Abstract

To increase the brightness of broad area laser diodes, it is necessary to tailor the optical properties of their waveguide region. For this purpose, there is the need for simulation tools which can predict the optical properties of the complete device and thus of the outcoupled light. In the present publication, we show a numerical method to calculate typical intensity distributions of the multimode beam inside a high-power semiconductor laser. The model considers effects of mode competition and the influence of the gain medium on the optical field. Simulation results show a good agreement with near and far field measurements of the analyzed broad area laser diodes.

© 2013 Optical Society of America

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References

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  1. A. Büttner and U. Zeitner, “Experimental Realization of Monolithic Diffractive Broad-Area Polymeric Waveguide Dye Lasers,” IEEE J. Quantum Electron. 43(7), 545–551 (2007).
    [Crossref]
  2. A. Büttner, U. D. Zeitner, and R. Kowarschik, “Design considerations for high-brightness diffractive broad-area lasers,” J. Opt. Soc. Am. B 22, 796 (2005).
    [Crossref]
  3. C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators (United States Governm. Pr. Office, 1950).
  4. A. G. Fox and T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 51(1), 80–89 (1963).
    [Crossref]
  5. B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, “Ambipolar diffusion of photoexcited carriers in bulk GaAs,” Appl. Phys. Lett. 97(26), 262119 (2010).
    [Crossref]
  6. L. A. Coldren, S. W. Corzine, and M. Mashanovitch, Diode lasers and photonic integrated circuits, 2nd ed. (Wiley, 2012).
  7. J. Luttinger and W. Kohn, “Motion of Electrons and Holes in Perturbed Periodic Fields,” Phys. Rev. 97(4), 869–883 (1955).
    [Crossref]
  8. D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
    [Crossref]
  9. A. E. Siegman, “How to (Maybe) Measure Laser Beam Quality,” in OSA Trends in Optics and Photonics, Vol. 17 (1998), MQ1.
  10. M. D. Feit and J. A. Fleck., “Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams,” J. Opt. Soc. Am. B 5(3), 633 (1988).
    [Crossref]

2010 (1)

B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, “Ambipolar diffusion of photoexcited carriers in bulk GaAs,” Appl. Phys. Lett. 97(26), 262119 (2010).
[Crossref]

2007 (1)

A. Büttner and U. Zeitner, “Experimental Realization of Monolithic Diffractive Broad-Area Polymeric Waveguide Dye Lasers,” IEEE J. Quantum Electron. 43(7), 545–551 (2007).
[Crossref]

2005 (1)

1992 (1)

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[Crossref]

1988 (1)

1963 (1)

A. G. Fox and T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 51(1), 80–89 (1963).
[Crossref]

1955 (1)

J. Luttinger and W. Kohn, “Motion of Electrons and Holes in Perturbed Periodic Fields,” Phys. Rev. 97(4), 869–883 (1955).
[Crossref]

Büttner, A.

A. Büttner and U. Zeitner, “Experimental Realization of Monolithic Diffractive Broad-Area Polymeric Waveguide Dye Lasers,” IEEE J. Quantum Electron. 43(7), 545–551 (2007).
[Crossref]

A. Büttner, U. D. Zeitner, and R. Kowarschik, “Design considerations for high-brightness diffractive broad-area lasers,” J. Opt. Soc. Am. B 22, 796 (2005).
[Crossref]

Feit, M. D.

Fleck, J. A.

Fox, A. G.

A. G. Fox and T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 51(1), 80–89 (1963).
[Crossref]

Hagan, D. J.

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[Crossref]

Hutchings, D. C.

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[Crossref]

Kohn, W.

J. Luttinger and W. Kohn, “Motion of Electrons and Holes in Perturbed Periodic Fields,” Phys. Rev. 97(4), 869–883 (1955).
[Crossref]

Kowarschik, R.

Li, T.

A. G. Fox and T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 51(1), 80–89 (1963).
[Crossref]

Luttinger, J.

J. Luttinger and W. Kohn, “Motion of Electrons and Holes in Perturbed Periodic Fields,” Phys. Rev. 97(4), 869–883 (1955).
[Crossref]

Ruzicka, B. A.

B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, “Ambipolar diffusion of photoexcited carriers in bulk GaAs,” Appl. Phys. Lett. 97(26), 262119 (2010).
[Crossref]

Samassekou, H.

B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, “Ambipolar diffusion of photoexcited carriers in bulk GaAs,” Appl. Phys. Lett. 97(26), 262119 (2010).
[Crossref]

Sheik-Bahae, M.

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[Crossref]

Stryland, E. W.

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[Crossref]

Werake, L. K.

B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, “Ambipolar diffusion of photoexcited carriers in bulk GaAs,” Appl. Phys. Lett. 97(26), 262119 (2010).
[Crossref]

Zeitner, U.

A. Büttner and U. Zeitner, “Experimental Realization of Monolithic Diffractive Broad-Area Polymeric Waveguide Dye Lasers,” IEEE J. Quantum Electron. 43(7), 545–551 (2007).
[Crossref]

Zeitner, U. D.

Zhao, H.

B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, “Ambipolar diffusion of photoexcited carriers in bulk GaAs,” Appl. Phys. Lett. 97(26), 262119 (2010).
[Crossref]

Appl. Phys. Lett. (1)

B. A. Ruzicka, L. K. Werake, H. Samassekou, and H. Zhao, “Ambipolar diffusion of photoexcited carriers in bulk GaAs,” Appl. Phys. Lett. 97(26), 262119 (2010).
[Crossref]

IEEE J. Quantum Electron. (1)

A. Büttner and U. Zeitner, “Experimental Realization of Monolithic Diffractive Broad-Area Polymeric Waveguide Dye Lasers,” IEEE J. Quantum Electron. 43(7), 545–551 (2007).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Quantum Electron. (1)

D. C. Hutchings, M. Sheik-Bahae, D. J. Hagan, and E. W. Stryland, “Kramers-Kronig relations in nonlinear optics,” Opt. Quantum Electron. 24(1), 1–30 (1992).
[Crossref]

Phys. Rev. (1)

J. Luttinger and W. Kohn, “Motion of Electrons and Holes in Perturbed Periodic Fields,” Phys. Rev. 97(4), 869–883 (1955).
[Crossref]

Proc. IEEE (1)

A. G. Fox and T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 51(1), 80–89 (1963).
[Crossref]

Other (3)

A. E. Siegman, “How to (Maybe) Measure Laser Beam Quality,” in OSA Trends in Optics and Photonics, Vol. 17 (1998), MQ1.

C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators (United States Governm. Pr. Office, 1950).

L. A. Coldren, S. W. Corzine, and M. Mashanovitch, Diode lasers and photonic integrated circuits, 2nd ed. (Wiley, 2012).

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Figures (6)

Fig. 1
Fig. 1 Change of carrier density vs. carrier density for different power and current densities for two different injection current densities (2500 and 1500 A/cm2) and 8 optical power densities (0,0.005..0.095 W/µm)

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Fig. 2
Fig. 2 Schematic sketch of the algorithm

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Fig. 3
Fig. 3 Near field diameter (top, red) and farfield full angle (bottom, blue) of an AlGaAs broad area laser (100µm stripe width, 4mm resonator length) vs. injection current; Simulation results (triangles) are compared with measurements (squares)

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Fig. 4
Fig. 4 Optical output power (bottom, red) and beam parameter product (top, blue) vs. injection current; Simulation results (triangles) are compared with measurements (squares)

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Fig. 5
Fig. 5 Simulated (red) and measured (blue) intensity distributions. Left: on the outcoupling facet (near field), right: and angular distribution of the output beam (far field)

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Fig. 6
Fig. 6 Distribution of excited carriers and optical power density inside the waveguide and change of the refractive index. The stripe width of the contacted region is 100 µm, the resonator length is 4 mm.

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Equations (15)

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Z ^ U i ( x,y,z )= λ i U i ( x,y,z ),
l i =1− ‖ λ i ‖ 2 .
U 0 ( x,y, z 0 )= ∑ i=0 n ( ξ i U i ( x,y, z 0 ) ) + U rest
U j 0 ( x,y, z 0 )= ∑ i=0 n ( [ ∏ k=0 j−1 ξ i,k λ i ]⋅ U i ( x,y, z 0 ) ) + Z ^ ∘...∘ Z ^ ︸ j−1   times U rest .
‖ ∏ k= j 0 m ξ i,k λ i ‖≈1 for  U i  is existing mode ‖ ∏ k= j 0 m ξ i,k λ i ‖≈0 for  U i  is below threshold ‖ Z ^ ∘...∘ Z ^ ︸ m   times U rest ‖≈0 for non-stationary parts of U 0 .
g i = 1 ‖ λ i ‖ 2 .
1 n avg +1 ∑ j= j 0 j 0 + n avg ∬ ∑ i ‖ ξ i,j λ i U i ( x,y, z OC ) ‖ 2  dxdy∼ P out
1 n avg +1 ∑ j= j 0 j 0 + n avg ∬ ‖ ξ i,j λ i U i ( x,y, z OC ) ‖ 2  dxdy∼ P i .
1 n avg +1 ∑ j= j 0 j 0 + n avg ∑ i ‖ ξ i,j λ i U i ( x,y,z ) ‖ 2 = ∑ i 1 n avg +1 [ ∑ j= j 0 j 0 + n avg ‖ ξ i,j λ i ‖ 2 ] ︸ = 1  if i∈Ω ,   ≈0  otherwise ⋅ ‖ U i ( x,y,z ) ‖ 2 = ∑ i∈Ω ‖ U i ( x,y,z ) ‖ 2 .
dN dt = −R( N )⋅N ︸ (a) − g( N )⋅ p( x,z )⋅dx hν ⋅Γ⋅dz ︸ (b) + d N I ( x,z ) ︸ (c) +d N diff ︸ ( d )
R( N )= A ︸ (a) + B(N)⋅N ︸ (b) + C⋅ N 2 ︸ (c) ,
L Diff ≈ D AM ⋅τ ≪ 20c m 2 s −1 ⋅0.5ns =1μm.
d N 0 ( x,z ) dt ≈0  →   N 0 ( x,z )= N 0 ( p( x,z ),I( x,z ) ).
p j+1 ( x,z )=( 1−α ) p j ( x,z )+α⋅ ε 0 ∫ ‖ U j+1 0 ( x,y,z ) ‖ 2 dy .
N 0 ( x,z ) j+1 =( 1−β )⋅ N 0 ( x,z ) j +β⋅ N 0 ( p j+1 ( x,z ),I( x,z ) ).

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