Abstract

Semiconductor laser devices based on triangular resonators can provide cheap, compact, and high performance optical sources for optical communications, computing, defense, and biological applications. I modify the original structure by introducing three trenches and analyze their effects on the electro magnetic modes propagating in the triangular cavity. I also analyze the coupling of light into single- mode waveguides. These analyses are conducted by using two-dimensional finite difference time-domain methods. Results show that the introduction of such trenches can considerably reduce the quality factors of most of the modes, but one mode is not significantly degraded, providing nearly single-mode operation. The effects of radiation losses are further investigated by introducing a photonic crystal shielding around the triangular structure. Finally I solve the rate equations to obtain the steady-state response for these structures.

© 2008 Optical Society of America

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References

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  1. O. Painter, R. K. Lee, A. Scherrer, A. Yariv, J. D. O'Brien, and P. D. Dapkus, “Two-dimensional photonic bandgap defect mode laser,” Science 284, 1819-1821 (1999).
    [CrossRef] [PubMed]
  2. H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353-1365 (2002).
    [CrossRef]
  3. D. S. Song, S. H. Kim, H. G. Park, C. K. Kim, and Y. H. Lee, “Single-fundamental-mode photonic crystal surface-emitting lasers,” Appl. Phys. Lett. 80, 3901-3903 (2002).
    [CrossRef]
  4. H. T. Hattori, V. M. Schneider, R. M. Cazo, and C. L. Barbosa, “Analysis of strategies to improve the directionality of square lattice band-edge photonic crystal structures,” Appl. Opt. 44, 3069-3076 (2005).
    [CrossRef] [PubMed]
  5. R. M. Cazo, C. L. Barbosa, H. T. Hattori, and V. M. Schneider, “Steady-state analysis of a directional square lattice band-edge photonic crystal laser,” Microw. Opt. Technol. Lett. 46, 210-214 (2005).
    [CrossRef]
  6. H. T. Hattori, I. McKerracher, H. H. Tan, C. Jagadish, and R. M. De La Rue, “In-plane coupling of light from InP-based photonic crystal band-edge lasers into single-mode waveguides,” IEEE J. Quantum Electron. 43, 279-286 (2007).
    [CrossRef]
  7. C. Seassal, C. Monat, J. Mouette, E. Touraille, B. Ben Bhakir, H. T. Hattori, J. L. Leclercq, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “InP bonded membrane photonics components and circuits: toward 2.5 dimensional micro-nano-photonics,” IEEE J. Sel. Top. Quantum Electron. 11, 395-407 (2005).
    [CrossRef]
  8. T. Baba, “Photonic crystals and microdisk cavities based on GaInAsP/InP system,” IEEE J. Sel. Top. Quantum Electron. 3, 808-830 (1997).
    [CrossRef]
  9. M. Fujita, A. Sakai, and T. Baba, “Ultra-small and ultra-low threshold microdisk injection laser--design, fabrication, lasing characteristics and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
    [CrossRef]
  10. A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62, 561-563 (1993).
    [CrossRef]
  11. S. J. Choi, K. Djordjev, and P. D. Dapkus, “Microdisk lasers vertically coupled to output waveguides,” IEEE Photonics Technol. Lett. 15, 1330-1332 (2003).
    [CrossRef]
  12. S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors in 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175-1182(2006).
    [CrossRef]
  13. H. T. Hattori, C. Seassal, E. Touraille, P. Rojo-Romeo, X. Letartre, G. Hollinger, P. Viktorovitch, L. DiCioccio, M. Zussy, L. El Melhaoui, and J. M. Fedeli, “Heterogeneous integration of microdisk lasers on silicon strip waveguides for optical interconnects,” IEEE Photonics Technol. Lett. 18, 223-225(2006).
    [CrossRef]
  14. S. Ando, N. Kobayashi, and H. Ando, “Triangular-facet laser with optical waveguides grown by selective area metalorganic chemical vapor deposition,” Jpn. J. Appl. Phys. 35, L411-L413(1996).
    [CrossRef]
  15. S. Ando, N. Kobayashi, and H. Ando, “Triangular-facet lasers coupled by a rectangular optical waveguide,” Jpn. J. Appl. Phys. 36, L76-L78 (1997).
    [CrossRef]
  16. Y. Z. Huang, W. H. Guo, and Q. M. Wang, “Analysis and numerical simulation of eigenmode characteristics for semiconductor lasers with an equilateral triangle micro-resonator,” IEEE J. Quantum Electron. 37, 100-107 (2001).
    [CrossRef]
  17. Y. Z. Huang, W. H. Guo, L. J. Yu, and H. B. Lei, “Analysis of semiconductor microlasers with an equilateral triangle resonator by rate equations,” IEEE J. Quantum Electron. 37, 1259-1264 (2001).
    [CrossRef]
  18. Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, “Room-temperature continuous-wave electrically injected InP-GaInAsP equilateral-triangle-resonator lasers,” IEEE Photonics Technol. Lett. 19, 963-965 (2007).
    [CrossRef]
  19. W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, “Mode quality factor based on far-field emission for square resonators,” IEEE Photonics Technol. Lett. 16, 479-481 (2004).
    [CrossRef]
  20. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Spectral shift and Q-change of circular and square-shaped optical micro-cavity modes due to periodic sidewall surface roughness,” J. Opt. Soc. Am. B 21, 1792-1796 (2004).
    [CrossRef]
  21. Fullwave 4.0 RSOFT design group, 1999, http://www.rsoftdesign.com
  22. H. Altug and J. Vuckovic, “Photonic crystal nanocavity array laser,” Opt. Express 13, 8819-8828 (2005)
    [CrossRef] [PubMed]
  23. L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, 1995).

2007 (2)

H. T. Hattori, I. McKerracher, H. H. Tan, C. Jagadish, and R. M. De La Rue, “In-plane coupling of light from InP-based photonic crystal band-edge lasers into single-mode waveguides,” IEEE J. Quantum Electron. 43, 279-286 (2007).
[CrossRef]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, “Room-temperature continuous-wave electrically injected InP-GaInAsP equilateral-triangle-resonator lasers,” IEEE Photonics Technol. Lett. 19, 963-965 (2007).
[CrossRef]

2006 (2)

S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors in 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175-1182(2006).
[CrossRef]

H. T. Hattori, C. Seassal, E. Touraille, P. Rojo-Romeo, X. Letartre, G. Hollinger, P. Viktorovitch, L. DiCioccio, M. Zussy, L. El Melhaoui, and J. M. Fedeli, “Heterogeneous integration of microdisk lasers on silicon strip waveguides for optical interconnects,” IEEE Photonics Technol. Lett. 18, 223-225(2006).
[CrossRef]

2005 (4)

C. Seassal, C. Monat, J. Mouette, E. Touraille, B. Ben Bhakir, H. T. Hattori, J. L. Leclercq, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “InP bonded membrane photonics components and circuits: toward 2.5 dimensional micro-nano-photonics,” IEEE J. Sel. Top. Quantum Electron. 11, 395-407 (2005).
[CrossRef]

H. T. Hattori, V. M. Schneider, R. M. Cazo, and C. L. Barbosa, “Analysis of strategies to improve the directionality of square lattice band-edge photonic crystal structures,” Appl. Opt. 44, 3069-3076 (2005).
[CrossRef] [PubMed]

R. M. Cazo, C. L. Barbosa, H. T. Hattori, and V. M. Schneider, “Steady-state analysis of a directional square lattice band-edge photonic crystal laser,” Microw. Opt. Technol. Lett. 46, 210-214 (2005).
[CrossRef]

H. Altug and J. Vuckovic, “Photonic crystal nanocavity array laser,” Opt. Express 13, 8819-8828 (2005)
[CrossRef] [PubMed]

2004 (2)

W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, “Mode quality factor based on far-field emission for square resonators,” IEEE Photonics Technol. Lett. 16, 479-481 (2004).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Spectral shift and Q-change of circular and square-shaped optical micro-cavity modes due to periodic sidewall surface roughness,” J. Opt. Soc. Am. B 21, 1792-1796 (2004).
[CrossRef]

2003 (1)

S. J. Choi, K. Djordjev, and P. D. Dapkus, “Microdisk lasers vertically coupled to output waveguides,” IEEE Photonics Technol. Lett. 15, 1330-1332 (2003).
[CrossRef]

2002 (2)

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353-1365 (2002).
[CrossRef]

D. S. Song, S. H. Kim, H. G. Park, C. K. Kim, and Y. H. Lee, “Single-fundamental-mode photonic crystal surface-emitting lasers,” Appl. Phys. Lett. 80, 3901-3903 (2002).
[CrossRef]

2001 (2)

Y. Z. Huang, W. H. Guo, and Q. M. Wang, “Analysis and numerical simulation of eigenmode characteristics for semiconductor lasers with an equilateral triangle micro-resonator,” IEEE J. Quantum Electron. 37, 100-107 (2001).
[CrossRef]

Y. Z. Huang, W. H. Guo, L. J. Yu, and H. B. Lei, “Analysis of semiconductor microlasers with an equilateral triangle resonator by rate equations,” IEEE J. Quantum Electron. 37, 1259-1264 (2001).
[CrossRef]

1999 (2)

O. Painter, R. K. Lee, A. Scherrer, A. Yariv, J. D. O'Brien, and P. D. Dapkus, “Two-dimensional photonic bandgap defect mode laser,” Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

M. Fujita, A. Sakai, and T. Baba, “Ultra-small and ultra-low threshold microdisk injection laser--design, fabrication, lasing characteristics and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
[CrossRef]

1997 (2)

T. Baba, “Photonic crystals and microdisk cavities based on GaInAsP/InP system,” IEEE J. Sel. Top. Quantum Electron. 3, 808-830 (1997).
[CrossRef]

S. Ando, N. Kobayashi, and H. Ando, “Triangular-facet lasers coupled by a rectangular optical waveguide,” Jpn. J. Appl. Phys. 36, L76-L78 (1997).
[CrossRef]

1996 (1)

S. Ando, N. Kobayashi, and H. Ando, “Triangular-facet laser with optical waveguides grown by selective area metalorganic chemical vapor deposition,” Jpn. J. Appl. Phys. 35, L411-L413(1996).
[CrossRef]

1993 (1)

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62, 561-563 (1993).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. F. J. Levi, R. E. Slusher, S. L. McCall, J. L. Glass, S. J. Pearton, and R. A. Logan, “Directional light coupling from microdisk lasers,” Appl. Phys. Lett. 62, 561-563 (1993).
[CrossRef]

D. S. Song, S. H. Kim, H. G. Park, C. K. Kim, and Y. H. Lee, “Single-fundamental-mode photonic crystal surface-emitting lasers,” Appl. Phys. Lett. 80, 3901-3903 (2002).
[CrossRef]

IEEE J. Quantum Electron. (4)

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y. H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353-1365 (2002).
[CrossRef]

H. T. Hattori, I. McKerracher, H. H. Tan, C. Jagadish, and R. M. De La Rue, “In-plane coupling of light from InP-based photonic crystal band-edge lasers into single-mode waveguides,” IEEE J. Quantum Electron. 43, 279-286 (2007).
[CrossRef]

Y. Z. Huang, W. H. Guo, and Q. M. Wang, “Analysis and numerical simulation of eigenmode characteristics for semiconductor lasers with an equilateral triangle micro-resonator,” IEEE J. Quantum Electron. 37, 100-107 (2001).
[CrossRef]

Y. Z. Huang, W. H. Guo, L. J. Yu, and H. B. Lei, “Analysis of semiconductor microlasers with an equilateral triangle resonator by rate equations,” IEEE J. Quantum Electron. 37, 1259-1264 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (4)

S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors in 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175-1182(2006).
[CrossRef]

C. Seassal, C. Monat, J. Mouette, E. Touraille, B. Ben Bhakir, H. T. Hattori, J. L. Leclercq, X. Letartre, P. Rojo-Romeo, and P. Viktorovitch, “InP bonded membrane photonics components and circuits: toward 2.5 dimensional micro-nano-photonics,” IEEE J. Sel. Top. Quantum Electron. 11, 395-407 (2005).
[CrossRef]

T. Baba, “Photonic crystals and microdisk cavities based on GaInAsP/InP system,” IEEE J. Sel. Top. Quantum Electron. 3, 808-830 (1997).
[CrossRef]

M. Fujita, A. Sakai, and T. Baba, “Ultra-small and ultra-low threshold microdisk injection laser--design, fabrication, lasing characteristics and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
[CrossRef]

IEEE Photonics Technol. Lett. (4)

H. T. Hattori, C. Seassal, E. Touraille, P. Rojo-Romeo, X. Letartre, G. Hollinger, P. Viktorovitch, L. DiCioccio, M. Zussy, L. El Melhaoui, and J. M. Fedeli, “Heterogeneous integration of microdisk lasers on silicon strip waveguides for optical interconnects,” IEEE Photonics Technol. Lett. 18, 223-225(2006).
[CrossRef]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, Y. Du, and Z. C. Fan, “Room-temperature continuous-wave electrically injected InP-GaInAsP equilateral-triangle-resonator lasers,” IEEE Photonics Technol. Lett. 19, 963-965 (2007).
[CrossRef]

W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, “Mode quality factor based on far-field emission for square resonators,” IEEE Photonics Technol. Lett. 16, 479-481 (2004).
[CrossRef]

S. J. Choi, K. Djordjev, and P. D. Dapkus, “Microdisk lasers vertically coupled to output waveguides,” IEEE Photonics Technol. Lett. 15, 1330-1332 (2003).
[CrossRef]

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

Jpn. J. Appl. Phys. (2)

S. Ando, N. Kobayashi, and H. Ando, “Triangular-facet laser with optical waveguides grown by selective area metalorganic chemical vapor deposition,” Jpn. J. Appl. Phys. 35, L411-L413(1996).
[CrossRef]

S. Ando, N. Kobayashi, and H. Ando, “Triangular-facet lasers coupled by a rectangular optical waveguide,” Jpn. J. Appl. Phys. 36, L76-L78 (1997).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

R. M. Cazo, C. L. Barbosa, H. T. Hattori, and V. M. Schneider, “Steady-state analysis of a directional square lattice band-edge photonic crystal laser,” Microw. Opt. Technol. Lett. 46, 210-214 (2005).
[CrossRef]

Opt. Express (1)

Science (1)

O. Painter, R. K. Lee, A. Scherrer, A. Yariv, J. D. O'Brien, and P. D. Dapkus, “Two-dimensional photonic bandgap defect mode laser,” Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Other (2)

Fullwave 4.0 RSOFT design group, 1999, http://www.rsoftdesign.com

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

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Figures (10)

Fig. 1
Fig. 1

Schematic of the basic equilateral triangular microlaser.

Fig. 2
Fig. 2

Basic ETR. (a) Magnetic field spectrum ( H y ) at the center of the waveguide. (b) Magnetic field ( H y ) at λ = 1042.8 nm . (c) Magnetic field ( H y ) distribution at λ = 1091.1 nm .

Fig. 3
Fig. 3

Top view of the ETR with three trenches.

Fig. 4
Fig. 4

ETR with three trenches with W 2 = 1.0 μm and L 2 = 1.5 μm . (a) Magnetic field spectrum ( H y ) at the center of the waveguide. (b) Magnetic field ( H y ) at λ = 1088.7 nm .

Fig. 5
Fig. 5

(a) Quality factor as a function of W 2 for L 2 = 1.5 μm . (b) Quality factor as a function of L 2 for W 2 = 1.0 .

Fig. 6
Fig. 6

Top view of the PhC ETR.

Fig. 7
Fig. 7

ETR with a PhC shielding L 2 = 1.5 μm . (a) Magnetic field spectrum ( H y ) at the center of the waveguide. (b) Magnetic field distribution ( H y ) at λ = 1057.1 nm .

Fig. 8
Fig. 8

Top view of the ETR with a PhC shielding and three PhC trenches.

Fig. 9
Fig. 9

ETR with a PhC shielding and three PhC trenches L 2 = 1.5 μm . (a) Magnetic field spectrum ( H y ) at the center of the waveguide. (b) Magnetic field distribution ( H y ) at λ = 1052.6 nm .

Fig. 10
Fig. 10

Steady-state response for the ETR with three trenches and W 2 = 1.0 μm and L 2 = 1.5 μm without the PhC shielding. The solid curve is for λ p = 800 nm and the solid curve with square markers is for λ p = 670 nm .

Tables (1)

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Table 1 Typical Laser Parameters

Equations (10)

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λ p , m = 3 n eff L 1 ( p 3 θ / π ) 2 + 3 ( m + 1 ) 2 ,
θ = π + 2 tan 1 [ 3 β p / ( 2 γ o ) ] .
3 β p L 1 + 6 θ = 2 ,
3 κ m L 1 = 2 ( m + 1 ) π ,
γ o = β p 2 / 4 + 3 κ m 2 ( 2 π λ ) 2 .
d N d t = η P in λ p h c o V a ( A N + B N 2 + C N 3 ) Γ G ( N ) S ,
d S d t = Γ G ( N ) S + β B N 2 S τ p ,
τ p = Q λ l 2 π c o ,
G ( N ) = v g G o ln ( N N t r ) ,
P out = η a h c o λ l S V mode τ mirror ,

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