Laser Action in Dye Doped Liquid Crystals:. from Periodic Structures to Random Media

October 26, 2009 14:43 WSPC/145-JNOPM 00472

Journal of Nonlinear Optical Physics & MaterialsVol. 18, No. 3 (2009) 349–365c© World Scientific Publishing Company

LASER ACTION IN DYE DOPED LIQUID CRYSTALS: FROMPERIODIC STRUCTURES TO RANDOM MEDIA

A. DE LUCA∗,‡, V. BARNA†, S. FERJANI∗, R. CAPUTO∗, C. VERSACE∗,N. SCARAMUZZA∗, R. BARTOLINO∗, C. UMETON∗ and G. STRANGI∗

∗LICRYL CNR-INFM and Center of Excellence CEMIF.CALDepartment of Physics, University of Calabria, I-87036 Rende (CS), Italy

†Faculty of Physics, University of Bucharest, PO Box Mg-11, 077125Bucharest, Magurele, Romania

‡[email protected]

Received 7 August 2009

The birefringence and natural ability to form periodic structures make cholesteric liquidcrystalline (CLC — chiral nematics) materials particularly attractive as 1D photonicband gap systems. If a CLC is doped with dye fluorescent molecules, in such a way thatthe maximum peak of fluorescence matches one of the edges of the selective stop band,laser action is expected at that spectral position. By confining the helical super-structureof chiral liquid crystals in polymeric micro-cavity channels, a tunable microcavity laserarray was achieved. In multiple scattering systems, the propagation of the light wavesis quite different, as optical scattering may induce a phase transition in the photontransport behavior. Beyond a critical scattering level, the system makes a transitioninto a strongly localized state and light transmission is inhibited. This effect can be usedas a photon trapping mechanism to obtain laser action in the presence of a gain medium.Random lasing modes come from interference effects which survive in disordered systemsand open a particular chapter in the study of the interplay between localization andamplification. Here, experiments performed on systems having different order degreeand confinement are presented and possible technological implications are discussed.

Keywords: Laser action; liquid crystals; periodic structures; random media.

1. Introduction

The diffusion and transport of light waves in complex dielectric structures haveencouraged a wide number of experimental and theoretical investigations, revealingone of the most challenging and exciting scientific areas of the past decade. Thepropagation of electromagnetic waves in periodically structured dielectric systemsand the linear and non linear optical phenomena in completely disordered systemsdoped with gain media represent two opposite sides of this promising scientificbranch. The literature demonstrates that much has been done in these extremeareas, but the huge intermediate world constituted by the partially ordered systemsstill remains almost unexplored. The study of laser emission properties in ordered

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350 A. De Luca et al.

and periodic systems has known an extraordinary revival in the last years; evenbecause of the remarkable development of experimental techniques which allow thedesign of photonic crystal structures whose dimensions fall in the nanoscale range.1

Surprisingly, active random media repeatedly demonstrated to be suitable candi-dates for obtaining diffusive laser action, mainly based on the resonant feedbackmechanisms in multiple scattering, thus eliminating the need for an external cavity,like in the case of regular lasers. Light localization and interference effects which sur-vive the multiple scattering events have been invoked to explain the random lasingobserved in many exotic and complex systems.2–8 The study of laser action extendsfrom periodic highly ordered materials (i.e., photonic crystals) to completely disor-dered systems such as powders, suspensions of microspheres, or strongly scatteringmaterials. Since first proposed by Letokhov9 in 1968, random lasers have been inten-sively studied, both theoretically and experimentally. The arbitrary walk of lightwaves inside random media results in the confinement of light within the material,walk long enough for the amplification to become efficient. Letokhov predicted thatthe combination of multiple scattering and light amplification would lead to a formof laser. In fact, when the diffusive photon transport in completely disordered sys-tems encounters the condition klt ∼ 1 (k being the magnitude of the local wavevector and lt the transport mean free path) an almost complete localization of lightwaves can occur. This effect is known as Anderson localization, by analogy to theelectronic model proposed by Philip W. Anderson in 1958 in the famous article‘Absence of diffusion in certain random lattices’.10 He described the vanishing ofelectron propagation in the regime of very strong multiple scattering due to inter-ference effects in electronic lattices where disorder was introduced as impurities;this concept served as a model for metal-insulator transitions. On the other hand,weak localization of light waves is considered to be a particular case of interferenceeffects, predicted and observed in random media and in partially ordered systemsfor klt > 1 (the Ioffe-Regel criterion for localization).11–15 Indeed, the performedcoherent backscattering experiments demonstrated that interference effects survivethe scattering regime and an enhancement of light intensity in the back directionis observed. This enhancement is called the cone of coherent backscattering anddenotes a marker for the fascinating effect of weak localization of light.10, 16

Cholesteric Liquid Crystals (CLC) possess a helical periodic superstructurewhich provides a 1D spatial modulation of the refractive index.17 These systemsbehave as photonic band gap systems (PBG), i.e., they exhibit a window in theelectromagnetic spectrum where wave propagation is forbidden. This is due to amechanism known in literature as distributed feedback (DFB), and has the con-sequence that the sample behaves as a mirrorless optical resonator. If the CLCmaterial is doped with fluorescent guest molecules, a gain enhancement of the radi-ation propagating in the structure is possible. Kogelnik and Shank18 were the first toreport laser action in mirrorless periodic Bragg DFB structures, while laser actionin chiral liquid crystals was predicted by Goldberg and Schnur.19 On the other


Laser Action in Dye Doped Liquid Crystals 351

hand, Nematic Liquid Crystals (NLC) are uniaxial fluids with rod-like moleculesaligned on average along a local anisotropy axis called molecular director, n(r, t).The spontaneous fluctuations of the director, represented by n(r, t) = n0 + δn(r, t),lead to fluctuations in the local dielectric tensor, εαβ = ε⊥δαβ + (ε‖ − ε⊥)nαnβ

being the main responsible effect for the recurrent multiple scattering events thata light wave experiences while propagating through the NLC medium.20 The scat-tering of visible light by a NLC is higher, by a factor of the order of 106, thanthe scattering by conventional isotropic fluids.17 The fluctuations in the dielectrictensor come from two different sources: (i) fluctuations in ε⊥ and ε‖ due to small,local changes in the density, temperature, etc.; (ii) fluctuations in the orientationof n, this being the dominant effect, which is specific for nematic liquid crystallinematerials. When the scattering is increased beyond a threshold value, the systemmakes a transition into a localized state, where light propagation is inhibited owingto interference in multiple scattering. The weak localization of light in an ampli-fying scattering medium supports stimulated emission through resonant and non-resonant optical feedback. Such a laser action is usually called diffusive or randomlasing.

Here, experimental studies about the synergetic behavior of light entrapmentand gain amplification observed in systems with different order degree, from self-organized periodic structures to scattering disordered media, are reported. In partic-ular, we discuss how the optical feedback needed for laser mode selection processesis provided by the investigated systems. We primarily consider the possibility ofobtaining lasing action in a periodic structure, in particular a POLICRYPS-likegrating.21 The sharp and parallel channels of a POLICRYPS grating can behaveas an array of optical resonators, each of them working as a micro-laser. Then wereport the study of the light emission properties from fiber-like cylindrical micro-cavities hosting helixed liquid crystals doped with fluorescent guest molecules. Thelevel of confinement ensures an increase of the axial resonant cavity length, whilemaintaining a small modal volume. Cylindrical geometry favors the existence ofa very complex structure of the chiral liquid crystal as evidenced by optical andstructural investigations. Furthermore we present a review of the main characteris-tics for the emission properties in systems consisting of partially ordered and highlyanisotropic confined nematic liquid crystals doped with fluorescent guest molecules,for which we recently reported the first experimental observations of a random laseraction.20, 22 The study of the emission properties for the above mentioned systemsemphasizes the peculiar behavior of the diffusive laser action; in particular, ran-domness of laser emission has been observed in time, space and frequency. Thespatial distribution of the emitted light assumes a speckle-like profile accompaniedby strong intensity fluctuations and slight shifts of the resonant peaks occur foreach pump pulse. The random laser relevant length scales (i.e., the scattering meanpath length lt, the gain length lg and the sample size) have been found to be ingood agreement with the random laser theory.



2. Lasing in DFB Periodic Structures: Organic Gratingsand Cylindrical Microcavities

In the last years many efforts have been spent in research for the realization of lasingdevices based on organic systems: good candidate materials for achieving this resultare cholesteric liquid crystals (CLC). It is well-known that CLC materials possessa helical periodic superstructure which provides a 1D spatial modulation of therefractive index.17 Taking into account that a CLC material provides distributedfeedback, a typical geometry for obtaining lasing action in dye-doped CLC materialsis the one reported in Ref. 23 where the CLC is sandwiched between two glass slabswith the helical axis directed perpendicular to them. An issue with chiral liquidcrystals is that the index modulation is low so that, in order to achieve sufficientfeedback, the resonant cavity needs to be long enough to allow a high number ofhelical periods. This is not possible with the typical cells used for the experimentscited above, where typical thickness is of the order of tens of microns and the typicalpitch of CLC helices is of the order of the visible wavelengths.

2.1. POLICRYPS structure

There are many advantages in using POLICRYPS as an host structure for dye-doped CLC helices. The sharp and parallel channels of POLICRYPS can behave asan array of optical resonators, each of them working as a micro-laser. The lengthof the single channel is not limited by the sample geometry, and in principle, thesingle cavity can be several centimetres long, thus allowing thousands of periods forthe CLC helices. At the same time, its volume can be reduced at will by changingthe periodicity of the structure. Optical resonators with these two features presenta high quality factor Q and correspond to very efficient micro-cavity lasers. Suchan array of micro-lasers has been experimentally realized in a POLICRYPS struc-ture.2 A small amount (0.7wt. %) of Irgacure 2100 and Darocur 1173 photoinitiators(1:1 wt. %, Ciba Specialty Chemicals) was used to reinforce the polymeric networkand a 0.09wt. % of Pyrromethene dye (Exciton) was added, which represented thegain medium of our system. Other components were 29.9wt. % BL088 cholestericliquid crystal (Merck), 69.3wt. % of NOA-61 monomer (Norland). The mixture wasintroduced by capillarity between two indium tin oxide (ITO) coated glass platesseparated by 13.5µm thick mylar spacers. The sample was then prepared by follow-ing our typical recipe for obtaining POLICRYPS. The only difference is that thecuring temperature was sensitively higher in order to bring the CLC material in theisotropic phase during curing. At the end of the whole process, an almost completephase separation was obtained, giving rise to helixed liquid crystal channels period-ically separated by polymer walls. A scanning electron microscopy analysis of thesample showed a periodicity of 5 µm with a microcavity width of about 1.5µm. Thesystem was optically pumped with the second harmonic (λ = 532nm) of a Nd:YAGlaser. The laser beam was focused onto the sample by means of a cylindrical lens(f = 100mm) and linearly polarized perpendicularly to the microchannels. The



long axis of the section was oriented perpendicularly to the orientation of the poly-meric walls, therefore, the obtained profile (long axis of approx. 5mm) assured thesimultaneous excitation of multiple microchannels. Above a certain pump power,stimulated emission was achieved emerging from the microcavities in a directionparallel to the glass plates and along the microchannels. At their end, highly sen-sitive emission measurements were performed in a restricted cone angle of about0.1 rad. The sketch in Fig. 1 shows this lasing scenario of the micro-lasers array.The stimulated emission emerging from the microchannels was circularly polariseddemonstrating that the distributed feedback mechanism due to the CLC helices isthe cause of the observed phenomenon.

The dependence of the emission intensity and spectral linewidth (FWHM) onthe input pump energy are reported in Fig. 2.

At low excitation energies, both the emission intensity and the linewidth show aquasilinear dependence on the pump energy. Above a characteristic threshold (thepump energy per excited sample area was about 5 mJ/cm2, which corresponds toabout 25nJ/pulse) the emission intensity suddenly starts to increase nonlinearly.Also, above this energetic pump limit, the emission linewidth breaks off from theprevious trend and begins to significantly decrease. The observed pump energyvalue at which the power explosion and line narrowing effects occur (25 nJ/pulse)is one order of magnitude lower than in the case of conventional dye doped systemspreviously investigated under the same experimental conditions. Further experi-mental studies revealed a couple of striking features for the presented system: thepossibility to tune the lasing wavelength by varying the temperature and to controlthe lasing intensity by applying an electric field perpendicular to the helical axisorientation. These properties were found to be fully reversible, as shown in Ref. 2.

Fig. 1. Sketch of a multilaser array realized in a POLICRYPS grating.



Fig. 2. Emission intensity and line-width dependence on input pump energy. Above the thresholdof 25 nJ/pulse, the reported curves change from initial regimes while lasing occurs.

Fig. 3. Spatial distribution of the laser emission emerging from the mirrorless microcavity laserarray. The periodicity of maximum intensities is 5 µm. This value is in agreement with the tailoreddistance between the polymeric microchannels.

A striking scenario is presented in Fig. 3 showing the spatial distribution ofthe laser emission emerging from the microcavity laser array. A high sensitivityand resolution (1390× 1024 12bit PixelFlyQe by PCO) imaging CCD camera wasemployed in order to check the near-field modal profile of the stimulated emission.The images were acquired by scanning in the proximity of the output edge ofour sample cell, in a direction perpendicular to the micro-channels. The mappedintensity profile hereby obtained indicates that the maxima of lasing intensitieshave a spatial recurrence; the periodicity is found to be about 5µm, a value thatis in perfect agreement with the initial tailoring configuration (i.e., the distance



between the polymeric walls). The LC microchannels act as miniaturised mirror-less laser cavities, where the emitted laser light propagates along the liquid crystalhelical axis, which behaves as a Bragg resonator. This level of integration might leadto new photonic chip architectures and devices, such as zero-threshold microlaser,phased array, discrete cavity solitons, filters, and routers. Furthermore, by tailoringa proper array of electrodes, which enables the application of a local electric field,would give rise to electrically programmable phase holograms with interesting lightpolarisation properties. Then, by including different dyes in neighbour channels,and by using proper micro fibers connected at the exit, the result could be a multi-color microlaser array, with the possibility to control separately the intensity ofeach channel.

2.2. Cylindrical microcavities

We have also studied the light emission properties of novel fiber-like cylindricalmicrocavities hosting helixed liquid crystals doped with fluorescent guest molecules.The level of confinement ensures an increase of the axial resonant cavity length,while maintaining a small modal volume. Cylindrical geometry favors the existenceof a very complex structure of the chiral liquid crystal as evidenced by optical andstructural investigations which will be reported elsewhere. The long-range periodic-ity guarantees an enhancement of distributed feedback mechanism which is behindthe observed axial and radial low-threshold tunable lasing action. The aim of thisstudy was to gain understandings about the role played by the number of helicalperiods, the influence of the CLC bulk volume and different surface treatmentson the quality factor of the periodic mirrorless resonant system. The actual levelof confinement allows us to obtain interesting emission properties: laser action isexhibited both in the axial and radial directions at different spectral positions, indi-cating that waveguide effects are not responsible for the multidirectional emission.A striking point is represented by the spontaneous reconstruction of the helixed liq-uid crystal superstructural configuration inside the cylindrical microcavity, givingrise to a novel three-dimensional (3D) multidirectional lasing system. This com-plex system keeps the advantage of a 3D blue phase-like matrix24 while provid-ing a wider thermal operating range and laser wavelength tunability. The hostingcylindrical microcavities are represented by capillary tubes with various diametervalues ranging from 15 up to 200µm. Several treatments were applied to the innersurface of the cylindrical microcavities in order to induce a privileged molecularalignment. The presented results have been obtained by performing investigationson 20µm diameter polyimide treated cylindrical capillary tubes, since they showedthe strongest surface-liquid crystal interaction. The microstructure was filled bycapillarity with a mixture (M1) of 99.7wt. % BL094 right handed cholesteric liq-uid crystal (Merck) and 0.3wt. % of PM-597 Pyrromethene dye (Exciton). Theconfined cholesteric liquid crystal had a birefringence ∆n = 0.21 and showed anoptical bandgap spanning from 525 to 585nm. The high efficiency region of the



dye fluorescence spectrum and the red-edge stop band of BL094 present very closespectral positions (580 and 585nm) which maximizes the gain. Since this spectraloverlapping could present the inconvenient of confusing the eventual amplified spon-taneous emission effect with laser action, a second mixture (M2) was prepared byadding a small percentage of BL001 nematic liquid crystal (Merck). As a result, thelow-energy band edge red-shifted to 607nm. The cylindrical microcavity was opti-cally pumped (Fig. 4) with 3 ns pulses produced by a frequency-doubled (532 nm)Nd:YAG laser (NewWave, Tempest 20). The pump beam was focused by meansof a spherical lens (f = 100mm) perpendicular to the axial sample direction. Theradial and axial emission were collected within a restricted cone angle of ∼ 0.15 radby using a multichannel charge-coupled device (CCD) (Jobin-Yvon, Micro-HR). Byincreasing the pump energy above a certain threshold value, a highly directionallaser action was observed at the red edge of the stop band, both axially and radi-ally. The laser emissions were found to be circularly polarized, which indicates thatdistributed feedback mechanisms take place through circular Bragg reflection. TheLC microcylinder acts like a miniaturized mirrorless cavity laser, where the emit-ted laser light propagates along the liquid crystal helical axis which behaves as aBragg resonator. Recorded radial and axial lasing spectra present slightly differentwavelength positions and linewidths full width at half maximum (example in theinset of Fig. 4). The displayed lasing lines have a spectral position which correspondto the low-energy edge of the PBG and exhibit a very narrow stimulated emission

Fig. 4. Lasing action from a optically pumped cylindrical microcavity. Intense highly directionalaxial stimulated emission (at 587 nm) is observed on the background screen.



peak of only 0.5 nm width (limited by the resolution of the CCD spectrometer).The lowest measured lasing threshold was 250nJ/pulse for the radial direction and500nJ/pulse for the axial one. We experimentally found that the ratio r/p (wherer is the internal radius of the cylinder and p is the pitch of the chiral liquid crystal)is the parameter which controls the arrangement of the helical superstructure. Thesimultaneous radial and axial lasing indeed occurs when r/p ≤ 50, indicating thatthe interplay of the strong boundary conditions and the symmetry of the micro-cavity is responsible for the observed effect. In addition to the expected band edgelasing modes, low threshold defect lasing modes which occur within the selectivereflection band gap have been also observed. Defect mode laser action has beenpreviously mentioned in layered chiral liquid crystal polymer networks as a conse-quence of the induced phase jump in the optical field or dislocations, being respon-sible for opening spectrally narrow transmission modes within the stop band.25

Lasing is facilitated at these wavelengths since the photon dwell time is enhanced,giving ample opportunity for amplification by stimulated emission, as predicted byKopp26 and Yablonovitch.27 In the case of the presented cylindrical microstruc-ture, the spontaneous rearrangement of the local director fields produces particularhelical axis configurations which span from planar (axial) to escaped twisted radialgeometry (schematic in Fig. 5). This structural organization materializes in theappearance of point defect modes.28, 29 The local alteration of the sample whichdisrupts the periodicity of the structure leads to long-lived and, hence, spectrallynarrow laser defect modes within the gap, observed both axially and radially. It isworth noting that lasing wavelength of axial and radial defect modes are slightlydifferent, since the resonant wavelength for the defect mode depends on the totalphase slip which is given by the twist defect characteristics.

Fig. 5. Schematic of helical configurations in the cylindrical microcavities. Inset: Detail of thedifferent helical configurations, included the defect region.



3. Random Lasing in Bounded and Unbounded Geometries:Wedge Cells, Cylindrical Capillaries and Suspended Droplets

Interestingly, in nematic liquid crystals (NLCs) the propagation of light waves isquite different from isotropic fluids, since the recurrent optical scattering induces alocalization of light which can be used as a photon trapping mechanism to obtainlaser action in partially ordered and random systems. In this section, we report aseries of experiments carried out onto dye doped NLCs both confined in differentgeometries and even forming unbounded systems. Experiments show striking las-ing features which are typical of random laser action; nevertheless a remarkabledependence of the lasing characteristics on the degree of order is pointed out.

Two different types of confining geometries, mainly wedge cells and cylindricalglass capillaries (with untreated surfaces), and an unbounded configuration havebeen employed in our experiments. The confined systems were filled by capillaritywith a mixture made of nematic liquid crystal (BL001 — provided by Merck),having the following bulk phase sequence Cr.− (−10◦C)−Nematic− 63◦C− Iso,doped with 0.3wt. % of Pyrromethene 597 dye (from Exciton). The wedge cell wasconstituted by two glass-ITO plates separated by Mylar spacers, having a thicknessof 100µm at one edge and 1.5µm at the other one. The inner side of the plates wascovered with a rubbed polyimide thin film for inducing a homogeneous (planar)alignment of the NLC molecules at the interfaces. The cell was then filled allowingfor the flow direction to be along the rubbing direction and normal with respect tothe wedge. Upon observing the sample under a polarized microscope it showed aplanar alignment, with the optical axis sitting in the plane of the cell and parallel tothe rubbing direction. The pyrromethene dye molecules dissolved in the NLC at verylow concentration (0.3–0.5wt. %), proved to be completely miscible as evidencedby the almost complete absence of micro droplets of dye embedded in the nematicphase. The same mixture was also confined into micro cylindrical capillaries, withinner diameters between 50 and 250µm, without any preliminary surface treatment.At the same time, a droplet of the same mixture (diameter approx. 2mm) wasshaped by gravitational strength by means of a special syringe for contact anglemeasurements. The samples were optically pumped with 3–5ns pulses produced bya frequency-doubled (532 nm) Nd:YAG laser (NewWave, Tempest 20). The pumpbeam was focused onto the sample by means of a spherical lens (f = 100mm),yielding a beam waist of about 30µm at the focus position. The experimental set-up(Fig. 6) shows a combination of several optical elements (quarter-wave plates, half-wave plates and Glan-Thompson polarizers) used for selecting all the polarizationstates for the pump beam. A multichannel CCD spectrometer with a high spectralresolution (0.5 nm) and a fiber termination (FI) was employed for acquiring theemission spectra within a limited cone angle of approximately 0.05 rad. Preliminarymeasurements were performed on empty samples by checking the transmission andreflection spectra (UV-visible-near-infrared Cary 500 Spectrophotometer by Varian)in order to rule out any possible cavity effects due to the multiple reflections at the



Fig. 6. Sketch of the experimental setup line.

boundaries. Furthermore, by assuming the existence of a potential cavity effect thecalculated free spectral range was found to be far from the wavelength region ofthe lasing modes and their spectral line spacing.

3.1. Experimental results and discussion

When optically pumping the samples and increasing the input energy above acertain threshold value, a fluctuating speckle-like spot, typical of random lasers,appears on the background screen (Fig. 7). We have spectrally analyzed the result-ing emission, using the high resolution optical multichannel charge coupled device(CCD) spectrometer (Jobin-Yvon). At low pump energy regimes, the emission spec-tra show the typical spontaneous emission curve of the pyrromethene dye, indicatingthat NLC does not modify the fluorescence spectrum (Fig. 8(a)). Upon increasingthe pump power above a given threshold value (about 900nJ/pulse in the case of thewedge cell), discrete sharp peaks emerge from the residual fluorescence spectrum,while the output energy is found to be about 150nJ/pulse at room temperature(Fig. 8(b)). The line width of these sharp peaks is measured to be less than 0.5 nm,limited by the spectral resolution of the CCD. When the incident pump energyexceeds the threshold value, the peak intensity increases rapidly with the pumppower and more sharp peaks appear, since the balance gain-loss of these lossiestmodes becomes positive (Fig. 8(c)).

(a) (b) (c)

Fig. 7. Image of diffusive lasing from optically pumped wedge cell (a), cylindrical capillary (b)and suspended droplet. Intense stimulated emission is observed on the background screen.



Fig. 8. Fluorescence (a) and random lasing spectra (b, c) in the case of a wedge cell uponincreasing the pump energy. Discrete sharp peaks emerge from the residual spontaneous emissionfor pump energy of about 900 nJ/pulse.

Diffusive random lasing occurs in dye doped nematics by recurrent light scatter-ing, the lasing frequencies being determined by phase relationship of the counter-propagating scattered light waves. The weak localization of light owing to the strongoptical scattering gives rise to reciprocal paths within the gain medium. When thephase accumulation in reciprocal path is equal, constructive interference occursamong the backscattered amplitudes. Therefore, it is believed that the observedspectral blue shift of the lasing peaks with respect to the fluorescence maximum ismainly due to the interference effects which introduce coherence and feedback, lead-ing to lasing action. The stimulated emission sharp peaks prove that lasing effectdoes not depend mainly on the sample size, but the key role is played by the bulkydye doped nematics. A small difference can be noticed however, in terms of the ran-dom lasing pump energy threshold, for the two confining geometries (Fig. 9). Thedifferent order degree of these systems probably makes the difference; we obtain a1.2µJ/pulse value of the lasing energy threshold in the case of cylindrical confine-ment. Furthermore, in the case of micro capillary tubes, the random lasing peak

0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7

Fig. 9. Emission intensity versus pump energy for the wedge cell and capillary glass microtube.The two confining geometries present different threshold values of the input pump energy abovewhich random lasing is obtained.



wavelengths tend to be slightly redshifted with respect to the wedge cell confine-ment, owing to the phase relationships which depend somehow on the boundaryconstraints.

In the science of cavity lasers, a parameter of great interest because of thepromise of ‘thresholdless laser’ is the β factor. For a conventional laser, this isdefined as the ratio of the rate of spontaneous emission into the lasing modes tothe total rate of spontaneous emission (0 ≤ β ≤ 1) and determines the sharpnessof the laser threshold (β = 1 when all the spontaneous emission is radiated intothe lasing modes).30 In the case of our wedge sample, the output energy increasesalmost exponentially with the pump power and from calculations we obtained avalue β ∼ 0.08. The presented behavior suggests that a large part of the sponta-neous emission is radiated into the lasing modes because of the sufficient opticalfeedback (with respect to completely random systems) provided by the anisotropiccoherent backscattering medium. The radiative transfer is regulated by the orderof the system, meaning that the order parameter drives the amount of sponta-neous emission radiated into the lasing modes. This can explain the higher valueof the threshold pump energy in the case of the micro capillary sample, due toa lower alignment order. Figure 10(a) shows that the fluorescence emission inten-sity undergoes a significant lowering when the pump light is polarized perpendicu-larly to the NLC director (o-wave), in comparison with the case of light polarizedparallel to the director (e-wave). The polarization dependence of the scatteringintensity and the coupling of the optical field with the gain medium have to betaken into account for the observed anisotropy. The former effect is mainly dueto polarization dependence of the diffusion constant D for the emitted photons.A larger diffusion constant for the e-wave compared to the o-wave is generally

Fig. 10. Polar plot for a wedge (a) and capillary (b) dye doped nematic sample showing thedependence of the polarized fluorescence emission on the angle θ between the linearly polarizedlight and the local nematic director orientation.



measured. The latter aspect can be analyzed by considering the Fermi’s GoldenRule which clearly states that the molecular transitions and the rate of emissionstrongly depend on the coupling of the pump electric field E with the transitiondipole moment d of the dye molecules. Experimental results also emphasize that thefluorescent molecules adopt, to some extent, the local nematic order of the liquidcrystal, which results in an anisotropic orientational distribution of the transitiondipole moment. From Fig. 10 we can notice that polarized fluorescence measure-ments show a more pronounced anisotropy for the wedge sample. This is an expectedresult when comparing the better nematic alignment of the wedge cell with respectto the degenerate one within the untreated cylindrical capillary. This result onceagain confirms that the dipolar coupling modifies the quantum yield for fluores-cence and plays an important role in the light amplification process; some states ofpolarization of the pump pulses provide a larger number of spontaneously emittedphotons which are radiated in the lasing modes. It is worth pointing out that themaximum of lasing intensity is obtained for linearly polarized pump pulses with Eoriented along the local director (θ = 0◦), in good agreement with the polarizedfluorescence results as well as the polarization dependence of the scattering inten-sity. In order to gain further understanding of the diffusive laser action observedin partially ordered systems, the far field spatial distribution of the emitted lightwas analyzed. Lasing emission was captured in a limited cone angle (∼ 0.1 rad) bymeans of a high resolution and sensitivity CCD camera (1390 × 1024 12bit Pix-elFlyQe by PCO). Figure 11 depicts an interesting scenario of the random lasingemission pattern from dye doped nematic liquid crystals confined in a wedge geom-etry. The spatial intensity profile is formed by a series of bright tiny spots spatiallyoverlapped which create a richly structured pattern. The sequence of images wasobtained for four successive pump pulses and we can clearly observe that randomlasing changes both spatially and in terms of intensity. This emission mechanismis based on the diffusive process of spontaneously emitted photons by fluorescentguest molecules launched at random directions from random positions. These pho-tons are involved in a weak localization process within the gain medium becauseof recurrent multiple scattering. Since the condition for lasing comes from a carefulbalance between gain and loss, it is clear that in this case not for every pump pulsethe random walk inside the anisotropic medium gathers enough gain for the systemto lase.

4. Conclusion

A color tunable DFB microcavity laser was created by embedding dye doped helixedliquid crystals in holographically sculptured polymeric microchannels. The uniqueoptical and electrical properties of chiral liquid crystals play a determining role inthe mirror-less cavity limited by polymeric walls. The laser action was observed atthe low energy edge of the bandgap where a sharp increase of the photonic density ofstates (DOS) is expected. The emitted light was circularly polarized, corroborating



(a) (b)

(c) (d)

Fig. 11. Far field spatial distribution of the emission intensity profile in a wedge NLC sample inthe case of four successive (a, b, c, d) pump beam pulses (f = 10 Hz). An irregular intermittentbehavior (both spatial and temporal) of the emission is observed.

the idea that a distributed feedback mechanism is behind the presented lasing effect.The investigation of the spatial distribution of the emitted light shows a laser arraywhere each microchannel acts as an astigmatic resonant cavity producing an ellipticGaussian beam.

Scattering materials also proved to be extremely efficient to provide opticalfeedback for lasing effects. Here, it was observed and characterized the processof random laser action in confined dye doped nematics, for the case of variousboundary and un-boundary conditions (i.e., confinement geometry, bulk volumeand surface treatment). The underlying mechanism is mainly based on interfer-ence effects which survive to recurrent multiple scattering driven by nematic direc-tor fluctuations. Weakly localized light waves into dye doped nematic sample areresponsible for amplification while the resonance frequencies are selected throughinterference phenomena of the counter-propagating light waves within the local-ized loops: 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 reciprocalpaths by these photons is not null (as demonstrated by coherent backscatteringexperiments), thus resulting in equal phase accumulation during the open loops.If the gain length is comparable with the transport mean free path, the furtheremission of photons is stimulated before the recurrently scattered photons leavethe sample, thus triggering a coherent chain reaction. When the gain-loss balancebecomes positive, the optically pumped sample starts to lase. Unlike distributedfeedback mirror-less lasers, this system can be considered as a cavity-less micro-laser where the disorder unexpectedly plays the most important role, behaving asrandomly distributed feedback laser. We found that the random lasing peaks areextremely narrow banded (0.5 nm) and also that dye transition dipole momentsadopt, to some extent, the orientational order parameter of the nematic director,resulting in a control of the emission intensity by varying the polarization of theinput pump beam. Both confined systems (wedge and capillary), as well as the sus-pended droplet, possess the characteristics of a random laser and a detailed analysisof the far field modal profile for the emission intensity illustrate a series of spatiallyoverlapped tiny spots, creating a richly structured pattern which varies in timeand position. Many other new geometries for the lasing system are being designedand investigated, such as freely standing and freely suspended dye doped NLC thinfilms.

References

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Laser Action in Dye Doped Liquid Crystals:. from Periodic Structures to Random Media

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