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.

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  1. 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]
  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. Ozcelik and D. L. Akins, "Extremely low excitation threshold, superradiant, molecular aggregate lasing system," Appl. Phys. Lett. 71, 3057 (1997).
    [CrossRef]
  4. 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]
  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]
  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]
  20. D. B. Chesnut and A. Suna, "Fermion behaviour of one-dimensional excitons," J. Chem. Phys. 39, 146 (1963).
    [CrossRef]
  21. H. Fidder, J. Knoester, and D. A. Wiersma, "Optical properties of disordered molecular aggregates: Numerical study," J. Chem. Phys. 95, 7880 (1991).
    [CrossRef]
  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]
  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]
  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) [ JETP 67, 1741 (1988)].
  27. A. S. Davydov, {it Theory of molecular excitons, (Plenum Press, New York, 1971).
  28. H. Fidder, J. Terpstra, and D. A. Wiersma, "Dynamics of Frenkel excitons in disordered molecular aggregates," J. Chem. Phys. 94, 6895 (1991).
    [CrossRef]
  29. L. Daehne and E. Biller, "Huge splitting of dichroic absorption energies in ordered cyanine dye films," Phys. Chem. Chem. Phys. 1, 1727 (1999).
    [CrossRef]

Other (29)

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]

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]

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]

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]

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]

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]

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

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

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

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

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

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]

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

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

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]

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

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

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]

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) [ JETP 67, 1741 (1988)].

A. S. Davydov, {it Theory of molecular excitons, (Plenum Press, New York, 1971).

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

L. Daehne and E. Biller, "Huge splitting of dichroic absorption energies in ordered cyanine dye films," Phys. Chem. Chem. Phys. 1, 1727 (1999).
[CrossRef]

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Figures (2)

Fig. 1.
Fig. 1.

Amplitude reflection (r) and transmission (t) coefficients of a thin film with thickness L=λ comprised of linear chains with mean length =30 and standard deviation a=9 calculated at adiabatic scanning of the input field amplitude ei up and down for different values of the inhomogeneous width σ=(2π 2 a/ 3)·(U/ Γ ¯ ), where U/ Γ ¯ was varied. The rest of the parameters is: Ψ=2πd̄ 2 n 0/ħ Γ ¯ =-δ=7.

Fig. 2.
Fig. 2.

Examples of the spatial profiles of the field amplitude module inside the film at σ=2 obtained at adiabatic scanning of the input field amplitude up (a) and down (b). The rest of parameters is the same as in Fig. 1. The darkness of a local differential domain is proportional to the respective field amplitude module.

Equations (14)

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k = ( 2 N + 1 ) 1 2 n = 1 N sin π kn N + 1 n , k = 1 , 2 , . N ,
E k = ω 21 2 U cos π k N + 1 .
ρ ˙ 21 = ( i ω + Γ ) ρ 21 i d ε Z ,
Z ˙ = 2 i d ε [ ρ 12 ρ 21 ] Γ 1 ( Z + 1 ) ,
ε ( x , t ) = ε i ( x , t ) 2 π c 0 L d x t 𝓟 ( x , t x x c ) .
𝓟 = n 0 N p ( N ) d [ ρ 21 + ρ 12 ] ,
R ˙ = ( i δ + γ ) R + μ e Z ,
Z ˙ = 1 2 μ ( e R * + e * R ) γ 1 ( Z + 1 ) ,
e ( ξ , τ ) = e i ( τ ) e i ξ + Ψ 0 k i L d ξ e i ξ ξ N p ( N ) μ R ( ξ , τ ) ,
e r ( τ ) = e ( 0 , τ ) e 0 ( τ ) = Ψ 0 k i L d ξ e i ξ N p ( N ) μ R ( ξ , τ ) ,
e t ( τ ) = e ( kL , τ ) = e i ( τ ) e i k i L + Ψ 0 k i L d ξ e i ( k i L ξ ) N p ( N ) μ R ( ξ , τ ) .
p ( N ) = 1 2 π a exp [ ( N N ) 2 2 a 2 ] ,
d 2 e d ξ 2 + n 2 ( e 2 ) e = 0 ,
n 2 ( e 2 ) = 1 + 2 Ψ i + δ 1 + δ 2 + γ e 2 γ 1 ,

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