Abstract

Apodizing holographic gratings used in an external cavity have shown to be effective to control the modal content of multimode broad-area diode lasers, providing single longitudinal-mode and single lateral-mode emission. They can also be designed to provide Littrow reflection at two wavelengths. We observed stable oscillation at two wavelengths in a diode laser with an external cavity ended with such a grating. This is not a common behavior for homogeneously broadened gain media. We present simulations of the behavior of this laser based on a rate equation analysis. The effects of spatial hole burning and spontaneous emission are examined.

© 2002 Optical Society of America

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References

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  1. J.-F. Lepage, R. Massudi, G. Anctil, S. Gilbert, M. Piché, N. McCarthy, “Apodizing holographic gratings for the modal control of semiconductor lasers,” Appl. Opt. 36, 4993–4998 (1997).
    [CrossRef] [PubMed]
  2. Ch. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics, R.-J. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
    [CrossRef]
  3. J.-F. Lepage, N. McCarthy, “Apodizing holographic gratings for dual-wavelength operation of broad-area semiconductor lasers,” Appl. Opt. 37, 8420–8425 (1998).
    [CrossRef]
  4. T. Hidaka, Y. Hatano, “Simulaneous two wave oscillation LD using biperiodic binary grating,” Electron. Lett. 27, 1075–1076 (1991).
    [CrossRef]
  5. K.-S. Lee, C. Shu, “Stable and widely tunable dual-wavelength continuous wave operation of a semiconductor laser in a novel Fabry-Perot grating-lens external cavity,” IEEE J. Quantum Electron. 33, 1832–1838 (1997).
    [CrossRef]
  6. C.-L. Pan, C.-L. Wang, “A novel tunable dual-wavelength external-cavity laser diode array and its applications,” Opt. Quantum Electron. 28, 1239–1257 (1996).
    [CrossRef]
  7. S. Iio, M. Suehiro, T. Hirata, T. Hidaka, “Two-longitudinal-mode laser diodes,” IEEE Photon. Technol. Lett. 7, 959–961 (1995).
    [CrossRef]
  8. M. H. Mourad, J. P. Vilcot, D. Decoster, D. Marcenac, “Design and simulation of a dual mode semiconductor laser using sampled grating DFB structure,” IEE Proc. Optoelectron. 147, 37–42 (2000).
    [CrossRef]
  9. P.-C. Ku, C.-F. Lin, B.-L. Lee, “Multiple cross switching in a two-mode semiconductor laser,” Appl. Phys. Lett. 69, 3984–3986 (1996).
    [CrossRef]
  10. E. C. Mos, J. J. H. B. Schleipen, H. de Waardt, G.-D. Kloe, “Longitudinal mode-switching in dual external-cavity laser diode,” IEEE J. Quantum Electron. 36, 486–495 (2000).
    [CrossRef]
  11. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1985).
  12. B. Zee, “Broadening mechanism in semiconductor (GaAs) lasers: limitations to single mode power emission,” IEEE J. Quantum Electron. QE-14, 727–736 (1978).
    [CrossRef]
  13. A. Gearba, G. Cone, “Numerical analysis of laser mode competition and stability,” Phys. Lett. A 269, 112–119 (2000).
    [CrossRef]
  14. F. X. Kärtner, B. Braun, U. Keller, “Continuous-wave mode-locked solid state lasers with enhanced spatial hole burning. Part II: Theory,” Appl. Phys. B. 61, 569–579 (1995).
    [CrossRef]
  15. H. G. Danielmeyer, “Effects of drift and diffusion of excited states on spatial hole burning and laser oscillation,” J. Appl. Phys. 42, 3125–3132 (1971).
    [CrossRef]
  16. J. J. Zayhowski, “Limits imposed by spatial hole burning on the single-mode operation of standing-wave laser cavities,” Opt. Lett. 15, 431–433 (1990).
    [CrossRef] [PubMed]
  17. T. Kimura, K. Otsuka, M. Saruwatari, “Spatial hole-burning effects in a Nd3+:YAG laser,” IEEE J. Quantum Electron. QE-7, 225–230 (1971).
    [CrossRef]
  18. I. V. Hertel, A. S. Stamatovic, “Spatial hole burning and oligo-mode distance control in CW dye lasers,” IEEE J. Quantum Electron. QE-11, 210–212 (1975).
    [CrossRef]
  19. G. P. Agrawal, N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, New York, 1993).
  20. G. P. Agrawal, “Effect of gain and index nonlinearities on single-mode dynamics in semiconductor lasers,” IEEE J. Quantum Electron. 26, 1901–1909 (1990).
    [CrossRef]
  21. W. Brunner, R. Fisher, H. Paul, “Regular and chaotic behavior of multimode lasers,” J. Opt. Soc. Am. B 2, 202–210 (1985).
    [CrossRef]
  22. I. McMackin, C. Radzewicz, M. Beck, M. G. Raymer, “Instabilities and chaos in a multimode, standing wave, cw dye laser,” Phys. Rev. A 38, 820–832 (1988).
    [CrossRef] [PubMed]

2000 (3)

M. H. Mourad, J. P. Vilcot, D. Decoster, D. Marcenac, “Design and simulation of a dual mode semiconductor laser using sampled grating DFB structure,” IEE Proc. Optoelectron. 147, 37–42 (2000).
[CrossRef]

E. C. Mos, J. J. H. B. Schleipen, H. de Waardt, G.-D. Kloe, “Longitudinal mode-switching in dual external-cavity laser diode,” IEEE J. Quantum Electron. 36, 486–495 (2000).
[CrossRef]

A. Gearba, G. Cone, “Numerical analysis of laser mode competition and stability,” Phys. Lett. A 269, 112–119 (2000).
[CrossRef]

1998 (1)

1997 (2)

K.-S. Lee, C. Shu, “Stable and widely tunable dual-wavelength continuous wave operation of a semiconductor laser in a novel Fabry-Perot grating-lens external cavity,” IEEE J. Quantum Electron. 33, 1832–1838 (1997).
[CrossRef]

J.-F. Lepage, R. Massudi, G. Anctil, S. Gilbert, M. Piché, N. McCarthy, “Apodizing holographic gratings for the modal control of semiconductor lasers,” Appl. Opt. 36, 4993–4998 (1997).
[CrossRef] [PubMed]

1996 (2)

C.-L. Pan, C.-L. Wang, “A novel tunable dual-wavelength external-cavity laser diode array and its applications,” Opt. Quantum Electron. 28, 1239–1257 (1996).
[CrossRef]

P.-C. Ku, C.-F. Lin, B.-L. Lee, “Multiple cross switching in a two-mode semiconductor laser,” Appl. Phys. Lett. 69, 3984–3986 (1996).
[CrossRef]

1995 (2)

S. Iio, M. Suehiro, T. Hirata, T. Hidaka, “Two-longitudinal-mode laser diodes,” IEEE Photon. Technol. Lett. 7, 959–961 (1995).
[CrossRef]

F. X. Kärtner, B. Braun, U. Keller, “Continuous-wave mode-locked solid state lasers with enhanced spatial hole burning. Part II: Theory,” Appl. Phys. B. 61, 569–579 (1995).
[CrossRef]

1991 (1)

T. Hidaka, Y. Hatano, “Simulaneous two wave oscillation LD using biperiodic binary grating,” Electron. Lett. 27, 1075–1076 (1991).
[CrossRef]

1990 (2)

J. J. Zayhowski, “Limits imposed by spatial hole burning on the single-mode operation of standing-wave laser cavities,” Opt. Lett. 15, 431–433 (1990).
[CrossRef] [PubMed]

G. P. Agrawal, “Effect of gain and index nonlinearities on single-mode dynamics in semiconductor lasers,” IEEE J. Quantum Electron. 26, 1901–1909 (1990).
[CrossRef]

1988 (1)

I. McMackin, C. Radzewicz, M. Beck, M. G. Raymer, “Instabilities and chaos in a multimode, standing wave, cw dye laser,” Phys. Rev. A 38, 820–832 (1988).
[CrossRef] [PubMed]

1985 (1)

1978 (1)

B. Zee, “Broadening mechanism in semiconductor (GaAs) lasers: limitations to single mode power emission,” IEEE J. Quantum Electron. QE-14, 727–736 (1978).
[CrossRef]

1975 (1)

I. V. Hertel, A. S. Stamatovic, “Spatial hole burning and oligo-mode distance control in CW dye lasers,” IEEE J. Quantum Electron. QE-11, 210–212 (1975).
[CrossRef]

1971 (2)

T. Kimura, K. Otsuka, M. Saruwatari, “Spatial hole-burning effects in a Nd3+:YAG laser,” IEEE J. Quantum Electron. QE-7, 225–230 (1971).
[CrossRef]

H. G. Danielmeyer, “Effects of drift and diffusion of excited states on spatial hole burning and laser oscillation,” J. Appl. Phys. 42, 3125–3132 (1971).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, “Effect of gain and index nonlinearities on single-mode dynamics in semiconductor lasers,” IEEE J. Quantum Electron. 26, 1901–1909 (1990).
[CrossRef]

G. P. Agrawal, N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, New York, 1993).

Anctil, G.

Beck, M.

I. McMackin, C. Radzewicz, M. Beck, M. G. Raymer, “Instabilities and chaos in a multimode, standing wave, cw dye laser,” Phys. Rev. A 38, 820–832 (1988).
[CrossRef] [PubMed]

Braun, B.

F. X. Kärtner, B. Braun, U. Keller, “Continuous-wave mode-locked solid state lasers with enhanced spatial hole burning. Part II: Theory,” Appl. Phys. B. 61, 569–579 (1995).
[CrossRef]

Brunner, W.

Budzinski, Ch.

Ch. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics, R.-J. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Cone, G.

A. Gearba, G. Cone, “Numerical analysis of laser mode competition and stability,” Phys. Lett. A 269, 112–119 (2000).
[CrossRef]

Danielmeyer, H. G.

H. G. Danielmeyer, “Effects of drift and diffusion of excited states on spatial hole burning and laser oscillation,” J. Appl. Phys. 42, 3125–3132 (1971).
[CrossRef]

de Waardt, H.

E. C. Mos, J. J. H. B. Schleipen, H. de Waardt, G.-D. Kloe, “Longitudinal mode-switching in dual external-cavity laser diode,” IEEE J. Quantum Electron. 36, 486–495 (2000).
[CrossRef]

Decoster, D.

M. H. Mourad, J. P. Vilcot, D. Decoster, D. Marcenac, “Design and simulation of a dual mode semiconductor laser using sampled grating DFB structure,” IEE Proc. Optoelectron. 147, 37–42 (2000).
[CrossRef]

Dutta, N. K.

G. P. Agrawal, N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, New York, 1993).

Fisher, R.

Gearba, A.

A. Gearba, G. Cone, “Numerical analysis of laser mode competition and stability,” Phys. Lett. A 269, 112–119 (2000).
[CrossRef]

Gilbert, S.

Grunwald, R.

Ch. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics, R.-J. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Hatano, Y.

T. Hidaka, Y. Hatano, “Simulaneous two wave oscillation LD using biperiodic binary grating,” Electron. Lett. 27, 1075–1076 (1991).
[CrossRef]

Hertel, I. V.

I. V. Hertel, A. S. Stamatovic, “Spatial hole burning and oligo-mode distance control in CW dye lasers,” IEEE J. Quantum Electron. QE-11, 210–212 (1975).
[CrossRef]

Hidaka, T.

S. Iio, M. Suehiro, T. Hirata, T. Hidaka, “Two-longitudinal-mode laser diodes,” IEEE Photon. Technol. Lett. 7, 959–961 (1995).
[CrossRef]

T. Hidaka, Y. Hatano, “Simulaneous two wave oscillation LD using biperiodic binary grating,” Electron. Lett. 27, 1075–1076 (1991).
[CrossRef]

Hirata, T.

S. Iio, M. Suehiro, T. Hirata, T. Hidaka, “Two-longitudinal-mode laser diodes,” IEEE Photon. Technol. Lett. 7, 959–961 (1995).
[CrossRef]

Iio, S.

S. Iio, M. Suehiro, T. Hirata, T. Hidaka, “Two-longitudinal-mode laser diodes,” IEEE Photon. Technol. Lett. 7, 959–961 (1995).
[CrossRef]

Kärtner, F. X.

F. X. Kärtner, B. Braun, U. Keller, “Continuous-wave mode-locked solid state lasers with enhanced spatial hole burning. Part II: Theory,” Appl. Phys. B. 61, 569–579 (1995).
[CrossRef]

Keller, U.

F. X. Kärtner, B. Braun, U. Keller, “Continuous-wave mode-locked solid state lasers with enhanced spatial hole burning. Part II: Theory,” Appl. Phys. B. 61, 569–579 (1995).
[CrossRef]

Kimura, T.

T. Kimura, K. Otsuka, M. Saruwatari, “Spatial hole-burning effects in a Nd3+:YAG laser,” IEEE J. Quantum Electron. QE-7, 225–230 (1971).
[CrossRef]

Kloe, G.-D.

E. C. Mos, J. J. H. B. Schleipen, H. de Waardt, G.-D. Kloe, “Longitudinal mode-switching in dual external-cavity laser diode,” IEEE J. Quantum Electron. 36, 486–495 (2000).
[CrossRef]

Ku, P.-C.

P.-C. Ku, C.-F. Lin, B.-L. Lee, “Multiple cross switching in a two-mode semiconductor laser,” Appl. Phys. Lett. 69, 3984–3986 (1996).
[CrossRef]

Lee, B.-L.

P.-C. Ku, C.-F. Lin, B.-L. Lee, “Multiple cross switching in a two-mode semiconductor laser,” Appl. Phys. Lett. 69, 3984–3986 (1996).
[CrossRef]

Lee, K.-S.

K.-S. Lee, C. Shu, “Stable and widely tunable dual-wavelength continuous wave operation of a semiconductor laser in a novel Fabry-Perot grating-lens external cavity,” IEEE J. Quantum Electron. 33, 1832–1838 (1997).
[CrossRef]

Lepage, J.-F.

Lin, C.-F.

P.-C. Ku, C.-F. Lin, B.-L. Lee, “Multiple cross switching in a two-mode semiconductor laser,” Appl. Phys. Lett. 69, 3984–3986 (1996).
[CrossRef]

Marcenac, D.

M. H. Mourad, J. P. Vilcot, D. Decoster, D. Marcenac, “Design and simulation of a dual mode semiconductor laser using sampled grating DFB structure,” IEE Proc. Optoelectron. 147, 37–42 (2000).
[CrossRef]

Massudi, R.

McCarthy, N.

McMackin, I.

I. McMackin, C. Radzewicz, M. Beck, M. G. Raymer, “Instabilities and chaos in a multimode, standing wave, cw dye laser,” Phys. Rev. A 38, 820–832 (1988).
[CrossRef] [PubMed]

Mos, E. C.

E. C. Mos, J. J. H. B. Schleipen, H. de Waardt, G.-D. Kloe, “Longitudinal mode-switching in dual external-cavity laser diode,” IEEE J. Quantum Electron. 36, 486–495 (2000).
[CrossRef]

Mourad, M. H.

M. H. Mourad, J. P. Vilcot, D. Decoster, D. Marcenac, “Design and simulation of a dual mode semiconductor laser using sampled grating DFB structure,” IEE Proc. Optoelectron. 147, 37–42 (2000).
[CrossRef]

Otsuka, K.

T. Kimura, K. Otsuka, M. Saruwatari, “Spatial hole-burning effects in a Nd3+:YAG laser,” IEEE J. Quantum Electron. QE-7, 225–230 (1971).
[CrossRef]

Pan, C.-L.

C.-L. Pan, C.-L. Wang, “A novel tunable dual-wavelength external-cavity laser diode array and its applications,” Opt. Quantum Electron. 28, 1239–1257 (1996).
[CrossRef]

Paul, H.

Piché, M.

Pinz, I.

Ch. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics, R.-J. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Radzewicz, C.

I. McMackin, C. Radzewicz, M. Beck, M. G. Raymer, “Instabilities and chaos in a multimode, standing wave, cw dye laser,” Phys. Rev. A 38, 820–832 (1988).
[CrossRef] [PubMed]

Raymer, M. G.

I. McMackin, C. Radzewicz, M. Beck, M. G. Raymer, “Instabilities and chaos in a multimode, standing wave, cw dye laser,” Phys. Rev. A 38, 820–832 (1988).
[CrossRef] [PubMed]

Saruwatari, M.

T. Kimura, K. Otsuka, M. Saruwatari, “Spatial hole-burning effects in a Nd3+:YAG laser,” IEEE J. Quantum Electron. QE-7, 225–230 (1971).
[CrossRef]

Schäfer, D.

Ch. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics, R.-J. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Schleipen, J. J. H. B.

E. C. Mos, J. J. H. B. Schleipen, H. de Waardt, G.-D. Kloe, “Longitudinal mode-switching in dual external-cavity laser diode,” IEEE J. Quantum Electron. 36, 486–495 (2000).
[CrossRef]

Schönnagel, H.

Ch. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics, R.-J. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

Shu, C.

K.-S. Lee, C. Shu, “Stable and widely tunable dual-wavelength continuous wave operation of a semiconductor laser in a novel Fabry-Perot grating-lens external cavity,” IEEE J. Quantum Electron. 33, 1832–1838 (1997).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1985).

Stamatovic, A. S.

I. V. Hertel, A. S. Stamatovic, “Spatial hole burning and oligo-mode distance control in CW dye lasers,” IEEE J. Quantum Electron. QE-11, 210–212 (1975).
[CrossRef]

Suehiro, M.

S. Iio, M. Suehiro, T. Hirata, T. Hidaka, “Two-longitudinal-mode laser diodes,” IEEE Photon. Technol. Lett. 7, 959–961 (1995).
[CrossRef]

Vilcot, J. P.

M. H. Mourad, J. P. Vilcot, D. Decoster, D. Marcenac, “Design and simulation of a dual mode semiconductor laser using sampled grating DFB structure,” IEE Proc. Optoelectron. 147, 37–42 (2000).
[CrossRef]

Wang, C.-L.

C.-L. Pan, C.-L. Wang, “A novel tunable dual-wavelength external-cavity laser diode array and its applications,” Opt. Quantum Electron. 28, 1239–1257 (1996).
[CrossRef]

Zayhowski, J. J.

Zee, B.

B. Zee, “Broadening mechanism in semiconductor (GaAs) lasers: limitations to single mode power emission,” IEEE J. Quantum Electron. QE-14, 727–736 (1978).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B. (1)

F. X. Kärtner, B. Braun, U. Keller, “Continuous-wave mode-locked solid state lasers with enhanced spatial hole burning. Part II: Theory,” Appl. Phys. B. 61, 569–579 (1995).
[CrossRef]

Appl. Phys. Lett. (1)

P.-C. Ku, C.-F. Lin, B.-L. Lee, “Multiple cross switching in a two-mode semiconductor laser,” Appl. Phys. Lett. 69, 3984–3986 (1996).
[CrossRef]

Electron. Lett. (1)

T. Hidaka, Y. Hatano, “Simulaneous two wave oscillation LD using biperiodic binary grating,” Electron. Lett. 27, 1075–1076 (1991).
[CrossRef]

IEE Proc. Optoelectron. (1)

M. H. Mourad, J. P. Vilcot, D. Decoster, D. Marcenac, “Design and simulation of a dual mode semiconductor laser using sampled grating DFB structure,” IEE Proc. Optoelectron. 147, 37–42 (2000).
[CrossRef]

IEEE J. Quantum Electron. (6)

K.-S. Lee, C. Shu, “Stable and widely tunable dual-wavelength continuous wave operation of a semiconductor laser in a novel Fabry-Perot grating-lens external cavity,” IEEE J. Quantum Electron. 33, 1832–1838 (1997).
[CrossRef]

E. C. Mos, J. J. H. B. Schleipen, H. de Waardt, G.-D. Kloe, “Longitudinal mode-switching in dual external-cavity laser diode,” IEEE J. Quantum Electron. 36, 486–495 (2000).
[CrossRef]

B. Zee, “Broadening mechanism in semiconductor (GaAs) lasers: limitations to single mode power emission,” IEEE J. Quantum Electron. QE-14, 727–736 (1978).
[CrossRef]

T. Kimura, K. Otsuka, M. Saruwatari, “Spatial hole-burning effects in a Nd3+:YAG laser,” IEEE J. Quantum Electron. QE-7, 225–230 (1971).
[CrossRef]

I. V. Hertel, A. S. Stamatovic, “Spatial hole burning and oligo-mode distance control in CW dye lasers,” IEEE J. Quantum Electron. QE-11, 210–212 (1975).
[CrossRef]

G. P. Agrawal, “Effect of gain and index nonlinearities on single-mode dynamics in semiconductor lasers,” IEEE J. Quantum Electron. 26, 1901–1909 (1990).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Iio, M. Suehiro, T. Hirata, T. Hidaka, “Two-longitudinal-mode laser diodes,” IEEE Photon. Technol. Lett. 7, 959–961 (1995).
[CrossRef]

J. Appl. Phys. (1)

H. G. Danielmeyer, “Effects of drift and diffusion of excited states on spatial hole burning and laser oscillation,” J. Appl. Phys. 42, 3125–3132 (1971).
[CrossRef]

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

Opt. Lett. (1)

Opt. Quantum Electron. (1)

C.-L. Pan, C.-L. Wang, “A novel tunable dual-wavelength external-cavity laser diode array and its applications,” Opt. Quantum Electron. 28, 1239–1257 (1996).
[CrossRef]

Phys. Lett. A (1)

A. Gearba, G. Cone, “Numerical analysis of laser mode competition and stability,” Phys. Lett. A 269, 112–119 (2000).
[CrossRef]

Phys. Rev. A (1)

I. McMackin, C. Radzewicz, M. Beck, M. G. Raymer, “Instabilities and chaos in a multimode, standing wave, cw dye laser,” Phys. Rev. A 38, 820–832 (1988).
[CrossRef] [PubMed]

Other (3)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1985).

Ch. Budzinski, R. Grunwald, I. Pinz, D. Schäfer, H. Schönnagel, “Apodized outcouplers for unstable resonators,” in Innovative Optics and Phase Conjugate Optics, R.-J. Ahlers, T. T. Tschudi, eds., Proc. SPIE1500, 264–274 (1991).
[CrossRef]

G. P. Agrawal, N. K. Dutta, Semiconductor Lasers, 2nd ed. (Van Nostrand Reinhold, New York, 1993).

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Figures (10)

Fig. 1
Fig. 1

Schematic representation of the groove depth profile of (a) a one-wavelength apodizing grating and (b) a two-wavelength apodizing grating. Profile depth and period are not to scale with respect to the position.

Fig. 2
Fig. 2

Dual-wavelength cavity setup. The collimation is achieved with a collimating lens (f = 8 mm and a numerical aperture of 0.5). The active layer of width W is in the x, z plane; the polarization of the output beam from the diode laser is along the x axis (normal to the figure). HR and AR are high-reflectivity and antireflection coatings, respectively. L is ∼20 cm. The half-wave plate is identified by λ/2. The grating is a two-wavelength apodizing grating.

Fig. 3
Fig. 3

Spectrum of the diode laser with a dual-wavelength grating in the external cavity.

Fig. 4
Fig. 4

Time evolution of one mode in dual-mode operation.

Fig. 5
Fig. 5

Time evolution of one mode in dual-mode operation in the presence of a parasitic reflection from the λ/2 plate (unstable regime).

Fig. 6
Fig. 6

Normalized cross-saturation coefficient that is due to SHB for mode i in the presence of mode j as a function of wave-number difference. Dots indicate the natural positions of the longitudinal modes of the short cavity.

Fig. 7
Fig. 7

Time evolution of the photon population of modes 1 and 2: (a) without SHB (β i ij = 1.0) and (b) with SHB (β i ij = 1.5). In (b) the population in mode 2 is represented by a dashed line.

Fig. 8
Fig. 8

Steady-state photon population of modes 1 and 2 as a function of β i ij .

Fig. 9
Fig. 9

Steady-state photon population of modes 1 and 2 as a function of the external mirror reflectivity for mode 2. Continuous curves, with SHB (β i ij = 1.5); dashed curves, without SHB (β i ij = 1.0).

Fig. 10
Fig. 10

Steady-state photon population of modes 1 and 2 as a function of the spontaneous emission factor. Continuous curves, with SHB (β i ij = 1.5); dashed curves, without SHB (β i ij = 1.0).

Equations (38)

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

dIidt=αi-βiIi-θijIjIi,
C=θ12θ21β1β2>1
αz, ω=αoω1+Iz/Isat,
Iz=4 i=12 Iio sin2kiz,
gsωi; ωj=0Lg αz, ωi; ωj4 sin2kizdz
gsωi; ωjg01-3IioIsat-2IjoIsat1+12sin2LgΔk2LgΔk,
Δk=|ki-kj|,
go=2αoωiLg.
βi=3goIsat.
θijlingoIsat1+ΔkqΔklong.
Δk=qΔklong=qπLg;
θij=2goIsat.
gsωigo1-2IioIsat-2IjoIsat.
βi=θij=2goIsat.
dPi,kdt=Gi,k-γi,kPi,k+Rspk+κi,k cosζ±ϕi,
dϕi,kdt=-μkμgkωi-Ωi,k+12 βcGi,k-γi,k-κi,k2Pi,ksinζ±ϕi,
dNdt=r Ithqe-γeN-G1,aP1,a-G2,aP2,a,
GN=GNN-No,
GNss=Gws1+Pi+Pj/Psat,
Gws=GNrIthγeqe-No,
Psat=γeGN.
GiNss=Gws1+βiPi+θijPj/Gws,
θij=GwsPsat,
θijβi32 θij,
Gi,a=GNN-No-ΔGi,
ΔGi=GNss-GiNss.
βsp=K Γλ44π2μμ¯μgVΔλsp,
ϕi=ϕi,a-ϕi,b.
ωi=ωoi+Pi,aϕ˙i,a+Pi,bϕ˙i,bPi,a+Pi,b,
GN=cμgaΓagV.
γe=Anr+BNV+CAN2V2.
γi,a=cμgaαinta-lnR1R22La,
γi,b=cμgbαint b-lnR2R3ωi2Lb.
κi,k=cμgkLkPi,aPi,b1/2μlμk1-R2R21/2.
Rsp=βspBN2V.
Ithqe=NthγeNth.
No=Vαint aΓag.
Nth=No+γi,aVμgagΓc.

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