Abstract

1550nm AlGaInAsInP long rectangle resonator lasers with three sides surrounded by SiO2 and p electrode layers are fabricated by planar technology, and room-temperature continuous-wave lasing is realized for a laser with a length of 53μm and a width of 2μm. Multiple peaks with wavelength intervals of Fabry–Pérot mode intervals and mode Q factors of about 400 and a lasing mode with a Q factor over 8000 are observed from the lasing spectrum at threshold current. The numerical results of the FDTD simulation indicate that the lasing mode may be a whispering-gallery mode, which is a coupled mode of two high-order transverse modes of the waveguide.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, and Z. C. Fan, “Directional emission InP/InGaAsP square-resonator microlasers,” Opt. Lett. 33, 2170-2172 (2008).
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2010 (1)

K. J. Che, Y. D. Yang, and Y. Z. Huang, “Multimode resonances of metallic-confined square-resonator microlasers,” Appl. Phys. Lett. 96, 051104 (2010).
[CrossRef]

2009 (3)

2008 (2)

D. V. Batrak, A. P. Bogatov, A. E. Drakin, and D. R. Miftakhutdinov, “Modes of a semiconductor rectangular microcavity,” Quantum Electron. 38, 16-22 (2008).
[CrossRef]

Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, and Z. C. Fan, “Directional emission InP/InGaAsP square-resonator microlasers,” Opt. Lett. 33, 2170-2172 (2008).
[CrossRef] [PubMed]

2007 (3)

Y. D. Yang and Y. Z. Huang, “Mode analysis and Q-factor enhancement due to mode coupling in rectangle resonators,” IEEE J. Quantum Electron. 43, 497-502 (2007).
[CrossRef]

Y. D. Yang, Y. Z. Huang, and Q. Chen, “Comparison of Q-factors between TE and TM modes in 3-D Microsquares by FDTD simulation,” IEEE Photonics Technol. Lett. 19, 1831-1833 (2007).
[CrossRef]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, 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]

2004 (1)

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

2003 (3)

H. J. Moon, K. An, and J. H. Lee, “Single spatial-mode selection in a layered square microcavity laser,” Appl. Phys. Lett. 82, 2963-2965 (2003).
[CrossRef]

K. J. Vahala, “Optical microcavities,” Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, “Modes in square resonators,” IEEE J. Quantum Electron. 39, 1563-1566 (2003).
[CrossRef]

2002 (2)

M. Lohmeyer, “Mode expansion modeling of rectangular integrated optical microresonators,” Opt. Quantum Electron. 34, 541-557 (2002).
[CrossRef]

M. Hammer, “Resonant coupling of dielectric optical waveguides via rectangular microcavities: the coupled guided mode perspective,” Opt. Commun. 214, 155-170 (2002).
[CrossRef]

2001 (1)

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation,” IEEE Microw. Wirel. Compon. Lett. 11, 223-225 (2001).
[CrossRef]

1999 (1)

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
[CrossRef]

1997 (1)

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery mode disk resonators,” J. Lightwave Technol. 15, 2154-2165 (1997).
[CrossRef]

1992 (1)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

1983 (1)

Alexander, R. W.

An, K.

H. J. Moon, K. An, and J. H. Lee, “Single spatial-mode selection in a layered square microcavity laser,” Appl. Phys. Lett. 82, 2963-2965 (2003).
[CrossRef]

Baba, T.

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
[CrossRef]

Batrak, D. V.

D. V. Batrak, A. P. Bogatov, A. E. Drakin, and D. R. Miftakhutdinov, “Modes of a semiconductor rectangular microcavity,” Quantum Electron. 38, 16-22 (2008).
[CrossRef]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Bogatov, A. P.

D. V. Batrak, A. P. Bogatov, A. E. Drakin, and D. R. Miftakhutdinov, “Modes of a semiconductor rectangular microcavity,” Quantum Electron. 38, 16-22 (2008).
[CrossRef]

Cao, H.

Q. Song, H. Cao, S. T. Ho, and G. S. Solomon, “Near-IR subwavelength microdisk lasers,” Appl. Phys. Lett. 94, 061109 (2009).
[CrossRef]

Che, K. J.

K. J. Che, Y. D. Yang, and Y. Z. Huang, “Multimode resonances of metallic-confined square-resonator microlasers,” Appl. Phys. Lett. 96, 051104 (2010).
[CrossRef]

Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, and Z. C. Fan, “Directional emission InP/InGaAsP square-resonator microlasers,” Opt. Lett. 33, 2170-2172 (2008).
[CrossRef] [PubMed]

Chen, Q.

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, 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]

Y. D. Yang, Y. Z. Huang, and Q. Chen, “Comparison of Q-factors between TE and TM modes in 3-D Microsquares by FDTD simulation,” IEEE Photonics Technol. Lett. 19, 1831-1833 (2007).
[CrossRef]

Drakin, A. E.

D. V. Batrak, A. P. Bogatov, A. E. Drakin, and D. R. Miftakhutdinov, “Modes of a semiconductor rectangular microcavity,” Quantum Electron. 38, 16-22 (2008).
[CrossRef]

Fan, Z. C.

Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, and Z. C. Fan, “Directional emission InP/InGaAsP square-resonator microlasers,” Opt. Lett. 33, 2170-2172 (2008).
[CrossRef] [PubMed]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, 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]

Fujita, M.

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
[CrossRef]

Geluk, E. J.

Guo, W. H.

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

W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, “Modes in square resonators,” IEEE J. Quantum Electron. 39, 1563-1566 (2003).
[CrossRef]

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation,” IEEE Microw. Wirel. Compon. Lett. 11, 223-225 (2001).
[CrossRef]

Hagness, S. C.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery mode disk resonators,” J. Lightwave Technol. 15, 2154-2165 (1997).
[CrossRef]

A. Taflove and S. C. Hagness, in Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

Hammer, M.

M. Hammer, “Resonant coupling of dielectric optical waveguides via rectangular microcavities: the coupled guided mode perspective,” Opt. Commun. 214, 155-170 (2002).
[CrossRef]

Hill, M. T.

Ho, S. T.

Q. Song, H. Cao, S. T. Ho, and G. S. Solomon, “Near-IR subwavelength microdisk lasers,” Appl. Phys. Lett. 94, 061109 (2009).
[CrossRef]

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery mode disk resonators,” J. Lightwave Technol. 15, 2154-2165 (1997).
[CrossRef]

Hu, Y. H.

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, 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]

Huang, Y. Z.

K. J. Che, Y. D. Yang, and Y. Z. Huang, “Multimode resonances of metallic-confined square-resonator microlasers,” Appl. Phys. Lett. 96, 051104 (2010).
[CrossRef]

Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, and Z. C. Fan, “Directional emission InP/InGaAsP square-resonator microlasers,” Opt. Lett. 33, 2170-2172 (2008).
[CrossRef] [PubMed]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, 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]

Y. D. Yang, Y. Z. Huang, and Q. Chen, “Comparison of Q-factors between TE and TM modes in 3-D Microsquares by FDTD simulation,” IEEE Photonics Technol. Lett. 19, 1831-1833 (2007).
[CrossRef]

Y. D. Yang and Y. Z. Huang, “Mode analysis and Q-factor enhancement due to mode coupling in rectangle resonators,” IEEE J. Quantum Electron. 43, 497-502 (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 resonator,” IEEE Photonics Technol. Lett. 16, 479-481 (2004).
[CrossRef]

W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, “Modes in square resonators,” IEEE J. Quantum Electron. 39, 1563-1566 (2003).
[CrossRef]

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation,” IEEE Microw. Wirel. Compon. Lett. 11, 223-225 (2001).
[CrossRef]

Karouta, F.

Lee, J. H.

H. J. Moon, K. An, and J. H. Lee, “Single spatial-mode selection in a layered square microcavity laser,” Appl. Phys. Lett. 82, 2963-2965 (2003).
[CrossRef]

Leong, E. S. P.

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Li, W. J.

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation,” IEEE Microw. Wirel. Compon. Lett. 11, 223-225 (2001).
[CrossRef]

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Lohmeyer, M.

M. Lohmeyer, “Mode expansion modeling of rectangular integrated optical microresonators,” Opt. Quantum Electron. 34, 541-557 (2002).
[CrossRef]

Long, L. L.

Lu, Q. Y.

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

W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, “Modes in square resonators,” IEEE J. Quantum Electron. 39, 1563-1566 (2003).
[CrossRef]

Marell, M.

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Miftakhutdinov, D. R.

D. V. Batrak, A. P. Bogatov, A. E. Drakin, and D. R. Miftakhutdinov, “Modes of a semiconductor rectangular microcavity,” Quantum Electron. 38, 16-22 (2008).
[CrossRef]

Moon, H. J.

H. J. Moon, K. An, and J. H. Lee, “Single spatial-mode selection in a layered square microcavity laser,” Appl. Phys. Lett. 82, 2963-2965 (2003).
[CrossRef]

Ning, C. Z.

Nötzel, R.

Oei, Y. S.

Ordal, M. A.

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Rafizadeh, D.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery mode disk resonators,” J. Lightwave Technol. 15, 2154-2165 (1997).
[CrossRef]

Sakai, A.

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
[CrossRef]

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Smalbrugge, B.

Smit, M. K.

Solomon, G. S.

Q. Song, H. Cao, S. T. Ho, and G. S. Solomon, “Near-IR subwavelength microdisk lasers,” Appl. Phys. Lett. 94, 061109 (2009).
[CrossRef]

Song, Q.

Q. Song, H. Cao, S. T. Ho, and G. S. Solomon, “Near-IR subwavelength microdisk lasers,” Appl. Phys. Lett. 94, 061109 (2009).
[CrossRef]

Sun, M. H.

Sun, X. W.

Taflove, A.

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery mode disk resonators,” J. Lightwave Technol. 15, 2154-2165 (1997).
[CrossRef]

A. Taflove and S. C. Hagness, in Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

Veldhoven, P. J.

Wang, J.

Wang, S. J.

Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, and Z. C. Fan, “Directional emission InP/InGaAsP square-resonator microlasers,” Opt. Lett. 33, 2170-2172 (2008).
[CrossRef] [PubMed]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, 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]

Ward, C. A.

Xu, J.

Yang, Y.

Yang, Y. D.

K. J. Che, Y. D. Yang, and Y. Z. Huang, “Multimode resonances of metallic-confined square-resonator microlasers,” Appl. Phys. Lett. 96, 051104 (2010).
[CrossRef]

Y. Z. Huang, K. J. Che, Y. D. Yang, S. J. Wang, and Z. C. Fan, “Directional emission InP/InGaAsP square-resonator microlasers,” Opt. Lett. 33, 2170-2172 (2008).
[CrossRef] [PubMed]

Y. D. Yang, Y. Z. Huang, and Q. Chen, “Comparison of Q-factors between TE and TM modes in 3-D Microsquares by FDTD simulation,” IEEE Photonics Technol. Lett. 19, 1831-1833 (2007).
[CrossRef]

Y. D. Yang and Y. Z. Huang, “Mode analysis and Q-factor enhancement due to mode coupling in rectangle resonators,” IEEE J. Quantum Electron. 43, 497-502 (2007).
[CrossRef]

Yu, L. J.

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

W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, “Modes in square resonators,” IEEE J. Quantum Electron. 39, 1563-1566 (2003).
[CrossRef]

Zhang, C. F.

Zhang, F.

Zhu, Y. C.

Appl. Opt. (1)

Appl. Phys. Lett. (4)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Q. Song, H. Cao, S. T. Ho, and G. S. Solomon, “Near-IR subwavelength microdisk lasers,” Appl. Phys. Lett. 94, 061109 (2009).
[CrossRef]

H. J. Moon, K. An, and J. H. Lee, “Single spatial-mode selection in a layered square microcavity laser,” Appl. Phys. Lett. 82, 2963-2965 (2003).
[CrossRef]

K. J. Che, Y. D. Yang, and Y. Z. Huang, “Multimode resonances of metallic-confined square-resonator microlasers,” Appl. Phys. Lett. 96, 051104 (2010).
[CrossRef]

IEEE J. Quantum Electron. (2)

W. H. Guo, Y. Z. Huang, Q. Y. Lu, and L. J. Yu, “Modes in square resonators,” IEEE J. Quantum Electron. 39, 1563-1566 (2003).
[CrossRef]

Y. D. Yang and Y. Z. Huang, “Mode analysis and Q-factor enhancement due to mode coupling in rectangle resonators,” IEEE J. Quantum Electron. 43, 497-502 (2007).
[CrossRef]

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

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673-681 (1999).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett. (1)

W. H. Guo, W. J. Li, and Y. Z. Huang, “Computation of resonant frequencies and quality factors of cavities by FDTD technique and Padé approximation,” IEEE Microw. Wirel. Compon. Lett. 11, 223-225 (2001).
[CrossRef]

IEEE Photonics Technol. Lett. (3)

Y. D. Yang, Y. Z. Huang, and Q. Chen, “Comparison of Q-factors between TE and TM modes in 3-D Microsquares by FDTD simulation,” IEEE Photonics Technol. Lett. 19, 1831-1833 (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 resonator,” IEEE Photonics Technol. Lett. 16, 479-481 (2004).
[CrossRef]

Y. Z. Huang, Y. H. Hu, Q. Chen, S. J. Wang, 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]

J. Lightwave Technol. (1)

S. C. Hagness, D. Rafizadeh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery mode disk resonators,” J. Lightwave Technol. 15, 2154-2165 (1997).
[CrossRef]

Nature (1)

K. J. Vahala, “Optical microcavities,” Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. Hammer, “Resonant coupling of dielectric optical waveguides via rectangular microcavities: the coupled guided mode perspective,” Opt. Commun. 214, 155-170 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

M. Lohmeyer, “Mode expansion modeling of rectangular integrated optical microresonators,” Opt. Quantum Electron. 34, 541-557 (2002).
[CrossRef]

Quantum Electron. (1)

D. V. Batrak, A. P. Bogatov, A. E. Drakin, and D. R. Miftakhutdinov, “Modes of a semiconductor rectangular microcavity,” Quantum Electron. 38, 16-22 (2008).
[CrossRef]

Other (1)

A. Taflove and S. C. Hagness, in Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

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Figures (8)

Fig. 1
Fig. 1

Scanning electron microscope images of (a) a rectangle resonator after the ICP etching process and (b) a rectangle resonator after top Ti–Pt–Au p contact is formed. (c) Schematic of the long rectangle resonator lasers encapsulated by p electrode metal.

Fig. 2
Fig. 2

Output power coupled to a multimode optical fiber (solid curve) and applied voltage (dashed curve) versus injection current for a rectangular waveguide laser with length of 53 μ m and width of 2 μ m at room temperature.

Fig. 3
Fig. 3

Laser spectra of a rectangle resonator laser with length of 53 μ m and width of 2 μ m at injection current of 25 mA at room temperature. The inset shows the lasing mode at current of 17 mA .

Fig. 4
Fig. 4

Mode interval (circle) and mode Q factors (solid square) of multiple peaks from 1480 to 1530 nm are plotted as functions of mode wavelengths. The solid line is the mode interval of Fabry–Pérot resonator with a group index of n g = 3.0715 + 0.366 E .

Fig. 5
Fig. 5

Detail spectra of a lasing mode at injection currents of 20, 25, 30, and 35 mA , respectively.

Fig. 6
Fig. 6

Intensity spectra of q = 0 (dashed curve) and q = 4 (solid curve) modes for a rectangle resonator with width of 2 μ m , and lengths of (a) 10 μ m and (b) 53 μ m obtained by FDTD simulation.

Fig. 7
Fig. 7

Field pattern of magnetic field component H z for (a) q = 0 mode at 1509.7 nm ; q = 4 modes at (b) 1501.2 nm and (c) 1523.7 nm in the region of 3.5 μ m × 2 μ m near the output facet for the 53 μ m × 2 μ m rectangle resonator by FDTD simulation. The solid curves indicate positions of the p electrode metal, Si O 2 , and the resonator.

Fig. 8
Fig. 8

Fourier transform (FT) of cavity-mode field patterns in Figs. 7a, 7b, 7c plotted in (a), (b), and (c), respectively.

Tables (1)

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Table 1 Mode Wavelengths and Q Factors for Fundamental and Fourth-order Transverse Modes in Long Rectangle Resonator with Length of 53 μ m and Width of 2 μ m Obtained by FDTD Simulation

Equations (8)

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F p ( x ) = { cos ( κ x x φ x ) | x | L 2 cos ( κ x L 2 φ x ) exp [ γ x ( x L 2 ) ] x > L 2 cos ( κ x L 2 φ x ) exp [ γ x ( x + L 2 ) ] x < L 2 } ,
κ x 2 + κ y 2 = N 2 k 0 2 ,
κ v 2 + γ v 2 = ( N 2 1 ) k 0 2 , v = x , y ,
κ x tan ( κ x L 2 φ x ) = N 2 γ x ,
κ y tan ( κ y a 2 φ y ) = N 2 γ y .
{ k x L = ( p + 1 ) π k y a = ( q + 1 ) π } .
λ = 2 π N ( ( q + 1 ) π a ) 2 + ( ( p + 1 ) π L ) 2 .
Δ λ λ 3 4 π N 2 L ( 2 N π λ ) 2 ( ( q + 1 ) π a ) 2 .

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