Abstract

We propose a new method for transverse-mode control in vertical-cavity surface-emitting lasers based on the idea of a Bragg waveguide. This method involves patterning concentric annuli into the top Bragg reflector of a vertical-cavity surface-emitting laser, inducing a cylindrical Bragg waveguide across the laser cavity. We use the effective-index approximation to evaluate the waveguiding effect of patterning the top Bragg reflector. A waveguide model has been developed to design the ideal Bragg waveguide for a specified HE11 mode. The model also calculates the field and power distributions and the optical confinement for the given mode.

© 1999 Optical Society of America

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References

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  1. K. Tai, J. D. Wynn, Y. H. Wang, and A. Y. Cho, “Selfaligned fibre pigtailed surface emitting lasers on Si submounts,” Electron. Lett. 27, 2030–2032 (1991).
    [CrossRef]
  2. Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold vertical cavity surface emitting lasers with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).
    [CrossRef]
  3. C. Jung, R. Jager, M. Grabherr, P. Schnitzer, R. Michalzik, B. Weigl, S. Muller, and K. J. Ebeling, “4.8 mW singlemode oxide confined top-surface emitting vertical-cavity laser diodes,” Electron. Lett. 33, 1790–1791 (1997).
    [CrossRef]
  4. Y. A. Wu, C. J. Chang-Hasnain, and R. Nabiev, “Single- mode emission from a passive-antiguide-region vertical-cavity surface emitting laser,” Electron. Lett. 29, 1861–1863 (1993).
    [CrossRef]
  5. P. Yeh and A. Yariv, “Theory of Bragg fiber,” J. Opt. Soc. Am. 68, 1196–1201 (1978).
    [CrossRef]
  6. M. J. Adams and M. J. Fisher, “Optically resonant structure,” European patent application 95, 306, 917.6 (September 29, 1995).
  7. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), Chap. 5.
  8. G. R. Hadley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett. 20, 1483–1485 (1995).
    [CrossRef] [PubMed]
  9. E. R. Hegblom, I. Dubravko, B. J. Thibeault, and L. A. Coldren, “Scattering losses from dielectric apertures in vertical cavity lasers,” IEEE J. Quantum Electron. 3, 379–389 (1997).
    [CrossRef]
  10. T. E. Sale, Vertical Cavity Surface Emitting Lasers (Wiley, New York, 1995), Chap. 2.
  11. M. J. Adams, An Introduction to Optical Waveguides (Wiley-Interscience, New York, 1981), Chap. 7.
  12. N. J. Doran and K. J. Blow, “Cylindrical Bragg fibers: a design and feasibility study for optical communications,” J. Lightwave Technol. LT-1, 108–110 (1983).
  13. W. Nakwaski, “Thermal aspects of efficient operation of vertical cavity surface emitting lasers,” Opt. Quantum Electron. 28, 335–352 (1996).
    [CrossRef]
  14. J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Design of index guided vertical cavity lasers for low temperature-sensitivity, sub-milliamp thresholds, and single-mode operation,” IEEE J. Quantum Electron. 29, 1295–1307 (1993).
    [CrossRef]

1997 (2)

C. Jung, R. Jager, M. Grabherr, P. Schnitzer, R. Michalzik, B. Weigl, S. Muller, and K. J. Ebeling, “4.8 mW singlemode oxide confined top-surface emitting vertical-cavity laser diodes,” Electron. Lett. 33, 1790–1791 (1997).
[CrossRef]

E. R. Hegblom, I. Dubravko, B. J. Thibeault, and L. A. Coldren, “Scattering losses from dielectric apertures in vertical cavity lasers,” IEEE J. Quantum Electron. 3, 379–389 (1997).
[CrossRef]

1996 (1)

W. Nakwaski, “Thermal aspects of efficient operation of vertical cavity surface emitting lasers,” Opt. Quantum Electron. 28, 335–352 (1996).
[CrossRef]

1995 (2)

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold vertical cavity surface emitting lasers with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).
[CrossRef]

G. R. Hadley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett. 20, 1483–1485 (1995).
[CrossRef] [PubMed]

1993 (2)

Y. A. Wu, C. J. Chang-Hasnain, and R. Nabiev, “Single- mode emission from a passive-antiguide-region vertical-cavity surface emitting laser,” Electron. Lett. 29, 1861–1863 (1993).
[CrossRef]

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Design of index guided vertical cavity lasers for low temperature-sensitivity, sub-milliamp thresholds, and single-mode operation,” IEEE J. Quantum Electron. 29, 1295–1307 (1993).
[CrossRef]

1991 (1)

K. Tai, J. D. Wynn, Y. H. Wang, and A. Y. Cho, “Selfaligned fibre pigtailed surface emitting lasers on Si submounts,” Electron. Lett. 27, 2030–2032 (1991).
[CrossRef]

1983 (1)

N. J. Doran and K. J. Blow, “Cylindrical Bragg fibers: a design and feasibility study for optical communications,” J. Lightwave Technol. LT-1, 108–110 (1983).

1978 (1)

Blow, K. J.

N. J. Doran and K. J. Blow, “Cylindrical Bragg fibers: a design and feasibility study for optical communications,” J. Lightwave Technol. LT-1, 108–110 (1983).

Chang-Hasnain, C. J.

Y. A. Wu, C. J. Chang-Hasnain, and R. Nabiev, “Single- mode emission from a passive-antiguide-region vertical-cavity surface emitting laser,” Electron. Lett. 29, 1861–1863 (1993).
[CrossRef]

Cho, A. Y.

K. Tai, J. D. Wynn, Y. H. Wang, and A. Y. Cho, “Selfaligned fibre pigtailed surface emitting lasers on Si submounts,” Electron. Lett. 27, 2030–2032 (1991).
[CrossRef]

Coldren, L. A.

E. R. Hegblom, I. Dubravko, B. J. Thibeault, and L. A. Coldren, “Scattering losses from dielectric apertures in vertical cavity lasers,” IEEE J. Quantum Electron. 3, 379–389 (1997).
[CrossRef]

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Design of index guided vertical cavity lasers for low temperature-sensitivity, sub-milliamp thresholds, and single-mode operation,” IEEE J. Quantum Electron. 29, 1295–1307 (1993).
[CrossRef]

Corzine, S. W.

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Design of index guided vertical cavity lasers for low temperature-sensitivity, sub-milliamp thresholds, and single-mode operation,” IEEE J. Quantum Electron. 29, 1295–1307 (1993).
[CrossRef]

Doran, N. J.

N. J. Doran and K. J. Blow, “Cylindrical Bragg fibers: a design and feasibility study for optical communications,” J. Lightwave Technol. LT-1, 108–110 (1983).

Dubravko, I.

E. R. Hegblom, I. Dubravko, B. J. Thibeault, and L. A. Coldren, “Scattering losses from dielectric apertures in vertical cavity lasers,” IEEE J. Quantum Electron. 3, 379–389 (1997).
[CrossRef]

Ebeling, K. J.

C. Jung, R. Jager, M. Grabherr, P. Schnitzer, R. Michalzik, B. Weigl, S. Muller, and K. J. Ebeling, “4.8 mW singlemode oxide confined top-surface emitting vertical-cavity laser diodes,” Electron. Lett. 33, 1790–1791 (1997).
[CrossRef]

Geels, R. S.

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Design of index guided vertical cavity lasers for low temperature-sensitivity, sub-milliamp thresholds, and single-mode operation,” IEEE J. Quantum Electron. 29, 1295–1307 (1993).
[CrossRef]

Grabherr, M.

C. Jung, R. Jager, M. Grabherr, P. Schnitzer, R. Michalzik, B. Weigl, S. Muller, and K. J. Ebeling, “4.8 mW singlemode oxide confined top-surface emitting vertical-cavity laser diodes,” Electron. Lett. 33, 1790–1791 (1997).
[CrossRef]

Hadley, G. R.

Hatori, N.

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold vertical cavity surface emitting lasers with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).
[CrossRef]

Hayashi, Y.

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold vertical cavity surface emitting lasers with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).
[CrossRef]

Hegblom, E. R.

E. R. Hegblom, I. Dubravko, B. J. Thibeault, and L. A. Coldren, “Scattering losses from dielectric apertures in vertical cavity lasers,” IEEE J. Quantum Electron. 3, 379–389 (1997).
[CrossRef]

Iga, K.

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold vertical cavity surface emitting lasers with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).
[CrossRef]

Jager, R.

C. Jung, R. Jager, M. Grabherr, P. Schnitzer, R. Michalzik, B. Weigl, S. Muller, and K. J. Ebeling, “4.8 mW singlemode oxide confined top-surface emitting vertical-cavity laser diodes,” Electron. Lett. 33, 1790–1791 (1997).
[CrossRef]

Jung, C.

C. Jung, R. Jager, M. Grabherr, P. Schnitzer, R. Michalzik, B. Weigl, S. Muller, and K. J. Ebeling, “4.8 mW singlemode oxide confined top-surface emitting vertical-cavity laser diodes,” Electron. Lett. 33, 1790–1791 (1997).
[CrossRef]

Koyama, F.

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold vertical cavity surface emitting lasers with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).
[CrossRef]

Matsutani, A.

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold vertical cavity surface emitting lasers with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).
[CrossRef]

Michalzik, R.

C. Jung, R. Jager, M. Grabherr, P. Schnitzer, R. Michalzik, B. Weigl, S. Muller, and K. J. Ebeling, “4.8 mW singlemode oxide confined top-surface emitting vertical-cavity laser diodes,” Electron. Lett. 33, 1790–1791 (1997).
[CrossRef]

Mukaihara, T.

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold vertical cavity surface emitting lasers with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).
[CrossRef]

Muller, S.

C. Jung, R. Jager, M. Grabherr, P. Schnitzer, R. Michalzik, B. Weigl, S. Muller, and K. J. Ebeling, “4.8 mW singlemode oxide confined top-surface emitting vertical-cavity laser diodes,” Electron. Lett. 33, 1790–1791 (1997).
[CrossRef]

Nabiev, R.

Y. A. Wu, C. J. Chang-Hasnain, and R. Nabiev, “Single- mode emission from a passive-antiguide-region vertical-cavity surface emitting laser,” Electron. Lett. 29, 1861–1863 (1993).
[CrossRef]

Nakwaski, W.

W. Nakwaski, “Thermal aspects of efficient operation of vertical cavity surface emitting lasers,” Opt. Quantum Electron. 28, 335–352 (1996).
[CrossRef]

Ohnoki, N.

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold vertical cavity surface emitting lasers with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).
[CrossRef]

Schnitzer, P.

C. Jung, R. Jager, M. Grabherr, P. Schnitzer, R. Michalzik, B. Weigl, S. Muller, and K. J. Ebeling, “4.8 mW singlemode oxide confined top-surface emitting vertical-cavity laser diodes,” Electron. Lett. 33, 1790–1791 (1997).
[CrossRef]

Scott, J. W.

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Design of index guided vertical cavity lasers for low temperature-sensitivity, sub-milliamp thresholds, and single-mode operation,” IEEE J. Quantum Electron. 29, 1295–1307 (1993).
[CrossRef]

Tai, K.

K. Tai, J. D. Wynn, Y. H. Wang, and A. Y. Cho, “Selfaligned fibre pigtailed surface emitting lasers on Si submounts,” Electron. Lett. 27, 2030–2032 (1991).
[CrossRef]

Thibeault, B. J.

E. R. Hegblom, I. Dubravko, B. J. Thibeault, and L. A. Coldren, “Scattering losses from dielectric apertures in vertical cavity lasers,” IEEE J. Quantum Electron. 3, 379–389 (1997).
[CrossRef]

Wang, Y. H.

K. Tai, J. D. Wynn, Y. H. Wang, and A. Y. Cho, “Selfaligned fibre pigtailed surface emitting lasers on Si submounts,” Electron. Lett. 27, 2030–2032 (1991).
[CrossRef]

Weigl, B.

C. Jung, R. Jager, M. Grabherr, P. Schnitzer, R. Michalzik, B. Weigl, S. Muller, and K. J. Ebeling, “4.8 mW singlemode oxide confined top-surface emitting vertical-cavity laser diodes,” Electron. Lett. 33, 1790–1791 (1997).
[CrossRef]

Wu, Y. A.

Y. A. Wu, C. J. Chang-Hasnain, and R. Nabiev, “Single- mode emission from a passive-antiguide-region vertical-cavity surface emitting laser,” Electron. Lett. 29, 1861–1863 (1993).
[CrossRef]

Wynn, J. D.

K. Tai, J. D. Wynn, Y. H. Wang, and A. Y. Cho, “Selfaligned fibre pigtailed surface emitting lasers on Si submounts,” Electron. Lett. 27, 2030–2032 (1991).
[CrossRef]

Yariv, A.

Yeh, P.

Electron. Lett. (4)

K. Tai, J. D. Wynn, Y. H. Wang, and A. Y. Cho, “Selfaligned fibre pigtailed surface emitting lasers on Si submounts,” Electron. Lett. 27, 2030–2032 (1991).
[CrossRef]

Y. Hayashi, T. Mukaihara, N. Hatori, N. Ohnoki, A. Matsutani, F. Koyama, and K. Iga, “Record low threshold vertical cavity surface emitting lasers with native oxide confinement structure,” Electron. Lett. 31, 560–561 (1995).
[CrossRef]

C. Jung, R. Jager, M. Grabherr, P. Schnitzer, R. Michalzik, B. Weigl, S. Muller, and K. J. Ebeling, “4.8 mW singlemode oxide confined top-surface emitting vertical-cavity laser diodes,” Electron. Lett. 33, 1790–1791 (1997).
[CrossRef]

Y. A. Wu, C. J. Chang-Hasnain, and R. Nabiev, “Single- mode emission from a passive-antiguide-region vertical-cavity surface emitting laser,” Electron. Lett. 29, 1861–1863 (1993).
[CrossRef]

IEEE J. Quantum Electron. (2)

E. R. Hegblom, I. Dubravko, B. J. Thibeault, and L. A. Coldren, “Scattering losses from dielectric apertures in vertical cavity lasers,” IEEE J. Quantum Electron. 3, 379–389 (1997).
[CrossRef]

J. W. Scott, R. S. Geels, S. W. Corzine, and L. A. Coldren, “Design of index guided vertical cavity lasers for low temperature-sensitivity, sub-milliamp thresholds, and single-mode operation,” IEEE J. Quantum Electron. 29, 1295–1307 (1993).
[CrossRef]

J. Lightwave Technol. (1)

N. J. Doran and K. J. Blow, “Cylindrical Bragg fibers: a design and feasibility study for optical communications,” J. Lightwave Technol. LT-1, 108–110 (1983).

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

W. Nakwaski, “Thermal aspects of efficient operation of vertical cavity surface emitting lasers,” Opt. Quantum Electron. 28, 335–352 (1996).
[CrossRef]

Other (4)

T. E. Sale, Vertical Cavity Surface Emitting Lasers (Wiley, New York, 1995), Chap. 2.

M. J. Adams, An Introduction to Optical Waveguides (Wiley-Interscience, New York, 1981), Chap. 7.

M. J. Adams and M. J. Fisher, “Optically resonant structure,” European patent application 95, 306, 917.6 (September 29, 1995).

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), Chap. 5.

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of a bottom-emitting VCSEL with a patterned phase-matching layer. QW, quantum well.

Fig. 2
Fig. 2

Schematic diagrams of the concentric annuli and the resultant changes in refractive index for (a) a type I and (b) a type II Bragg waveguide. The shaded annuli correspond to high-index material.

Fig. 3
Fig. 3

Structure of a bottom-emitting 975-nm VCSEL. 1 Å = 0.1 nm.

Fig. 4
Fig. 4

Resultant change in index as a function of etch depth for the 975-nm bottom-emitting VCSEL structure in Fig. 3.

Fig. 5
Fig. 5

Minimum annulus width as a function of Δn for two type I 975-nm BW’s with core radii of 20 µm (filled circles) and 40 µm (filled triangles).

Fig. 6
Fig. 6

Radial variation of H (solid curve) for the HE11 mode for a type I Bragg waveguide. n1=3.496, n2=3.5, and an effective refractive index of 3.4956 give a core radius of 7.06 µm. The index profile is also shown (dashed line).

Fig. 7
Fig. 7

Radial variation of H (solid curve) for the HE11 mode for a type II Bragg waveguide. n1=3.5, n2=3.496, and an effective refractive index of 3.4956 give a core radius of 3.39 µm. The index profile is also shown (dashed line).

Fig. 8
Fig. 8

Optical confinement factor as a function of core radius for (a) type I and (b) type II BW’s.

Tables (1)

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Table 1 Refractive Indices of the Materials as Used in the Modela

Equations (8)

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

Δn=ncav(Δλ/λ).
[t2+kt2]Ez(r,θ)Hz(r,θ)=0,
ki=(k2ni2-β2)1/2,
H=H(k1 r)r<ρCJ0(k2r)+DY0(k2r)r>ρ,
H(k1ρ)=CJ0(k2ρ)+DY0(k2ρ),
H(k1ρ)=(k2/k1)[CJ0(k2ρ)+DY0(k2ρ)].
ρ0=ηλ2πn12-neff2.
aiλ4ni2-neff2.

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