Abstract

For a two-dimensional quasi-stadium laser diode, we demonstrate stable excitation of the lowest-order transverse ring modes by optimally designing the confocal end mirrors of the laser cavity based on extended Fox–Li mode calculations. We observe kink-free light output versus injection current characteristics and highly directional single-peak emissions corresponding to the diamond-shaped trajectory in the cavity. These results provide convincing evidence for selective excitation of the lowest-order transverse modes.

© 2013 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, Appl. Phys. Lett. 60, 289 (1992).
    [CrossRef]
  2. C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
    [CrossRef]
  3. T. Fukushima, T. Harayama, P. Davis, P. O. Vaccaro, T. Nishimura, and T. Aida, Opt. Lett. 27, 1430 (2002).
    [CrossRef]
  4. G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
    [CrossRef]
  5. W. Fang, H. Cao, and G. S. Solomon, Appl. Phys. Lett. 90, 081108 (2007).
    [CrossRef]
  6. T. Tanaka, M. Hentschel, T. Fukushima, and T. Harayama, Phys. Rev. Lett. 98, 033902 (2007).
    [CrossRef]
  7. S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, Phys. Rev. A 80, 031801(R) (2009).
    [CrossRef]
  8. T. Harayama and S. Shinohara, Laser Photonics Rev. 5, 247 (2011).
    [CrossRef]
  9. T. Fukushima, T. Harayama, T. Miyasaka, and P. O. Vaccaro, J. Opt. Soc. Am. B 21, 935 (2004).
    [CrossRef]
  10. T. Fukushima and T. Harayama, IEEE J. Sel. Top. Quantum Electron. 10, 1039 (2004).
    [CrossRef]
  11. T. Fukushima, T. Tanaka, and T. Harayama, Appl. Phys. Lett. 86, 171103 (2005).
    [CrossRef]
  12. T. Fukushima, T. Tanaka, and T. Harayama, Appl. Phys. Lett. 87, 191103 (2005).
    [CrossRef]
  13. M. Choi, T. Tanaka, T. Fukushima, and T. Harayama, Appl. Phys. Lett. 88, 211110 (2006).
    [CrossRef]
  14. T. Fukushima and T. Harayama, in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference/Conference on Photonic Applications Systems and Technologies, Technical Digest (CD) (Optical Society of America, 2006), paper JWB4.
  15. T. Fukushima, S. Sunada, T. Harayama, K. Sakaguchi, and Y. Tokuda, Appl. Opt. 51, 2515 (2012).
    [CrossRef]
  16. A. E. Siegman, Lasers (University Science, 1986).
  17. T. Fukushima, S. A. Biellak, Y. Sun, and A. E. Siegman, Opt. Express 2, 21 (1998).
    [CrossRef]
  18. T. Fukushima, J. Lightwave Technol. 18, 2208 (2000).
    [CrossRef]
  19. H. C. Casey and M. B. Panish, Heterostructure Lasers (Academic, 1978).

2012 (1)

2011 (1)

T. Harayama and S. Shinohara, Laser Photonics Rev. 5, 247 (2011).
[CrossRef]

2009 (1)

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, Phys. Rev. A 80, 031801(R) (2009).
[CrossRef]

2007 (2)

W. Fang, H. Cao, and G. S. Solomon, Appl. Phys. Lett. 90, 081108 (2007).
[CrossRef]

T. Tanaka, M. Hentschel, T. Fukushima, and T. Harayama, Phys. Rev. Lett. 98, 033902 (2007).
[CrossRef]

2006 (1)

M. Choi, T. Tanaka, T. Fukushima, and T. Harayama, Appl. Phys. Lett. 88, 211110 (2006).
[CrossRef]

2005 (2)

T. Fukushima, T. Tanaka, and T. Harayama, Appl. Phys. Lett. 86, 171103 (2005).
[CrossRef]

T. Fukushima, T. Tanaka, and T. Harayama, Appl. Phys. Lett. 87, 191103 (2005).
[CrossRef]

2004 (2)

T. Fukushima and T. Harayama, IEEE J. Sel. Top. Quantum Electron. 10, 1039 (2004).
[CrossRef]

T. Fukushima, T. Harayama, T. Miyasaka, and P. O. Vaccaro, J. Opt. Soc. Am. B 21, 935 (2004).
[CrossRef]

2003 (1)

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

2002 (1)

2000 (1)

1998 (2)

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef]

T. Fukushima, S. A. Biellak, Y. Sun, and A. E. Siegman, Opt. Express 2, 21 (1998).
[CrossRef]

1992 (1)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Aida, T.

Biellak, S. A.

Cao, H.

W. Fang, H. Cao, and G. S. Solomon, Appl. Phys. Lett. 90, 081108 (2007).
[CrossRef]

Capasso, F.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef]

Casey, H. C.

H. C. Casey and M. B. Panish, Heterostructure Lasers (Academic, 1978).

Chang, R. K.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Chern, G. D.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

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, Science 280, 1556 (1998).
[CrossRef]

Choi, M.

M. Choi, T. Tanaka, T. Fukushima, and T. Harayama, Appl. Phys. Lett. 88, 211110 (2006).
[CrossRef]

Davis, P.

Faist, J.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef]

Fang, W.

W. Fang, H. Cao, and G. S. Solomon, Appl. Phys. Lett. 90, 081108 (2007).
[CrossRef]

Fukushima, T.

T. Fukushima, S. Sunada, T. Harayama, K. Sakaguchi, and Y. Tokuda, Appl. Opt. 51, 2515 (2012).
[CrossRef]

T. Tanaka, M. Hentschel, T. Fukushima, and T. Harayama, Phys. Rev. Lett. 98, 033902 (2007).
[CrossRef]

M. Choi, T. Tanaka, T. Fukushima, and T. Harayama, Appl. Phys. Lett. 88, 211110 (2006).
[CrossRef]

T. Fukushima, T. Tanaka, and T. Harayama, Appl. Phys. Lett. 86, 171103 (2005).
[CrossRef]

T. Fukushima, T. Tanaka, and T. Harayama, Appl. Phys. Lett. 87, 191103 (2005).
[CrossRef]

T. Fukushima and T. Harayama, IEEE J. Sel. Top. Quantum Electron. 10, 1039 (2004).
[CrossRef]

T. Fukushima, T. Harayama, T. Miyasaka, and P. O. Vaccaro, J. Opt. Soc. Am. B 21, 935 (2004).
[CrossRef]

T. Fukushima, T. Harayama, P. Davis, P. O. Vaccaro, T. Nishimura, and T. Aida, Opt. Lett. 27, 1430 (2002).
[CrossRef]

T. Fukushima, J. Lightwave Technol. 18, 2208 (2000).
[CrossRef]

T. Fukushima, S. A. Biellak, Y. Sun, and A. E. Siegman, Opt. Express 2, 21 (1998).
[CrossRef]

T. Fukushima and T. Harayama, in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference/Conference on Photonic Applications Systems and Technologies, Technical Digest (CD) (Optical Society of America, 2006), paper JWB4.

Gmachl, C.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef]

Harayama, T.

T. Fukushima, S. Sunada, T. Harayama, K. Sakaguchi, and Y. Tokuda, Appl. Opt. 51, 2515 (2012).
[CrossRef]

T. Harayama and S. Shinohara, Laser Photonics Rev. 5, 247 (2011).
[CrossRef]

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, Phys. Rev. A 80, 031801(R) (2009).
[CrossRef]

T. Tanaka, M. Hentschel, T. Fukushima, and T. Harayama, Phys. Rev. Lett. 98, 033902 (2007).
[CrossRef]

M. Choi, T. Tanaka, T. Fukushima, and T. Harayama, Appl. Phys. Lett. 88, 211110 (2006).
[CrossRef]

T. Fukushima, T. Tanaka, and T. Harayama, Appl. Phys. Lett. 86, 171103 (2005).
[CrossRef]

T. Fukushima, T. Tanaka, and T. Harayama, Appl. Phys. Lett. 87, 191103 (2005).
[CrossRef]

T. Fukushima and T. Harayama, IEEE J. Sel. Top. Quantum Electron. 10, 1039 (2004).
[CrossRef]

T. Fukushima, T. Harayama, T. Miyasaka, and P. O. Vaccaro, J. Opt. Soc. Am. B 21, 935 (2004).
[CrossRef]

T. Fukushima, T. Harayama, P. Davis, P. O. Vaccaro, T. Nishimura, and T. Aida, Opt. Lett. 27, 1430 (2002).
[CrossRef]

T. Fukushima and T. Harayama, in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference/Conference on Photonic Applications Systems and Technologies, Technical Digest (CD) (Optical Society of America, 2006), paper JWB4.

Hentschel, M.

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, Phys. Rev. A 80, 031801(R) (2009).
[CrossRef]

T. Tanaka, M. Hentschel, T. Fukushima, and T. Harayama, Phys. Rev. Lett. 98, 033902 (2007).
[CrossRef]

Johnson, N. M.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Kneissl, M.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Miyasaka, T.

Narimanov, E. E.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef]

Nishimura, T.

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, Science 280, 1556 (1998).
[CrossRef]

Panish, M. B.

H. C. Casey and M. B. Panish, Heterostructure Lasers (Academic, 1978).

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Sakaguchi, K.

Sasaki, T.

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, Phys. Rev. A 80, 031801(R) (2009).
[CrossRef]

Shinohara, S.

T. Harayama and S. Shinohara, Laser Photonics Rev. 5, 247 (2011).
[CrossRef]

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, Phys. Rev. A 80, 031801(R) (2009).
[CrossRef]

Siegman, A. E.

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, Science 280, 1556 (1998).
[CrossRef]

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

Solomon, G. S.

W. Fang, H. Cao, and G. S. Solomon, Appl. Phys. Lett. 90, 081108 (2007).
[CrossRef]

Stone, A. D.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef]

Sun, Y.

Sunada, S.

Tanaka, T.

T. Tanaka, M. Hentschel, T. Fukushima, and T. Harayama, Phys. Rev. Lett. 98, 033902 (2007).
[CrossRef]

M. Choi, T. Tanaka, T. Fukushima, and T. Harayama, Appl. Phys. Lett. 88, 211110 (2006).
[CrossRef]

T. Fukushima, T. Tanaka, and T. Harayama, Appl. Phys. Lett. 86, 171103 (2005).
[CrossRef]

T. Fukushima, T. Tanaka, and T. Harayama, Appl. Phys. Lett. 87, 191103 (2005).
[CrossRef]

Tokuda, Y.

Tureci, H. E.

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

Vaccaro, P. O.

Wiersig, J.

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, Phys. Rev. A 80, 031801(R) (2009).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (6)

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, Appl. Phys. Lett. 83, 1710 (2003).
[CrossRef]

W. Fang, H. Cao, and G. S. Solomon, Appl. Phys. Lett. 90, 081108 (2007).
[CrossRef]

T. Fukushima, T. Tanaka, and T. Harayama, Appl. Phys. Lett. 86, 171103 (2005).
[CrossRef]

T. Fukushima, T. Tanaka, and T. Harayama, Appl. Phys. Lett. 87, 191103 (2005).
[CrossRef]

M. Choi, T. Tanaka, T. Fukushima, and T. Harayama, Appl. Phys. Lett. 88, 211110 (2006).
[CrossRef]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, Appl. Phys. Lett. 60, 289 (1992).
[CrossRef]

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

T. Fukushima and T. Harayama, IEEE J. Sel. Top. Quantum Electron. 10, 1039 (2004).
[CrossRef]

J. Lightwave Technol. (1)

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

Laser Photonics Rev. (1)

T. Harayama and S. Shinohara, Laser Photonics Rev. 5, 247 (2011).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

S. Shinohara, M. Hentschel, J. Wiersig, T. Sasaki, and T. Harayama, Phys. Rev. A 80, 031801(R) (2009).
[CrossRef]

Phys. Rev. Lett. (1)

T. Tanaka, M. Hentschel, T. Fukushima, and T. Harayama, Phys. Rev. Lett. 98, 033902 (2007).
[CrossRef]

Science (1)

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, Science 280, 1556 (1998).
[CrossRef]

Other (3)

A. E. Siegman, Lasers (University Science, 1986).

H. C. Casey and M. B. Panish, Heterostructure Lasers (Academic, 1978).

T. Fukushima and T. Harayama, in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference/Conference on Photonic Applications Systems and Technologies, Technical Digest (CD) (Optical Society of America, 2006), paper JWB4.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic diagram of the quasi-stadium laser cavity, showing the diamond-shaped stable periodic orbit bouncing at points A, B, C, and D inside the cavity.

Fig. 2.
Fig. 2.

Near-field patterns at the curved end mirror for (a) lowest-order ring mode and (b) second-lowest-order ring mode.

Fig. 3.
Fig. 3.

Relationship between the diffraction loss per round-trip and mirror width for the lowest- and second-lowest-order ring modes in the quasi-stadium laser cavity.

Fig. 4.
Fig. 4.

Light output power versus injection current characteristics for the quasi-stadium laser diode.

Fig. 5.
Fig. 5.

Lasing spectra of the quasi-stadium laser diode at output powers of (a) 5 mW, (b) 10 mW, (c) 15 mW, and (d) 20 mW.

Fig. 6.
Fig. 6.

Far-field emission patterns for the quasi-stadium laser diode at output powers of 5, 10, 15, and 20 mW.

Fig. 7.
Fig. 7.

Far-field emission pattern calculated for the lowest-order ring mode.

Equations (3)

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

Δλ=λ2neffA[1(λ/neff)(dneff/dλ)].
A=2(L2+W2)1/2.
θ=±sin1[neffW(L2+W2)1/2].

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