Abstract

A modal analysis at threshold is presented for linear Talbot-cavity semiconductor lasers with a finite number of array elements. The analysis self-consistently calculates the array supermode profiles and the loss each incurs owing to imperfect Talbot imaging, including edge diffraction losses. It is found that the decrease in mode discrimination between supermodes incurred by fabricating larger arrays can be offset by reducing the near-field fill factor.

© 1991 Optical Society of America

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  1. J. Katz, S. Margalit, A. Yariv, Appl. Phys. Lett. 42, 554 (1983).
    [CrossRef]
  2. D. Mehuys, K. Mitsunaga, L. Eng, W. K. Marshall, A. Yariv, Appl. Phys. Lett. 53, 1165 (1988).
    [CrossRef]
  3. L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, Electron. Lett. 25, 365 (1989).
    [CrossRef]
  4. J. R. Leger, M. L. Scott, W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
    [CrossRef]
  5. J. R. Leger, Appl. Phys. Lett. 55, 334 (1989).
    [CrossRef]
  6. F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, Appl. Phys. Lett. 55, 816 (1989).
    [CrossRef]
  7. A. A. Golubentsev, V. V. Likhanskii, A. P. Napartovich, Sov. Phys. JETP 66, 676 (1987).
  8. S. Wang, J. Z. Wilcox, M. Jansen, J. J. Yang, Appl. Phys. Lett. 48, 1770 (1986).
    [CrossRef]
  9. E. Kapon, J. Katz, A. Yariv, Appl. Phys. Lett. 10, 125 (1984).
  10. J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984).
    [CrossRef]
  11. Strictly speaking, the Talbot effect is valid only under a paraxial approximation, and thus additional coupling losses will occur if w/λ0 is too small. See J. R. Leger, G. J. Swanson, Opt. Lett. 15, 288 (1990).
    [CrossRef] [PubMed]
  12. R. G. Waarts, D. Nam, D. Mehuys, D. F. Welch, D. R. Scifres, “High-power, low-loss external Talbot-cavity laser,” Appl. Phys. Lett. (to be published).
  13. F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, Proc. Soc. Photo-Opt. Instrum. Eng. 1043, 100 (1989).

1990

1989

F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, Proc. Soc. Photo-Opt. Instrum. Eng. 1043, 100 (1989).

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, Electron. Lett. 25, 365 (1989).
[CrossRef]

J. R. Leger, Appl. Phys. Lett. 55, 334 (1989).
[CrossRef]

F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, Appl. Phys. Lett. 55, 816 (1989).
[CrossRef]

1988

J. R. Leger, M. L. Scott, W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

D. Mehuys, K. Mitsunaga, L. Eng, W. K. Marshall, A. Yariv, Appl. Phys. Lett. 53, 1165 (1988).
[CrossRef]

1987

A. A. Golubentsev, V. V. Likhanskii, A. P. Napartovich, Sov. Phys. JETP 66, 676 (1987).

1986

S. Wang, J. Z. Wilcox, M. Jansen, J. J. Yang, Appl. Phys. Lett. 48, 1770 (1986).
[CrossRef]

1984

E. Kapon, J. Katz, A. Yariv, Appl. Phys. Lett. 10, 125 (1984).

J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[CrossRef]

1983

J. Katz, S. Margalit, A. Yariv, Appl. Phys. Lett. 42, 554 (1983).
[CrossRef]

Ackley, D. E.

J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[CrossRef]

Botez, D.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, Electron. Lett. 25, 365 (1989).
[CrossRef]

J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[CrossRef]

Butler, J. K.

J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[CrossRef]

D’Amato, F. X.

F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, Proc. Soc. Photo-Opt. Instrum. Eng. 1043, 100 (1989).

F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, Appl. Phys. Lett. 55, 816 (1989).
[CrossRef]

Eng, L.

D. Mehuys, K. Mitsunaga, L. Eng, W. K. Marshall, A. Yariv, Appl. Phys. Lett. 53, 1165 (1988).
[CrossRef]

Golubentsev, A. A.

A. A. Golubentsev, V. V. Likhanskii, A. P. Napartovich, Sov. Phys. JETP 66, 676 (1987).

Jansen, M.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, Electron. Lett. 25, 365 (1989).
[CrossRef]

S. Wang, J. Z. Wilcox, M. Jansen, J. J. Yang, Appl. Phys. Lett. 48, 1770 (1986).
[CrossRef]

Kapon, E.

E. Kapon, J. Katz, A. Yariv, Appl. Phys. Lett. 10, 125 (1984).

Katz, J.

E. Kapon, J. Katz, A. Yariv, Appl. Phys. Lett. 10, 125 (1984).

J. Katz, S. Margalit, A. Yariv, Appl. Phys. Lett. 42, 554 (1983).
[CrossRef]

Leger, J. R.

Likhanskii, V. V.

A. A. Golubentsev, V. V. Likhanskii, A. P. Napartovich, Sov. Phys. JETP 66, 676 (1987).

Margalit, S.

J. Katz, S. Margalit, A. Yariv, Appl. Phys. Lett. 42, 554 (1983).
[CrossRef]

Marshall, W. K.

D. Mehuys, K. Mitsunaga, L. Eng, W. K. Marshall, A. Yariv, Appl. Phys. Lett. 53, 1165 (1988).
[CrossRef]

Mawst, L. J.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, Electron. Lett. 25, 365 (1989).
[CrossRef]

Mehuys, D.

D. Mehuys, K. Mitsunaga, L. Eng, W. K. Marshall, A. Yariv, Appl. Phys. Lett. 53, 1165 (1988).
[CrossRef]

R. G. Waarts, D. Nam, D. Mehuys, D. F. Welch, D. R. Scifres, “High-power, low-loss external Talbot-cavity laser,” Appl. Phys. Lett. (to be published).

Mitsunaga, K.

D. Mehuys, K. Mitsunaga, L. Eng, W. K. Marshall, A. Yariv, Appl. Phys. Lett. 53, 1165 (1988).
[CrossRef]

Nam, D.

R. G. Waarts, D. Nam, D. Mehuys, D. F. Welch, D. R. Scifres, “High-power, low-loss external Talbot-cavity laser,” Appl. Phys. Lett. (to be published).

Napartovich, A. P.

A. A. Golubentsev, V. V. Likhanskii, A. P. Napartovich, Sov. Phys. JETP 66, 676 (1987).

Peterson, G.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, Electron. Lett. 25, 365 (1989).
[CrossRef]

Roth, T. J.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, Electron. Lett. 25, 365 (1989).
[CrossRef]

Roychoudhuri, C.

F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, Appl. Phys. Lett. 55, 816 (1989).
[CrossRef]

F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, Proc. Soc. Photo-Opt. Instrum. Eng. 1043, 100 (1989).

Scifres, D. R.

R. G. Waarts, D. Nam, D. Mehuys, D. F. Welch, D. R. Scifres, “High-power, low-loss external Talbot-cavity laser,” Appl. Phys. Lett. (to be published).

Scott, M. L.

J. R. Leger, M. L. Scott, W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

Siebert, E. T.

F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, Proc. Soc. Photo-Opt. Instrum. Eng. 1043, 100 (1989).

F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, Appl. Phys. Lett. 55, 816 (1989).
[CrossRef]

Simmons, W. W.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, Electron. Lett. 25, 365 (1989).
[CrossRef]

Swanson, G. J.

Veldkamp, W. B.

J. R. Leger, M. L. Scott, W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

Waarts, R. G.

R. G. Waarts, D. Nam, D. Mehuys, D. F. Welch, D. R. Scifres, “High-power, low-loss external Talbot-cavity laser,” Appl. Phys. Lett. (to be published).

Wang, S.

S. Wang, J. Z. Wilcox, M. Jansen, J. J. Yang, Appl. Phys. Lett. 48, 1770 (1986).
[CrossRef]

Welch, D. F.

R. G. Waarts, D. Nam, D. Mehuys, D. F. Welch, D. R. Scifres, “High-power, low-loss external Talbot-cavity laser,” Appl. Phys. Lett. (to be published).

Wilcox, J. Z.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, Electron. Lett. 25, 365 (1989).
[CrossRef]

S. Wang, J. Z. Wilcox, M. Jansen, J. J. Yang, Appl. Phys. Lett. 48, 1770 (1986).
[CrossRef]

Yang, J. J.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, Electron. Lett. 25, 365 (1989).
[CrossRef]

S. Wang, J. Z. Wilcox, M. Jansen, J. J. Yang, Appl. Phys. Lett. 48, 1770 (1986).
[CrossRef]

Yariv, A.

D. Mehuys, K. Mitsunaga, L. Eng, W. K. Marshall, A. Yariv, Appl. Phys. Lett. 53, 1165 (1988).
[CrossRef]

E. Kapon, J. Katz, A. Yariv, Appl. Phys. Lett. 10, 125 (1984).

J. Katz, S. Margalit, A. Yariv, Appl. Phys. Lett. 42, 554 (1983).
[CrossRef]

Appl. Phys. Lett.

J. R. Leger, M. L. Scott, W. B. Veldkamp, Appl. Phys. Lett. 52, 1771 (1988).
[CrossRef]

J. R. Leger, Appl. Phys. Lett. 55, 334 (1989).
[CrossRef]

F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, Appl. Phys. Lett. 55, 816 (1989).
[CrossRef]

S. Wang, J. Z. Wilcox, M. Jansen, J. J. Yang, Appl. Phys. Lett. 48, 1770 (1986).
[CrossRef]

E. Kapon, J. Katz, A. Yariv, Appl. Phys. Lett. 10, 125 (1984).

J. K. Butler, D. E. Ackley, D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[CrossRef]

J. Katz, S. Margalit, A. Yariv, Appl. Phys. Lett. 42, 554 (1983).
[CrossRef]

D. Mehuys, K. Mitsunaga, L. Eng, W. K. Marshall, A. Yariv, Appl. Phys. Lett. 53, 1165 (1988).
[CrossRef]

Electron. Lett.

L. J. Mawst, D. Botez, T. J. Roth, W. W. Simmons, G. Peterson, M. Jansen, J. Z. Wilcox, J. J. Yang, Electron. Lett. 25, 365 (1989).
[CrossRef]

Opt. Lett.

Proc. Soc. Photo-Opt. Instrum. Eng.

F. X. D’Amato, E. T. Siebert, C. Roychoudhuri, Proc. Soc. Photo-Opt. Instrum. Eng. 1043, 100 (1989).

Sov. Phys. JETP

A. A. Golubentsev, V. V. Likhanskii, A. P. Napartovich, Sov. Phys. JETP 66, 676 (1987).

Other

R. G. Waarts, D. Nam, D. Mehuys, D. F. Welch, D. R. Scifres, “High-power, low-loss external Talbot-cavity laser,” Appl. Phys. Lett. (to be published).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the linear Talbot cavity that we analyze.

Fig. 2
Fig. 2

Supermode threshold gain for an eight-element array as a function of round-trip Talbot-cavity length, in units of ZT. The near-field fill factor is f = 0.08.

Fig. 3
Fig. 3

Supermode threshold gain of the ν = N and ν = N − 1 supermodes as a function of the number of array elements N for an array with f = 0.08, η = 0.5, and z = ZT/2.

Fig. 4
Fig. 4

Supermode threshold gain for the ν = 20 and ν = 19 supermodes as a function of the near-field fill factor for an array with N = 20, η = 0.5, and z = ZT/2.

Equations (5)

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

[ r 0 r exp ( i 2 σ L ) R r - I ] e = 0 ,
κ p q = exp ( i k z ) ( 1 + i 4 η / π f 2 ) 1 / 2 exp [ - 2 ( p - q ) 2 / f 2 1 - i 4 η / π f 2 ] ,
η = z / Z T ,
f = w / a .
g ν = 1 L ln ( 1 r 0 r ) + 1 L ln ( 1 λ ν ) .

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