Abstract

Fox–Li iteration-based algorithms form the core of steady-state design tools for high-power semiconductor lasers. The theoretical formalism is developed for Fox–Li iteration-based algorithms as applied to high-power lasers. This allows us to study their numerical properties, explain their behavior, and show the nature of the calculated approximate cavity modes. Lower-dimensional models are used to identify and explain the source of numerical instabilities and to find ways of improving the convergence rate of Fox–Li iteration algorithms. Finally, the results of the lower-dimensional analysis are verified by performing simulations of high-power tapered laser diodes in two dimensions using the finite-difference beam-propagation method.

© 2007 Optical Society of America

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  1. L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
    [Crossref]
  2. S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, 'Non-linear properties of tapered laser cavities,' IEEE J. Sel. Top. Quantum Electron. 9, 823-834 (2003).
    [Crossref]
  3. C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, 'A first-principles fully space-time resolved model of a semiconductor laser model,' J. Opt. B: Quantum Semiclassical Opt. 9, 681-692 (1997).
    [Crossref]
  4. E. Gering, O. Hess, and R. Wallenstein, 'Modelling of the performance of high-power diode amplifier systems with an opto-thermal microscopic spatio-temporal theory,' IEEE J. Quantum Electron. 35, 320-331 (1999).
    [Crossref]
  5. Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, 'Numerical simulation of broad-area high-power semiconductor laser amplifiers,' IEEE J. Quantum Electron. 33, 2240-2254 (1997).
    [Crossref]
  6. S. Mariojouls, S. Margott, A. Schmitt, M. Mikulla, J. Braunstein, G. Weimann, F. Lozes, and S. Bonnefont, 'Modelling of the performance of high-brightness tapered lasers,' Proc. SPIE 3944, 395-406 (2000).
    [Crossref]
  7. G. Fox and T. Li, 'Resonant modes in maser interferometer,' Bell Syst. Tech. J. 40, 453-459 (1961).
  8. G. P. Agrawal, 'Fast-Fourier-transform based beam-propagation model for stripe-geometry semiconductor laser: inclusion of axial effects,' J. Appl. Phys. 56, 3100-3109 (1984).
    [Crossref]
  9. E. Kreyszig, Introductory Functional Analysis with Applications (Wiley, 1978).
  10. S. Sujecki, J. Wykes, P. Sewell, A. Vukovic, T. M. Benson, E. C. Larkins, L. Borruel, and I. Esquivias, 'Optical properties of tapered laser cavities,' IEE Proc.: Optoelectron. 150, 246-252 (2003).
    [Crossref]
  11. J. J. Lim, T. M. Benson, and E. C. Larkins, 'Design of wide-emitter single-mode laser diodes,' IEEE J. Quantum Electron. 41, 506-516 (2005).
    [Crossref]

2005 (1)

J. J. Lim, T. M. Benson, and E. C. Larkins, 'Design of wide-emitter single-mode laser diodes,' IEEE J. Quantum Electron. 41, 506-516 (2005).
[Crossref]

2004 (1)

L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
[Crossref]

2003 (2)

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, 'Non-linear properties of tapered laser cavities,' IEEE J. Sel. Top. Quantum Electron. 9, 823-834 (2003).
[Crossref]

S. Sujecki, J. Wykes, P. Sewell, A. Vukovic, T. M. Benson, E. C. Larkins, L. Borruel, and I. Esquivias, 'Optical properties of tapered laser cavities,' IEE Proc.: Optoelectron. 150, 246-252 (2003).
[Crossref]

2000 (1)

S. Mariojouls, S. Margott, A. Schmitt, M. Mikulla, J. Braunstein, G. Weimann, F. Lozes, and S. Bonnefont, 'Modelling of the performance of high-brightness tapered lasers,' Proc. SPIE 3944, 395-406 (2000).
[Crossref]

1999 (1)

E. Gering, O. Hess, and R. Wallenstein, 'Modelling of the performance of high-power diode amplifier systems with an opto-thermal microscopic spatio-temporal theory,' IEEE J. Quantum Electron. 35, 320-331 (1999).
[Crossref]

1997 (2)

Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, 'Numerical simulation of broad-area high-power semiconductor laser amplifiers,' IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[Crossref]

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, 'A first-principles fully space-time resolved model of a semiconductor laser model,' J. Opt. B: Quantum Semiclassical Opt. 9, 681-692 (1997).
[Crossref]

1984 (1)

G. P. Agrawal, 'Fast-Fourier-transform based beam-propagation model for stripe-geometry semiconductor laser: inclusion of axial effects,' J. Appl. Phys. 56, 3100-3109 (1984).
[Crossref]

1961 (1)

G. Fox and T. Li, 'Resonant modes in maser interferometer,' Bell Syst. Tech. J. 40, 453-459 (1961).

Agrawal, G. P.

G. P. Agrawal, 'Fast-Fourier-transform based beam-propagation model for stripe-geometry semiconductor laser: inclusion of axial effects,' J. Appl. Phys. 56, 3100-3109 (1984).
[Crossref]

Auznneau, S.-C.

L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
[Crossref]

Benson, T. M.

J. J. Lim, T. M. Benson, and E. C. Larkins, 'Design of wide-emitter single-mode laser diodes,' IEEE J. Quantum Electron. 41, 506-516 (2005).
[Crossref]

L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
[Crossref]

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, 'Non-linear properties of tapered laser cavities,' IEEE J. Sel. Top. Quantum Electron. 9, 823-834 (2003).
[Crossref]

S. Sujecki, J. Wykes, P. Sewell, A. Vukovic, T. M. Benson, E. C. Larkins, L. Borruel, and I. Esquivias, 'Optical properties of tapered laser cavities,' IEE Proc.: Optoelectron. 150, 246-252 (2003).
[Crossref]

Bonnefont, S.

S. Mariojouls, S. Margott, A. Schmitt, M. Mikulla, J. Braunstein, G. Weimann, F. Lozes, and S. Bonnefont, 'Modelling of the performance of high-brightness tapered lasers,' Proc. SPIE 3944, 395-406 (2000).
[Crossref]

Borruel, L.

L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
[Crossref]

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, 'Non-linear properties of tapered laser cavities,' IEEE J. Sel. Top. Quantum Electron. 9, 823-834 (2003).
[Crossref]

S. Sujecki, J. Wykes, P. Sewell, A. Vukovic, T. M. Benson, E. C. Larkins, L. Borruel, and I. Esquivias, 'Optical properties of tapered laser cavities,' IEE Proc.: Optoelectron. 150, 246-252 (2003).
[Crossref]

Braunstein, J.

S. Mariojouls, S. Margott, A. Schmitt, M. Mikulla, J. Braunstein, G. Weimann, F. Lozes, and S. Bonnefont, 'Modelling of the performance of high-brightness tapered lasers,' Proc. SPIE 3944, 395-406 (2000).
[Crossref]

Dai, Z.

Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, 'Numerical simulation of broad-area high-power semiconductor laser amplifiers,' IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[Crossref]

Ebeling, K. J.

Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, 'Numerical simulation of broad-area high-power semiconductor laser amplifiers,' IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[Crossref]

Egan, A.

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, 'A first-principles fully space-time resolved model of a semiconductor laser model,' J. Opt. B: Quantum Semiclassical Opt. 9, 681-692 (1997).
[Crossref]

Erbert, G.

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, 'Non-linear properties of tapered laser cavities,' IEEE J. Sel. Top. Quantum Electron. 9, 823-834 (2003).
[Crossref]

Esquivias, I.

L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
[Crossref]

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, 'Non-linear properties of tapered laser cavities,' IEEE J. Sel. Top. Quantum Electron. 9, 823-834 (2003).
[Crossref]

S. Sujecki, J. Wykes, P. Sewell, A. Vukovic, T. M. Benson, E. C. Larkins, L. Borruel, and I. Esquivias, 'Optical properties of tapered laser cavities,' IEE Proc.: Optoelectron. 150, 246-252 (2003).
[Crossref]

Fox, G.

G. Fox and T. Li, 'Resonant modes in maser interferometer,' Bell Syst. Tech. J. 40, 453-459 (1961).

Gering, E.

E. Gering, O. Hess, and R. Wallenstein, 'Modelling of the performance of high-power diode amplifier systems with an opto-thermal microscopic spatio-temporal theory,' IEEE J. Quantum Electron. 35, 320-331 (1999).
[Crossref]

Hess, O.

E. Gering, O. Hess, and R. Wallenstein, 'Modelling of the performance of high-power diode amplifier systems with an opto-thermal microscopic spatio-temporal theory,' IEEE J. Quantum Electron. 35, 320-331 (1999).
[Crossref]

Indik, R. A.

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, 'A first-principles fully space-time resolved model of a semiconductor laser model,' J. Opt. B: Quantum Semiclassical Opt. 9, 681-692 (1997).
[Crossref]

Krakowski, M.

L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
[Crossref]

Kreyszig, E.

E. Kreyszig, Introductory Functional Analysis with Applications (Wiley, 1978).

Larkins, E. C.

J. J. Lim, T. M. Benson, and E. C. Larkins, 'Design of wide-emitter single-mode laser diodes,' IEEE J. Quantum Electron. 41, 506-516 (2005).
[Crossref]

L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
[Crossref]

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, 'Non-linear properties of tapered laser cavities,' IEEE J. Sel. Top. Quantum Electron. 9, 823-834 (2003).
[Crossref]

S. Sujecki, J. Wykes, P. Sewell, A. Vukovic, T. M. Benson, E. C. Larkins, L. Borruel, and I. Esquivias, 'Optical properties of tapered laser cavities,' IEE Proc.: Optoelectron. 150, 246-252 (2003).
[Crossref]

Li, T.

G. Fox and T. Li, 'Resonant modes in maser interferometer,' Bell Syst. Tech. J. 40, 453-459 (1961).

Lim, J. J.

J. J. Lim, T. M. Benson, and E. C. Larkins, 'Design of wide-emitter single-mode laser diodes,' IEEE J. Quantum Electron. 41, 506-516 (2005).
[Crossref]

Lozes, F.

S. Mariojouls, S. Margott, A. Schmitt, M. Mikulla, J. Braunstein, G. Weimann, F. Lozes, and S. Bonnefont, 'Modelling of the performance of high-brightness tapered lasers,' Proc. SPIE 3944, 395-406 (2000).
[Crossref]

Margott, S.

S. Mariojouls, S. Margott, A. Schmitt, M. Mikulla, J. Braunstein, G. Weimann, F. Lozes, and S. Bonnefont, 'Modelling of the performance of high-brightness tapered lasers,' Proc. SPIE 3944, 395-406 (2000).
[Crossref]

Mariojouls, S.

S. Mariojouls, S. Margott, A. Schmitt, M. Mikulla, J. Braunstein, G. Weimann, F. Lozes, and S. Bonnefont, 'Modelling of the performance of high-brightness tapered lasers,' Proc. SPIE 3944, 395-406 (2000).
[Crossref]

Michalzik, R.

Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, 'Numerical simulation of broad-area high-power semiconductor laser amplifiers,' IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[Crossref]

Mikulla, M.

S. Mariojouls, S. Margott, A. Schmitt, M. Mikulla, J. Braunstein, G. Weimann, F. Lozes, and S. Bonnefont, 'Modelling of the performance of high-brightness tapered lasers,' Proc. SPIE 3944, 395-406 (2000).
[Crossref]

Moloney, J. V.

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, 'A first-principles fully space-time resolved model of a semiconductor laser model,' J. Opt. B: Quantum Semiclassical Opt. 9, 681-692 (1997).
[Crossref]

Moreno, P.

L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
[Crossref]

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, 'Non-linear properties of tapered laser cavities,' IEEE J. Sel. Top. Quantum Electron. 9, 823-834 (2003).
[Crossref]

Ning, C. Z.

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, 'A first-principles fully space-time resolved model of a semiconductor laser model,' J. Opt. B: Quantum Semiclassical Opt. 9, 681-692 (1997).
[Crossref]

Rodriguez, D.

L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
[Crossref]

Schmitt, A.

S. Mariojouls, S. Margott, A. Schmitt, M. Mikulla, J. Braunstein, G. Weimann, F. Lozes, and S. Bonnefont, 'Modelling of the performance of high-brightness tapered lasers,' Proc. SPIE 3944, 395-406 (2000).
[Crossref]

Sewell, P.

L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
[Crossref]

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, 'Non-linear properties of tapered laser cavities,' IEEE J. Sel. Top. Quantum Electron. 9, 823-834 (2003).
[Crossref]

S. Sujecki, J. Wykes, P. Sewell, A. Vukovic, T. M. Benson, E. C. Larkins, L. Borruel, and I. Esquivias, 'Optical properties of tapered laser cavities,' IEE Proc.: Optoelectron. 150, 246-252 (2003).
[Crossref]

Sujecki, S.

L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
[Crossref]

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, 'Non-linear properties of tapered laser cavities,' IEEE J. Sel. Top. Quantum Electron. 9, 823-834 (2003).
[Crossref]

S. Sujecki, J. Wykes, P. Sewell, A. Vukovic, T. M. Benson, E. C. Larkins, L. Borruel, and I. Esquivias, 'Optical properties of tapered laser cavities,' IEE Proc.: Optoelectron. 150, 246-252 (2003).
[Crossref]

Sumpf, B.

L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
[Crossref]

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, 'Non-linear properties of tapered laser cavities,' IEEE J. Sel. Top. Quantum Electron. 9, 823-834 (2003).
[Crossref]

Unger, P.

Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, 'Numerical simulation of broad-area high-power semiconductor laser amplifiers,' IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[Crossref]

Vukovic, A.

S. Sujecki, J. Wykes, P. Sewell, A. Vukovic, T. M. Benson, E. C. Larkins, L. Borruel, and I. Esquivias, 'Optical properties of tapered laser cavities,' IEE Proc.: Optoelectron. 150, 246-252 (2003).
[Crossref]

Wallenstein, R.

E. Gering, O. Hess, and R. Wallenstein, 'Modelling of the performance of high-power diode amplifier systems with an opto-thermal microscopic spatio-temporal theory,' IEEE J. Quantum Electron. 35, 320-331 (1999).
[Crossref]

Weimann, G.

S. Mariojouls, S. Margott, A. Schmitt, M. Mikulla, J. Braunstein, G. Weimann, F. Lozes, and S. Bonnefont, 'Modelling of the performance of high-brightness tapered lasers,' Proc. SPIE 3944, 395-406 (2000).
[Crossref]

Wenzel, H.

L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
[Crossref]

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, 'Non-linear properties of tapered laser cavities,' IEEE J. Sel. Top. Quantum Electron. 9, 823-834 (2003).
[Crossref]

Wykes, J.

L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
[Crossref]

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, 'Non-linear properties of tapered laser cavities,' IEEE J. Sel. Top. Quantum Electron. 9, 823-834 (2003).
[Crossref]

S. Sujecki, J. Wykes, P. Sewell, A. Vukovic, T. M. Benson, E. C. Larkins, L. Borruel, and I. Esquivias, 'Optical properties of tapered laser cavities,' IEE Proc.: Optoelectron. 150, 246-252 (2003).
[Crossref]

Bell Syst. Tech. J. (1)

G. Fox and T. Li, 'Resonant modes in maser interferometer,' Bell Syst. Tech. J. 40, 453-459 (1961).

IEE Proc.: Optoelectron. (1)

S. Sujecki, J. Wykes, P. Sewell, A. Vukovic, T. M. Benson, E. C. Larkins, L. Borruel, and I. Esquivias, 'Optical properties of tapered laser cavities,' IEE Proc.: Optoelectron. 150, 246-252 (2003).
[Crossref]

IEEE J. Quantum Electron. (4)

J. J. Lim, T. M. Benson, and E. C. Larkins, 'Design of wide-emitter single-mode laser diodes,' IEEE J. Quantum Electron. 41, 506-516 (2005).
[Crossref]

L. Borruel, S. Sujecki, P. Moreno, J. Wykes, M. Krakowski, B. Sumpf, P. Sewell, S.-C. Auznneau, H. Wenzel, D. Rodriguez, T. M. Benson, E. C. Larkins, and I. Esquivias, 'Quasi-3D simulation of high-brightness tapered lasers,' IEEE J. Quantum Electron. 40, 463-472 (2004).
[Crossref]

E. Gering, O. Hess, and R. Wallenstein, 'Modelling of the performance of high-power diode amplifier systems with an opto-thermal microscopic spatio-temporal theory,' IEEE J. Quantum Electron. 35, 320-331 (1999).
[Crossref]

Z. Dai, R. Michalzik, P. Unger, and K. J. Ebeling, 'Numerical simulation of broad-area high-power semiconductor laser amplifiers,' IEEE J. Quantum Electron. 33, 2240-2254 (1997).
[Crossref]

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

S. Sujecki, L. Borruel, J. Wykes, P. Moreno, B. Sumpf, P. Sewell, H. Wenzel, T. M. Benson, G. Erbert, I. Esquivias, and E. C. Larkins, 'Non-linear properties of tapered laser cavities,' IEEE J. Sel. Top. Quantum Electron. 9, 823-834 (2003).
[Crossref]

J. Appl. Phys. (1)

G. P. Agrawal, 'Fast-Fourier-transform based beam-propagation model for stripe-geometry semiconductor laser: inclusion of axial effects,' J. Appl. Phys. 56, 3100-3109 (1984).
[Crossref]

J. Opt. B: Quantum Semiclassical Opt. (1)

C. Z. Ning, J. V. Moloney, A. Egan, and R. A. Indik, 'A first-principles fully space-time resolved model of a semiconductor laser model,' J. Opt. B: Quantum Semiclassical Opt. 9, 681-692 (1997).
[Crossref]

Proc. SPIE (1)

S. Mariojouls, S. Margott, A. Schmitt, M. Mikulla, J. Braunstein, G. Weimann, F. Lozes, and S. Bonnefont, 'Modelling of the performance of high-brightness tapered lasers,' Proc. SPIE 3944, 395-406 (2000).
[Crossref]

Other (1)

E. Kreyszig, Introductory Functional Analysis with Applications (Wiley, 1978).

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Figures (6)

Fig. 1
Fig. 1

Tapered laser diode.

Fig. 2
Fig. 2

Longitudinal discretization for CSM and SSM.

Fig. 3
Fig. 3

Dependence of the photon density on the iteration number of the fixed-point sequence of Eq. (8) (a) of the right-hand side of Eq. (8) and (b) on the photon density.

Fig. 4
Fig. 4

Dependence of the photon density on the iteration number of the fixed-point sequence of Eq. (12) at (a) 2 and (b) 10 times the threshold current; p = 0.6 .

Fig. 5
Fig. 5

Dependence of the photon density at the rear facet associated with the forward-propagating wave on the iteration number at 10 times the threshold current with (a) 4 and (b) 10 longitudinal sections.

Fig. 6
Fig. 6

Light–current characteristic calculated by CSM with 40 longitudinal sections.

Tables (5)

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Table 1 Simulation Parameters

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Table 2 Summary of 1D CSM and SSM Simulations Using 40 Longitudinal Sections

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Table 3 Summary of 2D CSM Simulations (Spontaneous Emission Term Not Included)

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Table 4 Summary of 2D CSM Simulations (Spontaneous Emission Term Included)

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Table 5 Summary of 2D CSM Simulations at a Bias Current of 3.4 A (Spontaneous Emission Term Included) a

Equations (32)

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D 2 N x 2 = η i J q d + N τ + Γ g ( N ) h ν ( ϕ f 2 + ϕ b 2 ) ,
[ ϕ b ( z = z ) ϕ f ( z = z ) ] = [ 0 T o b 0 T o f ] [ ϕ b ( z = 0 ) ϕ f ( z = 0 ) ] .
T o f = exp z = 0 z [ j β r ( 1 + L m β r 2 + 1 ) ] d z ,
T o b = exp z = L z [ j β r ( 1 + L m β r 2 + 1 ) ] d z R f exp z = 0 L [ j β r ( 1 + L m β r 2 + 1 ) ] d z .
ϕ f 2 n + 1 ( x ) = O f 1 ϕ f 1 n ( x ) = T f 2 ϕ f 1 n ( x ) ,
ϕ f 3 n + 1 ( x ) = O f 2 O f 1 ϕ f 1 n ( x ) = T f 3 ϕ f 1 n ( x ) ,
ϕ f M n + 1 ( x ) = m = 1 M 1 O f m ϕ f 1 n ( x ) = T f M ϕ f 1 n ( x ) ,
ϕ b M n + 1 ( x ) = R f m = 1 M O f m ϕ f 1 n ( x ) = T b M ϕ f 1 n ( x ) ,
ϕ b 1 n + 1 ( x ) = m = 1 M 1 O b m R f m = 1 M O f m ϕ f 1 n ( x ) = T b 1 ϕ f 1 n ( x ) ,
ϕ f 1 n + 1 ( x ) = R b m = 1 M O b m R f m = 1 M O f m ϕ f 1 n ( x ) = T f 1 ϕ f 1 n ( x ) ,
N k n + 1 ( x ) = T e k ( ϕ f k n + 1 ( x ) 2 + ϕ b k n + 1 ( x ) 2 ) ,
ϕ f 2 n + 1 ( x ) = T f 2 ϕ f 1 n ( x ) ; N 2 n + 1 2 ( x ) = T e 2 ( ϕ f 2 n + 1 ( x ) 2 + ϕ b 2 n ( x ) 2 ) ,
ϕ f 3 n + 1 ( x ) = T f 3 ϕ f 1 n ( x ) ; N 3 n + 1 2 ( x ) = T e 3 ( ϕ f 3 n + 1 ( x ) 2 + ϕ b 3 n ( x ) 2 ) ,
ϕ f M n + 1 ( x ) = T f M ϕ f 1 n ( x ) ; N M n + 1 2 ( x ) = T e M ( ϕ f M n + 1 ( x ) 2 + ϕ b M n ( x ) 2 ) ,
ϕ b M n + 1 ( x ) = T b M ϕ f 1 n ( x ) ; N M n + 1 ( x ) = T e M ( ϕ f M n + 1 ( x ) 2 + ϕ b M n + 1 ( x ) 2 ) ,
ϕ b 1 n + 1 ( x ) = T b 1 ϕ f 1 n ( x ) ; N 1 n + 1 2 ( x ) = T e 1 ( ϕ f 1 n + 1 ( x ) 2 + ϕ b 1 n ( x ) 2 ) ,
ϕ f 1 n + 1 ( x ) = T f 1 ϕ f 1 n ( x ) ; N 1 n + 1 ( x ) = T e 1 ( ϕ f 1 n + 1 ( x ) 2 + ϕ b 1 n + 1 ( x ) 2 ) .
[ ϕ f 2 n + 1 ( x ) ϕ f 3 n + 1 ( x ) ϕ f M n + 1 ( x ) ϕ b M n + 1 ( x ) ϕ b 1 n + 1 ( x ) ϕ f 1 n + 1 ( x ) ] = [ 0 0 0 0 0 T f 2 0 0 0 0 0 T f 3 0 0 0 0 0 T f M 0 0 0 0 0 T b M 0 0 0 0 0 T b 1 0 0 0 0 0 T f 1 ] [ ϕ f 2 n ( x ) ϕ f 3 n ( x ) ϕ f M n ( x ) ϕ b M n ( x ) ϕ b 1 n ( x ) ϕ f 1 n ( x ) ] .
[ P f 2 n + 1 P f 3 n + 1 P f M n + 1 P b M n + 1 P b 1 n + 1 P f 1 n + 1 ] = [ 0 0 0 0 0 T f 2 1 D 0 0 0 0 0 T f 3 1 D 0 0 0 0 0 T f M 1 D 0 0 0 0 0 T b M 1 D 0 0 0 0 0 T b 1 1 D 0 0 0 0 0 T f 1 1 D ] [ P f 2 n P f 3 n P f M n P b M n P b 1 n P f 1 n ] ,
T f m 1 1 D = m = 1 m 1 exp ( g m Δ z ) , for m 1 = 2 , , M ,
T b m 1 1 D = m = M m 1 exp ( g m Δ z ) R f m = 1 M exp ( g m Δ z ) , for m 1 = 1 , , M ,
T f 1 1 D = R b m = 1 M exp ( g m Δ z ) R f m = 1 M exp ( g m Δ z ) , for m 1 = 1 ,
N m n + 1 = η I m q V m + v g a N t r ( P f m n + 1 + P b m n + 1 ) 1 τ + v g a ( P f m n + 1 + P b m n + 1 ) ,
P n + 1 = P n exp ( [ Γ v g a ( η I q V + v g a N t r P n 1 τ + v g a P n N t r ) 1 τ p ] 2 L v g ) ,
P n + 1 = P n exp ( [ Γ v g a ( η I q V + v g a N t r P n 1 τ + v g a P n N t r ) + Γ β τ P n η I q V + v g a N t r P n 1 τ + v g a P n 1 τ p ] 2 L v g ) ,
P n + 1 * p = P n exp ( [ Γ v g a ( N n N t r ) + Γ β N n τ P n 1 τ p ] 2 L v g * p ) ,
N n + 1 * p = η I q V + v g a N t r P n + 1 * p 1 τ + v g a P n + 1 * p .
ε = f n f n 1 , f n f n 1 f n + f n 1 , f n + f n 1 ,

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