Abstract

We investigate the modal losses and field distributions of different order transverse modes supported by the photonic crystal Bragg structure using a transfer matrix method. We find that only the fundamental transverse mode has a single-lobed near field and far field and there exists a trade-off between ensuring lasing in the fundamental transverse mode and reducing the threshold. Employing these design principles, we experimentally demonstrate a large-area, edge-emitting, and single-mode semiconductor photonic crystal Bragg laser with a single-lobed, diffraction-limited far field under continuous wave condition.

© 2007 Optical Society of America

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  1. A. Yariv, Opt. Lett. 27, 936 (2002).
    [CrossRef]
  2. I. Vurgaftman and J. R. Meyer, IEEE J. Quantum Electron. 38, 592 (2002).
    [CrossRef]
  3. C. S. Kim, W. W. Bewley, C. L. Canedy, I. Vurgaftman, M. Kim, and J. R. Meyer, IEEE Photon. Technol. Lett. 16, 1250 (2004).
    [CrossRef]
  4. S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
    [CrossRef] [PubMed]
  5. D. Ohnishi, T. Okano, M. Imada, and S. Noda, Opt. Express 12, 1562 (2004).
    [CrossRef] [PubMed]
  6. L. Zhu, J. M. Choi, G. A. DeRose, A. Yariv, and A. Scherer, Opt. Lett. 31, 1863 (2006).
    [CrossRef] [PubMed]
  7. H. Hofmann, H. Scherer, S. Deubert, M. Kamp, and A. Forchel, Appl. Phys. Lett. 90, 121 (2007).
  8. L. Zhu, G. A. DeRose, A. Scherer, and A. Yariv, Opt. Lett. 32, 1256 (2007).
    [CrossRef] [PubMed]
  9. L. Zhu, X. K. Sun, G. A. DeRose, A. Scherer, and A. Yariv, Appl. Phys. Lett. 90, 26116 (2007).
  10. L. Zhu, P. Chak, J. K. S. Poon, G. A. DeRose, A. Scherer, and A. Yariv, Opt. Express 15, 5966 (2007).
    [CrossRef] [PubMed]
  11. R. J. Lang, K. D. Zurko, A. Hardy, S. Demars, A. Schoenfelder, and D. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
    [CrossRef]
  12. L. Zhu, A. Yariv, and A. Scherer, "Modal gain analysis of transverse Bragg resonance waveguide lasers with and without transverse defects" IEEE J. Quantum Electron. (to be published).
  13. D. Botez and D. R. Scifres, Diode Laser Arrays (Cambridge U. Press, 1986), p. 12.

2007

H. Hofmann, H. Scherer, S. Deubert, M. Kamp, and A. Forchel, Appl. Phys. Lett. 90, 121 (2007).

L. Zhu, X. K. Sun, G. A. DeRose, A. Scherer, and A. Yariv, Appl. Phys. Lett. 90, 26116 (2007).

L. Zhu, G. A. DeRose, A. Scherer, and A. Yariv, Opt. Lett. 32, 1256 (2007).
[CrossRef] [PubMed]

L. Zhu, P. Chak, J. K. S. Poon, G. A. DeRose, A. Scherer, and A. Yariv, Opt. Express 15, 5966 (2007).
[CrossRef] [PubMed]

2006

2004

D. Ohnishi, T. Okano, M. Imada, and S. Noda, Opt. Express 12, 1562 (2004).
[CrossRef] [PubMed]

C. S. Kim, W. W. Bewley, C. L. Canedy, I. Vurgaftman, M. Kim, and J. R. Meyer, IEEE Photon. Technol. Lett. 16, 1250 (2004).
[CrossRef]

2002

I. Vurgaftman and J. R. Meyer, IEEE J. Quantum Electron. 38, 592 (2002).
[CrossRef]

A. Yariv, Opt. Lett. 27, 936 (2002).
[CrossRef]

2001

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
[CrossRef] [PubMed]

1998

R. J. Lang, K. D. Zurko, A. Hardy, S. Demars, A. Schoenfelder, and D. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

Bewley, W. W.

C. S. Kim, W. W. Bewley, C. L. Canedy, I. Vurgaftman, M. Kim, and J. R. Meyer, IEEE Photon. Technol. Lett. 16, 1250 (2004).
[CrossRef]

Botez, D.

D. Botez and D. R. Scifres, Diode Laser Arrays (Cambridge U. Press, 1986), p. 12.

Canedy, C. L.

C. S. Kim, W. W. Bewley, C. L. Canedy, I. Vurgaftman, M. Kim, and J. R. Meyer, IEEE Photon. Technol. Lett. 16, 1250 (2004).
[CrossRef]

Chak, P.

Choi, J. M.

Chutinan, A.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
[CrossRef] [PubMed]

Demars, S.

R. J. Lang, K. D. Zurko, A. Hardy, S. Demars, A. Schoenfelder, and D. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

DeRose, G. A.

Deubert, S.

H. Hofmann, H. Scherer, S. Deubert, M. Kamp, and A. Forchel, Appl. Phys. Lett. 90, 121 (2007).

Forchel, A.

H. Hofmann, H. Scherer, S. Deubert, M. Kamp, and A. Forchel, Appl. Phys. Lett. 90, 121 (2007).

Hardy, A.

R. J. Lang, K. D. Zurko, A. Hardy, S. Demars, A. Schoenfelder, and D. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

Hofmann, H.

H. Hofmann, H. Scherer, S. Deubert, M. Kamp, and A. Forchel, Appl. Phys. Lett. 90, 121 (2007).

Imada, M.

D. Ohnishi, T. Okano, M. Imada, and S. Noda, Opt. Express 12, 1562 (2004).
[CrossRef] [PubMed]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
[CrossRef] [PubMed]

Kamp, M.

H. Hofmann, H. Scherer, S. Deubert, M. Kamp, and A. Forchel, Appl. Phys. Lett. 90, 121 (2007).

Kim, C. S.

C. S. Kim, W. W. Bewley, C. L. Canedy, I. Vurgaftman, M. Kim, and J. R. Meyer, IEEE Photon. Technol. Lett. 16, 1250 (2004).
[CrossRef]

Kim, M.

C. S. Kim, W. W. Bewley, C. L. Canedy, I. Vurgaftman, M. Kim, and J. R. Meyer, IEEE Photon. Technol. Lett. 16, 1250 (2004).
[CrossRef]

Lang, R. J.

R. J. Lang, K. D. Zurko, A. Hardy, S. Demars, A. Schoenfelder, and D. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

Meyer, J. R.

C. S. Kim, W. W. Bewley, C. L. Canedy, I. Vurgaftman, M. Kim, and J. R. Meyer, IEEE Photon. Technol. Lett. 16, 1250 (2004).
[CrossRef]

I. Vurgaftman and J. R. Meyer, IEEE J. Quantum Electron. 38, 592 (2002).
[CrossRef]

Mochizuki, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
[CrossRef] [PubMed]

Noda, S.

D. Ohnishi, T. Okano, M. Imada, and S. Noda, Opt. Express 12, 1562 (2004).
[CrossRef] [PubMed]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
[CrossRef] [PubMed]

Ohnishi, D.

Okano, T.

S. Poon, J. K.

Scherer, A.

L. Zhu, P. Chak, J. K. S. Poon, G. A. DeRose, A. Scherer, and A. Yariv, Opt. Express 15, 5966 (2007).
[CrossRef] [PubMed]

L. Zhu, X. K. Sun, G. A. DeRose, A. Scherer, and A. Yariv, Appl. Phys. Lett. 90, 26116 (2007).

L. Zhu, G. A. DeRose, A. Scherer, and A. Yariv, Opt. Lett. 32, 1256 (2007).
[CrossRef] [PubMed]

L. Zhu, J. M. Choi, G. A. DeRose, A. Yariv, and A. Scherer, Opt. Lett. 31, 1863 (2006).
[CrossRef] [PubMed]

L. Zhu, A. Yariv, and A. Scherer, "Modal gain analysis of transverse Bragg resonance waveguide lasers with and without transverse defects" IEEE J. Quantum Electron. (to be published).

Scherer, H.

H. Hofmann, H. Scherer, S. Deubert, M. Kamp, and A. Forchel, Appl. Phys. Lett. 90, 121 (2007).

Schoenfelder, A.

R. J. Lang, K. D. Zurko, A. Hardy, S. Demars, A. Schoenfelder, and D. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

Scifres, D. R.

D. Botez and D. R. Scifres, Diode Laser Arrays (Cambridge U. Press, 1986), p. 12.

Sun, X. K.

L. Zhu, X. K. Sun, G. A. DeRose, A. Scherer, and A. Yariv, Appl. Phys. Lett. 90, 26116 (2007).

Vurgaftman, I.

C. S. Kim, W. W. Bewley, C. L. Canedy, I. Vurgaftman, M. Kim, and J. R. Meyer, IEEE Photon. Technol. Lett. 16, 1250 (2004).
[CrossRef]

I. Vurgaftman and J. R. Meyer, IEEE J. Quantum Electron. 38, 592 (2002).
[CrossRef]

Welch, D.

R. J. Lang, K. D. Zurko, A. Hardy, S. Demars, A. Schoenfelder, and D. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

Yariv, A.

L. Zhu, G. A. DeRose, A. Scherer, and A. Yariv, Opt. Lett. 32, 1256 (2007).
[CrossRef] [PubMed]

L. Zhu, P. Chak, J. K. S. Poon, G. A. DeRose, A. Scherer, and A. Yariv, Opt. Express 15, 5966 (2007).
[CrossRef] [PubMed]

L. Zhu, X. K. Sun, G. A. DeRose, A. Scherer, and A. Yariv, Appl. Phys. Lett. 90, 26116 (2007).

L. Zhu, J. M. Choi, G. A. DeRose, A. Yariv, and A. Scherer, Opt. Lett. 31, 1863 (2006).
[CrossRef] [PubMed]

A. Yariv, Opt. Lett. 27, 936 (2002).
[CrossRef]

L. Zhu, A. Yariv, and A. Scherer, "Modal gain analysis of transverse Bragg resonance waveguide lasers with and without transverse defects" IEEE J. Quantum Electron. (to be published).

Yokoyama, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
[CrossRef] [PubMed]

Zhu, L.

L. Zhu, X. K. Sun, G. A. DeRose, A. Scherer, and A. Yariv, Appl. Phys. Lett. 90, 26116 (2007).

L. Zhu, P. Chak, J. K. S. Poon, G. A. DeRose, A. Scherer, and A. Yariv, Opt. Express 15, 5966 (2007).
[CrossRef] [PubMed]

L. Zhu, G. A. DeRose, A. Scherer, and A. Yariv, Opt. Lett. 32, 1256 (2007).
[CrossRef] [PubMed]

L. Zhu, J. M. Choi, G. A. DeRose, A. Yariv, and A. Scherer, Opt. Lett. 31, 1863 (2006).
[CrossRef] [PubMed]

L. Zhu, A. Yariv, and A. Scherer, "Modal gain analysis of transverse Bragg resonance waveguide lasers with and without transverse defects" IEEE J. Quantum Electron. (to be published).

Zurko, K. D.

R. J. Lang, K. D. Zurko, A. Hardy, S. Demars, A. Schoenfelder, and D. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

Appl. Phys. Lett.

H. Hofmann, H. Scherer, S. Deubert, M. Kamp, and A. Forchel, Appl. Phys. Lett. 90, 121 (2007).

L. Zhu, X. K. Sun, G. A. DeRose, A. Scherer, and A. Yariv, Appl. Phys. Lett. 90, 26116 (2007).

IEEE J. Quantum Electron.

R. J. Lang, K. D. Zurko, A. Hardy, S. Demars, A. Schoenfelder, and D. Welch, IEEE J. Quantum Electron. 34, 2196 (1998).
[CrossRef]

I. Vurgaftman and J. R. Meyer, IEEE J. Quantum Electron. 38, 592 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

C. S. Kim, W. W. Bewley, C. L. Canedy, I. Vurgaftman, M. Kim, and J. R. Meyer, IEEE Photon. Technol. Lett. 16, 1250 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Science

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, Science 293, 1123 (2001).
[CrossRef] [PubMed]

Other

L. Zhu, A. Yariv, and A. Scherer, "Modal gain analysis of transverse Bragg resonance waveguide lasers with and without transverse defects" IEEE J. Quantum Electron. (to be published).

D. Botez and D. R. Scifres, Diode Laser Arrays (Cambridge U. Press, 1986), p. 12.

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of a two-dimensional photonic crystal Bragg laser. a is the transverse lattice constant, b is the longitudinal lattice constant, and θ t i l t is the facet tilt angle. (b) The cross-section structure of a fabricated PC Bragg laser.

Fig. 2
Fig. 2

(a) Modal losses for different order TBR modes as a function of the modal angle (solid curve) and the grating transmission spectrum (dashed curve). (b) Electrical field distributions for the three lowest-order TBR modes.

Fig. 3
Fig. 3

Modal losses for the fundamental TBR mode (solid curve) and intermodal discrimination between the fundamental TBR mode and second-order TBR mode (dashed curve) as a function of the transverse coupling coefficient.

Fig. 4
Fig. 4

Measurement results of the PC Bragg lasers with different etch depths. All the measurements are taken at I = 1.6 i th . (a.1)–(a.3) Spectrum, near field, and far field of the PC Bragg laser with 305 nm etch depth. (b.1)–(b.3) Spectrum, near field, and far field of the PC Bragg laser with 430 nm etch depth. The insets in (a-2) and (b-2) are direct infrared images of the laser facets.

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