Abstract

Aperiodic lattices are a promising route to achieving tunable or multi-frequency lasing, but their threshold spectrum remains largely unstudied. We find that holographically designed aperiodic lattices can possess a multimode spectral response, containing both defect and band-edge photonic states. Under the influence of facet feedback the aperiodic lattice maintains remarkable spectral control at multiple frequencies over a wide bandwidth. This control arises from enhancement to the photon density of states at the designed frequencies, reducing the threshold of modes in the Fabry Perot coupled aperiodic lattice laser. Our results suggest that aperiodic lattice lasers are robust against fabrication imperfections, as exemplified by experimental demonstrations in prior work.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  5. V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29(6), 1824–1834 (1993).
    [Crossref]
  6. I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, “Design of widely tunable semiconductor lasers and the concept of binary superimposed gratings (BSG’s),” IEEE J. Quantum Electron. 34(4), 729–741 (1998).
    [Crossref]
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    [Crossref]
  10. G. Adolfsson, J. Bengtsson, and A. Larsson, “Spectral engineering of semiconductor Fabry-Perot laser cavities in the weakly and strongly perturbed regimes,” J. Opt. Soc. Am. B 27(1), 118 (2010).
    [Crossref]
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    [Crossref]
  13. S. Chakraborty, O. Marshall, C. W. Hsin, M. Khairuzzaman, H. Beere, and D. Ritchie, “Discrete mode tuning in terahertz quantum cascade lasers,” Opt. Express 20(26), B306–B314 (2012).
    [Crossref] [PubMed]
  14. S. Chakraborty, O. P. Marshall, T. G. Folland, Y.-J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
    [Crossref] [PubMed]
  15. C. Sibilia, I. S. Nefedov, M. Scalora, and M. Bertolotti, “Electromagnetic mode density for finite quasi-periodic structures,” J. Opt. Soc. Am. B 15(7), 1947 (1998).
    [Crossref]
  16. T. G. Folland and S. Chakraborty, “Dual-frequency defect-mode lasing in Aperiodic Distributed Feedback (ADFB) cavities,” IEEE Photonics Technol. Lett. 28(15), 1617–1620 (2016).
    [Crossref]
  17. O. P. Marshall, S. Chakraborty, M. Khairuzzaman, T. Folland, A. Gholinia, H. E. Beere, and D. A. Ritchie, “Electronically tunable aperiodic distributed feedback terahertz lasers,” J. Appl. Phys. 113(20), 203103 (2013).
    [Crossref]
  18. O. P. Marshall, M. Khairuzzaman, H. E. Beere, D. A. Ritchie, and S. Chakraborty, “Broadband photonic control for dual-mode terahertz laser emission,” Appl. Phys. Lett. 102(18), 181106 (2013).
    [Crossref]
  19. J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 4107–4121 (1996).
    [Crossref] [PubMed]
  20. A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
    [Crossref]
  21. N. Laman, S. S. Harsha, D. Grischkowsky, and J. S. Melinger, “High-resolution waveguide THz spectroscopy of biological molecules,” Biophys. J. 94(3), 1010–1020 (2008).
    [Crossref] [PubMed]

2016 (2)

S. Chakraborty, O. P. Marshall, T. G. Folland, Y.-J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
[Crossref] [PubMed]

T. G. Folland and S. Chakraborty, “Dual-frequency defect-mode lasing in Aperiodic Distributed Feedback (ADFB) cavities,” IEEE Photonics Technol. Lett. 28(15), 1617–1620 (2016).
[Crossref]

2013 (2)

O. P. Marshall, S. Chakraborty, M. Khairuzzaman, T. Folland, A. Gholinia, H. E. Beere, and D. A. Ritchie, “Electronically tunable aperiodic distributed feedback terahertz lasers,” J. Appl. Phys. 113(20), 203103 (2013).
[Crossref]

O. P. Marshall, M. Khairuzzaman, H. E. Beere, D. A. Ritchie, and S. Chakraborty, “Broadband photonic control for dual-mode terahertz laser emission,” Appl. Phys. Lett. 102(18), 181106 (2013).
[Crossref]

2012 (2)

S. Chakraborty, O. P. Marshall, M. Khairuzzaman, C.-W. Hsin, H. E. Beere, and D. A. Ritchie, “Longitudinal computer-generated holograms for digital frequency control in electronically tunable terahertz lasers,” Appl. Phys. Lett. 101(12), 121103 (2012).
[Crossref]

S. Chakraborty, O. Marshall, C. W. Hsin, M. Khairuzzaman, H. Beere, and D. Ritchie, “Discrete mode tuning in terahertz quantum cascade lasers,” Opt. Express 20(26), B306–B314 (2012).
[Crossref] [PubMed]

2010 (2)

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).

G. Adolfsson, J. Bengtsson, and A. Larsson, “Spectral engineering of semiconductor Fabry-Perot laser cavities in the weakly and strongly perturbed regimes,” J. Opt. Soc. Am. B 27(1), 118 (2010).
[Crossref]

2008 (2)

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
[Crossref]

N. Laman, S. S. Harsha, D. Grischkowsky, and J. S. Melinger, “High-resolution waveguide THz spectroscopy of biological molecules,” Biophys. J. 94(3), 1010–1020 (2008).
[Crossref] [PubMed]

2006 (2)

S. O’Brien, A. Amann, R. Fehse, S. Osborne, E. P. O’Reilly, and J. M. Rondinelli, “Spectral manipulation in Fabry-Perot lasers: perturbative inverse scattering approach,” J. Opt. Soc. Am. B 23(6), 1046 (2006).
[Crossref]

S. Chakraborty, T. Chakraborty, S. P. Khanna, E. H. Linfield, A. G. Davies, J. Fowler, C. H. Worrall, H. E. Beere, and D. A. Ritchie, “Spectral engineering of terahertz quantum cascade lasers using focused ion beam etched photonic lattices,” Electron. Lett. 42(7), 404 (2006).
[Crossref]

2005 (1)

S. Chakraborty, M. C. Parker, and R. J. Mears, “A Fourier (k-) space design approach for controllable photonic band and localization states in aperiodic lattices,” Photonics Nanostructures – Fundam. Appl. 3, 139–147 (2005).

2002 (1)

1998 (2)

I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, “Design of widely tunable semiconductor lasers and the concept of binary superimposed gratings (BSG’s),” IEEE J. Quantum Electron. 34(4), 729–741 (1998).
[Crossref]

C. Sibilia, I. S. Nefedov, M. Scalora, and M. Bertolotti, “Electromagnetic mode density for finite quasi-periodic structures,” J. Opt. Soc. Am. B 15(7), 1947 (1998).
[Crossref]

1996 (1)

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 4107–4121 (1996).
[Crossref] [PubMed]

1994 (1)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896 (1994).
[Crossref]

1993 (1)

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29(6), 1824–1834 (1993).
[Crossref]

1976 (1)

H. Haus and C. Shank, “Antisymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. 12(9), 532–539 (1976).
[Crossref]

Adolfsson, G.

Amann, A.

Anis, H.

I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, “Design of widely tunable semiconductor lasers and the concept of binary superimposed gratings (BSG’s),” IEEE J. Quantum Electron. 34(4), 729–741 (1998).
[Crossref]

Avrutsky, I. A.

I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, “Design of widely tunable semiconductor lasers and the concept of binary superimposed gratings (BSG’s),” IEEE J. Quantum Electron. 34(4), 729–741 (1998).
[Crossref]

Beere, H.

Beere, H. E.

O. P. Marshall, S. Chakraborty, M. Khairuzzaman, T. Folland, A. Gholinia, H. E. Beere, and D. A. Ritchie, “Electronically tunable aperiodic distributed feedback terahertz lasers,” J. Appl. Phys. 113(20), 203103 (2013).
[Crossref]

O. P. Marshall, M. Khairuzzaman, H. E. Beere, D. A. Ritchie, and S. Chakraborty, “Broadband photonic control for dual-mode terahertz laser emission,” Appl. Phys. Lett. 102(18), 181106 (2013).
[Crossref]

S. Chakraborty, O. P. Marshall, M. Khairuzzaman, C.-W. Hsin, H. E. Beere, and D. A. Ritchie, “Longitudinal computer-generated holograms for digital frequency control in electronically tunable terahertz lasers,” Appl. Phys. Lett. 101(12), 121103 (2012).
[Crossref]

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).

S. Chakraborty, T. Chakraborty, S. P. Khanna, E. H. Linfield, A. G. Davies, J. Fowler, C. H. Worrall, H. E. Beere, and D. A. Ritchie, “Spectral engineering of terahertz quantum cascade lasers using focused ion beam etched photonic lattices,” Electron. Lett. 42(7), 404 (2006).
[Crossref]

Beltram, F.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).

Bendickson, J. M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 4107–4121 (1996).
[Crossref] [PubMed]

Bengtsson, J.

Bertolotti, M.

Bloemer, M. J.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896 (1994).
[Crossref]

Bowden, C. M.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896 (1994).
[Crossref]

Burnett, A. D.

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
[Crossref]

Chakraborty, S.

S. Chakraborty, O. P. Marshall, T. G. Folland, Y.-J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
[Crossref] [PubMed]

T. G. Folland and S. Chakraborty, “Dual-frequency defect-mode lasing in Aperiodic Distributed Feedback (ADFB) cavities,” IEEE Photonics Technol. Lett. 28(15), 1617–1620 (2016).
[Crossref]

O. P. Marshall, S. Chakraborty, M. Khairuzzaman, T. Folland, A. Gholinia, H. E. Beere, and D. A. Ritchie, “Electronically tunable aperiodic distributed feedback terahertz lasers,” J. Appl. Phys. 113(20), 203103 (2013).
[Crossref]

O. P. Marshall, M. Khairuzzaman, H. E. Beere, D. A. Ritchie, and S. Chakraborty, “Broadband photonic control for dual-mode terahertz laser emission,” Appl. Phys. Lett. 102(18), 181106 (2013).
[Crossref]

S. Chakraborty, O. P. Marshall, M. Khairuzzaman, C.-W. Hsin, H. E. Beere, and D. A. Ritchie, “Longitudinal computer-generated holograms for digital frequency control in electronically tunable terahertz lasers,” Appl. Phys. Lett. 101(12), 121103 (2012).
[Crossref]

S. Chakraborty, O. Marshall, C. W. Hsin, M. Khairuzzaman, H. Beere, and D. Ritchie, “Discrete mode tuning in terahertz quantum cascade lasers,” Opt. Express 20(26), B306–B314 (2012).
[Crossref] [PubMed]

S. Chakraborty, T. Chakraborty, S. P. Khanna, E. H. Linfield, A. G. Davies, J. Fowler, C. H. Worrall, H. E. Beere, and D. A. Ritchie, “Spectral engineering of terahertz quantum cascade lasers using focused ion beam etched photonic lattices,” Electron. Lett. 42(7), 404 (2006).
[Crossref]

S. Chakraborty, M. C. Parker, and R. J. Mears, “A Fourier (k-) space design approach for controllable photonic band and localization states in aperiodic lattices,” Photonics Nanostructures – Fundam. Appl. 3, 139–147 (2005).

Chakraborty, T.

S. Chakraborty, T. Chakraborty, S. P. Khanna, E. H. Linfield, A. G. Davies, J. Fowler, C. H. Worrall, H. E. Beere, and D. A. Ritchie, “Spectral engineering of terahertz quantum cascade lasers using focused ion beam etched photonic lattices,” Electron. Lett. 42(7), 404 (2006).
[Crossref]

Chuang, Z.-M.

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29(6), 1824–1834 (1993).
[Crossref]

Coldren, L. A.

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29(6), 1824–1834 (1993).
[Crossref]

Cunningham, J. E.

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
[Crossref]

Davies, A. G.

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
[Crossref]

S. Chakraborty, T. Chakraborty, S. P. Khanna, E. H. Linfield, A. G. Davies, J. Fowler, C. H. Worrall, H. E. Beere, and D. A. Ritchie, “Spectral engineering of terahertz quantum cascade lasers using focused ion beam etched photonic lattices,” Electron. Lett. 42(7), 404 (2006).
[Crossref]

Dowling, J. P.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 4107–4121 (1996).
[Crossref] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896 (1994).
[Crossref]

Ellis, D. S.

I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, “Design of widely tunable semiconductor lasers and the concept of binary superimposed gratings (BSG’s),” IEEE J. Quantum Electron. 34(4), 729–741 (1998).
[Crossref]

Faist, J.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).

Fan, W.

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
[Crossref]

Fehse, R.

Folland, T.

O. P. Marshall, S. Chakraborty, M. Khairuzzaman, T. Folland, A. Gholinia, H. E. Beere, and D. A. Ritchie, “Electronically tunable aperiodic distributed feedback terahertz lasers,” J. Appl. Phys. 113(20), 203103 (2013).
[Crossref]

Folland, T. G.

T. G. Folland and S. Chakraborty, “Dual-frequency defect-mode lasing in Aperiodic Distributed Feedback (ADFB) cavities,” IEEE Photonics Technol. Lett. 28(15), 1617–1620 (2016).
[Crossref]

S. Chakraborty, O. P. Marshall, T. G. Folland, Y.-J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
[Crossref] [PubMed]

Fowler, J.

S. Chakraborty, T. Chakraborty, S. P. Khanna, E. H. Linfield, A. G. Davies, J. Fowler, C. H. Worrall, H. E. Beere, and D. A. Ritchie, “Spectral engineering of terahertz quantum cascade lasers using focused ion beam etched photonic lattices,” Electron. Lett. 42(7), 404 (2006).
[Crossref]

Gholinia, A.

O. P. Marshall, S. Chakraborty, M. Khairuzzaman, T. Folland, A. Gholinia, H. E. Beere, and D. A. Ritchie, “Electronically tunable aperiodic distributed feedback terahertz lasers,” J. Appl. Phys. 113(20), 203103 (2013).
[Crossref]

Grigorenko, A. N.

S. Chakraborty, O. P. Marshall, T. G. Folland, Y.-J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
[Crossref] [PubMed]

Grischkowsky, D.

N. Laman, S. S. Harsha, D. Grischkowsky, and J. S. Melinger, “High-resolution waveguide THz spectroscopy of biological molecules,” Biophys. J. 94(3), 1010–1020 (2008).
[Crossref] [PubMed]

Harsha, S. S.

N. Laman, S. S. Harsha, D. Grischkowsky, and J. S. Melinger, “High-resolution waveguide THz spectroscopy of biological molecules,” Biophys. J. 94(3), 1010–1020 (2008).
[Crossref] [PubMed]

Haus, H.

H. Haus and C. Shank, “Antisymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. 12(9), 532–539 (1976).
[Crossref]

Hsin, C. W.

Hsin, C.-W.

S. Chakraborty, O. P. Marshall, M. Khairuzzaman, C.-W. Hsin, H. E. Beere, and D. A. Ritchie, “Longitudinal computer-generated holograms for digital frequency control in electronically tunable terahertz lasers,” Appl. Phys. Lett. 101(12), 121103 (2012).
[Crossref]

Jayaraman, V.

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29(6), 1824–1834 (1993).
[Crossref]

Khairuzzaman, M.

O. P. Marshall, S. Chakraborty, M. Khairuzzaman, T. Folland, A. Gholinia, H. E. Beere, and D. A. Ritchie, “Electronically tunable aperiodic distributed feedback terahertz lasers,” J. Appl. Phys. 113(20), 203103 (2013).
[Crossref]

O. P. Marshall, M. Khairuzzaman, H. E. Beere, D. A. Ritchie, and S. Chakraborty, “Broadband photonic control for dual-mode terahertz laser emission,” Appl. Phys. Lett. 102(18), 181106 (2013).
[Crossref]

S. Chakraborty, O. P. Marshall, M. Khairuzzaman, C.-W. Hsin, H. E. Beere, and D. A. Ritchie, “Longitudinal computer-generated holograms for digital frequency control in electronically tunable terahertz lasers,” Appl. Phys. Lett. 101(12), 121103 (2012).
[Crossref]

S. Chakraborty, O. Marshall, C. W. Hsin, M. Khairuzzaman, H. Beere, and D. Ritchie, “Discrete mode tuning in terahertz quantum cascade lasers,” Opt. Express 20(26), B306–B314 (2012).
[Crossref] [PubMed]

Khanna, S. P.

S. Chakraborty, T. Chakraborty, S. P. Khanna, E. H. Linfield, A. G. Davies, J. Fowler, C. H. Worrall, H. E. Beere, and D. A. Ritchie, “Spectral engineering of terahertz quantum cascade lasers using focused ion beam etched photonic lattices,” Electron. Lett. 42(7), 404 (2006).
[Crossref]

Kim, Y.-J.

S. Chakraborty, O. P. Marshall, T. G. Folland, Y.-J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
[Crossref] [PubMed]

Kononenko, V. K.

Laman, N.

N. Laman, S. S. Harsha, D. Grischkowsky, and J. S. Melinger, “High-resolution waveguide THz spectroscopy of biological molecules,” Biophys. J. 94(3), 1010–1020 (2008).
[Crossref] [PubMed]

Larsson, A.

Linfield, E. H.

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
[Crossref]

S. Chakraborty, T. Chakraborty, S. P. Khanna, E. H. Linfield, A. G. Davies, J. Fowler, C. H. Worrall, H. E. Beere, and D. A. Ritchie, “Spectral engineering of terahertz quantum cascade lasers using focused ion beam etched photonic lattices,” Electron. Lett. 42(7), 404 (2006).
[Crossref]

Mahler, L.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).

Marshall, O.

Marshall, O. P.

S. Chakraborty, O. P. Marshall, T. G. Folland, Y.-J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
[Crossref] [PubMed]

O. P. Marshall, S. Chakraborty, M. Khairuzzaman, T. Folland, A. Gholinia, H. E. Beere, and D. A. Ritchie, “Electronically tunable aperiodic distributed feedback terahertz lasers,” J. Appl. Phys. 113(20), 203103 (2013).
[Crossref]

O. P. Marshall, M. Khairuzzaman, H. E. Beere, D. A. Ritchie, and S. Chakraborty, “Broadband photonic control for dual-mode terahertz laser emission,” Appl. Phys. Lett. 102(18), 181106 (2013).
[Crossref]

S. Chakraborty, O. P. Marshall, M. Khairuzzaman, C.-W. Hsin, H. E. Beere, and D. A. Ritchie, “Longitudinal computer-generated holograms for digital frequency control in electronically tunable terahertz lasers,” Appl. Phys. Lett. 101(12), 121103 (2012).
[Crossref]

Mears, R. J.

S. Chakraborty, M. C. Parker, and R. J. Mears, “A Fourier (k-) space design approach for controllable photonic band and localization states in aperiodic lattices,” Photonics Nanostructures – Fundam. Appl. 3, 139–147 (2005).

Melinger, J. S.

N. Laman, S. S. Harsha, D. Grischkowsky, and J. S. Melinger, “High-resolution waveguide THz spectroscopy of biological molecules,” Biophys. J. 94(3), 1010–1020 (2008).
[Crossref] [PubMed]

Nefedov, I. S.

Novoselov, K. S.

S. Chakraborty, O. P. Marshall, T. G. Folland, Y.-J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
[Crossref] [PubMed]

O’Brien, S.

O’Reilly, E. P.

Osborne, S.

Parker, M. C.

S. Chakraborty, M. C. Parker, and R. J. Mears, “A Fourier (k-) space design approach for controllable photonic band and localization states in aperiodic lattices,” Photonics Nanostructures – Fundam. Appl. 3, 139–147 (2005).

Ritchie, D.

Ritchie, D. A.

O. P. Marshall, M. Khairuzzaman, H. E. Beere, D. A. Ritchie, and S. Chakraborty, “Broadband photonic control for dual-mode terahertz laser emission,” Appl. Phys. Lett. 102(18), 181106 (2013).
[Crossref]

O. P. Marshall, S. Chakraborty, M. Khairuzzaman, T. Folland, A. Gholinia, H. E. Beere, and D. A. Ritchie, “Electronically tunable aperiodic distributed feedback terahertz lasers,” J. Appl. Phys. 113(20), 203103 (2013).
[Crossref]

S. Chakraborty, O. P. Marshall, M. Khairuzzaman, C.-W. Hsin, H. E. Beere, and D. A. Ritchie, “Longitudinal computer-generated holograms for digital frequency control in electronically tunable terahertz lasers,” Appl. Phys. Lett. 101(12), 121103 (2012).
[Crossref]

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).

S. Chakraborty, T. Chakraborty, S. P. Khanna, E. H. Linfield, A. G. Davies, J. Fowler, C. H. Worrall, H. E. Beere, and D. A. Ritchie, “Spectral engineering of terahertz quantum cascade lasers using focused ion beam etched photonic lattices,” Electron. Lett. 42(7), 404 (2006).
[Crossref]

Rondinelli, J. M.

Scalora, M.

C. Sibilia, I. S. Nefedov, M. Scalora, and M. Bertolotti, “Electromagnetic mode density for finite quasi-periodic structures,” J. Opt. Soc. Am. B 15(7), 1947 (1998).
[Crossref]

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 4107–4121 (1996).
[Crossref] [PubMed]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896 (1994).
[Crossref]

Shank, C.

H. Haus and C. Shank, “Antisymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. 12(9), 532–539 (1976).
[Crossref]

Sibilia, C.

Smirnov, A. G.

Tager, A.

I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, “Design of widely tunable semiconductor lasers and the concept of binary superimposed gratings (BSG’s),” IEEE J. Quantum Electron. 34(4), 729–741 (1998).
[Crossref]

Tredicucci, A.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).

Ushakov, D. V.

Walther, C.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).

Wiersma, D. S.

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).

Worrall, C. H.

S. Chakraborty, T. Chakraborty, S. P. Khanna, E. H. Linfield, A. G. Davies, J. Fowler, C. H. Worrall, H. E. Beere, and D. A. Ritchie, “Spectral engineering of terahertz quantum cascade lasers using focused ion beam etched photonic lattices,” Electron. Lett. 42(7), 404 (2006).
[Crossref]

Xu, J. M.

I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, “Design of widely tunable semiconductor lasers and the concept of binary superimposed gratings (BSG’s),” IEEE J. Quantum Electron. 34(4), 729–741 (1998).
[Crossref]

Appl. Phys. Lett. (2)

S. Chakraborty, O. P. Marshall, M. Khairuzzaman, C.-W. Hsin, H. E. Beere, and D. A. Ritchie, “Longitudinal computer-generated holograms for digital frequency control in electronically tunable terahertz lasers,” Appl. Phys. Lett. 101(12), 121103 (2012).
[Crossref]

O. P. Marshall, M. Khairuzzaman, H. E. Beere, D. A. Ritchie, and S. Chakraborty, “Broadband photonic control for dual-mode terahertz laser emission,” Appl. Phys. Lett. 102(18), 181106 (2013).
[Crossref]

Biophys. J. (1)

N. Laman, S. S. Harsha, D. Grischkowsky, and J. S. Melinger, “High-resolution waveguide THz spectroscopy of biological molecules,” Biophys. J. 94(3), 1010–1020 (2008).
[Crossref] [PubMed]

Electron. Lett. (1)

S. Chakraborty, T. Chakraborty, S. P. Khanna, E. H. Linfield, A. G. Davies, J. Fowler, C. H. Worrall, H. E. Beere, and D. A. Ritchie, “Spectral engineering of terahertz quantum cascade lasers using focused ion beam etched photonic lattices,” Electron. Lett. 42(7), 404 (2006).
[Crossref]

IEEE J. Quantum Electron. (3)

H. Haus and C. Shank, “Antisymmetric taper of distributed feedback lasers,” IEEE J. Quantum Electron. 12(9), 532–539 (1976).
[Crossref]

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29(6), 1824–1834 (1993).
[Crossref]

I. A. Avrutsky, D. S. Ellis, A. Tager, H. Anis, and J. M. Xu, “Design of widely tunable semiconductor lasers and the concept of binary superimposed gratings (BSG’s),” IEEE J. Quantum Electron. 34(4), 729–741 (1998).
[Crossref]

IEEE Photonics Technol. Lett. (1)

T. G. Folland and S. Chakraborty, “Dual-frequency defect-mode lasing in Aperiodic Distributed Feedback (ADFB) cavities,” IEEE Photonics Technol. Lett. 28(15), 1617–1620 (2016).
[Crossref]

J. Appl. Phys. (2)

O. P. Marshall, S. Chakraborty, M. Khairuzzaman, T. Folland, A. Gholinia, H. E. Beere, and D. A. Ritchie, “Electronically tunable aperiodic distributed feedback terahertz lasers,” J. Appl. Phys. 113(20), 203103 (2013).
[Crossref]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band edge laser: A new approach to gain enhancement,” J. Appl. Phys. 75(4), 1896 (1994).
[Crossref]

J. Opt. Soc. Am. B (4)

Mater. Today (1)

A. G. Davies, A. D. Burnett, W. Fan, E. H. Linfield, and J. E. Cunningham, “Terahertz spectroscopy of explosives and drugs,” Mater. Today 11(3), 18–26 (2008).
[Crossref]

Nat. Photonics (1)

L. Mahler, A. Tredicucci, F. Beltram, C. Walther, J. Faist, H. E. Beere, D. A. Ritchie, and D. S. Wiersma, “Quasi-periodic distributed feedback laser,” Nat. Photonics 4, 165–169 (2010).

Opt. Express (1)

Photonics Nanostructures – Fundam. Appl. (1)

S. Chakraborty, M. C. Parker, and R. J. Mears, “A Fourier (k-) space design approach for controllable photonic band and localization states in aperiodic lattices,” Photonics Nanostructures – Fundam. Appl. 3, 139–147 (2005).

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 53(4), 4107–4121 (1996).
[Crossref] [PubMed]

Science (1)

S. Chakraborty, O. P. Marshall, T. G. Folland, Y.-J. Kim, A. N. Grigorenko, and K. S. Novoselov, “Gain modulation by graphene plasmons in aperiodic lattice lasers,” Science 351(6270), 246–248 (2016).
[Crossref] [PubMed]

Other (1)

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2007).

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Figures (4)

Fig. 1
Fig. 1 a) Physical geometry of the AL. Lines represent low index; minimum line separation is Λ; horizontal dashes represent defects in multiples of Λ/2; b) FT of the AL and reflection gain for κLg = 8 just below threshold c) contour plot of reflectivity spectral gain as a function of frequency and material gain d) Modal threshold gain spectrum for two different grating coupling coefficients e) modal threshold gain for a series of coupling strengths.
Fig. 2
Fig. 2 Comparison between TMM calculations and emission spectra for device C reproduced from reference [12]; insets show simulated systems schematics a) AL group delay calculation, neff = 3.61, Λ = 14.1 µm and κLg = 8, b) AL threshold spectrum c) Coupled FP-AL threshold spectrum, Lc = 6.00 mm. Black dashes indicate FP cavity threshold; blue area arbitrarily illustrates the lowest threshold modes expected in experiments. Experimental spectra are taken at three different operational currents.
Fig. 3
Fig. 3 Lattice group delay and cavity threshold spectrum for a) neff = 3.615, Λ = 13.72 µm (fB = 3.022 THz) and Lc = 5.72 mm and b) neff = 3.615, Λ = 14.1 µm (fB = 2.941 THz) and Lc = 6.00 mm. These results are against the emission spectra for devices A & B at a series of 6 different operational currents, reproduced from reference [12].
Fig. 4
Fig. 4 Top shows τg for the lattice only, bottom is the modal threshold for a cavity with κLg = 2, neff = 3.61, Λ = 14.10 µm and Lc = 6.00 mm, various cavity assymetries. Inset shows geometry.

Equations (3)

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( F 0 R 0 )=M( F N R N )= P 1 S 1,2 P 2 ... P N1 S N1,N P N ( F N R N )=( T 11 T 12 T 21 T 22 )( F N R N )
P u =( e iφ 0 0 e iφ )
S u,v = 1 t u,v ( 1 r u,v r u,v 1 )

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