Abstract

A model, by combining Maxwell’s equations with all-parameters of Sellmeier’s fitting equations and four-level rate equations, is built to investigate linear dispersive effect on the property of random lasing modes. Computed results show that the first excited modes for both dispersive and non-dispersive scattering cases have almost the same resonant frequency but the spectral intensity for dispersive case is lower than that for non-dispersive case, and there exist more modes in the whole spectra for dispersive case. Further analysis demonstrates that threshold of random lasing in dispersive case is higher than that of the non-dispersive case.

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  1. N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
    [CrossRef]
  2. H. Cao, Y. Zhao, S. Ho, E. Seelig, Q. Wang, and R. Chang, “Random laser action in semiconductor powder,” Phys. Rev. Lett. 82(11), 2278–2281 (1999).
    [CrossRef]
  3. X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85(1), 70–73 (2000).
    [CrossRef] [PubMed]
  4. P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66(14), 144202 (2002).
    [CrossRef]
  5. C. M. Soukoulis, X. Jiang, J. Y. Xu, and H. Cao, “Dynamic response and relaxation oscillations in random lasers,” Phys. Rev. B 65(4), 041103–041106 (2002).
    [CrossRef]
  6. T. Ito and M. Tomita, “Polarization-dependent laser action in a two-dimensional random medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(2), 027601–027604 (2002).
    [CrossRef] [PubMed]
  7. S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93(5), 053903–053907 (2004).
    [CrossRef] [PubMed]
  8. X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69(10), 104202 (2004).
    [CrossRef]
  9. J. S. Liu, H. Lu, and C. Wang, “Spectral time evolution of quasistate modes in two-dimensional random media,” Acta Phys. Sin. 54, 3116 (2005) (in Chinese).
  10. J. S. Liu and Z. Xiong, “Theoretical investigation on the threshold property of localized modes based on spectral width in two-dimensional random media,” Opt. Commun. 268(2), 294–299 (2006).
    [CrossRef]
  11. J. S. Liu, H. Wang, and Z. Xiong, “Origin of light localization from orientational disorder in one and two-dimensional random media with uniaxial scatterers,” Phys. Rev. B 73(19), 195110 (2006).
    [CrossRef]
  12. C. Wang and J. S. Liu, “Polarization dependence of lasing modes in two-dimensional random lasers,” Phys. Lett. A 353(2-3), 269–272 (2006).
    [CrossRef]
  13. C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98(14), 143902 (2007).
    [CrossRef] [PubMed]
  14. H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
    [CrossRef] [PubMed]
  15. D. S. Wiersma, “The physics and applications of random lasers,” Nat. Phys. 4(5), 359–367 (2008).
    [CrossRef]
  16. O. Zaitsev and L. Deych, “Recent developments in the theory of multimode random lasers,” J. Opt. 12(2), 024001–024013 (2010).
    [CrossRef]
  17. R. M. Joseph and A. Taflove, “FDTD Maxwell’s equations modes for nonlinear electrodynamics and optics,” IEEE Trans. Antenn. Propag. 45(3), 364–374 (1997).
    [CrossRef]
  18. M. J. Weber, CRC Handbook of Optical Materials (CRC Press, 2003).
  19. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

2010

O. Zaitsev and L. Deych, “Recent developments in the theory of multimode random lasers,” J. Opt. 12(2), 024001–024013 (2010).
[CrossRef]

2008

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
[CrossRef] [PubMed]

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

2007

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98(14), 143902 (2007).
[CrossRef] [PubMed]

2006

J. S. Liu and Z. Xiong, “Theoretical investigation on the threshold property of localized modes based on spectral width in two-dimensional random media,” Opt. Commun. 268(2), 294–299 (2006).
[CrossRef]

J. S. Liu, H. Wang, and Z. Xiong, “Origin of light localization from orientational disorder in one and two-dimensional random media with uniaxial scatterers,” Phys. Rev. B 73(19), 195110 (2006).
[CrossRef]

C. Wang and J. S. Liu, “Polarization dependence of lasing modes in two-dimensional random lasers,” Phys. Lett. A 353(2-3), 269–272 (2006).
[CrossRef]

2005

J. S. Liu, H. Lu, and C. Wang, “Spectral time evolution of quasistate modes in two-dimensional random media,” Acta Phys. Sin. 54, 3116 (2005) (in Chinese).

2004

S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93(5), 053903–053907 (2004).
[CrossRef] [PubMed]

X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69(10), 104202 (2004).
[CrossRef]

2002

P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66(14), 144202 (2002).
[CrossRef]

C. M. Soukoulis, X. Jiang, J. Y. Xu, and H. Cao, “Dynamic response and relaxation oscillations in random lasers,” Phys. Rev. B 65(4), 041103–041106 (2002).
[CrossRef]

T. Ito and M. Tomita, “Polarization-dependent laser action in a two-dimensional random medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(2), 027601–027604 (2002).
[CrossRef] [PubMed]

2000

X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85(1), 70–73 (2000).
[CrossRef] [PubMed]

1999

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

1997

R. M. Joseph and A. Taflove, “FDTD Maxwell’s equations modes for nonlinear electrodynamics and optics,” IEEE Trans. Antenn. Propag. 45(3), 364–374 (1997).
[CrossRef]

1994

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[CrossRef]

Balachandran, R. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[CrossRef]

Cao, H.

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98(14), 143902 (2007).
[CrossRef] [PubMed]

X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69(10), 104202 (2004).
[CrossRef]

C. M. Soukoulis, X. Jiang, J. Y. Xu, and H. Cao, “Dynamic response and relaxation oscillations in random lasers,” Phys. Rev. B 65(4), 041103–041106 (2002).
[CrossRef]

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

Chang, R.

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

Deych, L.

O. Zaitsev and L. Deych, “Recent developments in the theory of multimode random lasers,” J. Opt. 12(2), 024001–024013 (2010).
[CrossRef]

Feng, S.

X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69(10), 104202 (2004).
[CrossRef]

Ge, L.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
[CrossRef] [PubMed]

Gomes, A. S. L.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[CrossRef]

Ho, S.

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

Ito, T.

T. Ito and M. Tomita, “Polarization-dependent laser action in a two-dimensional random medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(2), 027601–027604 (2002).
[CrossRef] [PubMed]

Jiang, X.

X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69(10), 104202 (2004).
[CrossRef]

C. M. Soukoulis, X. Jiang, J. Y. Xu, and H. Cao, “Dynamic response and relaxation oscillations in random lasers,” Phys. Rev. B 65(4), 041103–041106 (2002).
[CrossRef]

X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85(1), 70–73 (2000).
[CrossRef] [PubMed]

Joannopoulos, J. D.

X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69(10), 104202 (2004).
[CrossRef]

Joseph, R. M.

R. M. Joseph and A. Taflove, “FDTD Maxwell’s equations modes for nonlinear electrodynamics and optics,” IEEE Trans. Antenn. Propag. 45(3), 364–374 (1997).
[CrossRef]

Lawandy, N. M.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[CrossRef]

Liu, J. S.

J. S. Liu and Z. Xiong, “Theoretical investigation on the threshold property of localized modes based on spectral width in two-dimensional random media,” Opt. Commun. 268(2), 294–299 (2006).
[CrossRef]

J. S. Liu, H. Wang, and Z. Xiong, “Origin of light localization from orientational disorder in one and two-dimensional random media with uniaxial scatterers,” Phys. Rev. B 73(19), 195110 (2006).
[CrossRef]

C. Wang and J. S. Liu, “Polarization dependence of lasing modes in two-dimensional random lasers,” Phys. Lett. A 353(2-3), 269–272 (2006).
[CrossRef]

J. S. Liu, H. Lu, and C. Wang, “Spectral time evolution of quasistate modes in two-dimensional random media,” Acta Phys. Sin. 54, 3116 (2005) (in Chinese).

Lu, H.

J. S. Liu, H. Lu, and C. Wang, “Spectral time evolution of quasistate modes in two-dimensional random media,” Acta Phys. Sin. 54, 3116 (2005) (in Chinese).

Mujumdar, S.

S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93(5), 053903–053907 (2004).
[CrossRef] [PubMed]

Ricci, M.

S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93(5), 053903–053907 (2004).
[CrossRef] [PubMed]

Rotter, S.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
[CrossRef] [PubMed]

Sauvain, E.

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[CrossRef]

Sebbah, P.

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98(14), 143902 (2007).
[CrossRef] [PubMed]

P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66(14), 144202 (2002).
[CrossRef]

Seelig, E.

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

Soukoulis, C. M.

X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69(10), 104202 (2004).
[CrossRef]

C. M. Soukoulis, X. Jiang, J. Y. Xu, and H. Cao, “Dynamic response and relaxation oscillations in random lasers,” Phys. Rev. B 65(4), 041103–041106 (2002).
[CrossRef]

X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85(1), 70–73 (2000).
[CrossRef] [PubMed]

Stone, A. D.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
[CrossRef] [PubMed]

Taflove, A.

R. M. Joseph and A. Taflove, “FDTD Maxwell’s equations modes for nonlinear electrodynamics and optics,” IEEE Trans. Antenn. Propag. 45(3), 364–374 (1997).
[CrossRef]

Tomita, M.

T. Ito and M. Tomita, “Polarization-dependent laser action in a two-dimensional random medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(2), 027601–027604 (2002).
[CrossRef] [PubMed]

Torre, R.

S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93(5), 053903–053907 (2004).
[CrossRef] [PubMed]

Türeci, H. E.

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
[CrossRef] [PubMed]

Vanneste, C.

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98(14), 143902 (2007).
[CrossRef] [PubMed]

P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66(14), 144202 (2002).
[CrossRef]

Wang, C.

C. Wang and J. S. Liu, “Polarization dependence of lasing modes in two-dimensional random lasers,” Phys. Lett. A 353(2-3), 269–272 (2006).
[CrossRef]

J. S. Liu, H. Lu, and C. Wang, “Spectral time evolution of quasistate modes in two-dimensional random media,” Acta Phys. Sin. 54, 3116 (2005) (in Chinese).

Wang, H.

J. S. Liu, H. Wang, and Z. Xiong, “Origin of light localization from orientational disorder in one and two-dimensional random media with uniaxial scatterers,” Phys. Rev. B 73(19), 195110 (2006).
[CrossRef]

Wang, Q.

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

Wiersma, D. S.

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

S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93(5), 053903–053907 (2004).
[CrossRef] [PubMed]

Xiong, Z.

J. S. Liu, H. Wang, and Z. Xiong, “Origin of light localization from orientational disorder in one and two-dimensional random media with uniaxial scatterers,” Phys. Rev. B 73(19), 195110 (2006).
[CrossRef]

J. S. Liu and Z. Xiong, “Theoretical investigation on the threshold property of localized modes based on spectral width in two-dimensional random media,” Opt. Commun. 268(2), 294–299 (2006).
[CrossRef]

Xu, J. Y.

C. M. Soukoulis, X. Jiang, J. Y. Xu, and H. Cao, “Dynamic response and relaxation oscillations in random lasers,” Phys. Rev. B 65(4), 041103–041106 (2002).
[CrossRef]

Zaitsev, O.

O. Zaitsev and L. Deych, “Recent developments in the theory of multimode random lasers,” J. Opt. 12(2), 024001–024013 (2010).
[CrossRef]

Zhao, Y.

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

Zi, J.

X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69(10), 104202 (2004).
[CrossRef]

Acta Phys. Sin.

J. S. Liu, H. Lu, and C. Wang, “Spectral time evolution of quasistate modes in two-dimensional random media,” Acta Phys. Sin. 54, 3116 (2005) (in Chinese).

IEEE Trans. Antenn. Propag.

R. M. Joseph and A. Taflove, “FDTD Maxwell’s equations modes for nonlinear electrodynamics and optics,” IEEE Trans. Antenn. Propag. 45(3), 364–374 (1997).
[CrossRef]

J. Opt.

O. Zaitsev and L. Deych, “Recent developments in the theory of multimode random lasers,” J. Opt. 12(2), 024001–024013 (2010).
[CrossRef]

Nat. Phys.

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

Nature

N. M. Lawandy, R. M. Balachandran, A. S. L. Gomes, and E. Sauvain, “Laser action in strongly scattering media,” Nature 368(6470), 436–438 (1994).
[CrossRef]

Opt. Commun.

J. S. Liu and Z. Xiong, “Theoretical investigation on the threshold property of localized modes based on spectral width in two-dimensional random media,” Opt. Commun. 268(2), 294–299 (2006).
[CrossRef]

Phys. Lett. A

C. Wang and J. S. Liu, “Polarization dependence of lasing modes in two-dimensional random lasers,” Phys. Lett. A 353(2-3), 269–272 (2006).
[CrossRef]

Phys. Rev. B

X. Jiang, S. Feng, C. M. Soukoulis, J. Zi, J. D. Joannopoulos, and H. Cao, “Coupling, competition, and stability of modes in random lasers,” Phys. Rev. B 69(10), 104202 (2004).
[CrossRef]

J. S. Liu, H. Wang, and Z. Xiong, “Origin of light localization from orientational disorder in one and two-dimensional random media with uniaxial scatterers,” Phys. Rev. B 73(19), 195110 (2006).
[CrossRef]

P. Sebbah and C. Vanneste, “Random laser in the localized regime,” Phys. Rev. B 66(14), 144202 (2002).
[CrossRef]

C. M. Soukoulis, X. Jiang, J. Y. Xu, and H. Cao, “Dynamic response and relaxation oscillations in random lasers,” Phys. Rev. B 65(4), 041103–041106 (2002).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

T. Ito and M. Tomita, “Polarization-dependent laser action in a two-dimensional random medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(2), 027601–027604 (2002).
[CrossRef] [PubMed]

Phys. Rev. Lett.

S. Mujumdar, M. Ricci, R. Torre, and D. S. Wiersma, “Amplified extended modes in random lasers,” Phys. Rev. Lett. 93(5), 053903–053907 (2004).
[CrossRef] [PubMed]

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

X. Jiang and C. M. Soukoulis, “Time dependent theory for random lasers,” Phys. Rev. Lett. 85(1), 70–73 (2000).
[CrossRef] [PubMed]

C. Vanneste, P. Sebbah, and H. Cao, “Lasing with resonant feedback in weakly scattering random systems,” Phys. Rev. Lett. 98(14), 143902 (2007).
[CrossRef] [PubMed]

Science

H. E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong interactions in multimode random lasers,” Science 320(5876), 643–646 (2008).
[CrossRef] [PubMed]

Other

M. J. Weber, CRC Handbook of Optical Materials (CRC Press, 2003).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

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Figures (6)

Fig. 1
Fig. 1

Schematic illustration of 1D random medium.

Fig. 2
Fig. 2

Relative electric permittivity of Alumina (Al2O3) assuming no absorption as a function of wavelength in the visible range.

Fig. 3
Fig. 3

The spectral intensity in arbitrary units versus the wavelength in the case of the dispersive scattering medium, as shown in Fig. 1 at (a) WP = 1 × 108 s−1, (b) WP = 1 × 109 s−1, (c) WP = 1 × 1010 s−1, (d) WP = 1 × 1011 s−1, (e) WP = 1 × 1012 s−1, and (f) WP = 1 × 1013 s−1.

Fig. 4
Fig. 4

The plot of the peak intensity and spectral width of the lasing modes vs the pump rate W p in the case of the dispersive scattering medium.(a) The peak intensity for the three indicated modes, and the lasing threshold measured from the plots are W I0 = 1.1 × 1010 s−1, W I1 = 2 × 1010 s−1, and W I2 = 4 × 1010 s−1. (b) the peak intensity and spectral width for the mode λ0; and (c) the spectral width for the three indicated modes, and the lasing threshold measured from the plots are W w0 = 5 × 109 s−1, W w1 = 0.9 × 1010 s−1, and W w2 = 1.1 × 1010 s−1.

Fig. 5
Fig. 5

The spectral intensity in arbitrary units versus the wavelength in the case of the non-dispersive scattering medium. shown in Fig. 1 at (a) WP = 1 × 108 s−1, (b) WP = 1 × 109 s−1, (c) WP = 1 × 1010 s−1, (d) WP = 1 × 1011 s−1, (e) WP = 1 × 1012 s−1, and (f) WP = 1 × 1013 s−1.

Fig. 6
Fig. 6

The plot of the peak intensity and spectral width of the lasing modes vs the pump rate W p in the case of the non-dispersive scattering medium.(a) The peak intensity for the two indicated modes, and the lasing threshold measured from the plots are W I 0 ' = 4 × 109 s−1, and W I 1 ' = 5 × 1011 s−1. (b) the peak intensity and spectral width for the mode λ 0 ' ; and (c) the spectral width for the three indicated modes, and the lasing threshold measured from the plots are W W 0   ' = 3 × 109s−1, and W W 1   ' = 0.9 × 1010s−1.

Tables (1)

Tables Icon

Table 1 The Thresholds (WI0, WI0´), the Numbers of the Spectral Spikes (Nums)

Equations (20)

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

H y x = ε 0 ε 1 E z t + P g a i n t
E z x = μ 0 H y t
d N 1 d t = N 2 τ 21 W p N 1
d N 2 d t = N 3 τ 32 N 2 τ 21 E z ω l d P g a i n d t
d N 3 d t = N 4 τ 43 N 3 τ 32 + E z ω l d P g a i n d t
d N 4 d t = N 4 τ 43 + W p N 1
d 2 P g a i n / d t 2 + Δ ω l d P g a i n / d t + ω l 2 P g a i n = κ Δ N E 2 .
H y ( t , x ) x = D z ( t , x ) t
E z ( t , x ) x = μ 0 H y ( t , x ) t
D z ( t , x ) = ε 0 E z ( t , x ) + P l o r e n t z ( t , x )
P l o r e n t z ( t , x ) = i = 1 3 P i ( t , x )
P ˜ l o r e n t z ( ω ) = ε 0 E ˜ z ( ω ) i = 1 3 χ ˜ i ( ω )
ε ˜ r ( ω ) = n ˜ ( ω ) 2 = 1 + i = 1 3 χ ˜ i ( ω ) = 1 + i = 1 3 B i ω i 2 ω i 2 ω 2
2 P i ( t ) t 2 + ω i 2 P i ( t ) = ω i 2 B i ( D z ( t ) i = 1 3 P i ( t ) )
d 2 P 1 d t 2 + ω 1 2 ( 1 + B 1 ) P 1 + ω 1 2 B 1 P 2 = ω 1 2 B 1 D z
d 2 P 2 d t 2 + ω 2 2 ( 1 + B 2 ) P 2 + ω 2 2 B 2 P 2 = ω 2 2 B 2 D z
d 2 P 3 d t 2 + ω 3 2 ( 1 + B 3 ) P 3 + ω 3 2 B 3 P 2 = ω 3 2 B 3 D z
E z = 1 ε 0 ( D z P 1 P 2 P 3 )
H y x = ε 0 ε 2 E z t
E z x = μ 0 H y t

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