Abstract

The optical mechanism and dynamics of electron-trapping material under simultaneous illumination with two wavelengths is investigated. Our analytical model proves that the equilibrium-state luminescence of such a material can be controlled to produce highly nonlinear behavior with potential applications in nonlinear optical signal processing and optical realization of nonlinear dynamical systems. Combining this new approach with state-of-the-art fast spatial light modulators and CCD cameras that can precisely control and measure exposure, large arrays of nonlinear processing elements can be accommodated in a thin film of this material.

© 2008 Optical Society of America

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References

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  1. N. H. Farhat and D. Psaltis, "Optical implementation of associative memory based on models of neural networks," in Optical Signal Processing (Academic, 1987), pp. 129-162.
  2. S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering (Perseus, 2001).
  3. R. Pashaie and N. H. Farhat, "Dynamics of electron-trapping materials under blue light and near-infrared exposure: a new model," J. Opt. Soc. Am. B 24, 1927-1941 (2007).
    [CrossRef]
  4. R. Pashaie and N. H. Farhat, "Realization of receptive fields with excitatory and inhibitory responses on the equilibrium-state luminescence of electron trapping material thin film," Opt. Lett. 32, 1501-1503 (2007).
    [CrossRef] [PubMed]
  5. Z. Hua, L. Salamanca-Riba, M. Wuttig, and P. K. Soltani, "Temperature dependence of photoluminescence in SrS:Eu2+,Sm3+ thin films," J. Opt. Soc. Am. B 10, 1464-1469 (1993).
    [CrossRef]
  6. S. Jutamulia, G. Stori, J. Lindmayer, and W. Seiderman, "Use of electron trapping materials in optical signal processing. 1. Parallel Boolean logic," Appl. Opt. 29, 4806-4811 (1990).
    [CrossRef] [PubMed]
  7. S. Jutamulia, G. Storti, J. Lindmayer, and W. Seiderman, "Optical information processing systems and architectures," Proc. SPIE 1151, 83 (1990).
  8. A. D. McAulay, J. Wang, and C. T. Ma, "Optical orthogonal neural network associative memory with luminescence rebroadcasting devices," in Proceedings of the IEEE International Conference on Neural Networks (IEEE, 1989), Vol. 2, pp. 483-485.
  9. J. Lindmayer, "A new erasable optical memory," Solid State Technol. 31, 135-138 (1988).
    [CrossRef]
  10. Z. Wen and N. Farhat, "Dynamics of electron trapping materials for use in optoelectronic neurocomputing," Appl. Opt. 32, 7251-7265 (1993).
    [CrossRef] [PubMed]
  11. D. Dudley, W. M. Duncan, and J. Slaughter, "Emerging digital micromirror device (DMD) applications," Proc. SPIE 4985, 14-25 (2003).
    [CrossRef]

2007 (2)

2003 (1)

D. Dudley, W. M. Duncan, and J. Slaughter, "Emerging digital micromirror device (DMD) applications," Proc. SPIE 4985, 14-25 (2003).
[CrossRef]

1993 (2)

1990 (2)

S. Jutamulia, G. Stori, J. Lindmayer, and W. Seiderman, "Use of electron trapping materials in optical signal processing. 1. Parallel Boolean logic," Appl. Opt. 29, 4806-4811 (1990).
[CrossRef] [PubMed]

S. Jutamulia, G. Storti, J. Lindmayer, and W. Seiderman, "Optical information processing systems and architectures," Proc. SPIE 1151, 83 (1990).

1988 (1)

J. Lindmayer, "A new erasable optical memory," Solid State Technol. 31, 135-138 (1988).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc. Am. B (2)

Opt. Lett. (1)

Proc. SPIE (2)

S. Jutamulia, G. Storti, J. Lindmayer, and W. Seiderman, "Optical information processing systems and architectures," Proc. SPIE 1151, 83 (1990).

D. Dudley, W. M. Duncan, and J. Slaughter, "Emerging digital micromirror device (DMD) applications," Proc. SPIE 4985, 14-25 (2003).
[CrossRef]

Solid State Technol. (1)

J. Lindmayer, "A new erasable optical memory," Solid State Technol. 31, 135-138 (1988).
[CrossRef]

Other (3)

A. D. McAulay, J. Wang, and C. T. Ma, "Optical orthogonal neural network associative memory with luminescence rebroadcasting devices," in Proceedings of the IEEE International Conference on Neural Networks (IEEE, 1989), Vol. 2, pp. 483-485.

N. H. Farhat and D. Psaltis, "Optical implementation of associative memory based on models of neural networks," in Optical Signal Processing (Academic, 1987), pp. 129-162.

S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering (Perseus, 2001).

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Figures (7)

Fig. 1
Fig. 1

(a) Optical setup. A light source illuminates the optical device, and a detector measures the intensity of the light that passes through the optical device. (b) The normally available and the desired curve.

Fig. 2
Fig. 2

Energy bands and optical mechanism of electron-trapping materials. Interaction of photons with wavelength λ 1 can excite electrons from valence band to conduction band. Some of these electrons return to the valence band and release their extra energy in the form of spontaneous emission at wavelength λ 2 , while others tunnel to the trap energy level. Interaction of photons with wavelengths λ 1 and λ 3 with trapped electrons can detrap some of the trapped electrons.

Fig. 3
Fig. 3

System of water tanks as a similar dynamics in fluid mechanics to the optical mechanism of ETMs. In this system the depth of water, h 1 ( t ) , in tank 1, and h 2 ( t ) , in tank 2, are dual of the density of the electrons in the trap level and the valence band, respectively. If the cross-sectional areas of the tanks are equal and F ( t ) represents the inflow of water from the faucet, D 1 ( t ) and D 2 ( t ) are the outflow of water from drain 1 and drain 2, respectively, and P ( t ) is a function representing the pump action, then the state equations of this system are d h 1 ( t ) d t = a F ( t ) h 2 ( t ) b D 1 ( t ) h 1 ( t ) c D 2 ( t ) h 1 ( t ) , d h 2 ( t ) d t = e D 1 ( t ) h 1 ( t ) + f D 2 ( t ) h 1 ( t ) h P ( t ) h 2 ( t ) , and h 1 ( t ) + h 2 ( t ) = const. , where the parameters a, b, c, e, f, and h are positive real numbers. This set of equations is similar to the set of equations that defines the dynamics of ETM [Eq. (3, 4)].

Fig. 4
Fig. 4

(a) Typical charging curves of a completely erased ETM under exposure to light with wavelength λ 1 . (b) Typical discharging curves of a precharged ETM under exposure to light with wavelength λ 3 , and P t e ( t = 0 ) = 10 8 . In both graphs ξ c v R = 0.1 , κ v 1 = 0.03 , and κ t 1 = 0.3 . In the charging curves κ t 3 = 0.3 , and in the discharging curves κ t 3 = 0.08 . Wavelengths are λ 1 = 450 nm , λ 2 = 650 nm , and λ 3 = 1300 nm .

Fig. 5
Fig. 5

(a) Three-dimensional plot of the monotonically increasing concave function f ( P 1 ph , P 3 ph ) . (b) The equilibrium state plane of ETM where contours of constant luminescence are plotted as function of the intensities of the two illuminations. In both graphs the material parameters are κ v 1 = 0.03 , α = 0.1 , and β = 1.0 . Wavelengths are λ 1 = 450 nm , λ 2 = 650 nm , and λ 3 = 1300 nm .

Fig. 6
Fig. 6

Schematic of a typical optical setup. A thin film of ETM is exposed to two light sources with wavelengths λ 1 and λ 3 . In this setup, the first light source is the master, and the second one is the slave, which is linearly coupled to the first one. Acronyms O.F., LC, and D stand for optical filter, linear coupling system, and photodetector, respectively.

Fig. 7
Fig. 7

Linear coupling of two sources and the corresponding nonlinear curve.

Equations (39)

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P v e ( t ) = P v e ( t δ ) δ P 1 ph ξ v c 1 ξ c t T + δ P 1 ph ξ t c 1 ξ c v R + δ P 3 ph ξ t c 3 ξ c v R ,
P t e ( t ) = P t e ( t δ ) + δ P 1 ph ξ v c 1 ξ c t T δ P 1 ph ξ t c 1 ξ c v R δ P 3 ph ξ t c 3 ξ c v R .
d P v e ( t ) d t = κ v 1 ξ c t T P e P 1 ph P v e ( t ) + κ t 1 ξ c v R P e P 1 ph P t e ( t ) + κ t 3 ξ c v R P e P 3 ph P t e ( t ) ,
d P t e ( t ) d t = + κ v 1 ξ c t T P e P 1 ph P v e ( t ) κ t 1 ξ c v R P e P 1 ph P t e ( t ) κ t 3 ξ c v R P e P 3 ph P t e ( t ) ,
P 2 ph ( t ) = κ v 1 ξ c v R P e P 1 ph P v e ( t ) + κ t 1 ξ c v R P e P 1 ph P t e ( t ) + κ t 3 ξ c v R P e P 3 ph P t e ( t ) .
κ v 1 ξ c t T P 1 ph P ̃ v e = κ t 1 ξ c v R P 1 ph P ̃ t e + κ t 3 ξ c v R P 3 ph P ̃ t e ,
P ̃ v e = ( α + P 3 ph P 1 ph β ) P ̃ t e ,
P ̃ v e + P ̃ t e = P e .
P ̃ v e = α P 1 ph + β P 3 ph ( 1 + α ) P 1 ph + β P 3 ph P e ,
P ̃ t e = P 1 ph ( 1 + α ) P 1 ph + β P 3 ph P e .
1 κ v 1 P ̃ 2 ph = P 1 ph α P 1 ph + β P 3 ph ( 1 + α ) P 1 ph + β P 3 ph = f ( P 1 ph , P 3 ph ) .
f ( P 1 ph , P 3 ph ) f P 1 ph P ̂ 1 ph + f P 3 ph P ̂ 3 ph = α ( 1 + α ) ( P 1 ph ) 2 + 2 α β P 1 ph P 3 ph + β 2 ( P 3 ph ) 2 [ ( 1 + α ) P 1 ph + β P 3 ph ] 2 P ̂ 1 ph + β ( P 1 ph ) 2 [ ( 1 + α ) P 1 ph + β P 3 ph ] 2 P ̂ 3 ph ,
H ( f ) [ 2 f 2 P 1 ph 2 f P 1 ph P 3 ph 2 f P 3 ph P 1 ph 2 f 2 P 3 ph ] = 2 β 2 [ ( 1 + α ) P 1 ph + β P 3 ph ] 3 [ ( P 3 ph ) 2 P 1 ph P 3 ph P 1 ph P 3 ph ( P 1 ph ) 2 ] .
d P t e ( t ) d t = θ ϕ P t e ( t ) ,
θ = 1 P e κ v 1 ξ c t T P 1 ph ,
ϕ = 1 P e ( κ v 1 ξ c t T P 1 ph + κ t 1 ξ c v R P 1 ph + κ t 3 ξ c v R P 3 ph ) .
P t e ( t ) = θ ϕ 1 ϕ exp ( ϕ t ) .
Maximize ( Maximize P e ϕ ) ,
ξ c v R , ξ c t T , κ v 1 , κ t 1 , κ t 3 I 1 , I 3
Subject to :
P e ϕ = κ v 1 ξ c t T P 1 ph + κ t 1 ξ c v R P 1 ph + κ t 3 ξ c v R P 3 ph ,
I 1 [ I 1 Min , I 1 Max ] , I 3 [ I 3 Min , I 3 Max ] ,
P i ph = I i h ν i ,
0 < ξ c v R , ξ c t T , κ v 1 , κ t 1 , κ t 3 < 1 ,
ξ c v R + ξ c t T = 1 .
Maximize ( Maximize P ̃ 2 ph ) ,
ξ c v R , ξ c t T , κ v 1 , κ t 1 , κ t 3 I 1 , I 3
Subject to :
P ̃ 2 ph = κ v 1 P 1 ph κ t 1 P 1 ph ξ c v R + κ t 3 P 3 ph ξ c v R ( κ v 1 ξ c t T + κ t 1 ξ c v R ) P 1 ph + κ t 3 P 3 ph ξ c v R ,
I 1 [ I 1 Min , I 1 Max ] , I 3 [ I 3 Min , I 3 Max ]
P i ph = I i h ν i ,
0 < ξ c v R , ξ c t T , κ v 1 , κ t 1 , κ t 3 < 1 ,
ξ c v R + ξ c t T = 1 .
P ̃ 2 ph ξ c v R = κ v 1 P 1 ph ( κ t 1 P 1 ph + κ t 3 P 3 ph ) g 2 0 ,
P ̃ 2 ph κ v 1 = P 1 ph ξ c v R ( κ t 1 P 1 ph + κ t 3 P 3 ph ) ( κ t 1 P 1 ph ξ c t T + κ t 3 P 3 ph ξ c v R ) g 2 0 ,
P ̃ 2 ph κ t 1 = κ v 1 ( P 1 ph ) 2 ξ c v R ( κ v 1 P 1 ph ξ c v R + κ t 3 P 3 ph ξ c v R κ t 3 P 3 ph ξ c t T ) g 2 ,
P ̃ 2 ph κ t 3 = κ v 1 ( P 1 ph ) 2 ξ c v R ( κ v 1 ξ c v R + κ t 1 ξ c t T κ t 1 ξ c v R ) g 2 ,
g = κ v 1 P 1 ph ξ c v R + κ t 1 P 1 ph ξ c t T + κ t 3 P 3 ph ξ c v R .
I 3 = η I 1 + μ .

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