.

Pump level P pump of the 5 lowest order modes, under uniform pump profile, of (a) circular DFB, (b) disk-, and (c) ring- Bragg resonator lasers with surface emission power P em=0.01, 1, and 10 (in units of saturation power P sat).

Fig. 3.
Fig. 3.

Device-size-dependent pump level P pump and frequency detuning factor δ of the 3 lowest order modes, under uniform pump profile, of (a) circular DFB, (b) disk-, and (c) ring- Bragg resonator lasers. xb is the exterior boundary radius for all types of lasers. The inner disk radius x 0 of disk Bragg resonator laser is set to be xb /2. The inner and outer edges of the annular defect of ring Bragg resonator laser are set to be xL =xb /2-π and xR =xb /2+π. The modes are labeled in accord with those shown in Fig. 2. Dashed lines mark the values obtained at threshold and solid lines at P em=10.

Tables (1)

Tables Icon

Table 1. Threshold pump level Pth (in units of P0) and energy conversion efficiency ηex (in units of Psat/P0) of circular DFB, disk-, and ring- Bragg resonator lasers under different pump profiles

Equations (7)

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

dA(x)dx=u (x) A (x)vB(x)e2iδx,
dB(x)dx=u(x)B(x)+vA(x)e2iδx,
dA2dx=2 (gAh1r)A2vA*Be2iδxv*AB*e2iδx,
dB2dx = 2 ( gAh1r ) B2 + v A B* e2iδx + v* A* B e2iδx .
ddx (A2B2)=2gA(A2+B2)2h1rAeiδx+Beiδx2.
A(xb)2peripheralleakage +2h1rgratingAeiδx+Beiδx2dxverticallaseremission =20xbgA(A2+B2)dxpowergeneratedinthegainmedium,
I(x)=E(x)2=AHm(1)2+BHm(2)2+A*BHm(1)*Hm(2)+AB*Hm(1)Hm(2)*interferenceterms.

Metrics