Abstract

Effects of a solid matrix on the dye kinetic parameters for Rh800 were experimentally studied. Saturation intensity dependencies were measured with a seeding pulse amplification method using a picosecond and a femtosecond white light supercontinuum source. The kinetic parameters were obtained by fitting experimental dependencies with Yee’s finite-difference time-domain model coupled to the rate equations of the 4-level Rh800-system. The comparison of these parameters (Rh800-solid host) with liquid host parameters revealed a slight change of the radiative lifetime and a strong change of the non-radiative decay rate. This experimentally determined model enables predictive simulations of time-domain responses of active metamaterials.

© 2011 OSA

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  1. S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  3. Z.-G. Dong, H. Liu, T. Li, Z.-H. Zhu, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Phys. Rev. B 96, 044104 (2010).
  4. T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-index metamaterials: going optical,” IEEE J. Sel. Top. Quantum Electron. 12, 1106–1115 (2006).
    [CrossRef]
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    [CrossRef]

2011 (1)

L. J. Prokopeva, J. Borneman, and A. V. Kildishev, “Optical dispersion models for time-domain modeling of metal-dielectric nanostructures,” IEEE Trans. Magn. 47, 1150–1153 (2011).
[CrossRef]

2010 (4)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

M. P. Hatlo Andresen, A. V. Skaldebo, M. W. Haakestad, H. E. Krogstad, and J. Skaar, “Effect of gain saturation in a gain compensated perfect lens,” J. Opt. Soc. Am. B 27, 1610–1616 (2010).
[CrossRef]

Z.-G. Dong, H. Liu, T. Li, Z.-H. Zhu, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Phys. Rev. B 96, 044104 (2010).

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef] [PubMed]

2009 (2)

A. Fang, T. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79, 241104 (2009).
[CrossRef]

L. Zhili and L. Thylen, “On the accuracy and stability of several widely used FDTD approaches for modeling lorentz dielectrics,” IEEE Trans. Antennas Propag. 57, 3378 (2009).
[CrossRef]

2007 (1)

S. V. Zhukovsky and D. N. Chigrin, “Numerical modelling of lasing in microstructures,” Phys. Stat. Solidi B 244, 3515 (2007).
[CrossRef]

2006 (1)

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-index metamaterials: going optical,” IEEE J. Sel. Top. Quantum Electron. 12, 1106–1115 (2006).
[CrossRef]

1998 (1)

A. S. Nagra and R. A. York, “FDTD Analysis of Wave Propagation in Nonlinear Absorbing and Gain Media,” IEEE Trans. Antennas Propag. 46, 334 (1998).
[CrossRef]

1994 (1)

B. Bachteler, K.-H. Drexhage, J. Arden-Jacob, K.-T. Han, M. Koellner, R. Mueller, M. Sauer, S. Seeger, and J. Wolfrum, “Sensitive fluorescence detection in capillary electrophoresis using laser diodes and multiplex dyes,” J. Lumin. 62, 101 (1994).
[CrossRef]

1992 (1)

1988 (1)

P. Sperber, W. Spangler, B. Meier, and A. Penzkoffer, “Experimental and theoretical investigation of tunable picosecond pulse generation in longitudinally pumped dye laser generators and amplifiers,” Opt. Quantum. Electron. 20, 395 (1988).
[CrossRef]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302 (1966).
[CrossRef]

Arden-Jacob, J.

B. Bachteler, K.-H. Drexhage, J. Arden-Jacob, K.-T. Han, M. Koellner, R. Mueller, M. Sauer, S. Seeger, and J. Wolfrum, “Sensitive fluorescence detection in capillary electrophoresis using laser diodes and multiplex dyes,” J. Lumin. 62, 101 (1994).
[CrossRef]

Bachteler, B.

B. Bachteler, K.-H. Drexhage, J. Arden-Jacob, K.-T. Han, M. Koellner, R. Mueller, M. Sauer, S. Seeger, and J. Wolfrum, “Sensitive fluorescence detection in capillary electrophoresis using laser diodes and multiplex dyes,” J. Lumin. 62, 101 (1994).
[CrossRef]

Benfey, D. P.

Borneman, J.

L. J. Prokopeva, J. Borneman, and A. V. Kildishev, “Optical dispersion models for time-domain modeling of metal-dielectric nanostructures,” IEEE Trans. Magn. 47, 1150–1153 (2011).
[CrossRef]

Brown, D. C.

Cao, J.-X.

Z.-G. Dong, H. Liu, T. Li, Z.-H. Zhu, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Phys. Rev. B 96, 044104 (2010).

Chettiar, U. K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

Chigrin, D. N.

S. V. Zhukovsky and D. N. Chigrin, “Numerical modelling of lasing in microstructures,” Phys. Stat. Solidi B 244, 3515 (2007).
[CrossRef]

Davis, S. J.

Dong, Z.-G.

Z.-G. Dong, H. Liu, T. Li, Z.-H. Zhu, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Phys. Rev. B 96, 044104 (2010).

Drachev, V. P.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-index metamaterials: going optical,” IEEE J. Sel. Top. Quantum Electron. 12, 1106–1115 (2006).
[CrossRef]

Drexhage, K.-H.

B. Bachteler, K.-H. Drexhage, J. Arden-Jacob, K.-T. Han, M. Koellner, R. Mueller, M. Sauer, S. Seeger, and J. Wolfrum, “Sensitive fluorescence detection in capillary electrophoresis using laser diodes and multiplex dyes,” J. Lumin. 62, 101 (1994).
[CrossRef]

Fang, A.

A. Fang, T. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79, 241104 (2009).
[CrossRef]

Foutter, R. F.

Haakestad, M. W.

Hagness, S.

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

Hamm, J. M.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef] [PubMed]

Han, K.-T.

B. Bachteler, K.-H. Drexhage, J. Arden-Jacob, K.-T. Han, M. Koellner, R. Mueller, M. Sauer, S. Seeger, and J. Wolfrum, “Sensitive fluorescence detection in capillary electrophoresis using laser diodes and multiplex dyes,” J. Lumin. 62, 101 (1994).
[CrossRef]

Hatlo Andresen, M. P.

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison Wesley, 2001).

Hess, O.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef] [PubMed]

Kildishev, A. V.

L. J. Prokopeva, J. Borneman, and A. V. Kildishev, “Optical dispersion models for time-domain modeling of metal-dielectric nanostructures,” IEEE Trans. Magn. 47, 1150–1153 (2011).
[CrossRef]

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-index metamaterials: going optical,” IEEE J. Sel. Top. Quantum Electron. 12, 1106–1115 (2006).
[CrossRef]

Klar, T. A.

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-index metamaterials: going optical,” IEEE J. Sel. Top. Quantum Electron. 12, 1106–1115 (2006).
[CrossRef]

Koellner, M.

B. Bachteler, K.-H. Drexhage, J. Arden-Jacob, K.-T. Han, M. Koellner, R. Mueller, M. Sauer, S. Seeger, and J. Wolfrum, “Sensitive fluorescence detection in capillary electrophoresis using laser diodes and multiplex dyes,” J. Lumin. 62, 101 (1994).
[CrossRef]

Koschny, T.

A. Fang, T. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79, 241104 (2009).
[CrossRef]

Krogstad, H. E.

Li, T.

Z.-G. Dong, H. Liu, T. Li, Z.-H. Zhu, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Phys. Rev. B 96, 044104 (2010).

Lieberherr, M.

M. Lieberherr, p.39–46 (1988), “Laser induced fluorescence and scattering near interfaces,” Ph.D. thesis, ETH Zurich (1991).

Liu, H.

Z.-G. Dong, H. Liu, T. Li, Z.-H. Zhu, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Phys. Rev. B 96, 044104 (2010).

Meier, B.

P. Sperber, W. Spangler, B. Meier, and A. Penzkoffer, “Experimental and theoretical investigation of tunable picosecond pulse generation in longitudinally pumped dye laser generators and amplifiers,” Opt. Quantum. Electron. 20, 395 (1988).
[CrossRef]

Mueller, R.

B. Bachteler, K.-H. Drexhage, J. Arden-Jacob, K.-T. Han, M. Koellner, R. Mueller, M. Sauer, S. Seeger, and J. Wolfrum, “Sensitive fluorescence detection in capillary electrophoresis using laser diodes and multiplex dyes,” J. Lumin. 62, 101 (1994).
[CrossRef]

Nagra, A. S.

A. S. Nagra and R. A. York, “FDTD Analysis of Wave Propagation in Nonlinear Absorbing and Gain Media,” IEEE Trans. Antennas Propag. 46, 334 (1998).
[CrossRef]

Ni, X.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

Penzkoffer, A.

P. Sperber, W. Spangler, B. Meier, and A. Penzkoffer, “Experimental and theoretical investigation of tunable picosecond pulse generation in longitudinally pumped dye laser generators and amplifiers,” Opt. Quantum. Electron. 20, 395 (1988).
[CrossRef]

Piper, L. G.

Prokopeva, L. J.

L. J. Prokopeva, J. Borneman, and A. V. Kildishev, “Optical dispersion models for time-domain modeling of metal-dielectric nanostructures,” IEEE Trans. Magn. 47, 1150–1153 (2011).
[CrossRef]

Pusch, A.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef] [PubMed]

Sauer, M.

B. Bachteler, K.-H. Drexhage, J. Arden-Jacob, K.-T. Han, M. Koellner, R. Mueller, M. Sauer, S. Seeger, and J. Wolfrum, “Sensitive fluorescence detection in capillary electrophoresis using laser diodes and multiplex dyes,” J. Lumin. 62, 101 (1994).
[CrossRef]

Seeger, S.

B. Bachteler, K.-H. Drexhage, J. Arden-Jacob, K.-T. Han, M. Koellner, R. Mueller, M. Sauer, S. Seeger, and J. Wolfrum, “Sensitive fluorescence detection in capillary electrophoresis using laser diodes and multiplex dyes,” J. Lumin. 62, 101 (1994).
[CrossRef]

Shalaev, V. M.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-index metamaterials: going optical,” IEEE J. Sel. Top. Quantum Electron. 12, 1106–1115 (2006).
[CrossRef]

Siegman, A. E.

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

Skaar, J.

Skaldebo, A. V.

Soukoulis, C. M.

A. Fang, T. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79, 241104 (2009).
[CrossRef]

Spangler, W.

P. Sperber, W. Spangler, B. Meier, and A. Penzkoffer, “Experimental and theoretical investigation of tunable picosecond pulse generation in longitudinally pumped dye laser generators and amplifiers,” Opt. Quantum. Electron. 20, 395 (1988).
[CrossRef]

Sperber, P.

P. Sperber, W. Spangler, B. Meier, and A. Penzkoffer, “Experimental and theoretical investigation of tunable picosecond pulse generation in longitudinally pumped dye laser generators and amplifiers,” Opt. Quantum. Electron. 20, 395 (1988).
[CrossRef]

Taflove, A.

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

Thylen, L.

L. Zhili and L. Thylen, “On the accuracy and stability of several widely used FDTD approaches for modeling lorentz dielectrics,” IEEE Trans. Antennas Propag. 57, 3378 (2009).
[CrossRef]

Tsakmakidis, K. L.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef] [PubMed]

Wang, S.-M.

Z.-G. Dong, H. Liu, T. Li, Z.-H. Zhu, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Phys. Rev. B 96, 044104 (2010).

Wegener, M.

A. Fang, T. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79, 241104 (2009).
[CrossRef]

Wolfrum, J.

B. Bachteler, K.-H. Drexhage, J. Arden-Jacob, K.-T. Han, M. Koellner, R. Mueller, M. Sauer, S. Seeger, and J. Wolfrum, “Sensitive fluorescence detection in capillary electrophoresis using laser diodes and multiplex dyes,” J. Lumin. 62, 101 (1994).
[CrossRef]

Wuestner, S.

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef] [PubMed]

Xiao, S.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302 (1966).
[CrossRef]

York, R. A.

A. S. Nagra and R. A. York, “FDTD Analysis of Wave Propagation in Nonlinear Absorbing and Gain Media,” IEEE Trans. Antennas Propag. 46, 334 (1998).
[CrossRef]

Yuan, H.-K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

Zhang, X.

Z.-G. Dong, H. Liu, T. Li, Z.-H. Zhu, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Phys. Rev. B 96, 044104 (2010).

Zhili, L.

L. Zhili and L. Thylen, “On the accuracy and stability of several widely used FDTD approaches for modeling lorentz dielectrics,” IEEE Trans. Antennas Propag. 57, 3378 (2009).
[CrossRef]

Zhu, S.-N.

Z.-G. Dong, H. Liu, T. Li, Z.-H. Zhu, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Phys. Rev. B 96, 044104 (2010).

Zhu, Z.-H.

Z.-G. Dong, H. Liu, T. Li, Z.-H. Zhu, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Phys. Rev. B 96, 044104 (2010).

Zhukovsky, S. V.

S. V. Zhukovsky and D. N. Chigrin, “Numerical modelling of lasing in microstructures,” Phys. Stat. Solidi B 244, 3515 (2007).
[CrossRef]

Appl. Opt. (1)

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

T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-index metamaterials: going optical,” IEEE J. Sel. Top. Quantum Electron. 12, 1106–1115 (2006).
[CrossRef]

IEEE Trans. Antennas Propag. (3)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302 (1966).
[CrossRef]

A. S. Nagra and R. A. York, “FDTD Analysis of Wave Propagation in Nonlinear Absorbing and Gain Media,” IEEE Trans. Antennas Propag. 46, 334 (1998).
[CrossRef]

L. Zhili and L. Thylen, “On the accuracy and stability of several widely used FDTD approaches for modeling lorentz dielectrics,” IEEE Trans. Antennas Propag. 57, 3378 (2009).
[CrossRef]

IEEE Trans. Magn. (1)

L. J. Prokopeva, J. Borneman, and A. V. Kildishev, “Optical dispersion models for time-domain modeling of metal-dielectric nanostructures,” IEEE Trans. Magn. 47, 1150–1153 (2011).
[CrossRef]

J. Lumin. (1)

B. Bachteler, K.-H. Drexhage, J. Arden-Jacob, K.-T. Han, M. Koellner, R. Mueller, M. Sauer, S. Seeger, and J. Wolfrum, “Sensitive fluorescence detection in capillary electrophoresis using laser diodes and multiplex dyes,” J. Lumin. 62, 101 (1994).
[CrossRef]

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

Nature (1)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[CrossRef] [PubMed]

Opt. Quantum. Electron. (1)

P. Sperber, W. Spangler, B. Meier, and A. Penzkoffer, “Experimental and theoretical investigation of tunable picosecond pulse generation in longitudinally pumped dye laser generators and amplifiers,” Opt. Quantum. Electron. 20, 395 (1988).
[CrossRef]

Phys. Rev. B (2)

A. Fang, T. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B 79, 241104 (2009).
[CrossRef]

Z.-G. Dong, H. Liu, T. Li, Z.-H. Zhu, S.-M. Wang, J.-X. Cao, S.-N. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Phys. Rev. B 96, 044104 (2010).

Phys. Rev. Lett. (1)

S. Wuestner, A. Pusch, K. L. Tsakmakidis, J. M. Hamm, and O. Hess, “Overcoming Losses with Gain in a Negative Refractive Index Metamaterial,” Phys. Rev. Lett. 105, 127401 (2010).
[CrossRef] [PubMed]

Phys. Stat. Solidi B (1)

S. V. Zhukovsky and D. N. Chigrin, “Numerical modelling of lasing in microstructures,” Phys. Stat. Solidi B 244, 3515 (2007).
[CrossRef]

Other (4)

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

M. Lieberherr, p.39–46 (1988), “Laser induced fluorescence and scattering near interfaces,” Ph.D. thesis, ETH Zurich (1991).

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

E. Hecht, Optics, 4th ed. (Addison Wesley, 2001).

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Figures (2)

Fig. 1
Fig. 1

(a) Generic 4-level atomic system, (b) Experimental pump-probe setup.

Fig. 2
Fig. 2

Transmission results performed with 2 ps (a–d) and 103 fs (e–f) pulse duration at different probing wavelengths. (blue dots: experiment; solid red line: simulation; dashed green line: reduced simulation without the b1p/2-term in the SRE).

Tables (3)

Tables Icon

Table 1 Experimental Setup Parameters

Tables Icon

Table 2 Kinetic System Parameters

Tables Icon

Table 3 Fitted Kinetic Parameters For Rh800/Solid Film Vs. The Reference Data For Methanol Solution

Equations (9)

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N 0 = τ 10 1 N 1 f 30 N 1 = τ 21 1 N 2 τ 10 1 N 1 f 21 N 2 = τ 32 1 N 3 τ 21 1 N 2 + f 21 N 3 = τ 32 1 N 3 + f 30
P 30 + Δ ω 30 P 30 + ω 30 2 P 30 = κ 30 ( N 0 N 3 ) E P 21 + Δ ω 21 P 21 + ω 21 2 P 21 = κ 21 ( N 1 N 2 ) E
n = gn + w ( p + b 1 p / 2 ) e , n ( 0 ) = [ 0 , 0 , 0 ] T
p + b 1 p + b 0 2 p = k ( a 0 + a 1 n ) e T , p ( 0 ) = p ( 0 ) = 0
g = [ τ 10 1 τ 21 1 0 0 τ 21 1 τ 32 1 0 0 τ 32 1 ] , w = [ 0 w 21 0 w 21 w 30 0 ] , w i j = ɛ 0 E p 2 h ¯ N Σ ω i j , b 0 = diag ( ω 30 , ω 21 ) b 1 = diag ( Δ ω 30 , Δ ω 21 ) ,
a 0 = [ 1 0 ] , a 1 = [ 1 1 2 1 1 0 ] and k = 6 π c 3 N Σ n 1 diag ( γ r , 30 ω 30 2 , γ r , 12 ω 21 2 ) .
n 3 i + 1 = 2 γ 32 τ 2 + γ 32 τ n 3 i + W 30 d p 30 i + p ¯ 30 i Δ ω 30 τ / 4 2 + γ 32 τ e ¯ i , n 2 i + 1 = 2 γ 21 τ 2 + γ 21 τ n 2 i + γ 32 τ 2 + γ 21 τ n ¯ 3 i + W 21 d p 21 i + p ¯ 21 i Δ ω 21 τ / 4 2 + γ 21 τ e ¯ i , n 1 i + 1 = 2 γ 10 τ 2 + γ 10 τ n 1 i + γ 21 τ 2 + γ 10 τ n ¯ 2 i W 21 d p 21 i + p ¯ 21 i Δ ω 21 τ / 4 2 + γ 10 τ e ¯ i
p i + 1 2 p i + p i 1 τ 2 + b 1 p i + 1 p i 1 2 τ + b 0 2 p i = k ( a 0 + a 1 n i ) e T , i
d p i + 1 = 1 / 2 ( β 1 β 0 1 ) d p i + 1 / 2 ( β 1 + β 0 1 ) p ¯ i + α ( a 0 + a 1 n i + 1 ) e T , i + 1 , p ¯ i + 1 = p ¯ i + d p i + d p i + 1

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