Abstract

We propose a novel method for extracting light beams from diamond-shaped total-internal reflection modes in two-dimensional microcavity laser diodes by the use of intracavity air gaps. By fabricating such a laser diode, we experimentally demonstrate that the direction and longitudinal mode spacing of the output beams are in good accordance with theoretical calculations.

© 2007 Optical Society of America

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  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]
  2. A. F. J. Levi, R. E. Slusher, S. L. McCall, S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
    [CrossRef]
  3. R. K. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).
    [CrossRef]
  4. T. J. Kippenberg, J. Kalkman, A. Polman, and K. J. Vahala, "Demonstration of an erbium-doped microdisk laser on a silicon chip," Phys. Rev. A 74, 051802-1-051802-4 (2006).
    [CrossRef]
  5. K. Srinivasan, M. Borselli, O. Painter, A. Stintz, and S. Krishna, "Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots," Opt. Express 14, 1094-1105 (2006).
    [CrossRef] [PubMed]
  6. S. J. Choi, K. Djordjev, S. J. Choi, and P. D. Dapkus, "Microdisk lasers vertically coupled to output waveguides," IEEE Photon. Technol. Lett. 15, 1330-1332 (2003).
    [CrossRef]
  7. J. V. Campenhout, P. Rojo-Romeo, P. Regreny, C. Seassal, D. V. Thourhout, S. Verstuyft, L. D. Cioccio, J.-M. Fedeli, C. Lagahe, and R. Baets, "Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on -insulator waveguide circuit," Opt. Express 15, 6744-6749 (2007).
    [CrossRef] [PubMed]
  8. J. U. Nöckel and A. D. Stone, "Ray and wave chaos in asymmetric resonant optical cavities," Nature 385, 45-47 (1997).
    [CrossRef]
  9. C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, "High-power directional emission from microlasers with chaotic resonators," Science 280, 1556-1564 (1998).
    [CrossRef] [PubMed]
  10. V. M. Apalkov and M. E. Raikh, "Directional emission from a microdisk resonator with a linear defect," Phys. Rev. B 70, 195317-1-195317-6 (2004).
    [CrossRef]
  11. J. Wiersig and M. Hentschel, "Unidirectional light emission from high-Q modes in optical microcavities," Phys. Rev. A 73, 031802-1-031802-4 (2006).
    [CrossRef]
  12. T. Fukushima and T. Harayama, "Stadium and quasi-stadium laser diodes," IEEE Sel. Top. Quantum Electron. 10, 1039-1051 (2004).
    [CrossRef]
  13. T. Fukushima, T. Harayama, T. Miyasaka, and P. O. Vaccaro, "Morphological dependence of lasing modes in two-dimensional quasi-stadium laser diodes," J. Opt. Soc. Am. B 21, 935-943 (2004).
    [CrossRef]
  14. H. E. Türeci, H. G. L. Schwefel, A. D. Stone, and E. E. Narimanov, "Gaussian-optical approach to stable periodic orbit resonances of partially chaotic dielectric micro-cavities," Opt. Express 10, 752-776 (2002).
    [PubMed]
  15. H. C. CaseyJr. and M. B. Panish, Heterostructure Lasers (Academic Press, New York, NY, 1978).

2007 (1)

2006 (1)

2004 (2)

2003 (1)

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

2002 (1)

1998 (1)

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, "High-power directional emission from microlasers with chaotic resonators," Science 280, 1556-1564 (1998).
[CrossRef] [PubMed]

1997 (1)

J. U. Nöckel and A. D. Stone, "Ray and wave chaos in asymmetric resonant optical cavities," Nature 385, 45-47 (1997).
[CrossRef]

1993 (1)

A. F. J. Levi, R. E. Slusher, S. L. McCall, S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
[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]

Baets, R.

Borselli, M.

Campenhout, J. V.

Capasso, F.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, "High-power directional emission from microlasers with chaotic resonators," Science 280, 1556-1564 (1998).
[CrossRef] [PubMed]

Cho, A. Y.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, "High-power directional emission from microlasers with chaotic resonators," Science 280, 1556-1564 (1998).
[CrossRef] [PubMed]

Choi, S. J.

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

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

Cioccio, L. D.

Dapkus, P. D.

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

Djordjev, K.

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

Faist, J.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, "High-power directional emission from microlasers with chaotic resonators," Science 280, 1556-1564 (1998).
[CrossRef] [PubMed]

Fedeli, J.-M.

Fukushima, T.

Gmachl, C.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, "High-power directional emission from microlasers with chaotic resonators," Science 280, 1556-1564 (1998).
[CrossRef] [PubMed]

Harayama, T.

Hobson, W. S.

A. F. J. Levi, R. E. Slusher, S. L. McCall, S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
[CrossRef]

Krishna, S.

Lagahe, C.

Levi, A. F. J.

A. F. J. Levi, R. E. Slusher, S. L. McCall, S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
[CrossRef]

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]

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]

McCall, S. L.

A. F. J. Levi, R. E. Slusher, S. L. McCall, S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
[CrossRef]

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]

Miyasaka, T.

Narimanov, E. E.

H. E. Türeci, H. G. L. Schwefel, A. D. Stone, and E. E. Narimanov, "Gaussian-optical approach to stable periodic orbit resonances of partially chaotic dielectric micro-cavities," Opt. Express 10, 752-776 (2002).
[PubMed]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, "High-power directional emission from microlasers with chaotic resonators," Science 280, 1556-1564 (1998).
[CrossRef] [PubMed]

Nöckel, J. U.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, "High-power directional emission from microlasers with chaotic resonators," Science 280, 1556-1564 (1998).
[CrossRef] [PubMed]

J. U. Nöckel and A. D. Stone, "Ray and wave chaos in asymmetric resonant optical cavities," Nature 385, 45-47 (1997).
[CrossRef]

Painter, O.

Pearton, S. J.

A. F. J. Levi, R. E. Slusher, S. L. McCall, S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
[CrossRef]

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]

Regreny, P.

Rojo-Romeo, P.

Schwefel, H. G. L.

Seassal, C.

Sivco, D. L.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, "High-power directional emission from microlasers with chaotic resonators," Science 280, 1556-1564 (1998).
[CrossRef] [PubMed]

Slusher, R. E.

A. F. J. Levi, R. E. Slusher, S. L. McCall, S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
[CrossRef]

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]

Srinivasan, K.

Stintz, A.

Stone, A. D.

H. E. Türeci, H. G. L. Schwefel, A. D. Stone, and E. E. Narimanov, "Gaussian-optical approach to stable periodic orbit resonances of partially chaotic dielectric micro-cavities," Opt. Express 10, 752-776 (2002).
[PubMed]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, "High-power directional emission from microlasers with chaotic resonators," Science 280, 1556-1564 (1998).
[CrossRef] [PubMed]

J. U. Nöckel and A. D. Stone, "Ray and wave chaos in asymmetric resonant optical cavities," Nature 385, 45-47 (1997).
[CrossRef]

Thourhout, D. V.

Türeci, H. E.

Vaccaro, P. O.

Verstuyft, S.

Appl. Phys. Lett. (2)

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]

A. F. J. Levi, R. E. Slusher, S. L. McCall, S. J. Pearton, and W. S. Hobson, "Room-temperature lasing action in In0.51Ga0.49P/In0.2Ga0.8As microcylinder laser diodes," Appl. Phys. Lett. 62, 2021-2023 (1993).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

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

IEEE Sel. Top. Quantum Electron. (1)

T. Fukushima and T. Harayama, "Stadium and quasi-stadium laser diodes," IEEE Sel. Top. Quantum Electron. 10, 1039-1051 (2004).
[CrossRef]

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

Nature (1)

J. U. Nöckel and A. D. Stone, "Ray and wave chaos in asymmetric resonant optical cavities," Nature 385, 45-47 (1997).
[CrossRef]

Opt. Express (3)

Science (1)

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, "High-power directional emission from microlasers with chaotic resonators," Science 280, 1556-1564 (1998).
[CrossRef] [PubMed]

Other (5)

V. M. Apalkov and M. E. Raikh, "Directional emission from a microdisk resonator with a linear defect," Phys. Rev. B 70, 195317-1-195317-6 (2004).
[CrossRef]

J. Wiersig and M. Hentschel, "Unidirectional light emission from high-Q modes in optical microcavities," Phys. Rev. A 73, 031802-1-031802-4 (2006).
[CrossRef]

R. K. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).
[CrossRef]

T. J. Kippenberg, J. Kalkman, A. Polman, and K. J. Vahala, "Demonstration of an erbium-doped microdisk laser on a silicon chip," Phys. Rev. A 74, 051802-1-051802-4 (2006).
[CrossRef]

H. C. CaseyJr. and M. B. Panish, Heterostructure Lasers (Academic Press, New York, NY, 1978).

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Figures (9)

Fig. 1.
Fig. 1.

Schematic diagram of 2-D microcavity laser diode having intracavity air gaps; (a) device structure; (b) definition of cavity parameters and cap layer shape; (c) contact area shape and electrode metal shape. (d) Diamond-shaped total internal reflection mode calculated using a Gaussian-optical approach [14].

Fig. 2.
Fig. 2.

Enlarged diagrams of (a) the air gap (Region A) and (b) the output port (Region B). The red lines indicate ray trajectories. The green lines are normal to the interfaces.

Fig. 3.
Fig. 3.

Calculated filtering characteristics of air gap; (a) reflectance and (b) transmittance.

Fig. 4.
Fig. 4.

Laser diode fabrication process: (a) etching of p-cap layer; (b) deposition of SiO2 film and formation of air gaps and 2-D laser cavity; (c) formation of p-electrode; (d) lapping, polishing, and formation of n-electrode.

Fig. 5.
Fig. 5.

Scanning electron microscope images of the 2-D laser diode: (a) general view; (b) enlargement of curved mirror; (c) enlargement of air gap.

Fig. 6.
Fig. 6.

Light output power versus injection current characteristics of the 2-D laser diode.

Fig. 7.
Fig. 7.

Far-field emission pattern from the output port: (a) wide angular range; (b) narrow angular range.

Fig. 8.
Fig. 8.

Lasing spectrum of the 2-D laser diode: (a) wide wavelength range; (b) narrow wavelength range far from the main peak at λ=868.8 nm.

Fig. 9.
Fig. 9.

Relationship between the spacing Δθ of the interference fringe peaks and optical path difference Δl between two output beams.

Tables (1)

Tables Icon

Table 1. Designed values of device parameters

Equations (10)

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Δ L = d cos β [ sin ( π 4 α + β ) cos ( π 4 α + β ) ] ,
θ = π φ sin 1 [ n eff sin ( 3 π 4 + 2 α φ ) ] ,
x m = L 2 + R R 2 ( W m 2 ) 2 ,
y m = W m 2 .
x c = x m tan ( φ π 2 ) ( L 4 ) tan ( π 4 2 α ) + y m L 4 tan ( φ π 2 ) + tan ( π 4 2 α ) ,
y c = ( x m + L 4 ) tan ( φ π 2 ) tan ( π 4 2 α ) + ( L 4 ) tan ( φ π 2 ) + y m tan ( π 4 2 α ) tan ( φ π 2 ) + tan ( π 4 2 α ) .
Δ θ sin 1 [ λ ( 2 y c ) ] ,
Δ λ = λ 2 n eff L s [ 1 ( λ n eff ) ( d n eff d λ ) ] + L a ,
L s = 4 2 { L 2 [ d cos ( π 4 α + β ) ] ( cos β ) } .
L a = 4 d cos β .

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