Abstract

We develop a theory of lasing of a collection of pumped active atoms without a resonator (either regular or random). Due to spontaneous emission into free space, phases of free space electromagnetic modes fluctuate. These phase fluctuations can be reduced to frequency fluctuations. The closer the frequency of fluctuation to the transition frequency of the active atoms, the higher lifetime of the fluctuation. We show that because of this, the average frequency of modes pulls toward the transition frequency. This leads to a maximum in the density of states of the electromagnetic field and a decrease of the mode group velocity. Consequently, the coupling of modes with atoms as well as the lifetime of fluctuations increase. Thus, mode pulling provides positive feedback. When the pump rate exceeds a certain threshold, the lifetime of one of the realized fluctuations diverges, and radiation becomes coherent.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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2019 (1)

2017 (4)

A. A. Zyablovsky, E. S. Andrianov, I. A. Nechepurenko, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Approach for describing spatial dynamics of quantum light-matter interaction in dispersive dissipative media,” Phys. Rev. A 95(5), 053835 (2017).
[Crossref]

V. Y. Shishkov, E. S. Andrianov, A. A. Pukhov, and A. P. Vinogradov, “Retardation of quantum uncertainty of two radiative dipoles,” Phys. Rev. A 95(6), 062115 (2017).
[Crossref]

S. Hartmann and W. Elsäßer, “A novel semiconductor-based, fully incoherent amplified spontaneous emission light source for ghost imaging,” Sci. Rep. 7(1), 41866 (2017).
[Crossref]

A. A. Zyablovsky, I. A. Nechepurenko, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, A. P. Vinogradov, and A. A. Lisyansky, “Optimum gain for plasmonic distributed feedback lasers,” Phys. Rev. B 95(20), 205417 (2017).
[Crossref]

2015 (2)

A. Nurmikko, “What future for quantum dot-based light emitters?” Nat. Nanotechnol. 10(12), 1001–1004 (2015).
[Crossref]

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6(1), 8056 (2015).
[Crossref]

2014 (2)

T. Pickering, J. M. Hamm, A. F. Page, S. Wuestner, and O. Hess, “Cavity-free plasmonic nanolasing enabled by dispersionless stopped light,” Nat. Commun. 5(1), 4972 (2014).
[Crossref]

M. T. Hill and M. C. Gather, “Advances in small lasers,” Nat. Photonics 8(12), 908–918 (2014).
[Crossref]

2013 (1)

2012 (1)

A. V. Dorofeenko, A. A. Zyablovsky, A. A. Pukhov, A. A. Lisyansky, and A. P. Vinogradov, “Light propagation in composite materials with gain layers,” Phys.-Usp. 55(11), 1080–1097 (2012).
[Crossref]

2011 (2)

M. Blazek, S. Hartmann, A. Molitor, and W. Elsaesser, “Unifying intensity noise and second-order coherence properties of amplified spontaneous emission sources,” Opt. Lett. 36(17), 3455–3457 (2011).
[Crossref]

M. Blazek and W. Elsäßer, “Coherent and thermal light: Tunable hybrid states with second-order coherence without first-order coherence,” Phys. Rev. A 84(6), 063840 (2011).
[Crossref]

2009 (1)

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009).
[Crossref]

2008 (1)

D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008).
[Crossref]

2004 (1)

A. P. Vinogradov and A. M. Merzlikin, “Band theory of light localization in one-dimensional disordered systems,” Phys. Rev. E 70(2), 026610 (2004).
[Crossref]

2001 (1)

H. Cao, Y. Ling, J. Xu, C. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86(20), 4524–4527 (2001).
[Crossref]

2000 (1)

H. J. Carmichael and M. O. Scully, “Statistical methods in quantum optics 1: Master equations and fokker-planck equations,” Phys. Today 53(3), 78–80 (2000).
[Crossref]

1999 (1)

H. Cao, Y. Zhao, S.-T. Ho, E. Seelig, Q. Wang, and R. P. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

1981 (1)

M. J. Mumma, D. Buhl, G. Chin, D. Deming, F. Espenak, T. Kostiuk, and D. Zipoy, “Discovery of natural gain amplification in the 10-micrometer carbon dioxide laser bands on Mars: a natural laser,” Science 212(4490), 45–49 (1981).
[Crossref]

1976 (1)

M. A. Johnson, M. A. Betz, R. A. McLaren, E. C. Sutton, and C. H. Townes, “Nonthermal 10 micron CO2 emission lines in the atmospheres of Mars and Venus,” Astrophys. J. 208, L145–L148 (1976).
[Crossref]

1973 (1)

R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow? A theory of single-quasimode laser operation,” Phys. Rev. A 7(5), 1788–1797 (1973).
[Crossref]

1972 (1)

V. S. Letokhov, “Laser action in stellar atmospheres,” IEEE J. Quantum Electron. 8(6), 615 (1972).
[Crossref]

1965 (1)

H. Weaver, D. R. W. Williams, N. H. Dieter, and W. T. Lum, “Observations of a strong unidentified microwave line and of emission from the OH molecule,” Nature 208(5005), 29–31 (1965).
[Crossref]

Andrianov, E. S.

I. V. Doronin, E. S. Andrianov, A. A. Zyablovsky, A. A. Pukhov, Y. E. Lozovik, A. P. Vinogradov, and A. A. Lisyansky, “Second-order coherence properties of amplified spontaneous emission,” Opt. Express 27(8), 10991–11005 (2019).
[Crossref]

A. A. Zyablovsky, E. S. Andrianov, I. A. Nechepurenko, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Approach for describing spatial dynamics of quantum light-matter interaction in dispersive dissipative media,” Phys. Rev. A 95(5), 053835 (2017).
[Crossref]

V. Y. Shishkov, E. S. Andrianov, A. A. Pukhov, and A. P. Vinogradov, “Retardation of quantum uncertainty of two radiative dipoles,” Phys. Rev. A 95(6), 062115 (2017).
[Crossref]

A. A. Zyablovsky, I. A. Nechepurenko, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, A. P. Vinogradov, and A. A. Lisyansky, “Optimum gain for plasmonic distributed feedback lasers,” Phys. Rev. B 95(20), 205417 (2017).
[Crossref]

Betz, M. A.

M. A. Johnson, M. A. Betz, R. A. McLaren, E. C. Sutton, and C. H. Townes, “Nonthermal 10 micron CO2 emission lines in the atmospheres of Mars and Venus,” Astrophys. J. 208, L145–L148 (1976).
[Crossref]

Blazek, M.

Bodnarchuk, M. I.

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6(1), 8056 (2015).
[Crossref]

Boitier, F.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009).
[Crossref]

Buhl, D.

M. J. Mumma, D. Buhl, G. Chin, D. Deming, F. Espenak, T. Kostiuk, and D. Zipoy, “Discovery of natural gain amplification in the 10-micrometer carbon dioxide laser bands on Mars: a natural laser,” Science 212(4490), 45–49 (1981).
[Crossref]

Cao, C.

H. Cao, Y. Ling, J. Xu, C. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86(20), 4524–4527 (2001).
[Crossref]

Cao, H.

H. Cao, Y. Ling, J. Xu, C. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86(20), 4524–4527 (2001).
[Crossref]

H. Cao, Y. Zhao, S.-T. Ho, E. Seelig, Q. Wang, and R. P. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Carmichael, H. J.

H. J. Carmichael and M. O. Scully, “Statistical methods in quantum optics 1: Master equations and fokker-planck equations,” Phys. Today 53(3), 78–80 (2000).
[Crossref]

Chang, R. P.

H. Cao, Y. Zhao, S.-T. Ho, E. Seelig, Q. Wang, and R. P. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Chin, G.

M. J. Mumma, D. Buhl, G. Chin, D. Deming, F. Espenak, T. Kostiuk, and D. Zipoy, “Discovery of natural gain amplification in the 10-micrometer carbon dioxide laser bands on Mars: a natural laser,” Science 212(4490), 45–49 (1981).
[Crossref]

De Luca, G.

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6(1), 8056 (2015).
[Crossref]

Deming, D.

M. J. Mumma, D. Buhl, G. Chin, D. Deming, F. Espenak, T. Kostiuk, and D. Zipoy, “Discovery of natural gain amplification in the 10-micrometer carbon dioxide laser bands on Mars: a natural laser,” Science 212(4490), 45–49 (1981).
[Crossref]

Dieter, N. H.

H. Weaver, D. R. W. Williams, N. H. Dieter, and W. T. Lum, “Observations of a strong unidentified microwave line and of emission from the OH molecule,” Nature 208(5005), 29–31 (1965).
[Crossref]

Dorofeenko, A. V.

A. A. Zyablovsky, E. S. Andrianov, I. A. Nechepurenko, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Approach for describing spatial dynamics of quantum light-matter interaction in dispersive dissipative media,” Phys. Rev. A 95(5), 053835 (2017).
[Crossref]

A. A. Zyablovsky, I. A. Nechepurenko, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, A. P. Vinogradov, and A. A. Lisyansky, “Optimum gain for plasmonic distributed feedback lasers,” Phys. Rev. B 95(20), 205417 (2017).
[Crossref]

A. V. Dorofeenko, A. A. Zyablovsky, A. A. Pukhov, A. A. Lisyansky, and A. P. Vinogradov, “Light propagation in composite materials with gain layers,” Phys.-Usp. 55(11), 1080–1097 (2012).
[Crossref]

Doronin, I. V.

Elsaesser, W.

Elsäßer, W.

S. Hartmann and W. Elsäßer, “A novel semiconductor-based, fully incoherent amplified spontaneous emission light source for ghost imaging,” Sci. Rep. 7(1), 41866 (2017).
[Crossref]

Elsässer, W.

Elsäßer, W.

M. Blazek and W. Elsäßer, “Coherent and thermal light: Tunable hybrid states with second-order coherence without first-order coherence,” Phys. Rev. A 84(6), 063840 (2011).
[Crossref]

Espenak, F.

M. J. Mumma, D. Buhl, G. Chin, D. Deming, F. Espenak, T. Kostiuk, and D. Zipoy, “Discovery of natural gain amplification in the 10-micrometer carbon dioxide laser bands on Mars: a natural laser,” Science 212(4490), 45–49 (1981).
[Crossref]

Fabre, C.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009).
[Crossref]

Fiebig, M.

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6(1), 8056 (2015).
[Crossref]

Gather, M. C.

M. T. Hill and M. C. Gather, “Advances in small lasers,” Nat. Photonics 8(12), 908–918 (2014).
[Crossref]

Godard, A.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009).
[Crossref]

Haken, H.

H. Haken, Laser light dynamics (North-Holland Physics Publishing1985).

Hamm, J. M.

T. Pickering, J. M. Hamm, A. F. Page, S. Wuestner, and O. Hess, “Cavity-free plasmonic nanolasing enabled by dispersionless stopped light,” Nat. Commun. 5(1), 4972 (2014).
[Crossref]

Hartmann, S.

Heiss, W.

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6(1), 8056 (2015).
[Crossref]

Hess, O.

T. Pickering, J. M. Hamm, A. F. Page, S. Wuestner, and O. Hess, “Cavity-free plasmonic nanolasing enabled by dispersionless stopped light,” Nat. Commun. 5(1), 4972 (2014).
[Crossref]

Hill, M. T.

M. T. Hill and M. C. Gather, “Advances in small lasers,” Nat. Photonics 8(12), 908–918 (2014).
[Crossref]

Ho, S.-T.

H. Cao, Y. Zhao, S.-T. Ho, E. Seelig, Q. Wang, and R. P. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Humer, M.

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6(1), 8056 (2015).
[Crossref]

Johansson, S.

V. S. Letokhov and S. Johansson, Astrophysical Lasers (Oxford University Press, 2009).

Johnson, M. A.

M. A. Johnson, M. A. Betz, R. A. McLaren, E. C. Sutton, and C. H. Townes, “Nonthermal 10 micron CO2 emission lines in the atmospheres of Mars and Venus,” Astrophys. J. 208, L145–L148 (1976).
[Crossref]

Kostiuk, T.

M. J. Mumma, D. Buhl, G. Chin, D. Deming, F. Espenak, T. Kostiuk, and D. Zipoy, “Discovery of natural gain amplification in the 10-micrometer carbon dioxide laser bands on Mars: a natural laser,” Science 212(4490), 45–49 (1981).
[Crossref]

Kovalenko, M. V.

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6(1), 8056 (2015).
[Crossref]

Krieg, F.

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6(1), 8056 (2015).
[Crossref]

Kumar, P.

H. Cao, Y. Ling, J. Xu, C. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86(20), 4524–4527 (2001).
[Crossref]

Lamb, W. E.

R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow? A theory of single-quasimode laser operation,” Phys. Rev. A 7(5), 1788–1797 (1973).
[Crossref]

Lang, R.

R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow? A theory of single-quasimode laser operation,” Phys. Rev. A 7(5), 1788–1797 (1973).
[Crossref]

Letokhov, V. S.

V. S. Letokhov, “Laser action in stellar atmospheres,” IEEE J. Quantum Electron. 8(6), 615 (1972).
[Crossref]

V. S. Letokhov and S. Johansson, Astrophysical Lasers (Oxford University Press, 2009).

Ling, Y.

H. Cao, Y. Ling, J. Xu, C. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86(20), 4524–4527 (2001).
[Crossref]

Lisyansky, A. A.

I. V. Doronin, E. S. Andrianov, A. A. Zyablovsky, A. A. Pukhov, Y. E. Lozovik, A. P. Vinogradov, and A. A. Lisyansky, “Second-order coherence properties of amplified spontaneous emission,” Opt. Express 27(8), 10991–11005 (2019).
[Crossref]

A. A. Zyablovsky, I. A. Nechepurenko, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, A. P. Vinogradov, and A. A. Lisyansky, “Optimum gain for plasmonic distributed feedback lasers,” Phys. Rev. B 95(20), 205417 (2017).
[Crossref]

A. V. Dorofeenko, A. A. Zyablovsky, A. A. Pukhov, A. A. Lisyansky, and A. P. Vinogradov, “Light propagation in composite materials with gain layers,” Phys.-Usp. 55(11), 1080–1097 (2012).
[Crossref]

Lozovik, Y. E.

Lum, W. T.

H. Weaver, D. R. W. Williams, N. H. Dieter, and W. T. Lum, “Observations of a strong unidentified microwave line and of emission from the OH molecule,” Nature 208(5005), 29–31 (1965).
[Crossref]

McLaren, R. A.

M. A. Johnson, M. A. Betz, R. A. McLaren, E. C. Sutton, and C. H. Townes, “Nonthermal 10 micron CO2 emission lines in the atmospheres of Mars and Venus,” Astrophys. J. 208, L145–L148 (1976).
[Crossref]

Merzlikin, A. M.

A. P. Vinogradov and A. M. Merzlikin, “Band theory of light localization in one-dimensional disordered systems,” Phys. Rev. E 70(2), 026610 (2004).
[Crossref]

Molitor, A.

Mumma, M. J.

M. J. Mumma, D. Buhl, G. Chin, D. Deming, F. Espenak, T. Kostiuk, and D. Zipoy, “Discovery of natural gain amplification in the 10-micrometer carbon dioxide laser bands on Mars: a natural laser,” Science 212(4490), 45–49 (1981).
[Crossref]

Nechepurenko, I. A.

A. A. Zyablovsky, E. S. Andrianov, I. A. Nechepurenko, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Approach for describing spatial dynamics of quantum light-matter interaction in dispersive dissipative media,” Phys. Rev. A 95(5), 053835 (2017).
[Crossref]

A. A. Zyablovsky, I. A. Nechepurenko, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, A. P. Vinogradov, and A. A. Lisyansky, “Optimum gain for plasmonic distributed feedback lasers,” Phys. Rev. B 95(20), 205417 (2017).
[Crossref]

Nedelcu, G.

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6(1), 8056 (2015).
[Crossref]

Nurmikko, A.

A. Nurmikko, “What future for quantum dot-based light emitters?” Nat. Nanotechnol. 10(12), 1001–1004 (2015).
[Crossref]

Page, A. F.

T. Pickering, J. M. Hamm, A. F. Page, S. Wuestner, and O. Hess, “Cavity-free plasmonic nanolasing enabled by dispersionless stopped light,” Nat. Commun. 5(1), 4972 (2014).
[Crossref]

Pickering, T.

T. Pickering, J. M. Hamm, A. F. Page, S. Wuestner, and O. Hess, “Cavity-free plasmonic nanolasing enabled by dispersionless stopped light,” Nat. Commun. 5(1), 4972 (2014).
[Crossref]

Protesescu, L.

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6(1), 8056 (2015).
[Crossref]

Pukhov, A. A.

I. V. Doronin, E. S. Andrianov, A. A. Zyablovsky, A. A. Pukhov, Y. E. Lozovik, A. P. Vinogradov, and A. A. Lisyansky, “Second-order coherence properties of amplified spontaneous emission,” Opt. Express 27(8), 10991–11005 (2019).
[Crossref]

V. Y. Shishkov, E. S. Andrianov, A. A. Pukhov, and A. P. Vinogradov, “Retardation of quantum uncertainty of two radiative dipoles,” Phys. Rev. A 95(6), 062115 (2017).
[Crossref]

A. A. Zyablovsky, E. S. Andrianov, I. A. Nechepurenko, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Approach for describing spatial dynamics of quantum light-matter interaction in dispersive dissipative media,” Phys. Rev. A 95(5), 053835 (2017).
[Crossref]

A. A. Zyablovsky, I. A. Nechepurenko, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, A. P. Vinogradov, and A. A. Lisyansky, “Optimum gain for plasmonic distributed feedback lasers,” Phys. Rev. B 95(20), 205417 (2017).
[Crossref]

A. V. Dorofeenko, A. A. Zyablovsky, A. A. Pukhov, A. A. Lisyansky, and A. P. Vinogradov, “Light propagation in composite materials with gain layers,” Phys.-Usp. 55(11), 1080–1097 (2012).
[Crossref]

Rosencher, E.

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009).
[Crossref]

Scully, M. O.

H. J. Carmichael and M. O. Scully, “Statistical methods in quantum optics 1: Master equations and fokker-planck equations,” Phys. Today 53(3), 78–80 (2000).
[Crossref]

R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow? A theory of single-quasimode laser operation,” Phys. Rev. A 7(5), 1788–1797 (1973).
[Crossref]

M. O. Scully and M. S. Zubairy, Quantum optics (Cambridge University Press, 1997).

Seelig, E.

H. Cao, Y. Zhao, S.-T. Ho, E. Seelig, Q. Wang, and R. P. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Shishkov, V. Y.

V. Y. Shishkov, E. S. Andrianov, A. A. Pukhov, and A. P. Vinogradov, “Retardation of quantum uncertainty of two radiative dipoles,” Phys. Rev. A 95(6), 062115 (2017).
[Crossref]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Sutton, E. C.

M. A. Johnson, M. A. Betz, R. A. McLaren, E. C. Sutton, and C. H. Townes, “Nonthermal 10 micron CO2 emission lines in the atmospheres of Mars and Venus,” Astrophys. J. 208, L145–L148 (1976).
[Crossref]

Townes, C. H.

M. A. Johnson, M. A. Betz, R. A. McLaren, E. C. Sutton, and C. H. Townes, “Nonthermal 10 micron CO2 emission lines in the atmospheres of Mars and Venus,” Astrophys. J. 208, L145–L148 (1976).
[Crossref]

Vinogradov, A. P.

I. V. Doronin, E. S. Andrianov, A. A. Zyablovsky, A. A. Pukhov, Y. E. Lozovik, A. P. Vinogradov, and A. A. Lisyansky, “Second-order coherence properties of amplified spontaneous emission,” Opt. Express 27(8), 10991–11005 (2019).
[Crossref]

A. A. Zyablovsky, E. S. Andrianov, I. A. Nechepurenko, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Approach for describing spatial dynamics of quantum light-matter interaction in dispersive dissipative media,” Phys. Rev. A 95(5), 053835 (2017).
[Crossref]

V. Y. Shishkov, E. S. Andrianov, A. A. Pukhov, and A. P. Vinogradov, “Retardation of quantum uncertainty of two radiative dipoles,” Phys. Rev. A 95(6), 062115 (2017).
[Crossref]

A. A. Zyablovsky, I. A. Nechepurenko, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, A. P. Vinogradov, and A. A. Lisyansky, “Optimum gain for plasmonic distributed feedback lasers,” Phys. Rev. B 95(20), 205417 (2017).
[Crossref]

A. V. Dorofeenko, A. A. Zyablovsky, A. A. Pukhov, A. A. Lisyansky, and A. P. Vinogradov, “Light propagation in composite materials with gain layers,” Phys.-Usp. 55(11), 1080–1097 (2012).
[Crossref]

A. P. Vinogradov and A. M. Merzlikin, “Band theory of light localization in one-dimensional disordered systems,” Phys. Rev. E 70(2), 026610 (2004).
[Crossref]

Wang, Q.

H. Cao, Y. Zhao, S.-T. Ho, E. Seelig, Q. Wang, and R. P. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Weaver, H.

H. Weaver, D. R. W. Williams, N. H. Dieter, and W. T. Lum, “Observations of a strong unidentified microwave line and of emission from the OH molecule,” Nature 208(5005), 29–31 (1965).
[Crossref]

Wiersma, D. S.

D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008).
[Crossref]

Williams, D. R. W.

H. Weaver, D. R. W. Williams, N. H. Dieter, and W. T. Lum, “Observations of a strong unidentified microwave line and of emission from the OH molecule,” Nature 208(5005), 29–31 (1965).
[Crossref]

Wuestner, S.

T. Pickering, J. M. Hamm, A. F. Page, S. Wuestner, and O. Hess, “Cavity-free plasmonic nanolasing enabled by dispersionless stopped light,” Nat. Commun. 5(1), 4972 (2014).
[Crossref]

Xu, J.

H. Cao, Y. Ling, J. Xu, C. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86(20), 4524–4527 (2001).
[Crossref]

Yakunin, S.

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6(1), 8056 (2015).
[Crossref]

Zhao, Y.

H. Cao, Y. Zhao, S.-T. Ho, E. Seelig, Q. Wang, and R. P. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

Zipoy, D.

M. J. Mumma, D. Buhl, G. Chin, D. Deming, F. Espenak, T. Kostiuk, and D. Zipoy, “Discovery of natural gain amplification in the 10-micrometer carbon dioxide laser bands on Mars: a natural laser,” Science 212(4490), 45–49 (1981).
[Crossref]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum optics (Cambridge University Press, 1997).

Zyablovsky, A. A.

I. V. Doronin, E. S. Andrianov, A. A. Zyablovsky, A. A. Pukhov, Y. E. Lozovik, A. P. Vinogradov, and A. A. Lisyansky, “Second-order coherence properties of amplified spontaneous emission,” Opt. Express 27(8), 10991–11005 (2019).
[Crossref]

A. A. Zyablovsky, E. S. Andrianov, I. A. Nechepurenko, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Approach for describing spatial dynamics of quantum light-matter interaction in dispersive dissipative media,” Phys. Rev. A 95(5), 053835 (2017).
[Crossref]

A. A. Zyablovsky, I. A. Nechepurenko, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, A. P. Vinogradov, and A. A. Lisyansky, “Optimum gain for plasmonic distributed feedback lasers,” Phys. Rev. B 95(20), 205417 (2017).
[Crossref]

A. V. Dorofeenko, A. A. Zyablovsky, A. A. Pukhov, A. A. Lisyansky, and A. P. Vinogradov, “Light propagation in composite materials with gain layers,” Phys.-Usp. 55(11), 1080–1097 (2012).
[Crossref]

Astrophys. J. (1)

M. A. Johnson, M. A. Betz, R. A. McLaren, E. C. Sutton, and C. H. Townes, “Nonthermal 10 micron CO2 emission lines in the atmospheres of Mars and Venus,” Astrophys. J. 208, L145–L148 (1976).
[Crossref]

IEEE J. Quantum Electron. (1)

V. S. Letokhov, “Laser action in stellar atmospheres,” IEEE J. Quantum Electron. 8(6), 615 (1972).
[Crossref]

Nat. Commun. (2)

T. Pickering, J. M. Hamm, A. F. Page, S. Wuestner, and O. Hess, “Cavity-free plasmonic nanolasing enabled by dispersionless stopped light,” Nat. Commun. 5(1), 4972 (2014).
[Crossref]

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6(1), 8056 (2015).
[Crossref]

Nat. Nanotechnol. (1)

A. Nurmikko, “What future for quantum dot-based light emitters?” Nat. Nanotechnol. 10(12), 1001–1004 (2015).
[Crossref]

Nat. Photonics (1)

M. T. Hill and M. C. Gather, “Advances in small lasers,” Nat. Photonics 8(12), 908–918 (2014).
[Crossref]

Nat. Phys. (2)

F. Boitier, A. Godard, E. Rosencher, and C. Fabre, “Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors,” Nat. Phys. 5(4), 267–270 (2009).
[Crossref]

D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008).
[Crossref]

Nature (1)

H. Weaver, D. R. W. Williams, N. H. Dieter, and W. T. Lum, “Observations of a strong unidentified microwave line and of emission from the OH molecule,” Nature 208(5005), 29–31 (1965).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (4)

R. Lang, M. O. Scully, and W. E. Lamb, “Why is the laser line so narrow? A theory of single-quasimode laser operation,” Phys. Rev. A 7(5), 1788–1797 (1973).
[Crossref]

M. Blazek and W. Elsäßer, “Coherent and thermal light: Tunable hybrid states with second-order coherence without first-order coherence,” Phys. Rev. A 84(6), 063840 (2011).
[Crossref]

A. A. Zyablovsky, E. S. Andrianov, I. A. Nechepurenko, A. V. Dorofeenko, A. A. Pukhov, and A. P. Vinogradov, “Approach for describing spatial dynamics of quantum light-matter interaction in dispersive dissipative media,” Phys. Rev. A 95(5), 053835 (2017).
[Crossref]

V. Y. Shishkov, E. S. Andrianov, A. A. Pukhov, and A. P. Vinogradov, “Retardation of quantum uncertainty of two radiative dipoles,” Phys. Rev. A 95(6), 062115 (2017).
[Crossref]

Phys. Rev. B (1)

A. A. Zyablovsky, I. A. Nechepurenko, E. S. Andrianov, A. V. Dorofeenko, A. A. Pukhov, A. P. Vinogradov, and A. A. Lisyansky, “Optimum gain for plasmonic distributed feedback lasers,” Phys. Rev. B 95(20), 205417 (2017).
[Crossref]

Phys. Rev. E (1)

A. P. Vinogradov and A. M. Merzlikin, “Band theory of light localization in one-dimensional disordered systems,” Phys. Rev. E 70(2), 026610 (2004).
[Crossref]

Phys. Rev. Lett. (2)

H. Cao, Y. Zhao, S.-T. Ho, E. Seelig, Q. Wang, and R. P. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
[Crossref]

H. Cao, Y. Ling, J. Xu, C. Cao, and P. Kumar, “Photon statistics of random lasers with resonant feedback,” Phys. Rev. Lett. 86(20), 4524–4527 (2001).
[Crossref]

Phys. Today (1)

H. J. Carmichael and M. O. Scully, “Statistical methods in quantum optics 1: Master equations and fokker-planck equations,” Phys. Today 53(3), 78–80 (2000).
[Crossref]

Phys.-Usp. (1)

A. V. Dorofeenko, A. A. Zyablovsky, A. A. Pukhov, A. A. Lisyansky, and A. P. Vinogradov, “Light propagation in composite materials with gain layers,” Phys.-Usp. 55(11), 1080–1097 (2012).
[Crossref]

Sci. Rep. (1)

S. Hartmann and W. Elsäßer, “A novel semiconductor-based, fully incoherent amplified spontaneous emission light source for ghost imaging,” Sci. Rep. 7(1), 41866 (2017).
[Crossref]

Science (1)

M. J. Mumma, D. Buhl, G. Chin, D. Deming, F. Espenak, T. Kostiuk, and D. Zipoy, “Discovery of natural gain amplification in the 10-micrometer carbon dioxide laser bands on Mars: a natural laser,” Science 212(4490), 45–49 (1981).
[Crossref]

Other (4)

V. S. Letokhov and S. Johansson, Astrophysical Lasers (Oxford University Press, 2009).

A. E. Siegman, Lasers (University Science Books, 1986).

M. O. Scully and M. S. Zubairy, Quantum optics (Cambridge University Press, 1997).

H. Haken, Laser light dynamics (North-Holland Physics Publishing1985).

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Figures (3)

Fig. 1.
Fig. 1. The dependence of the intensity of output radiation and ${g^{(2)}}({\omega _{TLS}},0)$ on the pump rate for the cavity-free system exhibiting the coherence threshold ${\gamma _{coh}}$ (shown by the vertical dashed line). The solid thick and the thin curves are output intensities obtained by solving the Maxwell-Bloch equation with and without noise, respectively. The computer simulation is performed for $G({{N_c}} ){L_{am}} = 26$ ($n = 32.0 \times {10^{17}}\,c{m^{ - 3}}$). The dashed blue curve is the second-order correlation function, ${g^{(2)}}({\omega _{TLS}},0)$.
Fig. 2.
Fig. 2. Spectra of the free-space mode with the free-space eigenfrequency $\omega = 0.978{\omega _{TLS}}$ for different pump rates: ${\gamma _P} = {\gamma _D}$ (the dotted blue curve), ${\gamma _P} = 1.5{\gamma _D}$ (the solid green curve), and ${\gamma _P} = 2{\gamma _D}$ (the dashed red curve) for an extended system. Below the threshold, the maximum of the spectrum is at $\omega = 0.978{\omega _{TLS}}$ (marked by the vertical black line); with an increase in the pump rate, the maximum at the atom transition frequency grows. $G({{N_c}} ){L_{am}} = 26$.
Fig. 3.
Fig. 3. The dependence of the mean frequency on the wavenumber for ${\gamma _P} = 2{\gamma _D}$ (the dashed blue curve) and ${\gamma _P} = 1000{\gamma _D}$ (the solid red curve). The DOSs near the transition frequency for ${\gamma _P} = 2{\gamma _D}$ (the dashed blue curve) and ${\gamma _P} = 1000{\gamma _D}$ (the solid red curve) are shown in the inset. The side maxima correspond to antisymmetric solutions, which have weaker interaction with atoms.

Equations (22)

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

ddtaj=(γa/2iΔj)ajikatomsΩjkσk,
ddtσk=σk(γP+γD+γdeph)/2+iDkjmodesΩjkaj+Fkσ,
ddtDk=(γPγD)(γP+γD)Dk+2ijmodesΩjk(ajσkajσk),
g(2)(τ)=I(t)I(t+τ)/I(t)2,
εgain(ω)1εgain(ω)+1exp(iωcεgain(ω)Lam)=1
εgain(ω)=1αωTLSωiγdeph/2,
G=2ωcImεgain(ω)ωcImεgain(ω).
|r(ωTLS)|=|εgain(ωTLS)1εgain(ωTLS)+1||Imεgain(ωTLS)|4cG4ωTLS.
|rFP(ωTLS)|=|exp(iωcεgain(ω)Lam)|1=exp(GcohLam/2)7.9102.
Aj(τ)=aj(tst+τ)aj(tst)/=aj(tst+τ)aj(tst)aj(tst)aj(tst)aj(tst)aj(tst)
Sj(ω)=Re0Aj(τ)exp(iωτ)dτ,
ω(kj)=0ωSj(ω)dω/0Sj(ω)dω.
ddtaj=(iΔjγa/2)ajiΩRNatσ,
ddtσ=γdephσ/2+iΩRDjmodeaj,
ddtD=(γPγD)(γPγD)D+2iΩ(σjmodeajσjmodeaj).
aj=iΩRNatγa/2+iΔjσ.
0=γdephσ/2+ΩR2σNatDjmode1γa/2+iΔj.
Dst=Dth=γaγσ4ΩR2Nat1jmode11+2iΔj/γaγaγσ4ΩR2Natξ,
ξjmode11+2iΔj/γa.
ξ=j=11+2iΔj/γa=2j=111+4Δ02(j1/2)2/γa2=π2Δ0/γatanh(π2Δ0/γa)
Dth=Δ0γσ2πΩR2Nattanh(πγa/2Δ0).
Dth=Δ0γσ2πΩR2Nat.

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