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Decelerating and stopping light is fundamental for optical processing, high performance sensor technologies and digital signal treatment, many of these applications relying on the ability of controlling the amplitude and phase of coherent light pulses. In this context, slow-light has been achieved by various methods, as coupling light into resonant media, Brillouin scattering in optical fibers, beam coupling in photorefractive and liquid crystal media or engineered dispersion in photonic crystals. Here, we present a different mechanism for slowing and storing light, which is based on photo-isomerization induced transparency of azo-dye molecules hosted in a chiral liquid crystal structure. Sharp spectral features of the medium absorption/dispersion, and the long population lifetime of the dye metastable state, enable the storage of light pulses with a significant retrieval after times much longer than the medium response time.
© 2013 Optical Society of America
1. Introduction
A variety of applications in precision interferometry [1] and telecommunication [2] have been driving latest interests in slowing down the group velocities of light pulses [3] and in stopping light [4]. Several slow-light schemes have been proposed and realized, based on various effects, such as electromagnetically induced transparency (EIT) in atomic media [5] and in optomechanical systems [6], coherent population oscillations (CPO) in solids [7, 8], stimulated Brillouin and Raman scattering in optical fibers [9–11], beam coupling in photorefractive crystals [12, 13] and wave-mixing in nematic liquid crystals [14, 15]. Among these schemes, a few methods to stop light pulses, hence, allowing the storage of light, have been experimentally achieved, namely, by using EIT in atoms [4, 16–20] and in solids [21, 22], and by stimulated Brillouin scattering in fibers [9]. Numerically, stopped light has also been proposed in coupled microcavities [23]. Here, we propose a novel mechanism for slowing and stopping light pulses, which is based on photo-isomerization induced transparency of azo-dye molecules hosted in a chiral nematic liquid crystal structure. Nonlinear optical phenomena are known to occur in azo-dye doped non-chiral nematics because of reorientational [24] and surface effects [25]. In our system the azo-dyes are hosted in a chiral structure, where the helical distribution of the liquid crystal molecules inhibits optically induced reorientation while letting the azo-dye molecules undergo conformational changes under light irradiation [26, 27]. As a consequence, trans-cis photo-isomerization of the dyes provides a mechanism for coherent resonance population excitation, which induces a corresponding modulation of the medium absorption. In a similar way as in the EIT, the change of the medium absorption results in the ability of the system to provide a transparency window when it is optically pumped. However, while in the EIT the energy levels are those of the atoms, or of the optical centers locked in a crystal lattice, here the involved energy levels are those of the molecular states associated to the trans and cis isomers of the azo-dyes. Therefore, photo-isomerization induced transparency is characterized by a much broader frequency bandwidth than the EIT. Besides, the macroscopic chiral structure of the liquid crystal host ensures a long coherence time of the dye states even at room temperature, hence, leading to large storage times without the need of low operating temperatures, as required, for instance, by EIT in solids [21, 22]. The dye-doped chiral medium also does not require any low frequency voltage to be applied to the cell, which is needed, for example, in the case of liquid crystal light-valves [14]. All these features greatly simplify the practical implementation of light storage/retrieval, where the slow/stopped light schemes will benefit from low power nonlinear optics and soft matter technology.
We first present the medium and its main properties, and we show that slow and stored light can be obtained by performing two-beam coupling experiments in the azo-dye doped chiral medium. For light pulses with a typical width of a few tens of milliseconds, the photo-isomerization induced transparency effect allows achieving slow-light with group velocities as low as 1 mm/s. Then, we demonstrate the storage and retrieval of light pulses, which is achieved thanks to the coherent optically induced population of the trans-cis dye isomers. Storage times as long as 160 ms are obtained under appropriate modulation of the pump beam and with a significant retrieval of the pulse. A theoretical analysis is developed in the second part of the paper, where the absorption/dispersion features of the medium are calculated.
The chiral medium and its photo-isomerization properties
The medium used in the experiment is a molecular mixture composed of a nematic liquid crystal host (E7) doped with the azobenzene dyes Methyl Red, MR, (0.5% in weight) and the chiral agent CB15 (41% in weight). The chiral mixture is injected between two planar rubbed polyvinyl alcohol(PVA)-coated glass plates with L=25 μm thick spacers. The helical structure of the chiral mixture is perpendicular to the confining walls, is right-handed and has a pitch P ≃ 360 nm. The azobenzene dyes undergo a trans-cis conformational change under irradiation from the UV to green visible light [26, 27]. The configurational change from the trans to the cis state is represented in Fig. 1(a) and corresponds, for instance, to a rotation of one of the central bonds about the double nitrogen bond. An equivalent energy diagram representing the photo-induced isomerization is shown in Fig. 1(b). Trans-cis transformations involve electronic transitions from the ground state to an excited state and occur at a fast rate. After de-excitation, a relaxation process takes place, leading to the cis form, which is metastable and slowly decays to the trans state. The cis-trans relaxation process is characterized by the decay rate Γ. To the extent of orientational order, the trans molecules have an elongated shape and are more effectively oriented along the liquid crystal host molecules than the V-shaped cis isomers. Under light irradiation, the trans-cis equilibrium concentration is altered, hence, the magnitude of the anisotropy of the guest-host system changes [26, 27].
Fig. 1 (a) Molecular structure of the azo-dyes; trans-cis conformational change occurs under light irradiation: in the trans state molecules are aligned along their long axis, in the cis state they are characterized by a V-like shape. (b) Equivalent energy diagram of the trans-cis photo-isomerization: after a fast excitation, molecules decay to the cis state, which is metastable and transforms back to trans with a slow decay rate Γ. (c) Pictorial representation of the azo-dye doped chiral medium : the dyes are represented by red rods (trans state) aligned with the helical structure of the chiral host; in the illuminated region the rods becomes V-shaped (cis state), altering the local order parameter.
The way in which we exploit the trans-cis states of the azo-dye isomers is that, because of the frustration due to the chiral texture, strong liquid crystal reorientations are inhibited. Indeed, chiral liquid crystals are characterized by a self-assembled helical structure of the molecules [28, 29]. The chiral texture, here is used to host the azo-dye molecules and to ensure a long relaxation time of the metastable cis population in the dark [26]. Note that image recording has been demonstrated in azobenzene liquid crystal films [30], where the trans-cis conformational change is at the basis of an order parameter change in the liquid crystalline texture. Azo-dye doped chiral nematics have also, recently, been demonstrated to provide gain for continuous pump and signal in two-wave mixing configuration [31] and phase conjugation and slow-light in four-wave mixing geometries [32], whereas efficient beam-coupling has also been achieved in dye-doped blue phases [33].
Photo-isomerization induced transparency is induced by selective illumination of the azo-dye doped chiral medium. As schematically represented in Fig. 1(c), in the presence of a light intensity distribution, as an interference fringe pattern, a trans - cis population distribution is created in the medium. Indeed, a cis state population is established in the illuminated regions, whereas the dark regions are mainly populated by the trans state. In summary, in the illuminated regions the concentration of the cis isomers is higher because the metastable state is continuously fed by the pump illumination : the dye molecules are excited to the upper state, then, rapidly decay to the cis metastable state, which slowly decay to the trans form. Because decaying to the trans form is slow and molecules are continuously excited, an excess of cis molecules is present in the illuminated regions, while the trans population is larger in the dark regions where the photo-excitation does not occur.
In order to model the photo-isomerization effect, let us consider the dynamics of the trans-cis transition under an uniform illumination of the sample. The density of the cis isomers, denoted by NC, can be described by the rate equation [34]
where I is the total light intensity of frequency ω impinging on the azo-dye doped medium, N is the total density of dye molecules, ΦTC and ΦCT are the quantum efficiencies of the trans⇒cis and cis⇒trans transitions, respectively, σT, σC are the absorption cross sections of the cis and trans isomers, respectively, and Γ is the decay rate for the cis ⇒ trans state in the absence of light, that is, the dark relaxation time of the cis population.The steady state solution of Eq. (1) is
where is the light saturation intensity for which the maximum concentration of NC is achieved. The medium absorption coefficient can be written as and, by replacing the expression for in Eq. (4), we obtain The large dichroism of the dye ensures that the absorption cross sections of the two isomers are quite different. For the azo-dyes used in our sample we typically have σT/σC ∼ 7. Therefore, the second term on the r.h.s. of Eq. (5) is always positive and an increase of the light intensity I produces a corresponding decrease of the light absorption.Moreover, Eq. (1) can be rewritten in the following form
where is the response time of the medium. We see that, in a similar way as the absorption coefficient, the medium response time depends on the light intensity I. The two quantities are, indeed, related to the density of molecules in the cis state. The response time τ has been measured as a function of the light intensity impinging on the medium. The results are plotted in Fig. 2. By fitting the data with Eq. (7), we obtain the saturation intensity ISAT = 0.37 mW / cm2 and the decay rate Γ = 5.29 s−1Fig. 2 Response time τ as a function of the total light intensity I incident on the sample; square: experimental data, line: fit with the theoretical curve.
2. Two-beam coupling experiments: slow and stored light
Slow and stopped light are achieved by performing two-beam coupling experiments. The experimental setup is shown in Fig. 3(a). A pump beam Ep and a pulse signal beam Es, both circularly polarized, are sent to the liquid crystal cell where they create an interference fringe pattern, thus, inducing a trans-cis population grating distribution. ES is time modulated by using an electro-optic modulator (EOM), whereas a shutter is used to switch on/off the pump beam.
Fig. 3 (a) Experimental setup: the pump EP and signal beam ES are produced by a cw solid state laser, λ = 532 nm, and sent to interfere in the dye doped chiral liquid crystal, LC-cell; quarter wave plates (QWP) are used to change the beam polarizations from linear to circular. ES is time modulated by an electro-optic modulator (EOM); a shutter is used to switch on/off the pump. The input ES and output pulse E0 are detected by the photodiodes, PD1 and PD2, respectively. (b) Experimental temporal traces of the input (blue line) and output (red line) pulses recorded for |AP|2 = 2.1 mW / cm2, |AS|2 = 0.1 mW / cm2 and input pulse duration 140 ms. The group delay of the output pulse is 31.3 ms. c) Broadening of the output pulse as a function of the input pulse duration.
The pulse is diffracted by the photo-isomerization grating induced in the medium. The time dependence of the output pulse is recorded by a photodiode (PD2) and compared with that of the input pulse (recorded with PD1.) In Fig. 3(b) the temporal evolutions of the input and output pulse are plotted on the same graph, for a pump intensity |AP|2 = 2.1 mW / cm2 and a signal intensity |AS|2 = 0.1 mW / cm2, where AP and AS are the amplitudes of the pump and signal, respectively. The input pulse width was of 140 ms and a group delay of 31.3 ms was observed for the output pulse. Correspondingly, the achieved group velocity is approximately vg = 0.8 mm/s. For durations of the input pulse shorter than 60 ms, we observe a broadening of the output pulse due to the frequency bandwidth of the photo-isomerization induced transparency window. The effective broadening is illustrated in Fig. 3(c), where the ratio of the output to the input pulse duration is plotted versus the input pulse duration.
To demonstrate the ability of the system to perform pulse storage and retrieval, the pump beam is turned off when the input pulse traverses the medium and then is turned on at a later time by using a shutter triggered by the input signal pulse. Plots of the measured input and output pulse intensities are presented in Fig. 4 for increasing values of the storage time during which the pump beam is off. The input pulse width is 20 ms. The switch-off time of the pump is about 20 ms after the maximum of the input pulse. This time-lag optimizes the maximum storage time, since it corresponds to the delay time provided by the slow-light effect, hence, ensures a maximum mapping of the input pulse onto the corresponding cis population created in the medium. The maximum achieved storage time, at which a significant output pulse is still retrieved, is about 160 ms. A magnification of the output pulse retrieved after 160 ms is shown in the inset of Fig. 4.
Fig. 4 Light storage: the output pulse is recovered after switching off the pump (dashed line); the off time is increased from bottom to top; the blue line is the input signal pulse, the red line is the output pulse. In the inset is shown a magnification of the output pulse stored and retrieved after 160 ms. The input pulse width is 20 ms.
The retrieval efficiency is plotted in Fig. 5 versus the storage time. For comparison, on the same graph it is also shown the retrieval efficiency obtained with an azo-dye doped non-chiral nematic cell under similar experimental conditions. In both cases, the storage time is normalized to the medium response time τ. It can be seen that when the azo-dyes are hosted by the chiral structure, the maximum storage time at which the pulse can be retrieved goes well beyond the response time of the cell (about a factor of 7). On the other hand, when the same dyes are hosted in a non-chiral nematic the storage time remains below the response time of the cell.
Fig. 5 Signal retrieval efficiency η = |A0|2/|AS|2 versus the storage time normalised to the medium response time τ; the efficiency of the dye-doped chiral (red circles) and non-chiral (blue circles) liquid crystal, LC, cell are compared.
Theoretical analysis
In order to model the two-beam coupling and associated slow light effects, we extend the model of the trans-cis dynamics to the case when the sample is illuminated by a spatially sinusoidal distribution of intensity. Briefly, we can consider that the total optical field incident on the medium is of the form
where AP and AS are the amplitude of the pump and, respectively, the signal beam, and the total light intensity illuminating the medium is given by the interference of the two beams where Im = |AP|2 + |AS|2 is the average light intensity and Δ = ωP −ωS is the frequency detuning between pump and signal. In our experiment, the pump and signal intensities are typically set at IP = |AP|2 = 2 mW / cm2 and IS = |AS|2 = 0.1 mW / cm2. Under these conditions, Im ≃ IP and |APAS| ≪ Im. Therefore, a solution for the rate equation, Eq(1), can be found where is the uniform value calculated before, Eq. (2), and is a complex number, with , describing the amplitude of the population grating. Under this assumption, we find for the solution [34] which strongly depends on the frequency detuning Δ. Correspondingly, the absorption can be written as and, by replacing Eqs. (2,11) in Eq. (12), we obtain the solution for α where the first term describes the uniform absorption and is the amplitude of the photo-induced grating, with the phase shift due to the non instantaneous response of the photo-isomerization process. Because the thickness L of the medium is smaller than the spatial period of the light interference pattern, the output scattered beam is under the Raman-Nath regime of diffraction and the total output field amplitude can be expressed as In the experiment, the output amplitude E0 is detected on the first diffracted order of the pump. By developing the output field, Eq. (16), in power series of modified Bessel functions and by considering that x ≡ |δαL| ≪ 1, we can use the following approximations: I0(x) ≃ 1, I1(x) ≃ x/2 and I2(x) ≃ 0, where In(x) is the modified Bessel function of order n, and obtain where k0 = 2kP − kS, ω0 = ωP + Δ and the equivalent absorption for the output detected intensity |E0|2 is with the output phase shift.The result for the calculated cis state density, Eq. (10) is shown in Fig. 6(a), where a strong dependency on the frequency detuning can be appreciated. Correspondingly, the medium absorption α0, expressed by Eq. (18), is characterized by a narrow transparency window around Δ = 0. The theoretical curve is displayed in Fig. 6(b) together with the experimental data obtained by measuring the medium absorption around resonance. While the pump detuning is varied by using an electro-optic modulator, the output signal intensity is recorded with a photodiode. The data and the theoretical curve show a good agreement. The associated phase change φ0 is shown in Fig. 6(c) and is very sharp at resonance. The group velocity can, then, be calculated as
from which we get the expression By using parameter values consistent with the typical characteristics of the azo-dyes, we calculate a minimal group velocity of vg = 0.8 mm/s, which occurs for Δ = 0. By considering the thickness of the medium, at this group velocity corresponds a group delay L/vg ≃ 31.25 ms, in agreement with the maximum group delay observed experimentally.Fig. 6 (a) Theoretically predicted variation of the cis state molecule concentration versus the frequency detuning Δ. The parameters used in the calculation are: ΦTC = 0.25, ΦCT = 0.4, Γ = 5.29 s−1, σT/σC = 7. (b) Corresponding absorption as a function of the frequency detuning; the black squares are experimental data, the continuous line is the theoretical curve. (c) Theoretically calculated phase shift as function of frequency detuning.
3. Conclusion
In conclusion, we have shown that slow and stopped light can be efficiently achieved through a new mechanism that is based on light induced photo-isomerization of azo-dye molecules hosted in a chiral liquid crystal medium. The photo-isomerization induced transparency, in analogy with EIT, provides a transparency window that can be exploited to slow-down and store light pulses. We have also shown that, while slow-light effects can be obtained even when the host is a non-chiral nematic, the storage effect is essentially related to the chiral structure of the liquid crystal host, which frustrates reorientational phenomena, hence, privileging the trans-cis population dynamics of the azo-dyes. In these conditions, the storage time becomes larger than the medium response time, since it becomes dictated by the long dark relaxation time of the metastable cis population to the trans ground state.
Acknowledgments
We acknowledge A. Iljin and Z. Cai for helpful discussions. D. Wei acknowledges financial support from the China Scholarship Council. We acknowledge financial support of the ANR international program, Project No. ANR-2010-INTB-402-02 ( ANR-CONICYT39), “COLORS”.
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