Abstract

We report the energy-transfer efficiency in a saturable absorber nonlinear media by two-coherent-wave coupling using the Doppler shift. Intensity-dependent nondegenerate two-beam coupling has been studied in Rhodamine 110-doped boric acid glass films. Two beams have been described in the limit of a weak probe and a relatively strong pump at the wavelength 488nm from a continuous-wave Ar+ laser. The results have been interpreted in terms of the four-level description of a saturable absorber. We obtained good agreement between the experimental and the theoretical results. Estimated values of the nonlinear parameters such as the saturation intensity, refractive index, and the response time of the optical nonlinearity have been obtained at different pump beam intensities for the first time, to our knowledge, in the Rhodamine 110-doped film.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  8. P. Xie and Z.-Q. Zhang, 'Nondegenerate two-beam coupling in Kerr nonlinear photonic crystals,' Phys. Rev. E 72, 036607 (2005).
    [CrossRef]
  9. P. Pagliusi and G. Cipparrone, 'Optical two-beam coupling for a surface-induced photorefractive effect in undoped liquid crystals,' Opt. Lett. 28, 2369-2371 (2003).
    [CrossRef] [PubMed]
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  12. G. Zhang, F. Bo, R. Dong, and J. Xu, 'Phase-coupling-induced ultraslow light propagation in solids at room temperature,' Phys. Rev. Lett. 93, 133903 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
  16. H. Fujiwara, K. Shio, and S. Miyanaga, 'Power transfer by nearly degenerate two-wave mixing in a saturable dye-doped film,' J. Opt. Soc. Am. B 8, 1740-1746 (1991).
    [CrossRef]
  17. R. Saxena, I. McMichael, and P. Yeh, 'Dynamics of refractive-index changes and two-beam coupling in resonant media,' Appl. Phys. B 51, 243-253 (1996).
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  18. I. McMichael, P. Yeh, and P. Beckwith, 'Nondegenerate two-wave mixing in ruby,' Opt. Lett. 13, 500-502 (1988).
    [CrossRef] [PubMed]
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    [CrossRef]
  22. I. C. Khoo and T. H. Liu, 'Theory and experiments on multiwave-mixing-mediated probe-beam amplification,' Phys. Rev. A 39, 4036-4044 (1989).
    [CrossRef] [PubMed]
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    [CrossRef]
  24. I. C. Khoo and P. Zhou, 'Transient multiwave mixing in a nonlinear medium,' Phys. Rev. A 41, 1544-1555 (1990).
    [CrossRef] [PubMed]
  25. A. V. Khomenko and I. Rocha-Mendoza, 'Vectorial two-beam coupling with arbitrary shifted photorefractive gratings: an analytical approach,' Phys. Rev. E 70, 066615 (2004).
    [CrossRef]
  26. T. Sassa, T. Muto, and T. Wada, 'Enhanced photorefractive two-beam coupling in low-Tg polymeric materials with a new device structure,' J. Opt. Soc. Am. B 21, 1255-1261 (2004).
    [CrossRef]
  27. I. C. Khoo and J. Ding, 'All-optical cw laser polarization conversion at 1.55 μm by two-beam coupling in nematic liquid crystal films,' Appl. Phys. Lett. 81, 2496-2498 (2002).
    [CrossRef]
  28. Y. Silberberg and I. Bar-Joseph, 'Instabilities, self-oscillation, and chaos in a simple nonlinear optical interaction,' Phys. Rev. Lett. 48, 1541-1543 (1982).
    [CrossRef]
  29. Y. Silberberg and I. Bar-Joseph, 'Optical instabilities in a nonlinear Kerr medium,' J. Opt. Soc. Am. B 1, 662-670 (1984).
    [CrossRef]
  30. S. A. Boothroyd, J. Chrostowskii, and M. S. O'Sullivan, 'Two-wave mixing by phase and absorption gratings in saturable absorbers,' J. Opt. Soc. Am. B 6, 766-771 (1989).
    [CrossRef]
  31. S. A. Boothroyd, J. Chrostowskii, and M. S. O'Sullivan, 'Determination of the phase of the complex nonlinear refractive index by transient two-wave mixing in saturable absorbers,' Opt. Lett. 14, 946-948 (1984).
    [CrossRef]
  32. P. Yeh, 'Exact solution of a nonlinear model of two-wave mixing in Kerr media,' J. Opt. Soc. Am. B 3, 747-750 (1986).
    [CrossRef]
  33. H. Zhou, X. Mi, Q. Jiang, R. Zhang, and P. Ye, 'Saturation effect in nondegenerate two-wave mixing,' Opt. Commun. 78, 382-386 (1990).
    [CrossRef]
  34. D. Grandelement, G. Grynberg, and M. Pinard, 'Observation of continuous-wave self-oscillation due to pressure-induced two-wave mixing in sodium,' Phys. Rev. Lett. 59, 40-43 (1987).
    [CrossRef]
  35. S. C. Zilio, J. C. Penforte, F. A. Gouveia, and M. J. V. Bell, 'Nearly degenerate two-wave mixing in saturable absorbers,' Opt. Commun. 86, 81-87 (1991).
    [CrossRef]
  36. H. L. Fragnito, S. F. Pereira, and A. Kiel, 'Self-diffraction in population gratings,' J. Opt. Soc. Am. B 4, 1309-1315 (1987).
    [CrossRef]

2005 (3)

R. Caputo, L. De Sio, A. Veltri, C. Umeton, and A. V. Sukhov, 'Model for two-beam coupling during the formation of holographic gratings with a nematic film-polymer-slice sequence structure,' Appl. Phys. Lett. 87, 141108 (2005).
[CrossRef]

P. Xie and Z.-Q. Zhang, 'Nondegenerate two-beam coupling in Kerr nonlinear photonic crystals,' Phys. Rev. E 72, 036607 (2005).
[CrossRef]

S. Serguei, E. Hernández, and M. Plata, 'Two-wave mixing of orthogonally polarized waves via anisotropic dynamic gratings in erbium-doped optical fiber,' J. Opt. Soc. Am. B 22, 1161-1166 (2005).
[CrossRef]

2004 (3)

G. Zhang, F. Bo, R. Dong, and J. Xu, 'Phase-coupling-induced ultraslow light propagation in solids at room temperature,' Phys. Rev. Lett. 93, 133903 (2004).
[CrossRef] [PubMed]

A. V. Khomenko and I. Rocha-Mendoza, 'Vectorial two-beam coupling with arbitrary shifted photorefractive gratings: an analytical approach,' Phys. Rev. E 70, 066615 (2004).
[CrossRef]

T. Sassa, T. Muto, and T. Wada, 'Enhanced photorefractive two-beam coupling in low-Tg polymeric materials with a new device structure,' J. Opt. Soc. Am. B 21, 1255-1261 (2004).
[CrossRef]

2003 (1)

2002 (2)

V. M. N. Passaro and D. Marseglia, 'Numerical analysis of vectorial two-beam coupling in photorefractive materials,' Opt. Express 10, 1384-1390 (2002).
[PubMed]

I. C. Khoo and J. Ding, 'All-optical cw laser polarization conversion at 1.55 μm by two-beam coupling in nematic liquid crystal films,' Appl. Phys. Lett. 81, 2496-2498 (2002).
[CrossRef]

2001 (1)

A. Sharan, R. C. Sharma, S. N. Sandhya, A. Ayyer, and K. K. Sharma, 'Modeling absorption in saturable absorbers,' Opt. Commun. 199, 267-275 (2001).
[CrossRef]

1998 (1)

1996 (3)

1994 (1)

1993 (1)

1991 (2)

H. Fujiwara, K. Shio, and S. Miyanaga, 'Power transfer by nearly degenerate two-wave mixing in a saturable dye-doped film,' J. Opt. Soc. Am. B 8, 1740-1746 (1991).
[CrossRef]

S. C. Zilio, J. C. Penforte, F. A. Gouveia, and M. J. V. Bell, 'Nearly degenerate two-wave mixing in saturable absorbers,' Opt. Commun. 86, 81-87 (1991).
[CrossRef]

1990 (2)

H. Zhou, X. Mi, Q. Jiang, R. Zhang, and P. Ye, 'Saturation effect in nondegenerate two-wave mixing,' Opt. Commun. 78, 382-386 (1990).
[CrossRef]

I. C. Khoo and P. Zhou, 'Transient multiwave mixing in a nonlinear medium,' Phys. Rev. A 41, 1544-1555 (1990).
[CrossRef] [PubMed]

1989 (3)

I. C. Khoo and T. H. Liu, 'Theory and experiments on multiwave-mixing-mediated probe-beam amplification,' Phys. Rev. A 39, 4036-4044 (1989).
[CrossRef] [PubMed]

S. A. Boothroyd, J. Chrostowskii, and M. S. O'Sullivan, 'Two-wave mixing by phase and absorption gratings in saturable absorbers,' J. Opt. Soc. Am. B 6, 766-771 (1989).
[CrossRef]

P. Yeh, 'Two-wave mixing in nonlinear media,' IEEE J. Quantum Electron. 25, 484-519 (1989).
[CrossRef]

1988 (1)

1987 (4)

W. R. Tompkin, R. W. Boyd, D. M. Hall, and P. A. Tick, 'Nonlinear-optical properties of lead-tin fluorophosphate glass containing acridine dyes,' J. Opt. Soc. Am. B 4, 1030-1034 (1987).
[CrossRef]

R. J. Mears, L. Reekie, I. M. Jauncey, and D. N. Payne, 'Low-noise erbium-doped fibre amplifier at 1.54 pm,' Electron. Lett. 23, 1026-1028 (1987).
[CrossRef]

D. Grandelement, G. Grynberg, and M. Pinard, 'Observation of continuous-wave self-oscillation due to pressure-induced two-wave mixing in sodium,' Phys. Rev. Lett. 59, 40-43 (1987).
[CrossRef]

H. L. Fragnito, S. F. Pereira, and A. Kiel, 'Self-diffraction in population gratings,' J. Opt. Soc. Am. B 4, 1309-1315 (1987).
[CrossRef]

1986 (1)

1984 (2)

1982 (1)

Y. Silberberg and I. Bar-Joseph, 'Instabilities, self-oscillation, and chaos in a simple nonlinear optical interaction,' Phys. Rev. Lett. 48, 1541-1543 (1982).
[CrossRef]

1980 (1)

J. Freinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, 'Photorefractive effects and light-induced charge migration in barium titanate,' J. Appl. Phys. 51, 1297-1305 (1980).
[CrossRef]

1972 (1)

A. Penzkofer, D. von der Linde, A. Laubereau, and W. Kaiser, 'Generation of single picosecond and subpicosecond light pulses,' Appl. Phys. Lett. 20, 351-354 (1972).
[CrossRef]

Ayyer, A.

A. Sharan, R. C. Sharma, S. N. Sandhya, A. Ayyer, and K. K. Sharma, 'Modeling absorption in saturable absorbers,' Opt. Commun. 199, 267-275 (2001).
[CrossRef]

Bar-Joseph, I.

Y. Silberberg and I. Bar-Joseph, 'Optical instabilities in a nonlinear Kerr medium,' J. Opt. Soc. Am. B 1, 662-670 (1984).
[CrossRef]

Y. Silberberg and I. Bar-Joseph, 'Instabilities, self-oscillation, and chaos in a simple nonlinear optical interaction,' Phys. Rev. Lett. 48, 1541-1543 (1982).
[CrossRef]

Beckwith, P.

Bell, M. J. V.

S. C. Zilio, J. C. Penforte, F. A. Gouveia, and M. J. V. Bell, 'Nearly degenerate two-wave mixing in saturable absorbers,' Opt. Commun. 86, 81-87 (1991).
[CrossRef]

Bo, F.

G. Zhang, F. Bo, R. Dong, and J. Xu, 'Phase-coupling-induced ultraslow light propagation in solids at room temperature,' Phys. Rev. Lett. 93, 133903 (2004).
[CrossRef] [PubMed]

Boothroyd, S. A.

Boyd, R. W.

Caputo, R.

R. Caputo, L. De Sio, A. Veltri, C. Umeton, and A. V. Sukhov, 'Model for two-beam coupling during the formation of holographic gratings with a nematic film-polymer-slice sequence structure,' Appl. Phys. Lett. 87, 141108 (2005).
[CrossRef]

Chen, J.

Cheng, T. Y.

Chrostowskii, J.

Cipparrone, G.

Daisy, R.

De Sio, L.

R. Caputo, L. De Sio, A. Veltri, C. Umeton, and A. V. Sukhov, 'Model for two-beam coupling during the formation of holographic gratings with a nematic film-polymer-slice sequence structure,' Appl. Phys. Lett. 87, 141108 (2005).
[CrossRef]

Ding, J.

I. C. Khoo and J. Ding, 'All-optical cw laser polarization conversion at 1.55 μm by two-beam coupling in nematic liquid crystal films,' Appl. Phys. Lett. 81, 2496-2498 (2002).
[CrossRef]

Dong, R.

G. Zhang, F. Bo, R. Dong, and J. Xu, 'Phase-coupling-induced ultraslow light propagation in solids at room temperature,' Phys. Rev. Lett. 93, 133903 (2004).
[CrossRef] [PubMed]

Fischer, B.

Fragnito, H. L.

Freinberg, J.

J. Freinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, 'Photorefractive effects and light-induced charge migration in barium titanate,' J. Appl. Phys. 51, 1297-1305 (1980).
[CrossRef]

Fujiwara, H.

Gouveia, F. A.

S. C. Zilio, J. C. Penforte, F. A. Gouveia, and M. J. V. Bell, 'Nearly degenerate two-wave mixing in saturable absorbers,' Opt. Commun. 86, 81-87 (1991).
[CrossRef]

Grandelement, D.

D. Grandelement, G. Grynberg, and M. Pinard, 'Observation of continuous-wave self-oscillation due to pressure-induced two-wave mixing in sodium,' Phys. Rev. Lett. 59, 40-43 (1987).
[CrossRef]

Grynberg, G.

D. Grandelement, G. Grynberg, and M. Pinard, 'Observation of continuous-wave self-oscillation due to pressure-induced two-wave mixing in sodium,' Phys. Rev. Lett. 59, 40-43 (1987).
[CrossRef]

Hall, D. M.

Heiman, D.

J. Freinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, 'Photorefractive effects and light-induced charge migration in barium titanate,' J. Appl. Phys. 51, 1297-1305 (1980).
[CrossRef]

Hellwarth, R. W.

J. Freinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, 'Photorefractive effects and light-induced charge migration in barium titanate,' J. Appl. Phys. 51, 1297-1305 (1980).
[CrossRef]

Hernández, E.

Horowitz, M.

Jauncey, I. M.

R. J. Mears, L. Reekie, I. M. Jauncey, and D. N. Payne, 'Low-noise erbium-doped fibre amplifier at 1.54 pm,' Electron. Lett. 23, 1026-1028 (1987).
[CrossRef]

Jiang, Q.

H. Zhou, X. Mi, Q. Jiang, R. Zhang, and P. Ye, 'Saturation effect in nondegenerate two-wave mixing,' Opt. Commun. 78, 382-386 (1990).
[CrossRef]

Kaiser, W.

A. Penzkofer, D. von der Linde, A. Laubereau, and W. Kaiser, 'Generation of single picosecond and subpicosecond light pulses,' Appl. Phys. Lett. 20, 351-354 (1972).
[CrossRef]

Khomenko, A. V.

A. V. Khomenko and I. Rocha-Mendoza, 'Vectorial two-beam coupling with arbitrary shifted photorefractive gratings: an analytical approach,' Phys. Rev. E 70, 066615 (2004).
[CrossRef]

Khoo, I. C.

I. C. Khoo and J. Ding, 'All-optical cw laser polarization conversion at 1.55 μm by two-beam coupling in nematic liquid crystal films,' Appl. Phys. Lett. 81, 2496-2498 (2002).
[CrossRef]

I. C. Khoo and P. Zhou, 'Transient multiwave mixing in a nonlinear medium,' Phys. Rev. A 41, 1544-1555 (1990).
[CrossRef] [PubMed]

I. C. Khoo and T. H. Liu, 'Theory and experiments on multiwave-mixing-mediated probe-beam amplification,' Phys. Rev. A 39, 4036-4044 (1989).
[CrossRef] [PubMed]

Kiel, A.

Kochner, W.

W. Kochner, Solid-State Laser Engineering, 3rd ed. (Springer, 1992), Chap. 8.

Laubereau, A.

A. Penzkofer, D. von der Linde, A. Laubereau, and W. Kaiser, 'Generation of single picosecond and subpicosecond light pulses,' Appl. Phys. Lett. 20, 351-354 (1972).
[CrossRef]

Liu, T. H.

I. C. Khoo and T. H. Liu, 'Theory and experiments on multiwave-mixing-mediated probe-beam amplification,' Phys. Rev. A 39, 4036-4044 (1989).
[CrossRef] [PubMed]

Marseglia, D.

McMichael, I.

Mears, R. J.

R. J. Mears, L. Reekie, I. M. Jauncey, and D. N. Payne, 'Low-noise erbium-doped fibre amplifier at 1.54 pm,' Electron. Lett. 23, 1026-1028 (1987).
[CrossRef]

Mi, X.

H. Zhou, X. Mi, Q. Jiang, R. Zhang, and P. Ye, 'Saturation effect in nondegenerate two-wave mixing,' Opt. Commun. 78, 382-386 (1990).
[CrossRef]

Miyanaga, S.

Muto, T.

O'Sullivan, M. S.

Pagliusi, P.

Passaro, V. M. N.

Payne, D. N.

R. J. Mears, L. Reekie, I. M. Jauncey, and D. N. Payne, 'Low-noise erbium-doped fibre amplifier at 1.54 pm,' Electron. Lett. 23, 1026-1028 (1987).
[CrossRef]

Peda'el, A.

Penforte, J. C.

S. C. Zilio, J. C. Penforte, F. A. Gouveia, and M. J. V. Bell, 'Nearly degenerate two-wave mixing in saturable absorbers,' Opt. Commun. 86, 81-87 (1991).
[CrossRef]

Penzkofer, A.

A. Penzkofer, D. von der Linde, A. Laubereau, and W. Kaiser, 'Generation of single picosecond and subpicosecond light pulses,' Appl. Phys. Lett. 20, 351-354 (1972).
[CrossRef]

Pereira, S. F.

Pinard, M.

D. Grandelement, G. Grynberg, and M. Pinard, 'Observation of continuous-wave self-oscillation due to pressure-induced two-wave mixing in sodium,' Phys. Rev. Lett. 59, 40-43 (1987).
[CrossRef]

Plata, M.

Rand, S.

Reddy, B. R.

Reekie, L.

R. J. Mears, L. Reekie, I. M. Jauncey, and D. N. Payne, 'Low-noise erbium-doped fibre amplifier at 1.54 pm,' Electron. Lett. 23, 1026-1028 (1987).
[CrossRef]

Rocha-Mendoza, I.

A. V. Khomenko and I. Rocha-Mendoza, 'Vectorial two-beam coupling with arbitrary shifted photorefractive gratings: an analytical approach,' Phys. Rev. E 70, 066615 (2004).
[CrossRef]

Sandhya, S. N.

A. Sharan, R. C. Sharma, S. N. Sandhya, A. Ayyer, and K. K. Sharma, 'Modeling absorption in saturable absorbers,' Opt. Commun. 199, 267-275 (2001).
[CrossRef]

Sassa, T.

Saxena, R.

R. Saxena, I. McMichael, and P. Yeh, 'Dynamics of refractive-index changes and two-beam coupling in resonant media,' Appl. Phys. B 51, 243-253 (1996).
[CrossRef]

I. McMichael, R. Saxena, T. Y. Cheng, Q. Shu, S. Rand, J. Chen, and H. Tuller, 'High-gain nondegenerate two-wave mixing in Cr:YAlO3,' Opt. Lett. 19, 1511-1513 (1994).
[CrossRef] [PubMed]

Serguei, S.

Sharan, A.

A. Sharan, R. C. Sharma, S. N. Sandhya, A. Ayyer, and K. K. Sharma, 'Modeling absorption in saturable absorbers,' Opt. Commun. 199, 267-275 (2001).
[CrossRef]

Sharma, K. K.

A. Sharan, R. C. Sharma, S. N. Sandhya, A. Ayyer, and K. K. Sharma, 'Modeling absorption in saturable absorbers,' Opt. Commun. 199, 267-275 (2001).
[CrossRef]

Sharma, R. C.

A. Sharan, R. C. Sharma, S. N. Sandhya, A. Ayyer, and K. K. Sharma, 'Modeling absorption in saturable absorbers,' Opt. Commun. 199, 267-275 (2001).
[CrossRef]

Shio, K.

Shu, Q.

Silberberg, Y.

Y. Silberberg and I. Bar-Joseph, 'Optical instabilities in a nonlinear Kerr medium,' J. Opt. Soc. Am. B 1, 662-670 (1984).
[CrossRef]

Y. Silberberg and I. Bar-Joseph, 'Instabilities, self-oscillation, and chaos in a simple nonlinear optical interaction,' Phys. Rev. Lett. 48, 1541-1543 (1982).
[CrossRef]

Simkin, D. J.

Skirtach, A. G.

Sukhov, A. V.

R. Caputo, L. De Sio, A. Veltri, C. Umeton, and A. V. Sukhov, 'Model for two-beam coupling during the formation of holographic gratings with a nematic film-polymer-slice sequence structure,' Appl. Phys. Lett. 87, 141108 (2005).
[CrossRef]

Tanguay, A. R.

J. Freinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, 'Photorefractive effects and light-induced charge migration in barium titanate,' J. Appl. Phys. 51, 1297-1305 (1980).
[CrossRef]

Tick, P. A.

Tompkin, W. R.

Tuller, H.

Umeton, C.

R. Caputo, L. De Sio, A. Veltri, C. Umeton, and A. V. Sukhov, 'Model for two-beam coupling during the formation of holographic gratings with a nematic film-polymer-slice sequence structure,' Appl. Phys. Lett. 87, 141108 (2005).
[CrossRef]

Vekateswarlu, P.

Veltri, A.

R. Caputo, L. De Sio, A. Veltri, C. Umeton, and A. V. Sukhov, 'Model for two-beam coupling during the formation of holographic gratings with a nematic film-polymer-slice sequence structure,' Appl. Phys. Lett. 87, 141108 (2005).
[CrossRef]

von der Linde, D.

A. Penzkofer, D. von der Linde, A. Laubereau, and W. Kaiser, 'Generation of single picosecond and subpicosecond light pulses,' Appl. Phys. Lett. 20, 351-354 (1972).
[CrossRef]

Wada, T.

Xie, P.

P. Xie and Z.-Q. Zhang, 'Nondegenerate two-beam coupling in Kerr nonlinear photonic crystals,' Phys. Rev. E 72, 036607 (2005).
[CrossRef]

Xu, J.

G. Zhang, F. Bo, R. Dong, and J. Xu, 'Phase-coupling-induced ultraslow light propagation in solids at room temperature,' Phys. Rev. Lett. 93, 133903 (2004).
[CrossRef] [PubMed]

Ye, P.

H. Zhou, X. Mi, Q. Jiang, R. Zhang, and P. Ye, 'Saturation effect in nondegenerate two-wave mixing,' Opt. Commun. 78, 382-386 (1990).
[CrossRef]

Yeh, P.

R. Saxena, I. McMichael, and P. Yeh, 'Dynamics of refractive-index changes and two-beam coupling in resonant media,' Appl. Phys. B 51, 243-253 (1996).
[CrossRef]

P. Yeh, 'Two-wave mixing in nonlinear media,' IEEE J. Quantum Electron. 25, 484-519 (1989).
[CrossRef]

I. McMichael, P. Yeh, and P. Beckwith, 'Nondegenerate two-wave mixing in ruby,' Opt. Lett. 13, 500-502 (1988).
[CrossRef] [PubMed]

P. Yeh, 'Exact solution of a nonlinear model of two-wave mixing in Kerr media,' J. Opt. Soc. Am. B 3, 747-750 (1986).
[CrossRef]

Zhang, G.

G. Zhang, F. Bo, R. Dong, and J. Xu, 'Phase-coupling-induced ultraslow light propagation in solids at room temperature,' Phys. Rev. Lett. 93, 133903 (2004).
[CrossRef] [PubMed]

Zhang, R.

H. Zhou, X. Mi, Q. Jiang, R. Zhang, and P. Ye, 'Saturation effect in nondegenerate two-wave mixing,' Opt. Commun. 78, 382-386 (1990).
[CrossRef]

Zhang, Z.-Q.

P. Xie and Z.-Q. Zhang, 'Nondegenerate two-beam coupling in Kerr nonlinear photonic crystals,' Phys. Rev. E 72, 036607 (2005).
[CrossRef]

Zhou, H.

H. Zhou, X. Mi, Q. Jiang, R. Zhang, and P. Ye, 'Saturation effect in nondegenerate two-wave mixing,' Opt. Commun. 78, 382-386 (1990).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

Opt. Express (1)

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[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

Two-coherent-wave coupling experimental setup. BAG, boric acid glass.

Fig. 2
Fig. 2

Laser-induced grating pattern in the two-beam coupling.

Fig. 3
Fig. 3

Four-level-model energy-level diagram.

Fig. 4
Fig. 4

Absorption spectrum of the Rhodamine 110-doped boric acid glass thin film in the wavelength region 300 600 nm .

Fig. 5
Fig. 5

Nonlinear absorption profile of the Rhodamine 110-doped boric acid glass film in the 10 5 to 10 W power region at the wavelength 488 nm and fitting in the four-level model.

Fig. 6
Fig. 6

(a) Piezomirror supply for frequency shift and (b) two-coherent-wave coupling signal at the Doppler shift of 4.0 Hz .

Fig. 7
Fig. 7

Pump–probe experiment when the piezomirror is off and the pump power is varied between the range 10 6 and 10 W .

Fig. 8
Fig. 8

Two-beam coupling signal with a fitted curve at the Doppler shift between 0 and 20 Hz .

Fig. 9
Fig. 9

Plot T 1 1 + S 0 versus dependence on the pump beam power for best-fitted value of T 1 .

Tables (3)

Tables Icon

Table 1 Two-Beam Coupling Signal in the Rhodamine 110-Doped Boric Acid Glass Thin Films a

Tables Icon

Table 2 Power-Dependent Two-Beam Coupling Signal in the Rhodamine 110-Doped Boric Acid Glass Thin Films

Tables Icon

Table 3 Best-Fitted Parameters of Rhodamine 110-Doped Boric Acid Glass film in the Four-Level Model of the Saturable Absorber

Equations (37)

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E 1 = E 0 + exp [ i ( k 0 + r ω 1 t + ϕ 0 ) ] .
E 2 = E 0 exp [ i ( k 0 r ω 2 t + ϕ 0 ) ] .
E = E 1 + E 2 .
I 0 ( x , t ) = I 0 + I 1 cos ( k x Ω t + Δ ϕ )
I 0 = { I 0 + + I 0 } ,
I 1 = 2 ( I 0 + I 0 ) 1 2 ,
P = ϵ 0 ( η 2 1 ) E + ϵ 0 ( η 0 χ 0 + η 1 χ 1 ) E
= P 1 + P 2 ,
P 1 = ϵ 0 ( η 2 1 + χ 0 ) E 0 ,
P 2 = ϵ 0 n 1 ( χ 1 χ 0 ) E .
d n 1 d t = ( 1 n 1 ) W 13 n 1 T 1 .
W 13 = σ 0 I ω ,
n 1 ( x , t ) = I ( 1 + S 0 ) n = A n exp [ i n ( K x Ω t + Δ ϕ ) ] ,
A 0 = S 0 ,
A n = ( 1 ) n + 1 { ( S 1 2 ) ( 1 + S 0 ) } n [ m = 1 n ( 1 i sign ( n ) m Ω T 1 ) ] for n 0 ,
S 1 = I 1 I s ,
T 1 = T 1 ( 1 + I 0 I s ) .
( c ω ) 2 2 E + [ η 2 + χ 0 + ( 1 1 + S 0 ) n = χ NL A n × exp i n ( K x Ω t + Δ ϕ ) ] E = 0 ,
d ϵ 0 + d z = i γ [ ( χ 0 + ( χ NL A * 0 1 + S 0 ) ϵ + 0 + ( χ NL A 1 1 + S 0 ) ϵ 0 exp ( i Δ ϕ ) ) ] ,
d ϵ 0 d z = i γ [ { ( χ * NL A * 1 ) ( 1 + S 0 ) } ϵ + 0 exp ( i Δ ϕ ) + { χ 0 + ( χ NL A * 0 ) ( 1 + S 0 ) } ϵ 0 ] ,
γ = ( 1 2 η cos θ ) ( ω c ) .
ϵ + 0 ( z ) = ϵ + 0 ( 0 ) exp [ i γ ( χ 0 + ( χ NL A 0 ) ( 1 + S 0 ) ) z ] .
ϵ 0 ( z ) = ϵ 0 ( 0 ) [ 1 + i γ { χ 0 + ( χ * NL ϵ + 0 ( 0 ) A * 1 ) ( 1 + ϵ 0 ( 0 ) S 0 ) } z ] exp [ i γ { χ 0 + ( χ NL A 0 ) ( 1 + S 0 ) } z ] .
ϵ + 0 ( z ) = [ 1 + i γ { χ 0 + ( χ * NL ϵ + 0 ( 0 ) A * 1 ) ( 1 + ϵ 0 ( 0 ) ) } z ]
× exp [ i γ { χ 0 + ( χ * NL ϵ + 0 ( 0 ) A * 1 ) ( 1 + ϵ 0 ( 0 ) S 0 ) } z ] .
[ γ { χ 0 + ( χ * NL ϵ + 0 ( 0 ) A * 1 ) ( 1 + ϵ 0 ( 0 ) S 0 ) } z ] 1 .
I 0 ( L ) = 1 2 ϵ 0 η c ϵ 0 ( L ) = I 0 ( 0 ) exp { 2 γ L ( χ 0 + ( χ NL S 0 ) ( 1 + S 0 ) ) } [ 1 + { 2 X ( χ NL + Ω T 1 χ NL ) } { ( 1 + Ω 2 T 1 2 ) } ] + { X 2 ( χ 2 NL + χ 2 NL ) ( 1 + Ω 2 T 1 2 ) } ,
I 0 ( L ) = I 0 ( 0 ) exp [ { ( α 0 L cos θ ) ( 1 + S 0 ) } { ( 1 + I 0 + β 0 ) ( I s α 0 ) } ] [ 1 + { 2 π n 2 L ( I 0 + I s ) ( r + Δ ) } { λ cos θ ( 1 + S 0 ) 2 ( 1 + Δ 2 ) } 2 ] + [ { 2 π n 2 L ( I 0 + I s ) ( I r Δ ) } { λ cos θ ( 1 + S 0 ) 2 ( 1 + Δ 2 ) } 2 ] ,
I 0 ( L , Δ ) = I 0 ( 0 ) [ { 1 + g L ( ( r + Δ ) ( 1 + Δ 2 ) ) } 2 + { g L ( ( 1 r Δ ) ( 1 + Δ 2 ) ) } 2 ] exp ( α eff L ) ,
α eff = { ( α 0 cos θ ) ( 1 + I 0 + I s ) } [ 1 + ( I 0 + β 0 ( I s α 0 ) ) ] ,
g = { 2 π n 2 ( I 0 + I s ) } { λ cos θ ( 1 + S 0 ) 2 } .
I 0 ( L , Δ ) = I 0 ( 0 ) exp [ { 2 g ( ( r + Δ ) 2 ( 1 + Δ 2 ) ) α eff } L ] .
I 0 ( L , 0 ) = I 0 ( 0 ) exp { α eff L } [ { 1 + g L r } 2 + { g L } 2 ] .
( I 0 ( L , 0 ) I 0 ( 0 ) ) = [ { 1 + ( 2 π n 2 ( I 0 + I s ) L ) ( λ cos θ ( 1 + S 0 ) 2 ) } 2 + { ( 2 π n 2 ( I 0 + I s ) L ) ( λ cos θ ( 1 + S 0 ) 2 ) } 2 ] exp [ { ( α 0 L ) ( 1 + ( β 0 L ) I 0 + ( α 0 L ) I s ) } { cos θ ( 1 + S 0 ) } ] .
Γ ( Δ ) = Δ I 0 ( L , Δ ) I 0 ( L , 0 ) = I 0 ( L , Δ ) I 0 ( L , Δ ) I 0 ( L , 0 ) ,
Γ ( Δ ) = [ 4 g L Δ ( 1 + Δ 2 ) ] [ ( 1 + g L r ) 2 + ( g L ) 2 ] ,
Γ ( Δ ) = [ 4 π L n 2 S 0 2 Δ ] [ λ cos θ ( 1 + S 0 ) 2 ( 1 + Δ 2 ) ] [ { 1 + ( 2 π n 2 L S 0 ) λ cos θ ( 1 + S 0 ) 2 } 2 + { ( 2 π n 2 L S 0 ) λ cos θ ( 1 + S 0 ) 2 } 2 ] .

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