All-optical guided-wave random laser in nematic liquid crystals

Spatial solitons can affect and enhance random lasing in optically-pumped dyedoped nematic liquid crystals. Upon launching two collinear beams in the sample, the first to pump the fluorescent guest molecules and the second to induce a reorientational soliton, strikingly the second beam not only guides the emitted photons in the soliton waveguide, but also enhances the lasing efficiency and modulates its spectral width. By altering the scattering paths of the emitted photons, the soliton also contributes to the selection of the lasing modes, as further confirmed by the observed kinks in the input/output characteristics. These experimental results demonstrate that random lasing can be efficiently controlled by a light beam which does not interact with the gain molecules, opening a route towards light-controlled random lasers. c © 2017 Optical Society of America OCIS codes: (190.5940) Self-action effects; (190.6135) Spatial solitons; (160.3380) Laser materials; (160.3710) Liquid


Introduction
Random lasing occurs when disorder in an optically amplifying medium provides multiple scattering events for emitted light, such that the resulting photon paths allow for amplification and stimulated emission, even in the absence of an actual cavity [1]. Since its prediction [2] and the first experimental demonstration [3], several efforts were devoted to obtaining random lasing (RL), foreseeing the development of low cost coherent sources [4]. To achieve random lasing, the significant scattering required from the active medium or the host was obtained in powders [3,5,6], optical fibers [7], biological tissues [8] and liquid crystals [9][10][11]. At the same time, the strong dependence of RL emission on environmental parameters offered unprecedented opportunities to tune the lasing properties through, e.g., temperature control [12], concentration of active molecules in host materials [13], grain size in powder systems [14], bias voltage [11,15], spatial profile of the pump beam [6,16]. By acting on the favoured scattering paths (equivalent to tuning the cavity in standard lasers), it was possible to select lasing modes [17,18] and lock them [19].
Liquid crystals are mesophases possessing a finite degree of positional and/or orientational order, due to their relatively weak intermolecular links [20]. In the nematic phase the positional order is negligible, while the long axes of the oriented molecules are aligned in an average direction, termed molecular director n and corresponding to the optic axis of the macroscopic uniaxial material [21]. RL can be obtained in nematic liquid crystals (NLC) by doping them with a pump-resonant active dye, as demonstrated in various systems [9,22]. The director distribution in NLC can be adjusted by the application of electric fields [15], making them excellent candidates for the tuning of random lasers. Another important property of NLC is their nonlinear optical response, with a dominant contribution from molecular reorientation through the torque provided by the electric field of light on the dipoles induced in the elongated molecules. When all-optical reorientation is produced by a finite size beam, the corresponding increase in refractive index for extraordinarily polarized waves leads to self-focusing and eventually self-confinement, with the propagation of an optical spatial soliton and the formation of a light-induced waveguide [23]. Spatial solitons and their control in nematic liquid crystals ("nematicons") have been extensively reported in the past two decades [23][24][25][26][27][28][29][30][31]; they form when a finite beam produces a graded director distribution and refractive index profile with self-focusing balancing out linear diffraction [23]. Such light-induced waveguides can confine co-polarized signals at other wavelengths [27], as well as light emitted through fluorescence or spontaneous emission [31][32][33]; moreover, distinct regimes allow for the effective synergy of diverse nonlinear responses in NLC and their mutual control in the presence of solitons [34][35][36]. In this work we control the RL emission of a planar dye-doped NLC sample exploiting all-optical reorientation to launch a soliton at a wavelength well removed from the guest-host absorption resonance. We demonstrate that, in analogy to other guiding geometries [37], the light-induced waveguide associated to a soliton can confine the emitted photons in the extraordinary polarization [33,38], enhancing the overall lasing efficiency. This approach to random lasing, combining a resonant light-matter interaction between the pump and the guest-host with a non-resonant one supporting beam self-confinement via reorientation, can be exploited for a novel generation of controllable cavity-less lasers.  The sample we used in the experiments, sketched in Fig. 1(a) and similar to that previously used, e.g., in [24,33,38], consists of two parallel glass slides separated by Mylar spacers, surface treated with polyimide to favor the NLC alignment at θ = ∠nẑ = π/4, thus maximizing the birefringent walkoff of the equivalent uniaxial and the nonlinearity experienced by an extraordinary -wave (e-) beam propagating with k parallel toẑ [30]. Two other thinner glass interfaces perpendicular to z seal the cell and provide anchoring with n parallel to y in order to optimize the coupling of radiation (input laser beam) into the extraordinary wave [24]. The cell is infiltrated by capillarity with a mixture of the commercial E7 NLC with a 0.3wt% of Pyrromethene dye (PM597). The latter dye is based on the fluoroboration of two pyrrole rings linked by a conjugated π-system chain, yielding the dipyrromethene-BF2 complexes also known as cyclic cyanine dyes; it has a fluorescence quantum yield approaching unity and can lase more efficiently than other common dyes such as rhodamine, also because of the low T-T absorption capacity over the lasing spectrum [9,39]. A similar mixture, with absorption peaked around 530nm, has been demonstrated to random lase in various configurations (wedge cells, drops, capillaries) and allow for temperature tuning [9,22,40]. It has been proven that the opticallyinduced molecular reorientation for wavelengths out of the dye absorption band is not affected by such a low concentration of fluorescent guest molecules in the nematic host [41]. Thus, PM597-E7 is an excellent guest-host system to investigate the interplay between the pumping beam and the reorienting beam for conveying all-optically controlled random laser emission.

Experimental setup and sample characterization
We employed two laser beams of different intensities and wavelengths to independently excite the two nonlinear mechanisms, namely fluorescence/lasing and reorientation, focusing them at the cell entrance through a microscope objective and additional optics to obtain comparable waists w 0 ≈ 4μm at the input facet. A microscope imaged the out-of-plane scattered light into a CCD camera, allowing for the acquisition of beam evolution in the principal propagation plane yz. At the output, a spectrometer equipped with a 100μm-core multimode fiber and a 100μm slit collected the emitted light and acquired the spectra. A continuous-wave near-infrared (NIR) y-polarized Gaussian beam at λ = 1.064μm was launched in the cell to excite a nematicon at powers P > 2mW, propagating with a transverse angular velocity (walkoff) δ = arctan[ a sin 2θ/( a + 2n 2 ⊥ + a cos 2θ)] with respect to the wavevector (k parallel toẑ) [24], according to the initial director alignment, with a = n 2 − n 2 ⊥ > 0 the optical anisotropy (n and n ⊥ being the refractive indices for fields parallel and orthogonal to the optic axis, respectively). We generated fluorescence and RL emission with a frequency-doubled Q-switched 6ns-pulse Nd:YAG source at wavelength 532nm and 20Hz repetition rate.  (d-f) Same as (a-c), but for P NIR = 6mW: the NIR-induced confinement enhances RL, with a higher gain accompanied by spectral narrowing. (g-i) Same as (a-c), for P NIR = 14mW: the spectra further narrow down and a kink appears in the input/output characteristic (g). Narrower profiles in (c)-(f)-(i) correspond to increasing pump energies.
The spectra obtained by pumping the material (in the absence of a NIR nematicon) with either k alongx (transverse geometry) or k parallel toẑ in the yz plane (principal plane of the NIR beam) exhibited RL emission peaked around 576nm, non-collinear to the pump beam owing to the optical anisotropy and to the randomness of the resonant feedback [9,15]. Since material anisotropy affects both the lasing efficiency and the emission polarization [15,42], the emitted light was an e-wave in the plane nẑ ≡ŷẑ despite the pump polarization, whereas the emission efficiency was maximum for a pump x-polarized perpendicular to the director, as previously reported in [38] but at variance with [9]. This polarization dependence suggests that the combined action of the two beams can yield efficient RL for an ordinary-wave (o-) pump collinear with the e-wave soliton ( Fig. 1(b), right), allowing the latter to confine the emitted light in the waveguide region if a suitable input tilt compensates for the limited beam overlap due to the angular walkoff of the soliton. The alternative configuration, an e-pump collinear with and confined by the e-soliton ( Fig. 1(b),left), would maximize the overlap of pump and fluorescence in the nematicon region, but at the expenses of the resulting emission. Figure 1(c) shows the acquired pictures of (top) the emitted (green-yellow) photons, (middle) the NIR beam featuring self-confinement and (bottom) the emitted (y-polarized) photons guided by the nematicon waveguide.

Results and discussion
As described above, we co-launched two co-planar beams sharing one and the same direction of their Poynting vectors in the medium, an ordinary (o-) polarized pump (visible) and an e-wave nematicon (NIR), adjusting their waists and tilt in order to maximize the overlap between the emitted fluorescent light and the green pump within the graded-index waveguide formed by the NIR soliton. As we demonstrated earlier [38], light-induced reorientation alters the scattering paths of the emission and limits diffraction, beneficially affecting the random lasing characteristics. Typical emission spectra of the emitted light (single realizations) below and above lasing threshold are shown in Fig. 2 with and without the presence of a NIR nematicon collinear with the o-pump beam. To gain a better insight on the phenomenon, we acquired the input/output characteristics as well as the output spectra of the generated radiation as we varied both the pump pulse energy and the soliton power, as shown in Fig. 3 after averaging over numerous (> 60) pulse realizations and employing a spectrometer with limited resolution (≈nm) in order to present and compare smooth (realization-independent) profiles. As a result, Fig. 3 the FWHM values are overestimated.
For P NIR = 2mW nonlinear reorientation gives rise to an NIR spatial soliton but contributes negligibly to the overall RL performance, as apparent in Figs. 3(a)-(c): the RL spectra without (not shown) and with the nematicon exhibit marginal differences. Things change when the soliton power increases as, e.g., for P NIR = 6mW (Figs. 3(d)-(f)): soliton induced reorientation features a higher RL efficiency and lowers the β-factor (Fig. 3(d)), with a moderate narrowing of the emission spectra as compared to the bulk case without nematicon (Figs. 3(e)-(f)).
Further increases in soliton power allow to access a the RL regime illustrated, e.g., in Fig.  3(g): for P NIR = 14mW the input/output curve above threshold initially exhibits a higher gain, later followed by a reduced slope at energies above E k ≈ 1.25μJ where a "kink" appears. Consistently with similar effects observed in other random lasing systems [43,44], this behavior can be attributed to the interaction/competition of several lasing modes in the large interaction volume defined by the cell length L, with a resulting saturation of the laser gain. Figure 4 collates RL input/output curves versus pump energy for various NIR soliton powers, up to P NIR = 18mW; at powers of 18mW and higher, nematicons tend to become less stable and exhibit trajectory fluctuations in the transverse plane. It is apparent that, although soliton-driven reorientation does not affect the RL threshold energy E th ≈ 0.7μJ, the transition to lasing gets sharper and the slope of the laser intensity versus pump energy/pulse initially increases with P NIR . The corresponding enhancement factors β, calculated from the emission spectra before (fluorescence) and after (RL) threshold at a pump energy E = 1μJ according to [45], are indicated in the legend for various nematicon powers. Surprisingly, the kink remains approximately positioned at E k ≈ 1.25μJ and it only appears in the presence of the nematicon, which is likely  to trigger a more efficient mode selection. A quantitative estimate of the interaction between the emitted photons and the pump, various scattering paths and their modulation by soliton reorientation, are beyond the scopes of this paper and will be discussed in future work together with a suitable model. Figure 5 illustrates the role of nematicons on random lasing, graphing RL spectra for various nematicon powers, as well as the corresponding FWHM and the peak emitted intensities (as acquired by the spectrometer). At a pump energy E ≈ 0.66μJ (Figs. 5(a) and 5(b)), below lasing threshold, the presence of a soliton collinear with the pump does not produce dramatic changes, with a moderate enhancement G = I P Ma x I P=0 ≈ 2 due to improved photon collection and a spectral narrowing > 0.25, as visible in Fig. 5(b). At energy E =≈ 1.0μJ (Figs. 5(c) and 5(d)), just above RL threshold, the gain enhancement is G ≈ 5 with narrowing S n ≈ 0.62, i.e., FWHM dropping from 24 to 9nm. Finally, at energy E = 1.53μJ above E k (Figs. 5(e) and 5(f)), G ≈ 8 with S n ≈ 0.55.

Conclusions
We experimentally investigated the interaction between two nonlinear effects occurring in dye-doped nematic liquid crystals, namely random lasing in scattering media and beam selfconfinement via a Kerr-like all-optical response. We demonstrated that an optical spatial soliton is able to modify the lasing properties of the strongly scattering random medium, altering the scattering paths and the resulting feedback available in the interaction volume. RL emission is assisted and enhanced by solitons through both light guiding and scattering modulation, resulting in gain enhancement, spectral narrowing and reduction in β-factor, mode selection and, eventually, kinks in the input/output characteristic. This report introduces a guest-host system where a passive nonlinear response (beam self-focusing and self-trapping) acts in synergy with an active mechanism (optical gain and laser action) to yield all-optical control of random las- (a) Emission spectra for nematicon powers from P NIR = 0mW (broadest) to P NIR = 18mW (narrowest) and (b) corresponding FWHM (circles) and peak emission intensity (squares) versus soliton power P NIR , for a pump energy E = 0.66μJ below threshold. (c-d) As in (a-b) but for E = 1μJ, above threshold.
(e-f) As in (a-b) or E = 1.53μJ, above the kink in Fig. 4.
ing in the presence of strong disorder. Among the several advantages illustrated above with these preliminary data, we pinpoint light-controlled emission using beams of different wavelengths and intensities, an extended interaction volume with a large number of lasing modes, power-controlled gain enhancement as well as spectral narrowing. Such features are promising towards the implementation of nonlinearly adjusted light sources and processors.