1. Introduction

The diffusion and transport of light waves in complex dielectric structures have spurred a vast range of experimental and theoretical work, revealing one of the most challenging and exciting scientific area of the past decade. The propagation of electromagnetic waves in periodically structured dielectric systems, i.e. photonic bandgap materials, and the linear and non linear optical phenomena in completely disordered systems doped with gain media represent two opposite sides of this promising scientific branch. The literature demonstrates that much has been done in these extreme areas, but the huge intermediate world constituted by the partially ordered systems still remains almost unexplored. The laser emission study in ordered and periodic systems has known an extraordinary revival in the last years; even because of the remarkable development of experimental techniques which allow to scale the photonic crystal structures down to the nanoscale with the aim to mould the flow of light [1]. Surprisingly, active random media repeatedly proved to be suitable for obtaining diffusive laser action, mainly based on the resonant feedback mechanisms in multiple scattering. Light localization and interference effects which survive to multiple scattering events have been invoked to explain the random lasing observed in many exotic and complex systems [2–9]. In fact, when the diffusive photon transport in completely disordered systems encounters the condition kl_t~ 1, being k is the magnitude of the local wave vector and l_t is the transport mean free path, an almost complete localization of light waves should occur. This effect is known as Anderson localization in analogy with the diffusion behaviour of electrons in some conductor lattices [10].

Weak localization of light waves is considered as a particular case of interference effects which were predicted and observed in random media and in partially ordered systems for kl_t > 1 [11–17]. Recently, coherent backscattering experiments performed with high accuracy apparatus manifested weak localization of light even in tensorial systems characterized by high optical anisotropy, like nematic liquid crystals [18]. These experiments show how the recurrent multiple scattering events exactly back enhance the scattered intensity giving rise to an anisotropic backscattering cone [19].

Nematic liquid crystals (NLC) are uniaxial fluids with rod-like molecules aligned on average along a local anisotropy axis which is represented by the unit vector n(r,t), the molecular director.

The spontaneous fluctuations of the director represented by n(r, t) = n ₀ + δn(r, t) leads to fluctuations in the local dielectric tensor ε_α,β = ε⊥δ_αβ + (ε_∥ -ε _⊥)n_α n_β which is the main effect responsible of the recurrent multiple scattering events as a light wave is propagating through the NLC medium. The scattering of visible light by NLC is higher, by a factor of the order of 10⁶, than the scattering by conventional isotropic fluids [20]. The fluctuations of ε_αβ come from two different sources: (1) fluctuations in ε _⊥ and ε_∥ due to small, local, changes in the density, temperature, etc.; (2) fluctuations in the orientation of n, this is the dominant effect which is specific of nematic liquid crystals. When the scattering is increased beyond a critical value, the system makes a transition in a localized state, where light propagation is inhibited owing to interference in multiple scattering. The weak localization of light in an amplifying scattering medium supports stimulated emission through resonant and nonresonant optical feedback. Such laser action is usually called diffusive or random lasing. In this letter, we mainly consider the multiple scattering of spontaneously emitted photons within the gain medium. These photons are characterized by different initial states of polarization which does not depend on the excitation polarization. The polarization of the excitation pulses and the scattering intensity is considered only in terms of quantum yields and photons available to be radiated into the lasing modes.

Here we report the first experimental observation of random laser action in a partially ordered and highly anisotropic NLC doped with fluorescent guest molecules. The study of laser emission in such system emphasizes the peculiar behaviour of diffusive laser action, randomness of laser emission was observed in time, space and frequency. In fact, the spatial distribution of the emitted light is speckle-like accompanied by strong intensity fluctuations and slight shifts of the resonant peaks occur for each pump pulse. The random laser relevant length scales, i.e. the scattering mean path length l, the gain length lg, and the sample size are found to be in good agreement with the random laser theory. In fact, the gain length at the onset of lasing is lg ~ V ^2/3/l -3.5 × 10^-2 mm, is in reasonable agreement with the value found experimentally at the lasing threshold pump intensity (4.4 × 10^-2 mm). In addition, the scattering mean path length was measured to be about an order of magnitude longer than the gain length providing ample opportunities to trigger the lasing effect.

2. Experimental

The nematic liquid crystal, BL001 provided by Merck, having the following bulk phase sequence Cr. - -10°C - Nematic - 63°C - Iso was doped with 0.3 wt% of Pyrromethene 597 dye (Exciton). The mixture was confined in a wedge cell constituted by two glass-ITO plates separated by Mylar spacers, with a thickness of 100 μm at one edge and 1.5 μm at the other one. The inner side of the plates were covered with rubbed polyimide alignment layers in order to induce a homogeneous alignment of the NLC molecules at the interface. Then, the wedge cell was filled by capillarity with the flow direction along the rubbing direction and normal with respect to the wedge. Upon observing the sample under a polarized microscope, it shows a planar alignment with the optical axis which lies in the plane of the cell parallel to the rubbing direction. The pyrromethene dye molecules dissolved in the NLC at very low concentration (0.3–0.5% by wt), proved to be completely miscible as evidenced by the almost complete absence of micro-droplets of dye embedded in the nematic phase. The wedge sample was optically pumped with 3–5 ns pulses produced by a frequency-doubled (532 nm) Nd:YAG laser (NewWave, Tempest 20). The pump beam was focused onto the thick region of the sample (about 100 μm) with a spherical lens (f = 100 mm) yielding a beam waist of about 30 μm at the focus position. The experimental set-up (see Fig. 1) presents a combination of optical elements (quarter-wave plates, half-wave plates and Glan-Thompson polarizers) in order to select all the states of polarization of the pump beam. A multichannel CCD spectrometer with a high spectral resolution (0.5 nm) and with a fiber termination was used to capture the emission spectra within a limited cone angle of 0.05 rad. The speckle-like pattern of the emission spot was imaged on a screen while simultaneously the emission spectrum was captured by means of the CCD spectrometer (see Fig. 1).

At low pump power, the emission spectra show the typical spontaneous emission curve of pyrromethene dye, indicating that NLC does not considerably modify the fluorescence spectrum (Fig. 2). Upon increasing the pump power above a given threshold value (about 900 nJ/pulse), discrete sharp peaks emerge from the residual fluorescent spectrum and the output energy was found to be about 150 nJ/pulse at room temperature. The line width of these sharp peaks were less than 0.5 nm, yielding a quality factor Q of this random cavities larger than 1000. When the incident pump energy exceeds the threshold value, the peak intensity increases much more rapidly with the pump power and more sharp peaks appear, because now the balance gain-loss of these lossiest modes become positive (see Fig. 2). Hence, diffusive lasing occurs in dye doped nematics by recurrent light scattering and the lasing frequencies are determined by phase relationship of the counter-propagating scattered light waves. In fact, the weak localization of light waves owing to the strong optical scattering gives rise to reciprocal paths within the gain medium.

 

Fig. 1. Schematic diagram of the experimental set-up: the picture shows the pump beam and the diffusive laser emission projected on the screen. Recurrent multiple light scattering in dye doped nematics provides the feedback for laser oscillations.

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When the phase accumulation in reciprocal path is equal, constructive interference occurs among the backscattered amplitudes. Therefore, we do believe that blue shift of the laser emission with respect to the fluorescence maximum is determined by interference effects which introduce coherence and feedback, leading to lasing action.

The inset of Fig. 2 shows the dependence of lasing intensity as a function of the orientation of the linear state of polarization of the pump beam. The lasing intensity undergoes a five-fold lowering when the pump light is polarized perpendicularly to the NLC director (o-wave) compared with the light polarized parallel to the director (e-wave). The polarization dependence of the scattering intensity and the coupling of the optical field with the gain medium have to be taken into account for the observed anisotropy. The former effect is mainly due to polarization dependence of the diffusion constant D for the emitted photons, indeed a larger diffusion constant for the e-wave compared to the o-wave is generally measured. The latter aspect can be analyzed by considering the Fermi’s Golden Rule which clearly states that the molecular transitions and the rate of emission strongly depend by the coupling of the pump electric field E and the transition dipole moment d of the dye molecules.

 

Fig. 2. Fluorescence and lasing spectra are reported. Discrete sharp peaks emerge from the residual spontaneous emission for pump energy of about 1.2 μJ/pulse. The inset shows the dependence of the lasing intensity on the angle θ between the linearly polarized light and the local nematic director orientation.

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Thus, these processes are governed by the projection E ∙ d. In addition, the experimental results emphasize that the fluorescent molecules adopt to some degree the local nematic order of the liquid crystal solvent, which results in an anisotropic orientational distribution of the transition dipole moment. In fact, polarized fluorescence measurements emphasize a strong dependence of the emission intensity on the pump polarization, as it is shown in the polar plot of Fig. 3.

It is worth to point out that the maximum of the lasing intensity was obtained for linearly polarized pump pulses with E oriented along the local director (θ =0°), being in good agreement with the polarized fluorescence results as well as the polarization dependence of the scattering intensity. This indicates that the dye molecules possess an anisotropic orientational distribution of the transition dipole moments along the local nematic director, with a dye order parameter S_D = 0.2 calculated as follows [21]:

Here F_∥ and F_⊥ are fluorescence intensities polarized parallel and perpendicular to the NLC director, respectively. Therefore, this confirms that the dipolar coupling modifies the quantum yield for fluorescence and plays an important role for the light amplification process; some states of polarization of the pump pulses provide a larger number of spontaneously emitted photons which are radiated in the lasing modes.

 

Fig. 3. Polar plot of the polarized fluorescence of the dye doped nematic sample. It is obtained by measuring the fluorescence intensity by analyzing the polarized emission at different angles about the local nematic director.

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Finally, in order to gain further understanding on the diffusive laser action observed in this partially ordered system, a comparative study of the emission properties of systems with different order degree was performed. We investigated the input-output characteristics and evaluated the β-factor of the following systems: 1) self-ordered dye doped helixed liquid crystals confined in conventional sandwich cell [22–26]; 2) laser dye solution containing ZnO nanoparticles [27]; 3) dye doped nematic liquid crystal confined in a wedge cell. While the first two systems have been widely investigated showing a lasing action with a well known input-output behaviour, the unexplored presented system presents a peculiar intermediate behaviour. In a conventional laser, β is defined as the ratio of the rate of spontaneous emission into the lasing modes to the total rate of spontaneous emission (0 ≤ β ≤ 1) , and determines the sharpness of the laser threshold [28]. In the science of cavity laser this parameter is of great interest because of the promise of “thresholdless laser” with β=1, in which all the spontaneous emission is radiated into the lasing modes. In figure 4 is reported the integrated emission intensity in function of the pump energy for the investigated systems characterized by different order degree. Unlike the sharpness of the lasing threshold observed in the self-ordered cholesteric cells (β ~ 0.01), in which a super-linear increase of the emission intensity is measured above the threshold, the input-output curve measured in the random medium shows a stretched-exponential behaviour characterized by β ~ 0.2. The partially ordered nematic sample shows a behaviour intermediate between these two extremes. In fact, the output energy increases almost exponentially with the pump power (β ~ 0.08). The presented behaviour suggests that a large part of the spontaneous emission is radiated into the lasing modes by of the optical feedback provided by the anisotropic coherent backscattering. Interestingly, upon increasing the temperature of the sample, the diminished nematic order parameter results in a smoother lasing threshold, approaching indeed the random system behaviour. Anyway, a detailed study of the aforementioned effect will be reported elsewhere.

 

Fig. 4. Light input-output curves for systems with different order degree are reported. The emission rate of ordered dye doped cholesterics with a periodic helical structure, disordered nanoparticles of ZnO dissolved in methanol solution and partially ordered nematic liquid crystals are compared.

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3. Conclusion

In conclusion, random laser action in highly anisotropic and partially ordered NLC has been observed. The underlying mechanism is mainly based on interference effects which survive to recurrent multiple scattering driven by nematic director fluctuations. Coherent backscattering experiments performed on similar systems have already proven that interference effects leads to weak localization of light waves [14]. Weakly localized light waves into dye doped nematic sample are responsible for amplification while the resonance frequencies are selected through interference phenomena of the counter-propagating light waves within the localized loops. For the sake of simplify, photons spontaneously emitted by the fluorescent guest molecules are launched at random directions from random positions within the excited volume. Because of the recurrent multiple scattering the probability to trace reciprocal paths by these photons is not null, as demonstrated by coherent backscattering experiments, thus resulting in equal phase accumulation during these open loops. Being the gain length comparable with the transport mean free path the emission of other photons is stimulated before the recurrently scattered photons leave the sample, triggering a coherent chain reaction. When the balance gain-loss becomes positive the optically excited dye doped nematic start to lase. Unlike distributed feedback mirror-less laser, this system can be considered as a cavity-less microlaser where the disorder unexpectedly plays the most important role, behaving as randomly distributed feedback laser. We found that the dye transition dipole moments adopt in some degree the orientational order parameter of the nematic director, resulting in a control of the emission intensity by varying the polarization of the pump beam. In addition, the evaluated β-factor for the presented system yields an intermediate value with respect to the random and fully ordered systems, suggesting that the order parameter drives the amount of spontaneous emission radiated into the lasing modes. Many further studies will be needed in order to gain full understandings of the diffusive laser action in nematic samples, indeed a wide series of experiments, simulations and extensive investigations have been planned. The aim of this letter is to report the experimental evidence of random lasing in nematics in order to enlighten the intriguing world of the partially ordered systems, and its peculiar emission properties when doped with gain media. Clearly, this could represent an exceptionally promising route for fundamental prospective studies with strong technological implications for integrated optical systems, nanophotonic and optoelectronic fields.