Abstract

By inserting index perturbations at certain positions along a semiconductor Fabry–Perot laser cavity the threshold gain for one or several of the longitudinal cavity modes can be selectively lowered to facilitate, e.g., single-mode or two-color operation. Previous design methods were limited to a fairly small number of perturbations, leading to only weakly perturbed cavities and thus a limited freedom in tailoring the spectral properties of the laser. In our approach we fully account for all multiple-reflection events and use a search space that permits any distribution of the locations and lengths of the perturbations. We are therefore able to design cavities with almost arbitrary spectral properties with very low threshold gain values for, e.g., the lasing modes of a two-color cavity. Constraining the design by reducing the geometrical freedom, which can be used to increase the smallest feature size to simplify fabrication, we seamlessly approach the weakly perturbed regime while maintaining much of the freedom for spectral engineering.

© 2009 Optical Society of America

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  1. B. Corbett and D. McDonald, “Single longitudinal mode ridge waveguide 1.3 μm Fabry-Perot laser by modal perturbation,” Electron. Lett. 31, 2181-2182 (1995).
    [CrossRef]
  2. D. Erni, M. Spühler, and J. Fröhlich, “Evolutionary optimization of non-periodic coupled-cavity semiconductor laser diodes,” Opt. Quantum Electron. 30, 287-303 (1998).
    [CrossRef]
  3. S. O'Brien and E. O'Reilly, “Theory of improved spectral purity in index patterned Fabry-Perot lasers,” Appl. Phys. Lett. 86, 1-3 (2005).
  4. S. O'Brien, A. Amann, R. Fehse, S. Osborne, E. O'Reilly, and J. Rondinelli, “Spectral manipulation in Fabry-Perot lasers: perturbative inverse scattering approach,” J. Opt. Soc. Am. B 23, 1046-1056 (2006).
    [CrossRef]
  5. R. Phelan, B. Kelly, J. O'Carroll, C. Herbert, A. Duke, and J. O'Gorman, “−40°C<T<95°C mode-hop-free operation of uncooled AlGaInAs-MQW discrete-mode laser diode with emission at λ=1.3 μm,” Electron. Lett. 45, 43-45 (2009).
    [CrossRef]
  6. S. Osborne, S. O'Brien, K. Buckley, R. Fehse, J. Patchell, B. Kelly, J. O'Gorman, and E. O'Reilly, “Two-colour Fabry-Perot laser with terahertz primary mode spacing,” Electron. Lett. 43, 224-225 (2007).
    [CrossRef]
  7. S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. Moloney, A. Moskalenko, M. Kira, S. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
    [CrossRef]
  8. S. Osborne, S. O'Brien, E. O'Reilly, P. Huggard, and B. Ellison, “Generation of CW 0.5 THz radiation by photomixing the output of a two-colour 1.49 μm Fabry-Perot diode laser,” Electron. Lett. 44, 296-297 (2008).
    [CrossRef]
  9. A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68, 4309-4341 (1997).
    [CrossRef]
  10. S. O'Brien, S. Osborne, K. Buckley, R. Fehse, A. Amann, E. O'Reilly, L. Barry, P. Anandarajah, J. Patchell, and J. O'Gorman, “Inverse scattering approach to multiwavelength Fabry-Perot laser design,” Phys. Rev. A 74, 063814 (2006).
    [CrossRef]
  11. S. Osborne, S. O'Brien, K. Buckley, R. Fehse, A. Amann, J. Patchell, B. Kelly, D. Jones, J. O'Gorman, and E. O'Reilly, “Design of single-mode and two-color Fabry-Perot lasers with patterned refractive index,” IEEE J. Sel. Top. Quantum Electron. 13, 1157-1163 (2007).
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2009 (1)

R. Phelan, B. Kelly, J. O'Carroll, C. Herbert, A. Duke, and J. O'Gorman, “−40°C<T<95°C mode-hop-free operation of uncooled AlGaInAs-MQW discrete-mode laser diode with emission at λ=1.3 μm,” Electron. Lett. 45, 43-45 (2009).
[CrossRef]

2008 (1)

S. Osborne, S. O'Brien, E. O'Reilly, P. Huggard, and B. Ellison, “Generation of CW 0.5 THz radiation by photomixing the output of a two-colour 1.49 μm Fabry-Perot diode laser,” Electron. Lett. 44, 296-297 (2008).
[CrossRef]

2007 (2)

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, J. Patchell, B. Kelly, J. O'Gorman, and E. O'Reilly, “Two-colour Fabry-Perot laser with terahertz primary mode spacing,” Electron. Lett. 43, 224-225 (2007).
[CrossRef]

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, A. Amann, J. Patchell, B. Kelly, D. Jones, J. O'Gorman, and E. O'Reilly, “Design of single-mode and two-color Fabry-Perot lasers with patterned refractive index,” IEEE J. Sel. Top. Quantum Electron. 13, 1157-1163 (2007).
[CrossRef]

2006 (2)

S. O'Brien, S. Osborne, K. Buckley, R. Fehse, A. Amann, E. O'Reilly, L. Barry, P. Anandarajah, J. Patchell, and J. O'Gorman, “Inverse scattering approach to multiwavelength Fabry-Perot laser design,” Phys. Rev. A 74, 063814 (2006).
[CrossRef]

S. O'Brien, A. Amann, R. Fehse, S. Osborne, E. O'Reilly, and J. Rondinelli, “Spectral manipulation in Fabry-Perot lasers: perturbative inverse scattering approach,” J. Opt. Soc. Am. B 23, 1046-1056 (2006).
[CrossRef]

2005 (1)

S. O'Brien and E. O'Reilly, “Theory of improved spectral purity in index patterned Fabry-Perot lasers,” Appl. Phys. Lett. 86, 1-3 (2005).

2004 (1)

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. Moloney, A. Moskalenko, M. Kira, S. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

1998 (1)

D. Erni, M. Spühler, and J. Fröhlich, “Evolutionary optimization of non-periodic coupled-cavity semiconductor laser diodes,” Opt. Quantum Electron. 30, 287-303 (1998).
[CrossRef]

1997 (2)

1995 (1)

B. Corbett and D. McDonald, “Single longitudinal mode ridge waveguide 1.3 μm Fabry-Perot laser by modal perturbation,” Electron. Lett. 31, 2181-2182 (1995).
[CrossRef]

1991 (1)

Allebach, J.

Amann, A.

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, A. Amann, J. Patchell, B. Kelly, D. Jones, J. O'Gorman, and E. O'Reilly, “Design of single-mode and two-color Fabry-Perot lasers with patterned refractive index,” IEEE J. Sel. Top. Quantum Electron. 13, 1157-1163 (2007).
[CrossRef]

S. O'Brien, S. Osborne, K. Buckley, R. Fehse, A. Amann, E. O'Reilly, L. Barry, P. Anandarajah, J. Patchell, and J. O'Gorman, “Inverse scattering approach to multiwavelength Fabry-Perot laser design,” Phys. Rev. A 74, 063814 (2006).
[CrossRef]

S. O'Brien, A. Amann, R. Fehse, S. Osborne, E. O'Reilly, and J. Rondinelli, “Spectral manipulation in Fabry-Perot lasers: perturbative inverse scattering approach,” J. Opt. Soc. Am. B 23, 1046-1056 (2006).
[CrossRef]

Anandarajah, P.

S. O'Brien, S. Osborne, K. Buckley, R. Fehse, A. Amann, E. O'Reilly, L. Barry, P. Anandarajah, J. Patchell, and J. O'Gorman, “Inverse scattering approach to multiwavelength Fabry-Perot laser design,” Phys. Rev. A 74, 063814 (2006).
[CrossRef]

Barry, L.

S. O'Brien, S. Osborne, K. Buckley, R. Fehse, A. Amann, E. O'Reilly, L. Barry, P. Anandarajah, J. Patchell, and J. O'Gorman, “Inverse scattering approach to multiwavelength Fabry-Perot laser design,” Phys. Rev. A 74, 063814 (2006).
[CrossRef]

Bengtsson, J.

Bründermann, E.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. Moloney, A. Moskalenko, M. Kira, S. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

Buckley, K.

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, J. Patchell, B. Kelly, J. O'Gorman, and E. O'Reilly, “Two-colour Fabry-Perot laser with terahertz primary mode spacing,” Electron. Lett. 43, 224-225 (2007).
[CrossRef]

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, A. Amann, J. Patchell, B. Kelly, D. Jones, J. O'Gorman, and E. O'Reilly, “Design of single-mode and two-color Fabry-Perot lasers with patterned refractive index,” IEEE J. Sel. Top. Quantum Electron. 13, 1157-1163 (2007).
[CrossRef]

S. O'Brien, S. Osborne, K. Buckley, R. Fehse, A. Amann, E. O'Reilly, L. Barry, P. Anandarajah, J. Patchell, and J. O'Gorman, “Inverse scattering approach to multiwavelength Fabry-Perot laser design,” Phys. Rev. A 74, 063814 (2006).
[CrossRef]

Corbett, B.

B. Corbett and D. McDonald, “Single longitudinal mode ridge waveguide 1.3 μm Fabry-Perot laser by modal perturbation,” Electron. Lett. 31, 2181-2182 (1995).
[CrossRef]

Duke, A.

R. Phelan, B. Kelly, J. O'Carroll, C. Herbert, A. Duke, and J. O'Gorman, “−40°C<T<95°C mode-hop-free operation of uncooled AlGaInAs-MQW discrete-mode laser diode with emission at λ=1.3 μm,” Electron. Lett. 45, 43-45 (2009).
[CrossRef]

Ellison, B.

S. Osborne, S. O'Brien, E. O'Reilly, P. Huggard, and B. Ellison, “Generation of CW 0.5 THz radiation by photomixing the output of a two-colour 1.49 μm Fabry-Perot diode laser,” Electron. Lett. 44, 296-297 (2008).
[CrossRef]

Erni, D.

D. Erni, M. Spühler, and J. Fröhlich, “Evolutionary optimization of non-periodic coupled-cavity semiconductor laser diodes,” Opt. Quantum Electron. 30, 287-303 (1998).
[CrossRef]

Fehse, R.

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, J. Patchell, B. Kelly, J. O'Gorman, and E. O'Reilly, “Two-colour Fabry-Perot laser with terahertz primary mode spacing,” Electron. Lett. 43, 224-225 (2007).
[CrossRef]

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, A. Amann, J. Patchell, B. Kelly, D. Jones, J. O'Gorman, and E. O'Reilly, “Design of single-mode and two-color Fabry-Perot lasers with patterned refractive index,” IEEE J. Sel. Top. Quantum Electron. 13, 1157-1163 (2007).
[CrossRef]

S. O'Brien, S. Osborne, K. Buckley, R. Fehse, A. Amann, E. O'Reilly, L. Barry, P. Anandarajah, J. Patchell, and J. O'Gorman, “Inverse scattering approach to multiwavelength Fabry-Perot laser design,” Phys. Rev. A 74, 063814 (2006).
[CrossRef]

S. O'Brien, A. Amann, R. Fehse, S. Osborne, E. O'Reilly, and J. Rondinelli, “Spectral manipulation in Fabry-Perot lasers: perturbative inverse scattering approach,” J. Opt. Soc. Am. B 23, 1046-1056 (2006).
[CrossRef]

Fröhlich, J.

D. Erni, M. Spühler, and J. Fröhlich, “Evolutionary optimization of non-periodic coupled-cavity semiconductor laser diodes,” Opt. Quantum Electron. 30, 287-303 (1998).
[CrossRef]

Havenith, M.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. Moloney, A. Moskalenko, M. Kira, S. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

Herbert, C.

R. Phelan, B. Kelly, J. O'Carroll, C. Herbert, A. Duke, and J. O'Gorman, “−40°C<T<95°C mode-hop-free operation of uncooled AlGaInAs-MQW discrete-mode laser diode with emission at λ=1.3 μm,” Electron. Lett. 45, 43-45 (2009).
[CrossRef]

Hoffmann, S.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. Moloney, A. Moskalenko, M. Kira, S. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

Hofmann, M.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. Moloney, A. Moskalenko, M. Kira, S. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

Huggard, P.

S. Osborne, S. O'Brien, E. O'Reilly, P. Huggard, and B. Ellison, “Generation of CW 0.5 THz radiation by photomixing the output of a two-colour 1.49 μm Fabry-Perot diode laser,” Electron. Lett. 44, 296-297 (2008).
[CrossRef]

Jennison, B.

Jones, D.

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, A. Amann, J. Patchell, B. Kelly, D. Jones, J. O'Gorman, and E. O'Reilly, “Design of single-mode and two-color Fabry-Perot lasers with patterned refractive index,” IEEE J. Sel. Top. Quantum Electron. 13, 1157-1163 (2007).
[CrossRef]

Kelly, B.

R. Phelan, B. Kelly, J. O'Carroll, C. Herbert, A. Duke, and J. O'Gorman, “−40°C<T<95°C mode-hop-free operation of uncooled AlGaInAs-MQW discrete-mode laser diode with emission at λ=1.3 μm,” Electron. Lett. 45, 43-45 (2009).
[CrossRef]

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, J. Patchell, B. Kelly, J. O'Gorman, and E. O'Reilly, “Two-colour Fabry-Perot laser with terahertz primary mode spacing,” Electron. Lett. 43, 224-225 (2007).
[CrossRef]

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, A. Amann, J. Patchell, B. Kelly, D. Jones, J. O'Gorman, and E. O'Reilly, “Design of single-mode and two-color Fabry-Perot lasers with patterned refractive index,” IEEE J. Sel. Top. Quantum Electron. 13, 1157-1163 (2007).
[CrossRef]

Kira, M.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. Moloney, A. Moskalenko, M. Kira, S. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

Koch, S.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. Moloney, A. Moskalenko, M. Kira, S. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

Matus, M.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. Moloney, A. Moskalenko, M. Kira, S. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

McDonald, D.

B. Corbett and D. McDonald, “Single longitudinal mode ridge waveguide 1.3 μm Fabry-Perot laser by modal perturbation,” Electron. Lett. 31, 2181-2182 (1995).
[CrossRef]

Moloney, J.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. Moloney, A. Moskalenko, M. Kira, S. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

Moskalenko, A.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. Moloney, A. Moskalenko, M. Kira, S. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

O'Brien, S.

S. Osborne, S. O'Brien, E. O'Reilly, P. Huggard, and B. Ellison, “Generation of CW 0.5 THz radiation by photomixing the output of a two-colour 1.49 μm Fabry-Perot diode laser,” Electron. Lett. 44, 296-297 (2008).
[CrossRef]

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, A. Amann, J. Patchell, B. Kelly, D. Jones, J. O'Gorman, and E. O'Reilly, “Design of single-mode and two-color Fabry-Perot lasers with patterned refractive index,” IEEE J. Sel. Top. Quantum Electron. 13, 1157-1163 (2007).
[CrossRef]

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, J. Patchell, B. Kelly, J. O'Gorman, and E. O'Reilly, “Two-colour Fabry-Perot laser with terahertz primary mode spacing,” Electron. Lett. 43, 224-225 (2007).
[CrossRef]

S. O'Brien, A. Amann, R. Fehse, S. Osborne, E. O'Reilly, and J. Rondinelli, “Spectral manipulation in Fabry-Perot lasers: perturbative inverse scattering approach,” J. Opt. Soc. Am. B 23, 1046-1056 (2006).
[CrossRef]

S. O'Brien, S. Osborne, K. Buckley, R. Fehse, A. Amann, E. O'Reilly, L. Barry, P. Anandarajah, J. Patchell, and J. O'Gorman, “Inverse scattering approach to multiwavelength Fabry-Perot laser design,” Phys. Rev. A 74, 063814 (2006).
[CrossRef]

S. O'Brien and E. O'Reilly, “Theory of improved spectral purity in index patterned Fabry-Perot lasers,” Appl. Phys. Lett. 86, 1-3 (2005).

O'Carroll, J.

R. Phelan, B. Kelly, J. O'Carroll, C. Herbert, A. Duke, and J. O'Gorman, “−40°C<T<95°C mode-hop-free operation of uncooled AlGaInAs-MQW discrete-mode laser diode with emission at λ=1.3 μm,” Electron. Lett. 45, 43-45 (2009).
[CrossRef]

O'Gorman, J.

R. Phelan, B. Kelly, J. O'Carroll, C. Herbert, A. Duke, and J. O'Gorman, “−40°C<T<95°C mode-hop-free operation of uncooled AlGaInAs-MQW discrete-mode laser diode with emission at λ=1.3 μm,” Electron. Lett. 45, 43-45 (2009).
[CrossRef]

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, J. Patchell, B. Kelly, J. O'Gorman, and E. O'Reilly, “Two-colour Fabry-Perot laser with terahertz primary mode spacing,” Electron. Lett. 43, 224-225 (2007).
[CrossRef]

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, A. Amann, J. Patchell, B. Kelly, D. Jones, J. O'Gorman, and E. O'Reilly, “Design of single-mode and two-color Fabry-Perot lasers with patterned refractive index,” IEEE J. Sel. Top. Quantum Electron. 13, 1157-1163 (2007).
[CrossRef]

S. O'Brien, S. Osborne, K. Buckley, R. Fehse, A. Amann, E. O'Reilly, L. Barry, P. Anandarajah, J. Patchell, and J. O'Gorman, “Inverse scattering approach to multiwavelength Fabry-Perot laser design,” Phys. Rev. A 74, 063814 (2006).
[CrossRef]

O'Reilly, E.

S. Osborne, S. O'Brien, E. O'Reilly, P. Huggard, and B. Ellison, “Generation of CW 0.5 THz radiation by photomixing the output of a two-colour 1.49 μm Fabry-Perot diode laser,” Electron. Lett. 44, 296-297 (2008).
[CrossRef]

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, A. Amann, J. Patchell, B. Kelly, D. Jones, J. O'Gorman, and E. O'Reilly, “Design of single-mode and two-color Fabry-Perot lasers with patterned refractive index,” IEEE J. Sel. Top. Quantum Electron. 13, 1157-1163 (2007).
[CrossRef]

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, J. Patchell, B. Kelly, J. O'Gorman, and E. O'Reilly, “Two-colour Fabry-Perot laser with terahertz primary mode spacing,” Electron. Lett. 43, 224-225 (2007).
[CrossRef]

S. O'Brien, A. Amann, R. Fehse, S. Osborne, E. O'Reilly, and J. Rondinelli, “Spectral manipulation in Fabry-Perot lasers: perturbative inverse scattering approach,” J. Opt. Soc. Am. B 23, 1046-1056 (2006).
[CrossRef]

S. O'Brien, S. Osborne, K. Buckley, R. Fehse, A. Amann, E. O'Reilly, L. Barry, P. Anandarajah, J. Patchell, and J. O'Gorman, “Inverse scattering approach to multiwavelength Fabry-Perot laser design,” Phys. Rev. A 74, 063814 (2006).
[CrossRef]

S. O'Brien and E. O'Reilly, “Theory of improved spectral purity in index patterned Fabry-Perot lasers,” Appl. Phys. Lett. 86, 1-3 (2005).

Osborne, S.

S. Osborne, S. O'Brien, E. O'Reilly, P. Huggard, and B. Ellison, “Generation of CW 0.5 THz radiation by photomixing the output of a two-colour 1.49 μm Fabry-Perot diode laser,” Electron. Lett. 44, 296-297 (2008).
[CrossRef]

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, A. Amann, J. Patchell, B. Kelly, D. Jones, J. O'Gorman, and E. O'Reilly, “Design of single-mode and two-color Fabry-Perot lasers with patterned refractive index,” IEEE J. Sel. Top. Quantum Electron. 13, 1157-1163 (2007).
[CrossRef]

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, J. Patchell, B. Kelly, J. O'Gorman, and E. O'Reilly, “Two-colour Fabry-Perot laser with terahertz primary mode spacing,” Electron. Lett. 43, 224-225 (2007).
[CrossRef]

S. O'Brien, A. Amann, R. Fehse, S. Osborne, E. O'Reilly, and J. Rondinelli, “Spectral manipulation in Fabry-Perot lasers: perturbative inverse scattering approach,” J. Opt. Soc. Am. B 23, 1046-1056 (2006).
[CrossRef]

S. O'Brien, S. Osborne, K. Buckley, R. Fehse, A. Amann, E. O'Reilly, L. Barry, P. Anandarajah, J. Patchell, and J. O'Gorman, “Inverse scattering approach to multiwavelength Fabry-Perot laser design,” Phys. Rev. A 74, 063814 (2006).
[CrossRef]

Othonos, A.

A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68, 4309-4341 (1997).
[CrossRef]

Patchell, J.

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, A. Amann, J. Patchell, B. Kelly, D. Jones, J. O'Gorman, and E. O'Reilly, “Design of single-mode and two-color Fabry-Perot lasers with patterned refractive index,” IEEE J. Sel. Top. Quantum Electron. 13, 1157-1163 (2007).
[CrossRef]

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, J. Patchell, B. Kelly, J. O'Gorman, and E. O'Reilly, “Two-colour Fabry-Perot laser with terahertz primary mode spacing,” Electron. Lett. 43, 224-225 (2007).
[CrossRef]

S. O'Brien, S. Osborne, K. Buckley, R. Fehse, A. Amann, E. O'Reilly, L. Barry, P. Anandarajah, J. Patchell, and J. O'Gorman, “Inverse scattering approach to multiwavelength Fabry-Perot laser design,” Phys. Rev. A 74, 063814 (2006).
[CrossRef]

Phelan, R.

R. Phelan, B. Kelly, J. O'Carroll, C. Herbert, A. Duke, and J. O'Gorman, “−40°C<T<95°C mode-hop-free operation of uncooled AlGaInAs-MQW discrete-mode laser diode with emission at λ=1.3 μm,” Electron. Lett. 45, 43-45 (2009).
[CrossRef]

Rondinelli, J.

Saito, S.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. Moloney, A. Moskalenko, M. Kira, S. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

Sakai, K.

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. Moloney, A. Moskalenko, M. Kira, S. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

Spühler, M.

D. Erni, M. Spühler, and J. Fröhlich, “Evolutionary optimization of non-periodic coupled-cavity semiconductor laser diodes,” Opt. Quantum Electron. 30, 287-303 (1998).
[CrossRef]

Sweeney, D.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

S. O'Brien and E. O'Reilly, “Theory of improved spectral purity in index patterned Fabry-Perot lasers,” Appl. Phys. Lett. 86, 1-3 (2005).

S. Hoffmann, M. Hofmann, E. Bründermann, M. Havenith, M. Matus, J. Moloney, A. Moskalenko, M. Kira, S. Koch, S. Saito, and K. Sakai, “Four-wave mixing and direct terahertz emission with two-color semiconductor lasers,” Appl. Phys. Lett. 84, 3585-3587 (2004).
[CrossRef]

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S. Osborne, S. O'Brien, E. O'Reilly, P. Huggard, and B. Ellison, “Generation of CW 0.5 THz radiation by photomixing the output of a two-colour 1.49 μm Fabry-Perot diode laser,” Electron. Lett. 44, 296-297 (2008).
[CrossRef]

R. Phelan, B. Kelly, J. O'Carroll, C. Herbert, A. Duke, and J. O'Gorman, “−40°C<T<95°C mode-hop-free operation of uncooled AlGaInAs-MQW discrete-mode laser diode with emission at λ=1.3 μm,” Electron. Lett. 45, 43-45 (2009).
[CrossRef]

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, J. Patchell, B. Kelly, J. O'Gorman, and E. O'Reilly, “Two-colour Fabry-Perot laser with terahertz primary mode spacing,” Electron. Lett. 43, 224-225 (2007).
[CrossRef]

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[CrossRef]

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

S. Osborne, S. O'Brien, K. Buckley, R. Fehse, A. Amann, J. Patchell, B. Kelly, D. Jones, J. O'Gorman, and E. O'Reilly, “Design of single-mode and two-color Fabry-Perot lasers with patterned refractive index,” IEEE J. Sel. Top. Quantum Electron. 13, 1157-1163 (2007).
[CrossRef]

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

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

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[CrossRef]

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[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Schematic illustration of a pixel-segmented Fabry–Perot cavity with a spatially varying effective index in the longitudinal direction. The effective index of a perturbed pixel segment is changed by Δ n , e.g., by narrowing the width of the ridge by sidewall etching. In this example Δ n < 0 , which is the case for a perturbation realized by narrowing the ridge waveguide.

Fig. 2
Fig. 2

Example of the dependence of the (a) real and (b) imaginary part of T 11 on the imaginary part of the effective index in the waveguide (related to the modal gain) and the wavelength of radiation, for a specific strongly perturbed cavity.

Fig. 3
Fig. 3

Curves of the zeros of the real and imaginary parts of T 11 in modal gain-wavelength space for (a) an unperturbed Fabry–Perot cavity and (b) for the same strongly perturbed two-color laser cavity as in Fig. 2. The solutions to T 11 = 0 , i.e., the resonance wavelengths of the lasing modes and their threshold gains are found at the intersections, as indicated with circles. Thus, in the displayed wavelength interval there are 23 cavity modes in each of these examples.

Fig. 4
Fig. 4

Close-up of a small portion of the modal gain-wavelength space around one of the cavity resonances. Shown are curves of the zeros of T 11 and T 11 , where the latter is found from a rigorous calculation of the new transfer matrix, T , resulting from changing the effective index in a pixel segment, and an exact solution of the lasing equation T 11 = 0 . The filled circles indicate the evaluation points used when calculating the solution to T 11 = 0 , using the efficient update formula for T from Eq. (10) in three points around the old solution ( n 0 , λ 0 ) , and the linear approximation in Eq. (12). The obtained solution is indicated by an open circle, and for clarity its deviation from the exact position, at the crossing of the curves for T 11 = 0 , was exaggerated.

Fig. 5
Fig. 5

Top, plot of the obtained error function for designed cavities as a function of pixel segment length. In this figure the symbol λ denotes the wavelength in the waveguide. Bottom, strength of the perturbation for the design solutions. The target threshold gain spectrum is shown in Fig. 6 along with the obtained threshold gain spectrum for a pixel segment length of d = 303 nm . The cavity length was 300 μ m , n = 3.4 , and Δ n = 0.01 .

Fig. 6
Fig. 6

Target and obtained threshold gain spectra for the designed cavities in Fig. 5 for a pixel segment length of d = 303 nm , using the unweighted (filled circles) and weighted (filled diamonds) error function in the optimization. To better see how well each mode reaches its target value, in the plots the obtained threshold gain spectra have been redshifted by the average deviation of the modes from the resonance wavelengths in the target spectrum (1.18 and 1.36 nm for the unweighted and weighted case, respectively). The nine central modes have an rms deviation from their target threshold gain values of 0.25 cm 1 for the unweighted design and of 0.035 cm 1 for the weighted design.

Fig. 7
Fig. 7

Evolution of the number of perturbed pixel segments, N p , and the error function, Q, as functions of the number of pixel segment optimizations during a design run for cavities with pixel segments that are s = 1 and s = 9 quarter-wavelengths long ( d 0.09 μ m and d 0.79 μ m , giving a total number of pixel segments N = 3432 and N = 382 , respectively). The dots indicate points where a single iteration has been completed.

Fig. 8
Fig. 8

Target and obtained threshold gain spectra for a two-color laser cavity designed such that two modes should experience a threshold gain reduction of 15 cm 1 . The inset shows the designed cavity with gray regions indicating positions of refractive index perturbations. The T 11 function of this cavity is illustrated in Figs. 2, 3b.

Fig. 9
Fig. 9

Target and obtained threshold gain spectra for a two-color laser cavity designed such that two modes should experience a threshold gain reduction of 1.0 cm 1 . The inset shows the designed cavity with gray regions indicating positions of refractive index perturbations.

Fig. 10
Fig. 10

Target and obtained threshold gain spectra for a two-color laser cavity designed such that two modes should experience a threshold gain reduction of 1.6 cm 1 . The upper case uses a cavity with as-cleaved facets, while the lower case assumes that a 95% high-reflectivity coating is applied to the left facet.

Equations (17)

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γ = 2 k n ,
T i , j = 1 t i , j ( 1 r i , j r i , j 1 ) ,
T P i = ( exp ( j β i d ) 0 0 exp ( + j β i d ) ) ,
T i = T i 1 , i T P i .
T = ( i = 1 N T i ) T N , N + 1 ,
T 11 = 0 .
Re [ T 11 ( n , λ ) ] = 0 ,
Im [ T 11 ( n , λ ) ] = 0 .
Im [ T 11 ( n = const. , λ ) ] = 0 .
T = T i 1 left T i 1 , i T P i T i , i + 1 T P i + 1 ( l = i + 2 N T l ) T N , N + 1 = T i 1 left T i 1 , i T P i T i , i + 1 T P i + 1 ( T i + 1 ) 1 T i 1 right ,
f ( n , λ ) = f 0 + f n Δ n + f λ Δ λ = 0 ,
g ( n , λ ) = g 0 + g n Δ n + g λ Δ λ = 0 ,
Δ λ = f 0 g n g 0 f n f n g λ g n f λ , Δ n = g 0 f λ f 0 g λ f n g λ g n f λ ,
Q = m [ γ th , target ( λ m ) γ th ( λ m ) ] 2 ,
Q w = m [ γ th , target ( λ m ) γ th ( λ m ) ] 2 w m [ γ th , target ( λ m ) , γ th ( λ m ) ] ,
d s λ 4 ( n + Δ n ) , s = 1 , 3 , 5 , ,
S p = N is Δ n n ,

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