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Optics Express

  • Editor: J. H. Eberly
  • Vol. 6, Iss. 12 — Jun. 5, 2000
  • pp: 227–235
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A thin film of short oriented linear Frenkel chains as an optical bistable element

Victor A. Malyshev and Enrique Conejero Jarque  »View Author Affiliations


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

A considerable attention has been recently drawn to the problem of strong coupling of organic polymers and molecular aggregates to resonant radiation. There have been reported cooperative emission in 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

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]

] and super-radiant lasing from J-aggregated cyanine dye molecules adsorbed onto colloidal silica [3

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

] and silver [4

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]

]. In addition, it has been theoretically argued that both an individual linear molecular aggregate [5

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

, 6

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

, 7

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

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]

] (more specifically, J-aggregate) and a film with thickness smaller than the emission wavelength (hereinafter, ultrathin) built up of such objects [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]

] may respond to the action of resonant irradiation in a bistable manner, showing a sudden switching of the aggregate population from a low level to a higher one as the pump intensity rises. Respectively, the same peculiarity occurs in the reflection from and in the transmission through such a system. An experimental observation of bistable behavior of an ensemble of J-aggregates would give us a real chance to create an all-optical switching unit which, integrated into an array, could serve as a macro-unit for a logical all-optical device.

2 Model

An elementary object of the ensemble we deal with represents a short (with length smaller than the emission wavelength) regular linear chain consisting of 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]

] so that any state with a fixed number of excitons nex can be constructed as a Slater determinant of nex one-exciton states

k=(2N+1)12n=1NsinπknN+1n,k=1,2,.N,
(1)

where |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=k=1N nk Ek , where nk =0,1 is the occupation number of the kth one-exciton state and Ek is the corresponding energy given by

Ek=ω212UcosπkN+1.
(2)

Here, 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]

]), while the transition between the bottoms of one-exciton and two-exciton bands is blue-shifted with regard to the former by an energy of 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]

] to treat the transition from the ground state to the bottom of the one-exciton band as an isolated inhomogeneously broadened (due to variance of chain lengths) transition. In what follows, we will also use this assumption as a basis of our approach and thus will model the ensemble of Frenkel chains as that of 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]

]. Regarding the incoming field εi , 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.

Under the above limitations, the time evolution of the film, subjected to the action of an external field εi , can be described in terms of the 2×2 density matrix ραβ (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

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]

])

ρ˙21=(iω+Γ)ρ21idεZ,
(3)
Z˙=2idε[ρ12ρ21]Γ1(Z+1),
(4)
ε(x,t)=εi(x,t)2πc0Ldxt𝓟(x,txxc).
(5)

Here, ħω=ħω 21-2U cos[π/(N+1)]≈ħω 21-2U+ 2/N 2 is the transition energy for an individual chain of size N (hereafter assumed to be large); Γ1 is the spontaneous emission constant of the optically active one-exciton state: Γ1=γ0 N with γ0 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 Γ1 by unity); Γ=Γ1/2+Γ2 is the dephasing constant, where Γ2 is the contribution not connected with radiative damping; d is the transition dipole moment of a chain of size N scaled as d=d 0N, 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:

𝓟=n0Np(N)d[ρ21+ρ12],
(6)

where n 0 is the density of chains in the film and p(N) denotes the chain length distribution function.

We are using in our study the wave equation in its integral form, Eq. (5). In contrast to its differential version, an obvious advantage of this approach is that the field can be explicitly calculated in any space-time point if one knows the spatial distribution of the electric polarization which, in turn, is found from constituent equations (3) and (4). The boundary conditions are not required. The background refraction index is not included in Eq. (5) because, in fact, this simply results in constant renormalizations [13

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]

].

We assume that the incident field has the form εi =Ei (t) cos(ωit-kix), where ωi and ki =ωi /c are the frequency and the wavenumber, respectively, while Ei (t) is the amplitude, slowly varying in scale of the optical period 2π/ωi . 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)Rexp(-it), ε=(1/2)E exp(-it)+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 Γ¯ and ei =d̄Ei /ħ Γ¯ (where =∑ Np(N)d and Γ¯ =∑ Np(N)Γ are the mean transition dipole moment and the mean relaxation constant, respectively) and dimensionless spatial ξ=kix and temporal τ=Γ¯ 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:

R˙=(iδ+γ)R+μeZ,
(7)
Z˙=12μ(eR*+e*R)γ1(Z+1),
(8)
e(ξ,τ)=ei(τ)eiξ+Ψ0kiLdξeiξξNp(N)μR(ξ,τ),
(9)

where δ=Δ/Γ¯ , γ=Γ/Γ¯ , µ=d/, γ11/Γ¯ , and Ψ=2πd̄ 2 n 0/ħ Γ¯ . We neglected in Eq. (9) the retardation effect, replacing t-|x-x′|/c by t since for a film of thickness of the order of the emission wavelength λ=2π/ki 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/d̄Ei , Δ-1) are much longer. One can therefore consider the field as propagating instantaneously.

The reflected and transmitted waves are simply given by the formulae:

er(τ)=e(0,τ)e0(τ)=Ψ0kiLdξeiξNp(N)μR(ξ,τ),
(10)
et(τ)=e(kL,τ)=ei(τ)eikiL+Ψ0kiLdξei(kiLξ)Np(N)μR(ξ,τ).
(11)

Further, we choose, as a distribution function p(N), a Gaussian centered around with standard deviation a

p(N)=12πaexp[(NN)22a2],
(12)

assuming a 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 21-2U+ 2/ 2-ħω)/ħ Γ¯ with standard deviation σ=2π 2 Ua/ħ Γ¯ 3. The quantity σ can be identified with the inhomogeneous width of the exciton absorption line, so that the limit σ>1 (or 2π 2 Ua/ 3>ħ Γ¯ in dimensional units) corresponds to the case of dominating inhomogeneous broadening. At σ<1, the exciton transition is homogeneously broadened.

The set of nonlinear equations (7)(11) constitutes the basis of our analysis of the optical response of a thin film consisting of linear Frenkel chains. We will be interested in the amplitude reflection and transmission coefficients, which are given by the formulae r=|[e(0,τ)-ei (τ)]/ei (τ)| and t=|e(kL,τ)/ei (τ)|, respectively.

3 Motivation

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.

The physical origin of the effects reported in Refs. [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]

, 13

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

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]

, 25

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]

] is attributed to saturation of the non-linear refraction index by the acting field. For an input field changing slowly in the scale of the relaxation times Γ-1, Γ11 (the case of our interest in the present study), the medium adiabatically follows the field. Under such conditions, the set of equations (7)(9) is equivalent to only one equation [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]

]:

d2edξ2+n2(e2)e=0,
(13)
n2(e2)=1+2Ψi+δ1+δ2+γe2γ1,
(14)

where 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 ei 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

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

]. This interface plays the role of an “artificial” mirror giving rise to a feedback necessary for the effects outlined above to occur.

4 Results

When studying the reflection from and transmission through a film consisting of 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. 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]

]) to get the optimal conditions for the effects we are looking for.

Figure 1 presents examples of the input field dependence of the reflection and transmission coefficients for a thin film of thickness L=λ. The data were obtained at adiabatic scanning of the input field amplitude ei 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).

Figure 2 shows spatial profiles of the amplitude module of the field inside the film versus the input field amplitude ei 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 ei 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:

(i) Despite the fact that the thickness of the system does not exceed one wavelength in vacuum λ, the field inside the film is not uniform at any amplitude of the input field. For not saturating magnitudes of the latter, this is simply explained by the fact that the (linear) refraction index in this case (at 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.

(ii) Comparison of the field profiles depicted in the plots (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

First, let us discuss the applicability of the two-level model used in this Paper. One should compare the typical energy spacing between the first and second exciton levels (E 2-E 1)/ħ Γ¯ ⋍3π 2(U/ħ Γ¯ )/ 2 with the switching magnitude of the input field ei . 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.

It is worthwhile to analyze the parameters of real systems in order to get insight into feasibility of the bistable mechanism we are dealing with. In this sense, the J-aggregates of PIC, as one of the most studied species of the type we need, seem to be suitable objects. The width of the red J-band of PIC-Br (centered at λ=576.1 nm), at low temperature, has an inhomogeneous nature and an order of magnitude of 30cm -1 (or 1ps -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]

]. The blue shift of the transition from one-to-two exciton bands with respect to that from the ground state to the one-exciton band for the red J-band has the same order. The polariton splitting is ΨΓ=2πd̄ 2 n 0/ħ=(3/16π 20 N̄n 0λ3, so that taking γ0=(1/3.7)ns -1 and N̄n 0=1018 cm -3 (an achievable concentration of molecules before aggregation), we obtain ΨΓ⋍1ps -1, i.e., the value that exceeds twice the halfwidth of the J-band 0.5ps -1 (σΓ in our notation). Hence, for the parameters used, we are under conditions needed the bistability to occur.

To conclude, it is to be noting that the authors of Ref. [29

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]

] reported a room-temperature formation of polariton states in ordered cyanine dye films. The latter thus can also be considered as a promising object from the viewpoint of our findings.

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.

6 Conclusions

In this Paper, we have numerically studied the optical bistable response of a thin film with thickness of the order of the emission wavelength, comprised of oriented linear Frenkel chains. We have taken into account a distribution of chains over lengths, resulting in an inhomogeneous broadening of the exciton optical transition.

From our study, the following conclusions can be drawn:

(i) within a certain range of driving parameters (resonance detuning, polariton splitting, and inhomogeneous width), the film really shows a bistable behavior with respect to both the reflection and transmission of the resonant light;

(ii) the bistability effect exists until the inhomogeneous width of the transition approaches the polariton splitting, i.e., for a fairly wide range of widths;

(iii) the parameters needed for the bistable behavior seem to be achievable for a thin film of J-aggregates of polymethine dyes and for some classes of conjugated polymers deposited onto a dielectric substrate such as poly(p-phenylene-vinylene) derivatives.

Acknowledgments

V. A. M. acknowledges a support from the INTAS (project 97-10434). E. C. J. acknowledges supports from the Spanish DGESEIC (project PB98-0268) as well as from the Junta de Castilla y León (project SA58/00B).

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. 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]

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) [JETP67, 1741 (1988)].

27.

A. S. Davydov, 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]

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

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