Abstract

We theoretically demonstrate that increase of absorption with constant gain in laser systems can lead to onset of laser generation. This counterintuitive absorption induced lasing (AIL) is explained by emergence of additional lasing modes created by an introduction of an absorbing medium with narrow linewidth. We show that this effect is universal and, in particular, can be encountered in simple Fabry-Perot-like systems and doped spherical dielectric nanoresonators. The predicted behavior is robust against detuning between the resonant frequencies of gain and absorbing medium.

© 2015 Optical Society of America

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References

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  1. H. Haken, Laser Theory (Springer, 1984).
  2. P. W. Milonni and J. H. Eberly, Laser Physics (Wiley, 2010).
    [Crossref]
  3. M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley Pub. Co., 1974).
  4. M. Liertzer, L. Ge, A. Cerjan, A. D. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
    [Crossref] [PubMed]
  5. R. El-Ganainy, M. Khajavikhan, and L. Ge, “Exceptional points and lasing self-termination in photonic molecules,” Phys. Rev. A 90, 013802 (2014).
    [Crossref]
  6. M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
    [Crossref] [PubMed]
  7. M. Chitsazi, S. Factor, J. Schindler, H. Ramezani, F. M. Ellis, and T. Kottos, “Experimental observation of lasing shutdown via asymmetric gain,” Phys. Rev. A 89, 043842 (2014).
    [Crossref]
  8. B. Peng, K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
    [Crossref] [PubMed]
  9. A. Mostafazadeh, “Spectral singularities and CPA-laser action in a weakly nonlinear PT-symmetric bilayer slab,” Stud. Appl. Math. 133, 353 (2014).
    [Crossref]
  10. L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
    [Crossref]
  11. L. Ge, Y. D. Chong, S. Rotter, H. E. Türeci, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 1023820 (2011).
    [Crossref]
  12. X. Liu, Q. Zhang, Q. Xiong, and T. C. Sum, “Tailoring the lasing modes in semiconductor nanowire cavities using intrinsic self-absorption,” Nano Lett. 13, 1080 (2013).
    [Crossref] [PubMed]
  13. S. Solimeno, B. Crosignani, and P. DiPorto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, 1986).
  14. S.-L. Chua, Y. Chong, A. D. Stone, M. Soljacic, and J. Bravo-Abad, “Low-threshold lasing action in photonic crystal slabs enabled by Fano resonances,” Opt. Express 19, 1539 (2011).
    [Crossref] [PubMed]
  15. B. Nistad and J. Skaar, “Causality and electromagnetic properties of active media,” Phys. Rev. E 78, 036603 (2008).
    [Crossref]
  16. A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749 (2012).
    [Crossref] [PubMed]
  17. U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5, 3402 (2014).
    [Crossref] [PubMed]
  18. K. L. v. d. Molen, P. Zijlstra, A. Lagendijl, and A. P. Mosk, “Laser threshold of Mie resonances,” Opt. Lett. 31, 1432 (2006).
    [Crossref] [PubMed]
  19. I. Liberal, I. Ederra, R. Gonzalo, and R. W. Ziolkowski, “Magnetic dipole super-resonances and their impact on mechanical forces at optical frequencies,” Opt. Express 22, 8640 (2014).
    [Crossref] [PubMed]
  20. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

2014 (7)

R. El-Ganainy, M. Khajavikhan, and L. Ge, “Exceptional points and lasing self-termination in photonic molecules,” Phys. Rev. A 90, 013802 (2014).
[Crossref]

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
[Crossref] [PubMed]

M. Chitsazi, S. Factor, J. Schindler, H. Ramezani, F. M. Ellis, and T. Kottos, “Experimental observation of lasing shutdown via asymmetric gain,” Phys. Rev. A 89, 043842 (2014).
[Crossref]

B. Peng, K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref] [PubMed]

A. Mostafazadeh, “Spectral singularities and CPA-laser action in a weakly nonlinear PT-symmetric bilayer slab,” Stud. Appl. Math. 133, 353 (2014).
[Crossref]

U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5, 3402 (2014).
[Crossref] [PubMed]

I. Liberal, I. Ederra, R. Gonzalo, and R. W. Ziolkowski, “Magnetic dipole super-resonances and their impact on mechanical forces at optical frequencies,” Opt. Express 22, 8640 (2014).
[Crossref] [PubMed]

2013 (1)

X. Liu, Q. Zhang, Q. Xiong, and T. C. Sum, “Tailoring the lasing modes in semiconductor nanowire cavities using intrinsic self-absorption,” Nano Lett. 13, 1080 (2013).
[Crossref] [PubMed]

2012 (2)

M. Liertzer, L. Ge, A. Cerjan, A. D. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref] [PubMed]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749 (2012).
[Crossref] [PubMed]

2011 (2)

L. Ge, Y. D. Chong, S. Rotter, H. E. Türeci, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 1023820 (2011).
[Crossref]

S.-L. Chua, Y. Chong, A. D. Stone, M. Soljacic, and J. Bravo-Abad, “Low-threshold lasing action in photonic crystal slabs enabled by Fano resonances,” Opt. Express 19, 1539 (2011).
[Crossref] [PubMed]

2010 (1)

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

2008 (1)

B. Nistad and J. Skaar, “Causality and electromagnetic properties of active media,” Phys. Rev. E 78, 036603 (2008).
[Crossref]

2006 (1)

Bender, C. M.

B. Peng, K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref] [PubMed]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Bozhevolnyi, S. I.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749 (2012).
[Crossref] [PubMed]

Brandstetter, M.

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
[Crossref] [PubMed]

Bravo-Abad, J.

Cerjan, A.

M. Liertzer, L. Ge, A. Cerjan, A. D. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref] [PubMed]

Chichkov, B. N.

U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5, 3402 (2014).
[Crossref] [PubMed]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749 (2012).
[Crossref] [PubMed]

Chitsazi, M.

M. Chitsazi, S. Factor, J. Schindler, H. Ramezani, F. M. Ellis, and T. Kottos, “Experimental observation of lasing shutdown via asymmetric gain,” Phys. Rev. A 89, 043842 (2014).
[Crossref]

Chong, Y.

Chong, Y. D.

L. Ge, Y. D. Chong, S. Rotter, H. E. Türeci, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 1023820 (2011).
[Crossref]

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

Chua, S.-L.

Crosignani, B.

S. Solimeno, B. Crosignani, and P. DiPorto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, 1986).

Deutsch, C.

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
[Crossref] [PubMed]

DiPorto, P.

S. Solimeno, B. Crosignani, and P. DiPorto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, 1986).

Eberly, J. H.

P. W. Milonni and J. H. Eberly, Laser Physics (Wiley, 2010).
[Crossref]

Ederra, I.

El-Ganainy, R.

R. El-Ganainy, M. Khajavikhan, and L. Ge, “Exceptional points and lasing self-termination in photonic molecules,” Phys. Rev. A 90, 013802 (2014).
[Crossref]

Ellis, F. M.

M. Chitsazi, S. Factor, J. Schindler, H. Ramezani, F. M. Ellis, and T. Kottos, “Experimental observation of lasing shutdown via asymmetric gain,” Phys. Rev. A 89, 043842 (2014).
[Crossref]

Eriksen, R. L.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749 (2012).
[Crossref] [PubMed]

Evlyukhin, A. B.

U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5, 3402 (2014).
[Crossref] [PubMed]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749 (2012).
[Crossref] [PubMed]

Factor, S.

M. Chitsazi, S. Factor, J. Schindler, H. Ramezani, F. M. Ellis, and T. Kottos, “Experimental observation of lasing shutdown via asymmetric gain,” Phys. Rev. A 89, 043842 (2014).
[Crossref]

Ge, L.

R. El-Ganainy, M. Khajavikhan, and L. Ge, “Exceptional points and lasing self-termination in photonic molecules,” Phys. Rev. A 90, 013802 (2014).
[Crossref]

M. Liertzer, L. Ge, A. Cerjan, A. D. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref] [PubMed]

L. Ge, Y. D. Chong, S. Rotter, H. E. Türeci, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 1023820 (2011).
[Crossref]

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

Gonzalo, R.

Haken, H.

H. Haken, Laser Theory (Springer, 1984).

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Khajavikhan, M.

R. El-Ganainy, M. Khajavikhan, and L. Ge, “Exceptional points and lasing self-termination in photonic molecules,” Phys. Rev. A 90, 013802 (2014).
[Crossref]

Klang, P.

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
[Crossref] [PubMed]

Kottos, T.

M. Chitsazi, S. Factor, J. Schindler, H. Ramezani, F. M. Ellis, and T. Kottos, “Experimental observation of lasing shutdown via asymmetric gain,” Phys. Rev. A 89, 043842 (2014).
[Crossref]

Lagendijl, A.

Lamb, W. E.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley Pub. Co., 1974).

Liberal, I.

Liertzer, M.

B. Peng, K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref] [PubMed]

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
[Crossref] [PubMed]

M. Liertzer, L. Ge, A. Cerjan, A. D. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref] [PubMed]

Liu, X.

X. Liu, Q. Zhang, Q. Xiong, and T. C. Sum, “Tailoring the lasing modes in semiconductor nanowire cavities using intrinsic self-absorption,” Nano Lett. 13, 1080 (2013).
[Crossref] [PubMed]

Milonni, P. W.

P. W. Milonni and J. H. Eberly, Laser Physics (Wiley, 2010).
[Crossref]

Molen, K. L. v. d.

Monifi, F.

B. Peng, K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref] [PubMed]

Mosk, A. P.

Mostafazadeh, A.

A. Mostafazadeh, “Spectral singularities and CPA-laser action in a weakly nonlinear PT-symmetric bilayer slab,” Stud. Appl. Math. 133, 353 (2014).
[Crossref]

Nistad, B.

B. Nistad and J. Skaar, “Causality and electromagnetic properties of active media,” Phys. Rev. E 78, 036603 (2008).
[Crossref]

Nori, F.

B. Peng, K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref] [PubMed]

Novikov, S. M.

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749 (2012).
[Crossref] [PubMed]

Ozdemir, K.

B. Peng, K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref] [PubMed]

Peng, B.

B. Peng, K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref] [PubMed]

Ramezani, H.

M. Chitsazi, S. Factor, J. Schindler, H. Ramezani, F. M. Ellis, and T. Kottos, “Experimental observation of lasing shutdown via asymmetric gain,” Phys. Rev. A 89, 043842 (2014).
[Crossref]

Reinhardt, C.

U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5, 3402 (2014).
[Crossref] [PubMed]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749 (2012).
[Crossref] [PubMed]

Rotter, S.

B. Peng, K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref] [PubMed]

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
[Crossref] [PubMed]

M. Liertzer, L. Ge, A. Cerjan, A. D. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref] [PubMed]

L. Ge, Y. D. Chong, S. Rotter, H. E. Türeci, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 1023820 (2011).
[Crossref]

Sargent, M.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley Pub. Co., 1974).

Schindler, J.

M. Chitsazi, S. Factor, J. Schindler, H. Ramezani, F. M. Ellis, and T. Kottos, “Experimental observation of lasing shutdown via asymmetric gain,” Phys. Rev. A 89, 043842 (2014).
[Crossref]

Schöberl, J.

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
[Crossref] [PubMed]

Scully, M. O.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley Pub. Co., 1974).

Skaar, J.

B. Nistad and J. Skaar, “Causality and electromagnetic properties of active media,” Phys. Rev. E 78, 036603 (2008).
[Crossref]

Solimeno, S.

S. Solimeno, B. Crosignani, and P. DiPorto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, 1986).

Soljacic, M.

Stone, A. D.

M. Liertzer, L. Ge, A. Cerjan, A. D. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref] [PubMed]

S.-L. Chua, Y. Chong, A. D. Stone, M. Soljacic, and J. Bravo-Abad, “Low-threshold lasing action in photonic crystal slabs enabled by Fano resonances,” Opt. Express 19, 1539 (2011).
[Crossref] [PubMed]

L. Ge, Y. D. Chong, S. Rotter, H. E. Türeci, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 1023820 (2011).
[Crossref]

L. Ge, Y. D. Chong, and A. D. Stone, “Steady-state ab initio laser theory: generalizations and analytic results,” Phys. Rev. A 82, 063824 (2010).
[Crossref]

Strasser, G.

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
[Crossref] [PubMed]

Sum, T. C.

X. Liu, Q. Zhang, Q. Xiong, and T. C. Sum, “Tailoring the lasing modes in semiconductor nanowire cavities using intrinsic self-absorption,” Nano Lett. 13, 1080 (2013).
[Crossref] [PubMed]

Türeci, H. E.

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
[Crossref] [PubMed]

M. Liertzer, L. Ge, A. Cerjan, A. D. Stone, H. E. Türeci, and S. Rotter, “Pump-induced exceptional points in lasers,” Phys. Rev. Lett. 108, 173901 (2012).
[Crossref] [PubMed]

L. Ge, Y. D. Chong, S. Rotter, H. E. Türeci, and A. D. Stone, “Unconventional modes in lasers with spatially varying gain and loss,” Phys. Rev. A 84, 1023820 (2011).
[Crossref]

Unterrainer, K.

M. Brandstetter, M. Liertzer, C. Deutsch, P. Klang, J. Schöberl, H. E. Türeci, G. Strasser, K. Unterrainer, and S. Rotter, “Reversing the pump dependence of a laser at an exceptional point,” Nat. Commun. 5, 4034 (2014).
[Crossref] [PubMed]

Xiong, Q.

X. Liu, Q. Zhang, Q. Xiong, and T. C. Sum, “Tailoring the lasing modes in semiconductor nanowire cavities using intrinsic self-absorption,” Nano Lett. 13, 1080 (2013).
[Crossref] [PubMed]

Yang, L.

B. Peng, K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref] [PubMed]

Yilmaz, H.

B. Peng, K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref] [PubMed]

Zhang, Q.

X. Liu, Q. Zhang, Q. Xiong, and T. C. Sum, “Tailoring the lasing modes in semiconductor nanowire cavities using intrinsic self-absorption,” Nano Lett. 13, 1080 (2013).
[Crossref] [PubMed]

Zijlstra, P.

Ziolkowski, R. W.

Zywietz, U.

U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses,” Nat. Commun. 5, 3402 (2014).
[Crossref] [PubMed]

A. B. Evlyukhin, S. M. Novikov, U. Zywietz, R. L. Eriksen, C. Reinhardt, S. I. Bozhevolnyi, and B. N. Chichkov, “Demonstration of magnetic dipole resonances of dielectric nanospheres in the visible region,” Nano Lett. 12, 3749 (2012).
[Crossref] [PubMed]

Nano Lett. (2)

X. Liu, Q. Zhang, Q. Xiong, and T. C. Sum, “Tailoring the lasing modes in semiconductor nanowire cavities using intrinsic self-absorption,” Nano Lett. 13, 1080 (2013).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 (a) Evolution of S–matrix poles for the case of a low Q resonator formed by a slab of length L = 2.25μm with permittivity of gain medium in the absence of pumping ε0 = 2, emission frequency of gain medium kG = 2.6μm−1 and linewidth of gain medium γG = 0.2μm−1 in the range of gain parameter 0 ≤ fG 1. Curves denote the amplitude condition of generation, Eq. (4a). Solid curve: passive system (fG = 0), dashed curve: fG = 0.5, dot-dashed curve: fG = 1. The box shows the point of poles condensation, located exactly at k = kG −iγG. Inset shows zoomed area around the pole lying close to the real axis. (b) The same as (a) for the case of a high Q resonator of length L = 10μm.
Fig. 2
Fig. 2 Two scenarios of the S–matrix poles evolution after reaching the overpumped state. (a) Position of poles of the L = 2.25μm cavity on the complex frequency plane for fG = 1.2. Curve denotes the amplitude condition, Eq. (4a). The black box shows the poles condensation point. (b) The same when absorption with central frequency kA = 2.5μm−1 and linewidth γA = γG/10 is added to the system. Gain and absorption values are set to fG = 1 and fA = 4. A new poles condensation point located at k = kAA emerges. Pole denoted by cyan color enters the upper half-plane. (c) Overpumped and lasing regions in the gain/loss parameters space.
Fig. 3
Fig. 3 Trajectory of the S–matrix pole responsible for absorption induced lasing at fixed gain fG = 1. The black box shows the point of poles condensation from which the pole begins to move. Numerical values on the graph correspond to those of the absorption strength fA at each point of the pole trajectory.
Fig. 4
Fig. 4 Lasing region in the gain-loss parameter space for the spherical laser formed by the nanoparticle of radius R = 1μm. Background permittivity of the nanoparticle medium ε0 = 4. Gain is applied at frequency kG = 1.9μm−1 and has linewidth γG = 0.1μm−1. Absorption line is centered at frequency kA = 2μm−1 with linewidth γA = 0.1γG.

Equations (8)

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ε ( k ) = ε 0 + 2 f A k A γ A k A 2 k 2 2 i k γ A 2 f G k G γ G k G 2 k 2 2 i k γ G ,
s ± = T ± R = ( exp ( i n k L ) ± r ) 1 r exp ( i n k L ) ,
1 r exp ( i n k L ) = 0.
Re [ i n k L + Ln r ] = 0 ,
Im [ i n k L + Ln r ] = 2 π m ,
a m = n ψ m ( n x ) ψ m ( x ) ψ m ( x ) ψ m ( n x ) n ψ m ( n x ) ξ m ( x ) ξ m ( x ) ψ m ( n x ) ,
b m = ψ m ( n x ) ψ n ( x ) n ψ m ( x ) ψ m ( n x ) ψ m ( n x ) ξ n ( x ) n ξ m ( x ) ψ m ( n x ) ,
Q s c = 2 π m = 1 ( ( 2 m + 1 ) ( | a m | 2 + | b m | 2 ) ) / k 2 .

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