Abstract

The transmittance of saturable nonlinear media under plane-wave excitation is analyzed for a Fabry–Perot geometry. The medium response is studied in terms of both a squared-field amplitude modulus and a time-averaged Poynting vector modulus. It was observed that both cases provide similar transmittance for the parameter range considered. For the nonlinearity proportional to the time-averaged Poynting vector modulus, a simple analytical expression for transmittance is derived as an Airy-type pattern. This allows us to perform a global analysis on the optical properties in terms of the nonlinear parameters and medium thickness. Several types of behavior were found at different parameter regions. Bistability happens only for excitation intensities around the saturation value. Finally, some possible implications of our results for bistable solitons are proposed.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. A. W. Snyder and A. P. Sheppard, "Bound-vector solitary waves in isotropic nonlinear dispersive media," Opt. Lett. 18, 1406-1408 (1993).
    [CrossRef] [PubMed]
  2. P. Vaveliuk, A. Lencina, P. C. de Oliveira, and N. Bolognini, "Photorefractive harmonic gratings within the shallow trap model," IEEE J. Quantum Electron. 38, 1541-1549 (2002).
    [CrossRef]
  3. W. Chen and D. L. Mills, "Optical response of a nonlinear dielectric film," Phys. Rev. B 35, 524-532 (1987).
    [CrossRef]
  4. A. Lencina, P. Vaveliuk, B. Ruiz, M. Tebaldi, and N. Bolognini, "Wave propagation and optical properties in slabs with light-induced free charge carriers," Phys. Rev. E 74, 056614 (2006).
    [CrossRef]
  5. A. Lencina and P. Vaveliuk, "Squared-field amplitude modulus and radiation intensity nonequivalence within nonlinear slabs," Phys. Rev. E 71, 056614 (2005).
    [CrossRef]
  6. M. Segev, "Optical spatial solitons," Opt. Quantum Electron. 30, 503-533 (1998).
    [CrossRef]
  7. J. Atai, Y. Chen, and J. M. Soto-Crespo, "Stability of three-dimensional self-trapped beams with a dark spot surrounded by bright rings of varying intensity," Phys. Rev. A 49, R3170-R3173 (1994).
    [CrossRef] [PubMed]
  8. P. W. Smith, Y. Silberberg, and D. A. B. Miller, "Mode locking of semiconductor lasers using saturable excitonic nonlinearities," J. Opt. Soc. Am. B 2, 1228-1236 (1985).
    [CrossRef]
  9. U. Keller, "Recent developments in compact ultrafast lasers," Nature 424, 831-838 (2003).
    [CrossRef] [PubMed]
  10. Y. S. Kivshar and B. Luther-Davies, "Dark optical solitons: physics and applications," Phys. Rep. 298, 81-197 (1998).
    [CrossRef]
  11. P. Vaveliuk, B. Ruiz, and A. Lencina, "Limits of the paraxial approximation in laser beams," Opt. Lett. 32, 927-929 (2007).
    [CrossRef] [PubMed]
  12. A. Lencina, B. Ruiz, and P. Vaveliuk, "Alternative method for wave propagation within bounded linear media: conceptual and practical implications," Optik (Stuttgart) (to be published).
  13. G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, "Bright and dark photovoltaic spatial solitons," Phys. Rev. A 50, R4457-R4460 (1994).
    [CrossRef] [PubMed]
  14. R. Redheffer, "Steen's equation and its generalizations," Aequ. Math. 58, 60-72 (1999).
  15. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 3rd ed. (World Scientific, 1998), p. 274.
  16. A. E. Kaplan, "Bistable solitons," Phys. Rev. Lett. 55, 1291-1294 (1985).
    [CrossRef] [PubMed]
  17. R. H. Enns and L. J. Mulder, "Bistable holes in nonlinear optical fibers," Opt. Lett. 14, 509-511 (1989).
    [CrossRef] [PubMed]

2007

2006

A. Lencina, P. Vaveliuk, B. Ruiz, M. Tebaldi, and N. Bolognini, "Wave propagation and optical properties in slabs with light-induced free charge carriers," Phys. Rev. E 74, 056614 (2006).
[CrossRef]

2005

A. Lencina and P. Vaveliuk, "Squared-field amplitude modulus and radiation intensity nonequivalence within nonlinear slabs," Phys. Rev. E 71, 056614 (2005).
[CrossRef]

2003

U. Keller, "Recent developments in compact ultrafast lasers," Nature 424, 831-838 (2003).
[CrossRef] [PubMed]

2002

P. Vaveliuk, A. Lencina, P. C. de Oliveira, and N. Bolognini, "Photorefractive harmonic gratings within the shallow trap model," IEEE J. Quantum Electron. 38, 1541-1549 (2002).
[CrossRef]

1999

R. Redheffer, "Steen's equation and its generalizations," Aequ. Math. 58, 60-72 (1999).

1998

M. Segev, "Optical spatial solitons," Opt. Quantum Electron. 30, 503-533 (1998).
[CrossRef]

Y. S. Kivshar and B. Luther-Davies, "Dark optical solitons: physics and applications," Phys. Rep. 298, 81-197 (1998).
[CrossRef]

1994

J. Atai, Y. Chen, and J. M. Soto-Crespo, "Stability of three-dimensional self-trapped beams with a dark spot surrounded by bright rings of varying intensity," Phys. Rev. A 49, R3170-R3173 (1994).
[CrossRef] [PubMed]

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, "Bright and dark photovoltaic spatial solitons," Phys. Rev. A 50, R4457-R4460 (1994).
[CrossRef] [PubMed]

1993

1989

1987

W. Chen and D. L. Mills, "Optical response of a nonlinear dielectric film," Phys. Rev. B 35, 524-532 (1987).
[CrossRef]

1985

Aequ. Math.

R. Redheffer, "Steen's equation and its generalizations," Aequ. Math. 58, 60-72 (1999).

IEEE J. Quantum Electron.

P. Vaveliuk, A. Lencina, P. C. de Oliveira, and N. Bolognini, "Photorefractive harmonic gratings within the shallow trap model," IEEE J. Quantum Electron. 38, 1541-1549 (2002).
[CrossRef]

J. Opt. Soc. Am. B

Nature

U. Keller, "Recent developments in compact ultrafast lasers," Nature 424, 831-838 (2003).
[CrossRef] [PubMed]

Opt. Lett.

Opt. Quantum Electron.

M. Segev, "Optical spatial solitons," Opt. Quantum Electron. 30, 503-533 (1998).
[CrossRef]

Phys. Rep.

Y. S. Kivshar and B. Luther-Davies, "Dark optical solitons: physics and applications," Phys. Rep. 298, 81-197 (1998).
[CrossRef]

Phys. Rev. A

G. C. Valley, M. Segev, B. Crosignani, A. Yariv, M. M. Fejer, and M. C. Bashaw, "Bright and dark photovoltaic spatial solitons," Phys. Rev. A 50, R4457-R4460 (1994).
[CrossRef] [PubMed]

J. Atai, Y. Chen, and J. M. Soto-Crespo, "Stability of three-dimensional self-trapped beams with a dark spot surrounded by bright rings of varying intensity," Phys. Rev. A 49, R3170-R3173 (1994).
[CrossRef] [PubMed]

Phys. Rev. B

W. Chen and D. L. Mills, "Optical response of a nonlinear dielectric film," Phys. Rev. B 35, 524-532 (1987).
[CrossRef]

Phys. Rev. E

A. Lencina, P. Vaveliuk, B. Ruiz, M. Tebaldi, and N. Bolognini, "Wave propagation and optical properties in slabs with light-induced free charge carriers," Phys. Rev. E 74, 056614 (2006).
[CrossRef]

A. Lencina and P. Vaveliuk, "Squared-field amplitude modulus and radiation intensity nonequivalence within nonlinear slabs," Phys. Rev. E 71, 056614 (2005).
[CrossRef]

Phys. Rev. Lett.

A. E. Kaplan, "Bistable solitons," Phys. Rev. Lett. 55, 1291-1294 (1985).
[CrossRef] [PubMed]

Other

A. Lencina, B. Ruiz, and P. Vaveliuk, "Alternative method for wave propagation within bounded linear media: conceptual and practical implications," Optik (Stuttgart) (to be published).

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 3rd ed. (World Scientific, 1998), p. 274.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

A harmonic plane wave of amplitude E 0 , propagating along the z direction, impinges on a parallel-plane-faces medium surrounded by an arbitrary linear dielectric. The wave is reflected and transmitted with coefficients r and t, respectively.

Fig. 2
Fig. 2

Transmittance T as a function of the dimensionless excitation parameter γ = I 0 I s a t at several saturation permittivities for SK and SP media. All figures with d ̃ = 2 π .

Fig. 3
Fig. 3

Transmittance T as a function of saturation permittivity ϵ s a t and dimensionless excitation parameter γ for an SP medium with d ̃ = 2 π .

Fig. 4
Fig. 4

Transmittance T as function of the dimensionless excitation parameter γ for an SP medium with varying thickness. All figures with ϵ s a t = 6 .

Equations (17)

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

S ( z ̃ ) = 1 I 0 S ( z ̃ ) u ̂ z ,
d 2 E d z ̃ 2 + ϵ t ( E ; S 0 ) E S 0 2 E 3 = 0 ,
[ E 2 ] z ̃ = d ̃ = S 0 ,
[ d E d z ̃ ] z ̃ = d ̃ = 0 ,
[ ( E 2 + S 0 ) 2 + ( E d E d z ̃ ) 2 4 E 2 ] z ̃ = 0 = 0 ,
T = t 2 = S 0 .
ϵ t = ϵ l + ϵ n l = ϵ l + ϵ s a t γ ψ 1 + γ ψ ,
ϵ n l ( S K ) ( z ̃ ) = ϵ s a t γ E 2 ( z ̃ ) 1 + γ E 2 ( z ̃ ) .
ϵ n l ( S P ) ( z ̃ ) = ϵ s a t γ S ( z ̃ ) 1 + γ S ( z ̃ ) .
d 2 u d z ̃ 2 + ϵ t ( β u 2 , β ) u 1 u 3 = 0 ,
[ u 2 ] z ̃ = d ̃ = 1 ,
[ d u d z ̃ ] z ̃ = d ̃ = 0 ,
[ ( u 2 + 1 ) 2 + ( u d u d z ̃ ) 2 4 u 2 S 0 ] z ̃ = 0 = 0 ,
T ( S P ) ( β , ϵ s a t , d ̃ ) = 1 1 + F sin 2 [ d ̃ ϵ l + ϵ s a t β ( 1 + β ) ] ,
F = [ 1 ϵ l + ϵ s a t β ( 1 + β ) ] 2 [ 4 ϵ l + ϵ s a t β ( 1 + β ) ] .
T ( S P ) ( ϵ s a t , d ̃ ) 1 1 + f sin 2 [ d ̃ ϵ l + ϵ s a t ] ,
f = [ 1 ϵ l + ϵ s a t ] 2 [ 4 ϵ l + ϵ s a t ] .

Metrics