Abstract

We applied the Fox-Li resonator theory to analyze the mode stability of concave mirror surface-emitting lasers. The numerical modeling incorporates the oxide aperture in the simple classical cavity by adding a non-uniform phase shifting layer to the flat mirror side. The calculation shows that there is a modal loss difference between the fundamental mode and the competing modes. The amount of loss difference depends upon cavity length and the thickness of the oxide aperture. In addition to loss difference, modal gain difference plays a key role in discriminating between the fundamental mode and the higher order transverse modes. The modal gain difference heavily depends upon the size of the oxide aperture and the field intensity distribution. To summarize, the geometry of the concave cavity affects the mode profile and the unique field profile of each transverse mode makes a difference in both modal loss and gain. Finally, this leads to a side-mode suppression.

© 2005 Optical Society of America

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References

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Appl. Phys. Lett.

Si-Hyun Park, Jaehoon Kim, Heonsu Jeon, Tan Sakong, Sung-Nam Lee, Suhee Chae, Y. Park, Chang-Hyun Jeong and Geun-Young Yeom, and Yong-Hoon Cho, �??Room-temperature GaN vertical-cavity surface-emitting laser operation in an extended cavity scheme,�?? Appl. Phys. Lett., 83, 2121-2121 (2003)
[CrossRef]

IEEE J. of Quantum Electron.

A. G. Fox and T. Li, �??Computation of optical resonator modes by the method of resonance excitation,�?? IEEE J. of Quantum Electron. QE-4, 460-465 (1968)
[CrossRef]

Y. G. Ju, J. H. Ser, and Y. H. Lee, "Analysis of metal-interlaced-grating vertical-cavity surface-emitting lasers using the modal method by modal expansion," IEEE J. of Quantum Electron. 33, 589-595 (1997)
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

S. A. Riyopoulos, D. Dialetis, J. Liu, and B. Riely, "Generic Representation of Active Cavity VCSEL Eigenmodes by Optimized Waist Gauss-Laguerre Modes,�?? IEEE J. Sel. Top. Quantum Electron. 7, 312-27 (2001)
[CrossRef]

IEEE Photon. Technol. Lett.

H. Martinsson, J. A. Vukusic, and A. Larsson, �??Single-mode power dependence on surface relief size for mode-stabilized oxide-confined vertical-cavity surface-emitting lasers,�?? IEEE Photon. Technol. Lett. 12, 1129-1131 (2000).
[CrossRef]

E. W. Young, K. D. Choquette, S. L. Chuan, K. M. Geib, A. J. Fischer, and A. A. Allerman, �??Single-transverse-mode vertical-cavity lasers under continuous and pulsed operation,�?? IEEE Photon. Technol. Lett. 13, 927-929 (2001)
[CrossRef]

J. of Appl. Phys.

S. H. Park, Y. Park, and H. Jeon, �??Theory of the mode stabilization mechanism in concave-micromirror-capped vertical-cavity surface-emitting lasers,�?? J. of Appl. Phys. 94, 1312-1317 (2003)
[CrossRef]

Jpn. J. Appl. Phys.

K. S. Kim, Y. H. Lee, B. Y. Jung and C. K. Hwangbo, �??Single mode operation of a curved-mirror vertical-emitting laser with an active distributed Bragg reflector,�?? Jpn. J. Appl. Phys. 41, L827-L829 (2002)
[CrossRef]

Opt. Express

Proc. SPIE

P. Brick, S. Lutgen, T. Albrecht, J. Luft, W. Spath, �??High-efficiency high-power semiconductor disc laser,�?? Proc. SPIE 4993, 50-56 (2003)
[CrossRef]

E. M. Strzelecka, J. G. McInerney, A. Mooradian, A. Lewis, A. V. Shchegrov, D. Lee, Wats, �??High-power high-brightness 980-nm lasers based on the extended cavity surface emitting lasers concept,�?? Proc. SPIE 4993, 57-67 (2003)
[CrossRef]

Other

A. E. Siegman, Laser, (Oxford University Press, 1986), Chap. 14

S. Corzine, Ph.D. dissertation, University of California at Santa Barbara, ch. 4. (1993)

E. R. Hegblom, �??Engineering oxide apertures in vertical cavity lasers,�?? Ph.D dissertation, University of California at Santa Barbara, ch. 4. (1999).

A. Mooradian, �??Coupled cavity high power semiconductor laser,�?? United States patent 6778582, (2004)

L.A. Coldren, S.P. DenBaars, O. Buchinsky, T. Margalith, D.A. Cohen, A.C. Abare, and M. Hansen, �??Blue and Green InGaN VCSEL Technology,�?? Final Report 1997-98 for MICRO Project 97-033 (1997) , <a href="http://www.ucop.edu/research/micro/97_98/97_033.pdf">http://www.ucop.edu/research/micro/97_98/97_033.pdf</a>

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Figures (8)

Fig. 1.
Fig. 1.

A schematic diagram of a concave mirror vertical-cavity with an oxide aperture.

Fig. 2.
Fig. 2.

Normalized field intensity of a mode obtained using the parameters in Table 1. Azimuthal mode number l=0. Phase shift=26°.

Fig. 3.
Fig. 3.

Power loss per iteration of the mode from Fig. 2.

Fig. 4.
Fig. 4.

Power loss as a function of cavity length., No oxide aperture is present

Fig. 5.
Fig. 5.

Power loss as a function of cavity length. The thickness of the oxide aperture is 0.03 µm.

Fig. 6.
Fig. 6.

Power loss as a function of cavity length. Thickness of the oxide aperture is 0.06 µm.

Fig. 7.
Fig. 7.

Confinement factor v.s. cavity length.

Fig. 8.
Fig. 8.

Transverse mode profiles used in Fig. 7. Radius of oxide aperture(rox)=6 µm, rox/mirror radius(a)=0.3

Tables (1)

Tables Icon

Table 1. The parameter values used in the modeling

Equations (3)

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W l ( n + 1 ) ( r ) = 0 a K l ( r , s ) W l ( n ) ( s ) sds
where { W l ( n ) : Radial field distribution function K l ( r , s ) : Kernal
E ( r , φ ) = W l ( r ) e jl φ

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