## A thin film of short oriented linear Frenkel chains as an optical bistable element

Optics Express, Vol. 6, Issue 12, pp. 227-235 (2000)

http://dx.doi.org/10.1364/OE.6.000227

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### Abstract

A numerical study of reflectivity and transmittivity of an ensemble of short oriented linear Frenkel chains, which forms a thin film with a thickness of the order of an optical wavelength, is carried out. The eigenstates of a single chain are considered to be of a collective (excitonic) origin. A distribution of chains over lengths resulting in inhomogeneous broadening of the exciton optical transition is taken into account. We report a bistable behavior of both reflectivity and transmittivity of the film in a spectral domain close to the exciton resonance, caused by saturation of the nonlinear refraction index. Estimates of driving parameters show that thin films of oriented J-aggregates of polymethine dyes deposited on a dielectric substrate seem to be a suitable object for observation of the predicted behavior.

© Optical Society of America

## 1 Introduction

*π*-conjugated polymer thin films [1

1. S. V. Frolov, W. Gellermann, M. Ozaki, K. Yoshino, and Z. V. Vardeny, “Cooperative Emission in π-Conjugated Polymer Thin Films,” Phys. Rev. Lett. **78**, 729 (1997). [CrossRef]

2. S. V. Frolov, Z. V. Vardeny, and K. Yoshino, “Cooperative and stimulated emission in poly(p-phenylene-vinylene) thin films and solutions,” Phys. Rev. B **57**, 9141 (1998). [CrossRef]

3. S. Özçelik and D. L. Akins, “Extremely low excitation threshold, superradiant, molecular aggregate lasing system,” Appl. Phys. Lett. **71**, 3057 (1997). [CrossRef]

4. S. Özçelik, I. Özçelik, and D. L. Akins, “Superradiant lasing from J-aggregated molecules adsorbed onto colloidal silver,” Appl. Phys. Lett. **73**, 1949 (1998). [CrossRef]

5. V. V. Gusev, “Mirrorless optical bistability in molecular aggregates with dipole-dipole interaction,” Adv. Mater. Opt. Electr. **1**, 235 (1992). [CrossRef]

6. V. Malyshev and P. Moreno, “Mirrorless optical bistability of linear molecular aggregates,” Phys. Rev. A **53**, 416 (1996). [CrossRef] [PubMed]

7. V. A. Malyshev, H. Glaeske, and K.-H. Feller, “Effect of exciton-exciton annihilation on optical bistability of a linear molecular aggregate,” Opt. Commun. **140**, 83 (1997). [CrossRef]

8. V. A. Malyshev, H. Glaeske, and K.-H. Feller, “Optical bistable response of an open Frenkel chain: Exciton-exciton annihilation and boundary effects,” Phys. Rev. A **58**, 670 (1998). [CrossRef]

9. V. A. Malyshev, H. Glaeske, and K.-H. Feller, “Bistable behavior of transmittivity of an ultrathin film comprised of linear molecular aggregates,” Opt. Commun. **169**, 177 (1999). [CrossRef]

9. V. A. Malyshev, H. Glaeske, and K.-H. Feller, “Bistable behavior of transmittivity of an ultrathin film comprised of linear molecular aggregates,” Opt. Commun. **169**, 177 (1999). [CrossRef]

10. M. G. Benedict and E. D. Trifonov, “Coherent reflection as superradiation from the boundary of a resonant medium,” Phys. Rev. A **38**, 2854 (1988). [CrossRef] [PubMed]

11. M. G. Benedict, V. A. Malyshev, E. D. Trifonov, and A. I. Zaitsev, “Reflection and transmission of ultrashort light pulses through a thin resonant medium: Local field effects,” Phys. Rev. A **43**, 3845 (1991). [CrossRef] [PubMed]

12. V. A. Malyshev and E. Conejero Jarque, “Optical hysteresis and instabilities inside the polariton band gap,” J. Opt. Soc. Am. B **12**, 1868 (1995). [CrossRef]

13. V. A. Malyshev and E. Conejero Jarque, “Spatial effects in nonlinear resonant reflection from the boundary of a dense semi-infinite two-level medium: Normal incidence,” J. Opt. Soc. Am. B **14**, 1167 (1997). [CrossRef]

14. E. Conejero Jarque and V. A. Malyshev, “Nonlinear reflection from a dense saturable absorber: from stability to chaos,” Opt. Commun. **142**, 66 (1997). [CrossRef]

15. J. T. Manassah and B. Gross, “Pulse reflectivity at a dense-gas-dielectric interface,” Opt. Commun. **131**, 408 (1996). [CrossRef]

16. J. T. Manassah and B. Gross, “Superradiant amplification in an optically dense gas,” Opt. Commun. **143**, 329 (1997). [CrossRef]

17. J. T. Manassah and B. Gross, “Reflected echo from a resonant two-level system,” Opt. Commun. **144**, 231 (1997). [CrossRef]

18. J. T. Manassah and B. Gross, “The different regimes of the optically dense amplifier,” Opt. Commun. **149**, 393 (1998). [CrossRef]

19. J. T. Manassah and B. Gross, “Amplification by an optically dense resonant two-level system embedded in a dielectric medium,” Opt. Commun. **155**, 213 (1998). [CrossRef]

12. V. A. Malyshev and E. Conejero Jarque, “Optical hysteresis and instabilities inside the polariton band gap,” J. Opt. Soc. Am. B **12**, 1868 (1995). [CrossRef]

13. V. A. Malyshev and E. Conejero Jarque, “Spatial effects in nonlinear resonant reflection from the boundary of a dense semi-infinite two-level medium: Normal incidence,” J. Opt. Soc. Am. B **14**, 1167 (1997). [CrossRef]

14. E. Conejero Jarque and V. A. Malyshev, “Nonlinear reflection from a dense saturable absorber: from stability to chaos,” Opt. Commun. **142**, 66 (1997). [CrossRef]

## 2 Model

*N*two-level molecules. Due to the inter-molecular dipolar coupling, the optically active states of the chain are the Frenkel exciton states. In the nearest-neighbor approximation, one-dimensional Frenkel excitons appear to be non-interacting fermions [20

20. D. B. Chesnut and A. Suna, “Fermion behaviour of one-dimensional excitons,” J. Chem. Phys. **39**, 146 (1963). [CrossRef]

*n*

_{ex}can be constructed as a Slater determinant of

*n*

_{ex}one-exciton states

*n*〉 is the ket-vector of excited state of the nth molecule. The energies of the one-dimensional exciton gas may take the values

*W*=

*n*

_{k}

*E*

_{k}, where

*n*

_{k}=0,1 is the occupation number of the

*k*th one-exciton state and

*E*

_{k}is the corresponding energy given by

*ω*

_{21}is the frequency of the transition in the isolated molecule;

*U*(chosen hereafter to be positive) is the nearest-neighbor dipole-dipole coupling. The optical transition from the ground state of the chain to the lowest state of the one-exciton band (

*k*=1) has the dominating oscillator strength, (81% of the entire one, see, for instance, Ref. [21

21. H. Fidder, J. Knoester, and D. A. Wiersma, “Optical properties of disordered molecular aggregates: Numerical study,” J. Chem. Phys. **95**, 7880 (1991). [CrossRef]

*E*

_{2}-

*E*

_{1}due to the fermionic nature of the one-dimensional Frenkel excitons. This fact was used in Ref. [9

9. V. A. Malyshev, H. Glaeske, and K.-H. Feller, “Bistable behavior of transmittivity of an ultrathin film comprised of linear molecular aggregates,” Opt. Commun. **169**, 177 (1999). [CrossRef]

*inhomogeneously broadened two-level systems*. However, the optical characteristics of the transition will be attributed to the lowest one-exciton state. We also assume that the transition dipole moments of all the chains are parallel to each other as well as to the film plane. Such conditions are achievable for thin films prepared by the spin-coating method [22

22. K. Misawa, K. Minoshima, H. Ono, and T. Kobayashi, “New fabrication method for highly oriented J-aggregates dispersed in polymer films,” Appl. Phys. Lett. **63**, 577 (1993). [CrossRef]

*ε*

_{i}, the on-resonance and normal incidence conditions are chosen. Besides, we will restrict ourselves without noticeable loss of generality to the case of the field polarization directed along the transition dipole moment. Hence, all the observables can be considered as scalars.

*ε*

_{i}, can be described in terms of the 2×2 density matrix

*ρ*

_{αβ}(

*α*,

*β*=1, 2) which determines the state of a chain of size

*N*. The density matrix equation and the Maxwell equation for the total field

*ε*, including the secondary field produced by the film, form the entire set of coupled nonlinear equations for description of the resonant optical response of the film. It reads (see, for instance, Refs. [10

10. M. G. Benedict and E. D. Trifonov, “Coherent reflection as superradiation from the boundary of a resonant medium,” Phys. Rev. A **38**, 2854 (1988). [CrossRef] [PubMed]

11. M. G. Benedict, V. A. Malyshev, E. D. Trifonov, and A. I. Zaitsev, “Reflection and transmission of ultrashort light pulses through a thin resonant medium: Local field effects,” Phys. Rev. A **43**, 3845 (1991). [CrossRef] [PubMed]

*ħω*=

*ħω*

_{21}-2

*U*cos[

*π*/(

*N*+1)]≈

*ħω*

_{21}-2

*U*+

*Uπ*

^{2}/

*N*

^{2}is the transition energy for an individual chain of size

*N*(hereafter assumed to be large); Γ

_{1}is the spontaneous emission constant of the optically active one-exciton state: Γ

_{1}=

_{γ0}

*N*with γ

_{0}being the analogous constant for an isolated molecule (for the sake of simplicity, we have replaced the numerical factor 8/

*π*

^{2}in the expression for Γ

_{1}by unity); Γ=Γ

_{1}/2+Γ

_{2}is the dephasing constant, where Γ

_{2}is the contribution not connected with radiative damping;

*d*is the transition dipole moment of a chain of size

*N*scaled as

*d*=

*d*

_{0}√

*N*, where

*d*

_{0}is the transition dipole moment for an isolated molecule;

*Z*=

*ρ*

_{22}-

*ρ*

_{11}is the population difference. The dots denote time derivatives. Formula (5) is nothing but an integral form of the Maxwell equation for a film, in which

*c*and

*L*stand for the speed of light and for the film thickness, respectively, and

*P*is the electric polarization:

*n*

_{0}is the density of chains in the film and

*p*(

*N*) denotes the chain length distribution function.

13. V. A. Malyshev and E. Conejero Jarque, “Spatial effects in nonlinear resonant reflection from the boundary of a dense semi-infinite two-level medium: Normal incidence,” J. Opt. Soc. Am. B **14**, 1167 (1997). [CrossRef]

*ε*

_{i}=

*E*

_{i}(

*t*) cos(

*ω*

_{i}

*t*-

*k*

_{i}

*x*), where

*ω*

_{i}and

*k*

_{i}=

*ω*

_{i}/

*c*are the frequency and the wavenumber, respectively, while

*E*

_{i}(

*t*) is the amplitude, slowly varying in scale of the optical period 2

*π*/

*ω*

_{i}. In order to describe adequately the reflection and transmission effects, we seek a solution of Eqs. (3–5) in the form:

*ρ*

_{21}=-(

*i*/2)

*R*exp(-

*iω*

_{i}

*t*),

*ε*=(1/2)

*E*exp(-

*iω*

_{i}

*t*)+

*c*.

*c*., where the complex amplitudes

*R*and

*E*are also slowly varying in time but not in space, and pass finally from Eqs. (3)–(5) to equations for the amplitudes

*R*,

*E*and for the population difference

*Z*. To make numerical calculations, it is convenient to write down these equations in a dimensionless form, introducing the dimensionless field amplitudes

*e*=

*d̄E*/

*ħ*

*e*

_{i}=

*d̄E*

_{i}/

*ħ*

*d̄*=∑

_{N}

*p*(

*N*)

*d*and

_{N}

*p*(

*N*)Γ are the mean transition dipole moment and the mean relaxation constant, respectively) and dimensionless spatial

*ξ*=

*k*

_{i}

*x*and temporal

*τ*=

*t*coordinates. Taking into account the resonant character of the problem under study and neglecting therefore the counter-rotating terms, we arrive at a truncated system of equations for the slowly varying magnitudes:

*δ*=Δ/

*γ*=Γ/

*µ*=

*d*/

*d̄*, γ

_{1}=Γ

_{1}/

*πd̄*

^{2}

*n*

_{0}/

*ħ*

*t*-|

*x*-

*x′*|/

*c*by

*t*since for a film of thickness of the order of the emission wavelength λ=2

*π*/

*k*

_{i}the actual passage time of the light through the film has an order of magnitude of the optical period while all the characteristic time scales of the problem at hand (Γ,

*ħ*/

*d̄E*

_{i}, Δ

^{-1}) are much longer. One can therefore consider the field as propagating instantaneously.

*p*(

*N*), a Gaussian centered around

*N̄*with standard deviation

*a*

*a*≪

*N̄*and replacing accordingly ∑

_{N}

*p*(

*N*) by ∫

*dNp*(

*N*). Under this assumption, it is easy to show that the distribution function of the detuning

*δ*also presents a Gaussian centered at

*δ*

_{0}=(

*ħω*

_{21}-2

*U*+

*Uπ*

^{2}/

*N̄*

^{2}-

*ħω*)/

*ħ*

*σ*=2

*π*

^{2}

*Ua*/

*ħ*

*N̄*

^{3}. The quantity

*σ*can be identified with the inhomogeneous width of the exciton absorption line, so that the limit

*σ*>1 (or 2

*π*

^{2}

*Ua*/

*N̄*

^{3}>

*ħ*

*σ*<1, the exciton transition is homogeneously broadened.

*r*=|[

*e*(0,

*τ*)-

*e*

_{i}(

*τ*)]/

*e*

_{i}(

*τ*)| and

*t*=|

*e*(

*kL*,

*τ*)/

*e*

_{i}(

*τ*)|, respectively.

## 3 Motivation

*L*≫λ) dense system of

*homogeneously broadened*two-level molecules [12

12. V. A. Malyshev and E. Conejero Jarque, “Optical hysteresis and instabilities inside the polariton band gap,” J. Opt. Soc. Am. B **12**, 1868 (1995). [CrossRef]

**14**, 1167 (1997). [CrossRef]

14. E. Conejero Jarque and V. A. Malyshev, “Nonlinear reflection from a dense saturable absorber: from stability to chaos,” Opt. Commun. **142**, 66 (1997). [CrossRef]

23. L. Roso-Franco, “Self-reflected Wave Inside a Very Dense Saturable Absorber,” Phys. Rev. Lett. **55**, 2149 (1985). [CrossRef] [PubMed]

24. L. Roso-Franco, “Propagation of light in a nonlinear absorber,” J. Opt. Soc. Am. B **4**, 1878 (1987). [CrossRef]

25. L. Roso-Franco and M. Ll. Pons, “Reflection of a plane wave at the boundary of a saturable absorber: normal incidence,” J. Mod. Opt. **37**, 1645 (1990). [CrossRef]

*L*≪λ, which makes possible to use the mean-field approach), another parameter, Ψ

*k*

_{i}

*L*, plays a similar role [9

**169**, 177 (1999). [CrossRef]

**12**, 1868 (1995). [CrossRef]

**14**, 1167 (1997). [CrossRef]

**142**, 66 (1997). [CrossRef]

*δ*=-Ψ.

**12**, 1868 (1995). [CrossRef]

**14**, 1167 (1997). [CrossRef]

**142**, 66 (1997). [CrossRef]

25. L. Roso-Franco and M. Ll. Pons, “Reflection of a plane wave at the boundary of a saturable absorber: normal incidence,” J. Mod. Opt. **37**, 1645 (1990). [CrossRef]

^{-1},

**12**, 1868 (1995). [CrossRef]

*n*(|

*e*|

^{2}) is the nonlinear refraction index. For the sake of simplicity, we have neglected in Eq. (14) the inhomogeneous broadening. Equation (14) explicitly includes the saturation effect: at higher amplitudes of the field,

*γ*|

*e*|

^{2}/

*γ*

_{1}≫Ψ, the refraction index goes to unity. In the opposite limit

*γ*|

*e*|

^{2}/

*γ*

_{1}≪Ψ, it approaches -1 at

*δ*=-Ψ. Such a behavior dictates the following scenario of the field-dependent reflection. At low (non-saturating) amplitudes of the input field

*e*

_{i}and of the field inside the film

*e*, the former is totally reflected from the absorber boundary. However, the molecules close to the boundary start to be saturated when the amplitude of both fields increases. As a result, the higher the field amplitudes, the deeper the field penetrates into the medium, and it is reflected from a very narrow interface between the saturated and non-saturated regions [23

23. L. Roso-Franco, “Self-reflected Wave Inside a Very Dense Saturable Absorber,” Phys. Rev. Lett. **55**, 2149 (1985). [CrossRef] [PubMed]

24. L. Roso-Franco, “Propagation of light in a nonlinear absorber,” J. Opt. Soc. Am. B **4**, 1878 (1987). [CrossRef]

## 4 Results

*in-homogeneously broadened*two-level systems, all the aforesaid should be kept in mind. Therefore, in what follows, we will also set

*δ*=-Ψ and consider Ψ>Ψ

_{c}=4.66 (Ψ

_{c}is the threshold of the bistability in reflection [12

**12**, 1868 (1995). [CrossRef]

*L*=λ. The data were obtained at adiabatic scanning of the input field amplitude

*e*

_{i}up and down so that in any momentum of time, all the characteristics (of the medium and of the field inside the film) arrived at their stationary values. ¿From this figure, one can conclude, first, that the system shows a stable hysteresis loop both in the reflectivity and in the transmittivity or, in other words, behaves in a bistable fashion until

*σ*<Ψ, i.e., until the inhomogeneous width approaches the polariton splitting. This is a quite clear limitation for bistability of this type to occur, since under the conditions of dominant inhomogeneous broadening (

*σ*>Ψ), the polariton splitting, being responsible for the effect at hand, vanishes. The second observation, evident from Fig. 1, is that the switching amplitudes of the input field do not depend strongly on the inhomogeneous width (at a fixed magnitude of Ψ).

*e*

_{i}which were calculated under the same parameters and conditions as the data presented in Fig. 1. The plots

*a*and

*b*correspond to adiabatic scanning of

*e*

_{i}up (

*a*) and down (

*b*), respectively. The darkness of a local differential domain is proportional to the field amplitude module. Observing these plots, we come to the following conclusions:

*δ*=-Ψ)

*n*≈-1, that, in turn, gives rise to decreasing the field amplitude on a scale much shorter than λ. At higher magnitudes of the input field, ranging within the bistable interval (see Fig. 1), the spatial inhomogeneity of the field demonstrates a global character, originating from the interplay between the forward and backward (in the present case, reflected from the back boundary of the film) waves.

*a*) and (

*b*) at a fix ed magnitude of the input field reveals that they differ one from the other so that one may say about the spatial hysteresis of the field inside the film.

## 5 Discussion

*E*

_{2}-

*E*

_{1})/

*ħ*

*π*

^{2}(

*U*/

*ħ*

*N̄*

^{2}with the switching magnitude of the input field

*e*

_{i}. For the parameters at hand, the former quantity ranges within the interval [3.3, 33] while the latter is approximately equal to 3. Therefore, we can conclude that our approach is correct and there is no necessity to include the one-to-two exciton transitions.

*cm*

^{-1}(or 1

*ps*

^{-1}in frequency units) [28

28. H. Fidder, J. Terpstra, and D. A. Wiersma, “Dynamics of Frenkel excitons in disordered molecular aggregates,” J. Chem. Phys. **94**, 6895 (1991). [CrossRef]

*πd̄*

^{2}

*n*

_{0}/

*ħ*=(3/16

*π*

^{2})γ

_{0}

*N̄n*

_{0}λ

^{3}, so that taking γ

_{0}=(1/3.7)

*ns*

^{-1}and

*N̄n*

_{0}=10

^{18}

*cm*

^{-3}(an achievable concentration of molecules before aggregation), we obtain ΨΓ⋍1

*ps*

^{-1}, i.e., the value that exceeds twice the halfwidth of the J-band 0.5

*ps*

^{-1}(

*σ*Γ in our notation). Hence, for the parameters used, we are under conditions needed the bistability to occur.

## 6 Conclusions

*p*-phenylene-vinylene) derivatives.

## Acknowledgments

## References and links

1. | S. V. Frolov, W. Gellermann, M. Ozaki, K. Yoshino, and Z. V. Vardeny, “Cooperative Emission in π-Conjugated Polymer Thin Films,” Phys. Rev. Lett. |

2. | S. V. Frolov, Z. V. Vardeny, and K. Yoshino, “Cooperative and stimulated emission in poly(p-phenylene-vinylene) thin films and solutions,” Phys. Rev. B |

3. | S. Özçelik and D. L. Akins, “Extremely low excitation threshold, superradiant, molecular aggregate lasing system,” Appl. Phys. Lett. |

4. | S. Özçelik, I. Özçelik, and D. L. Akins, “Superradiant lasing from J-aggregated molecules adsorbed onto colloidal silver,” Appl. Phys. Lett. |

5. | V. V. Gusev, “Mirrorless optical bistability in molecular aggregates with dipole-dipole interaction,” Adv. Mater. Opt. Electr. |

6. | V. Malyshev and P. Moreno, “Mirrorless optical bistability of linear molecular aggregates,” Phys. Rev. A |

7. | V. A. Malyshev, H. Glaeske, and K.-H. Feller, “Effect of exciton-exciton annihilation on optical bistability of a linear molecular aggregate,” Opt. Commun. |

8. | V. A. Malyshev, H. Glaeske, and K.-H. Feller, “Optical bistable response of an open Frenkel chain: Exciton-exciton annihilation and boundary effects,” Phys. Rev. A |

9. | V. A. Malyshev, H. Glaeske, and K.-H. Feller, “Bistable behavior of transmittivity of an ultrathin film comprised of linear molecular aggregates,” Opt. Commun. |

10. | M. G. Benedict and E. D. Trifonov, “Coherent reflection as superradiation from the boundary of a resonant medium,” Phys. Rev. A |

11. | M. G. Benedict, V. A. Malyshev, E. D. Trifonov, and A. I. Zaitsev, “Reflection and transmission of ultrashort light pulses through a thin resonant medium: Local field effects,” Phys. Rev. A |

12. | V. A. Malyshev and E. Conejero Jarque, “Optical hysteresis and instabilities inside the polariton band gap,” J. Opt. Soc. Am. B |

13. | V. A. Malyshev and E. Conejero Jarque, “Spatial effects in nonlinear resonant reflection from the boundary of a dense semi-infinite two-level medium: Normal incidence,” J. Opt. Soc. Am. B |

14. | E. Conejero Jarque and V. A. Malyshev, “Nonlinear reflection from a dense saturable absorber: from stability to chaos,” Opt. Commun. |

15. | J. T. Manassah and B. Gross, “Pulse reflectivity at a dense-gas-dielectric interface,” Opt. Commun. |

16. | J. T. Manassah and B. Gross, “Superradiant amplification in an optically dense gas,” Opt. Commun. |

17. | J. T. Manassah and B. Gross, “Reflected echo from a resonant two-level system,” Opt. Commun. |

18. | J. T. Manassah and B. Gross, “The different regimes of the optically dense amplifier,” Opt. Commun. |

19. | J. T. Manassah and B. Gross, “Amplification by an optically dense resonant two-level system embedded in a dielectric medium,” Opt. Commun. |

20. | D. B. Chesnut and A. Suna, “Fermion behaviour of one-dimensional excitons,” J. Chem. Phys. |

21. | H. Fidder, J. Knoester, and D. A. Wiersma, “Optical properties of disordered molecular aggregates: Numerical study,” J. Chem. Phys. |

22. | K. Misawa, K. Minoshima, H. Ono, and T. Kobayashi, “New fabrication method for highly oriented J-aggregates dispersed in polymer films,” Appl. Phys. Lett. |

23. | L. Roso-Franco, “Self-reflected Wave Inside a Very Dense Saturable Absorber,” Phys. Rev. Lett. |

24. | L. Roso-Franco, “Propagation of light in a nonlinear absorber,” J. Opt. Soc. Am. B |

25. | L. Roso-Franco and M. Ll. Pons, “Reflection of a plane wave at the boundary of a saturable absorber: normal incidence,” J. Mod. Opt. |

26. | A. M. Basharov, “Thin-film of two-level atoms - a simple model of optical bistability and self-pulsations,” Zh. Exp. Teor. Fiz.94, 12 (1988) [JETP67, 1741 (1988)]. |

27. | A. S. Davydov, |

28. | H. Fidder, J. Terpstra, and D. A. Wiersma, “Dynamics of Frenkel excitons in disordered molecular aggregates,” J. Chem. Phys. |

29. | L. Daehne and E. Biller, “Huge splitting of dichroic absorption energies in ordered cyanine dye films,” Phys. Chem. Chem. Phys. |

**OCIS Codes**

(190.1450) Nonlinear optics : Bistability

(190.4710) Nonlinear optics : Optical nonlinearities in organic materials

(230.1150) Optical devices : All-optical devices

**ToC Category:**

Research Papers

**History**

Original Manuscript: May 3, 2000

Published: June 5, 2000

**Citation**

Victor Malyshev and Enrique Jarque, "A thin film of short oriented linear Frenkel chains as an optical bistable element," Opt. Express **6**, 227-235 (2000)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-6-12-227

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### References

- S. V. Frolov, W. Gellermann, M. Ozaki, K. Yoshino, and Z. V. Vardeny, "Cooperative Emission in pi-Conjugated Polymer Thin Films," Phys. Rev. Lett. 78, 729 (1997). [CrossRef]
- S. V. Frolov, Z. V. Vardeny, and K. Yoshino, "Cooperative and stimulated emission in poly(p-phenylene-vinylene) thin films and solutions," Phys. Rev. B 57, 9141 (1998). [CrossRef]
- S. Ozcelik and D. L. Akins, "Extremely low excitation threshold, superradiant, molecular aggregate lasing system," Appl. Phys. Lett. 71, 3057 (1997). [CrossRef]
- S. Ozcelik, I. Ozcelik, and D. L. Akins, "Superradiant lasing from J-aggregated molecules adsorbed onto colloidal silver," Appl. Phys. Lett. 73, 1949 (1998). [CrossRef]
- V. V. Gusev, "Mirrorless optical bistability in molecular aggregates with dipole-dipole interaction," Adv. Mater. Opt. Electr. 1, 235 (1992). [CrossRef]
- V. Malyshev and P. Moreno, "Mirrorless optical bistability of linear molecular aggregates," Phys. Rev. A 53, 416 (1996). [CrossRef] [PubMed]
- V. A. Malyshev, H. Glaeske and K.-H. Feller, "Effect of exciton-exciton annihilation on optical bistability of a linear molecular aggregate," Opt. Commun. 140, 83 (1997). [CrossRef]
- V. A. Malyshev, H. Glaeske and K.-H. Feller, "Optical bistable response of an open Frenkel chain: Exciton-exciton annihilation and boundary effects," Phys. Rev. A 58, 670 (1998). [CrossRef]
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