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Role of the sample thickness on the performance of cholesteric liquid crystal lasers: Experimental, numerical, and analytical results
Abstract
We have studied the performance characteristics of a dye-doped cholesteric liquid crystal (CLC) laser as a function of the sample thickness. The study has been carried out both from the experimental and theoretical points of view. The theoretical model is based on the kinetic equations for the population of the excited states of the dye and for the power of light generated within the laser cavity. From the equations, the threshold pump radiation energyEth and the slope efficiency η are numerically calculated. Eth is rather insensitive to thickness changes, except for small thicknesses. In comparison, η shows a much more pronounced variation, exhibiting a maximum that determines the sample thickness for optimum laser performance. The predictions are in good accordance with the experimental results. Approximate analytical expressions for Eth and η as a function of the physical characteristics of the CLC laser are also proposed. These expressions present an excellent agreement with the numerical calculations. Finally, we comment on the general features of CLC layer and dye that lead to the best laser performance.
... This dye-doped chiral liquid crystal self-assembles between two parallel surfaces, typically made from glass, to form a laser cell, the fabrication of which uses common LC display manufacturing techniques. The optimum spacing between the two substrates has been shown to range from 10 m -20 m 7,11,12 . When the laser cell is appropriately excited with an optical source, liquid crystal laser emission is produced. ...
... While these dyes enable broad wavelength selectivity and most are soluble in the LC host, the four-level laser energy 17 structure of their molecules prohibits high repetition rate or continuous wave (CW) pumping. This is due to the undesirable population of triplet states, dye bleaching and thermal damage, all of which have detrimental effects to laser performance 7,12,18,19 . It is the purpose of the work presented in this paper to overcome some of these challenges and bring the practical application of LC lasers closer to realization. ...
... A smaller, cheaper and less complex pump source has often been discussed in the literature as the key to achieving commercial practicality for LC lasers 9,12,[20][21][22] . In particular, the use of semiconductor materials such as light emitting diodes (LEDs) or laser diodes (LDs) as pump sources has been alluded to throughout the literature over the past twenty years. ...
... It should be noted that the lasing measurements needed for a measuring of the director orientation as a function of coordinate in an individual GC zone are very similar to the ones performed in Sanz-Enguita et al. 6 where the lasing intensity was measured as a function of coordinate in a GC zone. In Sanz-Enguita et al. 6 nothing was said about the coordinate lasing frequency changes, however quite probable that the corresponding frequency measurements were also performed in Sanz-Enguita et al. 6 and can be used for obtaining an angular director distribution in the individual GC zone. ...
... It should be noted that the lasing measurements needed for a measuring of the director orientation as a function of coordinate in an individual GC zone are very similar to the ones performed in Sanz-Enguita et al. 6 where the lasing intensity was measured as a function of coordinate in a GC zone. In Sanz-Enguita et al. 6 nothing was said about the coordinate lasing frequency changes, however quite probable that the corresponding frequency measurements were also performed in Sanz-Enguita et al. 6 and can be used for obtaining an angular director distribution in the individual GC zone. ...
... It should be noted that the lasing measurements needed for a measuring of the director orientation as a function of coordinate in an individual GC zone are very similar to the ones performed in Sanz-Enguita et al. 6 where the lasing intensity was measured as a function of coordinate in a GC zone. In Sanz-Enguita et al. 6 nothing was said about the coordinate lasing frequency changes, however quite probable that the corresponding frequency measurements were also performed in Sanz-Enguita et al. 6 and can be used for obtaining an angular director distribution in the individual GC zone. ...
... Threshold and slope efficiency are common figures of merit for quantifying the performance of LC lasers, whereby the former is desirably minimized, and the latter maximized. Several studies have shown how different materials, pump and alignment geometries, and environmental conditions affect threshold and efficiency [14][15][16][17][18][19]. With regards to pump pulse duration, work by Cao et al. [20] showed an order of magnitude reduction in LC laser threshold using a 40 ps pump laser compared with a 7.5 ns source, but their study was limited to these two arbitrary data points, and no insight was provided into the effect on slope efficiency. ...
... With regards to pump pulse duration, work by Cao et al. [20] showed an order of magnitude reduction in LC laser threshold using a 40 ps pump laser compared with a 7.5 ns source, but their study was limited to these two arbitrary data points, and no insight was provided into the effect on slope efficiency. Theoretical work by Shtykov et al. [21] showed a reduction in LC laser threshold and an increase in slope efficiency with a decreasing duration of the rising edge of a hypothetical trapezoidal pump pulse, and Sanz-Enguita et al. [18] derived an equation showing the proportionality between threshold and pump pulse duration. However, such work has not been possible to verify experimentally using conventional (fixed pulse duration) pump sources. ...
Much work has been done to understand the factors that impact photonic band-edge liquid crystal (LC) laser threshold and slope efficiency, two parameters often stated to quantify performance. Conventionally, LC lasers are optically pumped using Q-switched lasers with a fixed pulse duration, and thus the effect of pump pulse duration on LC laser performance has received little attention. While some studies have been published at different pump pulse durations, these use different laser sources and experimental conditions, making the data incomparable. By exploiting a recent breakthrough in laser diode pumping, our experimental results prove and quantify the detrimental effect of an increase in pump pulse duration on LC laser performance. We also show that the dependency of threshold on pump pulse duration depends on how threshold is defined, owing to an ambiguity in the definition of pulse energy in systems where peak power and pulse duration can be independently controlled. For improved comparison within the literature on LC laser device performance, we thus propose an alternative convention, whereby threshold is stated in units of peak power density.
... CLCs are suitable to build distributed feedback lasers [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. These devices are made of CLC materials doped with fluorescent dyes whose emission spectra overlap with the band gap. ...
... In the case of multiple scattering a more complex angular redistribution of energy occurs. In fact, the laser light emitted along the helix decreases [13] and consequently the HWHM of the central peak increases. ...
The spot shapes of cholesteric liquid crystal lasers have been studied experimental and theoretically. A broad variety of profiles has been found depending on the oscillator architecture, thickness, and lasing conditions. Simple cells, lasing at the short-wavelength edge of the gap, give rise to simple spots, whereas if the laser wavelength is at the long-wavelength edge the spots are surrounded by rings. On the other hand, complex cells, which incorporate passive cholesteric mirrors connected with glass substrates, produce spots with many sharp concentric rings. In all cases we have demonstrated that the different intensity profiles can be explained as due to anomalous light scattering of the main laser propagating along the helical axis towards oblique directions. For simple cells, the beam divergence is essentially determined also by scattering, showing a decreasing tendency with the sample thickness. Complex cells have a much smaller beam divergence, and its value is limited by diffraction.
... A minimal layer thickness and a sufficient number of pitches in the layer is important to ensure a sufficiently high reflection and a well-defined band gap. This is important in various applications, such as low threshold CLC lasers [13] and color filters. The influence of the number of pitches on the optical reflection spectrum is shown in Figure 1a for perpendicular incidence, and for the following parameters: P = 376 nm, n e = 1.687 and n o = 1.508. ...
Nematic chiral liquid crystals (CLCs) are characterized by a helical arrangement of nematic LC molecules. A layer of CLC typically exhibits an optical reflection band due to Bragg reflection in the helical structure. When several layers of CLC are spin-coated and polymerized on top of each other without a barrier layer in between, defect modes can form in their reflection spectrum. By comparing experimental results and simulations, we investigate the origin of the defect modes, thereby revealing details on the behavior of the materials at the interfaces during deposition. Simulations show that these defect modes can originate from the migration of chiral dopant leading to a layer with a smaller pitch or from a discontinuity in the director orientation at the interface between two layers.
... The reflection wavelength according to the helical pitch can be tuned by external stimuli, such as electric field, 1-3 light, 4-6 and temperature. [7][8][9] This attractive optical property of CLCs is of great use for various applications such as displays, 10,11 lasers, [12][13][14] and sensors. 15,16 CLCs with cross-links in the polymer chain termed CLC elastomers (CLCEs) can deform largely accompanying a change in reflection wavelength. ...
Cholesteric liquid crystal elastomers (CLCEs), which exhibit selective reflection derived from a helical molecular structure, are receiving a great deal of attention because they deform largely due to the cross-linked polymer chains. Reflection wavelength of a CLCE film can be tuned by mechanical stretching that induces a change in the helical pitch. However, stretch-induced reflection wavelength tuning has some issues such as a large load required and a limited tuning range. In this paper, reflection wavelength of a CLCE film is tuned facilely and widely by bending. Outward and inward bendings cause blue and red shifts, respectively. Bending-buckling load required for the reflection tuning is much lower than stretching one, which is proved experimentally and theoretically. By considering the bending behavior of materials, we can impose large strain on a CLCE film and tune reflection wavelength over 300 nm, which is almost the whole region of visible light. This wideband reflection wavelength tuning by low-load bending leads to expanding applications of CLCEs.
... However, in practice some complication arises: If the reflectivity of the CLC mirrors is very high, the laser performance will be very poor, since most of the amplified radiation inside the cavity cannot escape, and will be eventually absorbed or scattered due to the distributed losses inside the cavity. This pernicious effect can dramatically reduce the slope efficiency of the laser as described in reference [33]. Nevertheless, the existence of a birefringent layer inside the cavity provides a mechanism for the light to escape from the cavity: When the phase retardation of the nematic layer is near but not exactly a full-wave plate, a small proportion of the reflected light is transformed from the reflecting circular polarisation state to the one with opposite handedness, which can escape from the cavity. ...
We present an experimental study of an electrically tunable laser based on liquid-crystal elements and analyse theoretically its main working principles. The laser structure includes two polymer-stabilised cholesteric-liquid-crystal slabs that act as polarisation-sensitive reflectors, and a dye-doped nematic layer sandwiched between them. The wavelength of lasing can be changed by modifying the optical retardation of the nematic layer by means of a low-amplitude square wave. For all wavelengths the laser light is circularly polarised with opposite handedness to that of the cholesteric mirrors. Good laser performance has been achieved, with low thresholds and quasi-continuous tuning ranges. The laser threshold varies with the wavelength, and was found to be highly dependent on the spatial location of the indium-tin-oxide (ITO) electrodes, inside or outside the laser resonator. A theoretical account for this effect is given using simulations based on the Berreman 4 × 4 matrix method.
... The dependence of lasing threshold on particle size can be attributed to changes in the resonant strength of the CLC cavity and the amount of nonquenched dye available for stimulated emission. 40,41 Analytical forms for lasing threshold originate from the laser rate equations 42 and/or density of state considerations, 41 but result in the following dependence on particle diameter: 40 ...
Minimally invasive methods for temperature sensing and thermal modulation in living tissues have extensive applications in biological research and clinical care. As alternatives to bioelectronic devices for this purpose, functional nanomaterials that self-assemble into optically active microstructures offer important features in remote sensing, injectability, and compact size. This paper introduces a transient, or bioresorbable, system based on injectable slurries of well-defined microparticles that serve as photopumped lasers with temperature-sensitive emission wavelengths (>4-300 nm °C-1). The resulting platforms can act as tissue-embedded thermal sensors and, simultaneously, as distributed vehicles for thermal modulation. Each particle consists of a spherical resonator formed by self-organized cholesteric liquid crystal molecules doped with fluorophores as gain media, encapsulated in thin shells of soft hydrogels that offer adjustable rates of bioresorption through chemical modification. Detailed studies highlight fundamental aspects of these systems including particle sensitivity, lasing threshold, and size. Additional experiments explore functionality as photothermal agents with active temperature feedback (ΔT = 1 °C) and potential routes in remote evaluation of thermal transport properties. Cytotoxicity evaluations support their biocompatibility, and ex vivo demonstrations in Casper fish illustrate their ability to measure temperature within biological tissues with resolution of 0.01 °C. This collective set of results demonstrates a range of multifunctional capabilities in thermal sensing and modulation.
... LC laser research has highlighted many of the technology's attractive features: high efficiencies (60%) have been achieved through optimized materials and cell construction [6][7][8][9], and a full range of visible wavelengths demonstrated [10]. Fine tuning of the laser wavelength has been achieved with electrical [11,12], mechanical [13,14] and thermal [15,16] methods. ...
Liquid crystal lasers have advantageous features, including continuous wavelength tuning at low cost. Although many potential applications have been highlighted, use of these lasers is not widespread, partially due to performance limitations. This paper presents a method of overcoming repetition rate limitations. A rapidly spinning stage is used to allow operation of a LC laser at 10 kHz: two orders of magnitude greater than possible with a static cell. Average power outputs of up to 3.5 mW are achieved along with an improvement in emission stability. Lastly, a mechanical wavelength-switching method is demonstrated. The spinning cell approach will enable research into the use of liquid crystal lasers in fluorescence imaging and display applications.
Liquid crystal lasers are typically pumped with Q-switched lasers, which provide the short pulse durations necessary to produce band-edge liquid crystal laser emission. However, the current cost and bulk of the pump laser, relative to the liquid crystal component, limit the application potential of liquid crystal laser technology. A low-cost and compact alternative pump source has often been discussed within the liquid crystal laser community but has not yet been demonstrated. In this paper, a 445 nm laser diode was integrated with carefully selected electronics in an attempt to reproduce equivalent pump conditions to that achieved from a Q-switched laser, and then used to pump a liquid crystal laser. Successful band-edge lasing was achieved, demonstrating, for the first time, a clear threshold and single mode, narrow linewidth emission. Red, green and blue outputs from different liquid crystal lasers were also realised when pumped with the same laser diode, demonstrating the broad wavelength selectivity of liquid crystal lasers using a single low-cost, compact device.
We have carried out polarisation and angle-resolved measurements of the light scattered from photonic cholesteric liquid crystals. Both in samples doped with laser dyes and in inactive (non-doped) samples we have observed pronounced directional dependences of the scattered light, finding angular ranges where the scattering is greatly enhanced and regions where the effect is almost suppressed. Moreover, the total amount of scattered light has also been found to depend strongly on the polarisation and direction of the incident beam. All the results have been interpreted successfully in terms of a simple expression proposed for the scattering cross section, in which the density of states of the ingoing and outgoing beams plays a major role. The expression would be applicable not only to cholesteric liquid crystals but to any one-dimensional photonic material.
Recently, there has been much activity in the field of localized optical modes, in particular, edge modes (EM) and defect modes (DM) in chiral liquid crystals (CLCs), mainly due to the possibilities for reaching a low lasing threshold for mirrorless distributed feedback (DFB) lasing in CLCs. In the present chapter, we study theoretically the influence of local absorption anisotropy on the characteristics of localized modes. We present analytical solutions for the EMs and DMs (associated with a local absorption anisotropy in CLCs) and consider some limiting cases simplifying the problem [15].
We study the optical properties of a cholesteric liquid crystal doped with a fluorescent dye in the regime of highly distorted helix without full helix unwinding. The distortion was achieved by applying a pulsed AC electric field, perpendicular to the helix axis. If the pulse is in the millisecond range, the helix is deformed but keeps its original pitch even for electric fields higher than the theoretical critical field for helix unwinding. In this field regime, very pronounced high-order photonic band gaps are observed, in agreement with our calculations. We theoretically explore the possibility of obtaining viable laser emission at the second-order photonic band gap, and experimentally find that lasing is not only possible but has a figure of merit similar to that of the usual laser at the main-gap region. Therefore, electric-field-induced high-order photonic band gaps are potentially useful for multiline laser applications.
The out-of-normal emission in cholesteric liquid-crystal lasers is studied experimental and theoretically. Apart from the well-known dominant laser in the direction of the helix axis, three other types of radiation, with cone-shaped spatial patterns, are identified and characterized. The physical mechanisms responsible for the different emissions are clarified. One of the radiations is a weak colorful lasing emission whose wavelength changes continuously depending on the propagation direction. The wavelengths of the other two radiations take place at the long-wavelength and short-wavelength edges of the photonic bandgap. These emissions are attributed to an anomalous scattering phenomenon that gives rise to energy transfer from the main laser beam to some specific directions where the amount of final photonic states is high. An expression for the scattering cross section, reminiscent of Fermi's golden rule for spontaneous emission in photonic structures, is proposed. Some other phenomena independent of the lasing occurrence but driven by the anomalous scattering are briefly presented.
The photon density of states in a cholesteric photonic crystal in the region of the photon band has been determined from the measured polarized luminescence spectra. The orientational ordering of the transition dipole moment in luminescence, as well as the ellipticity of light eigenmodes in the photonic crystal, has been taken into account when determining the density of states. Maxima in the spectrum of the density of states on two sides of the photonic band are related to the displacement of states from the band. The group velocity of light inside the photonic band exceeds the speed of light in vacuum.
The topic of cholesteric-liquid-crystal lasers is a rapidly expanding research area in the field of soft-matter photonics. The increasing interest in this field is due to the high versatility that these lasers may possibly present and the prospects of giving rise to new miniaturized devices. However, further improvements in their operation capabilities are still required for potential applications. In this paper, we critically analyze the main strategies proposed up to now to optimize their performance. We show theoretically and experimentally that possible innovations in the device structure cannot produce lasers with threshold energies below a certain limit. This limit is determined by the light scattering and absorption losses inside the liquid crystal. Even assuming the case of samples free of defects and perfectly non-absorbing, an intrinsic light scattering, typical of mesogens, still remains. Numerical estimates of the thresholds indicate that these lasers could hardly be driven by compact light sources such as current electroluminescent or light-emitting diodes. Since the improvement possibilities regarding cell architecture seem to be exhausted, the advance must come from the use of new dye molecules. These molecules should show enhanced emission cross-sections and be efficiently integrable within the mesogenic solvent. In addition, the fluorescent systems must present very small quantum yields to triplet states if continuous-wave lasing is sought. In this respect, quantum dots are an alternative to explore for further investigations.
An anomalous strong optical absorption was measured in a cholesteric liquid crystal (CLC) at both edges of its photonic band gap. The experiment was carried out by studying the luminescence generated by the CLC sample doped with a small amount of fluorescent dye. The material was excited with monochromatic light at different angles of incidence and polarisations. Clear peaks were found in the luminescence response at angles for which the pumping wavelength coincides with the positions of the gap edges. The effect is especially noticeable for excitation under circularly polarised light of the same handedness as that of the CLC helix, and it is the highest at the long-wavelength edge. The modification of the absorption is originated by the helicoidal (photonic) structure of the material, which drastically influences the propagation of electromagnetic waves at certain frequencies and polarisations. The results were analysed numerically using an extension of the Berreman method that incorporates absorption effects. Good agreement with the experiment was found.
Some dynamical aspects of fluorescence and lasing have been studied in a dye-doped cholesteric liquid crystal by measuring the response of the material to nanosecond optical pumping. It has been found that as the pumping energy is increased the fluorescence pulse duration decreases, reaching a minimum at the lasing threshold. Above the threshold the temporal profiles are irregular and consist of a set of narrow pulses whose measured duration is limited by the detector risetime (1 ns). The results are interpreted in terms of a recently proposed model [JETP, 118, 822 (2014)] that makes use of rate equations to account for the laser generation in cholesteric liquid crystals. The prediction of such equations for an experimental configuration appropriate for fluorescence lifetime measurements is analyzed.
Lasing in induced cholesteric liquid crystal (CLC) containing highly photosensitive azo chiral dopant (ChD) and pyrromethene laser dye was investigated. Due to the absence of excitation energy transfer from the dye molecules to the molecules of ChD in such a system, a low lasing threshold was achieved. When using violet and green light-emitting diodes, reversible frequency tuning was obtained in the range of about 30 nm with a tuning time 1–2 orders of magnitude smaller than in conventional CLC laser systems based on azo and azoxy photosensitive compounds. Further increase of the intensity of the excitation light by using a green laser pointer allowed us to achieve a record phototuning speed ( ∼ 21 nm in 148 ms).
This investigation is the first report of an optically stable and tunable laser using a quantum-dot (QD) embedded cholesteric liquid crystal (QD-CLC) microresonator with an added chiral-azobenzene moiety. The QD nanocrystal, CLC, and chiral-azobenzene play key roles in the highly stable fluorescence nano-emitter, microresonator, and photo-tuner in the photonic bandgap (PBG) of the CLC and associated lasing output, respectively. Experimental results show that both the PBG and lasing emission of the QD-CLC composite sample can be reversibly tuned under successive irradiation with UV and blue beams. The all-optical tunability of the laser is attributed to the successive elongation and shrinkage of the CLC pitch induced by UV- and blue beam-irradiation induced trans–cis and cis–trans back isomerizations of chiral-azobenzene, respectively. In addition, this composite laser has a high damage threshold (>85 μJ per pulse), and thus shows a uniquely high optical stability. This work has successfully opened up an opportunity for developing QD coherent light sources or lasers with good optical stability and tunability (e.g., optically stable and tunable single photon lasers).
We demonstrate high-precision, continuous, electrical tuning of a photonic band-edge laser based on a dye-doped cholesteric liquid crystal. A micro-patterned array of electrodes creates an electric field perpendicular to the cholesteric helix, which distorts the chiral order of the liquid crystal, thus shifting the resonant band edge modes. This configuration allows for smooth tuning of the laser emission in a wavelength range of about 3.5 nm, using low voltages (of the order of 10 V). (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4739840]
— Liquid-crystal lasers exhibit narrow linewidth, large coherence area, and low threshold laser emission. Moreover, the wavelength of the laser line can be readily tuned using a variety of different external stimuli, including electric fields. These combined features make them particularly attractive as compact tunable laser light sources. Recent experimental results with regards to the emission characteristics of chiral nematic photonic band-edge lasers are discussed. This type of liquid-crystal laser consists of a self-organizing one-dimensional photonic band structure and a gain medium in the form of a laser dye. Some of the generic features that are observed for these lasers are discussed, including the typical emission linewidth of the laser line, the change in emission energy of the laser for high excitation energies and high pump repetition rates, and the dependence of the excitation threshold and slope efficiency on the cell thickness. In addition, how the performance changes when either the molecular structure of the chiral nematic host or the gain medium is varied is considered. To conclude, results are presented on the laser emission for a wide-temperature-range blue phase I band-edge laser which consists of a self-organizing three-dimensional photonic band structure.
Cholesteric liquid crystals (CLCs) are one dimensional photonic band-gap materials. Due to distributed feedback, low threshold mirrorless lasing can occur in dye-doped and pure CLCs. In order to optimize the lasing conditions, we have studied the dependence of the lasing threshold on dye concentration and sample thickness. In particular, we have studied dye concentrations in the range of 0.1-3.0wt%, and cell thicknesses are in the range of 5-50µm. We have found that the system has a shallow lasing threshold minimum and can operate efficiently in the range of dye concentrations of 0.3-2.4wt% and sample thicknesses of 10-50µm. We discuss the physical processes responsible for the observed behaviour.
Helical structure induced in nematics by non-mesogenic optically active dopants (OAD) was studied by means of the distributed feedback laser (DFL) spectroscopy. A difference was found between laser generation frequencies and Bragg frequencies of the selective transmission spectra, attributed to the presence of two sublattices in the induced helical structure due to its distortion.
Despite numerous efforts, continuous wave (CW) lasing in dye doped, one-dimensional (1D) photonic bandgap cholesteric liquid crystal (CLC) structures has not been previously reported, to our knowledge. Here we report on the observation of lasing in such structures under both coherent (laser) and incoherent (LED) CW light excitation. To achieve this effect, we used a 1D-photonic bandgap structure made of a polymer stabilized CLC with a pitch gradient across the cell thickness. A spectral reflectivity profile of such a CLC structure reveals local minima in the area within a photonic stopband and close to it. The realization of lasing pumped by low power CW light sources opens the possibility of all-organic, compact, tunable CW lasers for display and medical applications.
This paper presents an overview of the results obtained in recent investigations of the control over the helical pitch under
irradiation and the use of these data for the design of compact broadband tunable lasers based on dye-doped cholesteric liquid
crystals. It is demonstrated that a reversible change in the lasing frequency can be achieved upon exposure to two low-power
light-emitting diodes. Another alternative approach to the generation of tunable laser radiation in the visible and ultraviolet
spectral regions (370–680 nm) in a specially designed cell with a cholesteric liquid crystal that is doped with several dyes
and possesses a helical pitch gradient is considered.
An analytic theory of localized edge modes in chiral liquid crystals (CLCs) is developed. Equations determining the edge-mode
frequencies are found and analytically solved in the case of low decaying modes and are solved numerically for the problem
parameter values typical for the experiment. The discrete edge-mode frequencies specified by the integer numbers n are located close to the stop-band edge frequencies outside the band. The expressions for the spatial distribution of the
n’s mode field in a CLC layer and for its temporal decay are presented. The possibilities of a reduction of the lasing threshold
due to the anomalously strong absorption effect are theoretically investigated for a distributed feedback lasing in CLCs.
It is shown that a minimum of the threshold pumping wave intensity may be reached, generally, for the pumping wave propagating
at an angle to the helical axis. However, for lucky values of the related parameters, it may be reached for the pumping wave
propagating along the helical axis. The lowest threshold pumping wave intensity occurs for the lasing at the first low-frequency
band-edge lasing mode and the pumping wave propagating at an angle to the spiral axis corresponding to the first angular absorption
maximum of the anomalously strong absorption effect at the high-frequency edge of the stop band. The study is performed in
the case of the average dielectric constant of the liquid crystal coinciding with the dielectric constant of the ambient material.
Numerical calculations of the distributed feedback lasing threshold at the edge-mode frequencies are performed for typical
values of the relevant parameters.
We have investigated the physical and optical properties of the left-handed chiral dopant ZLI-811 mixed in a nematic liquid crystal (LC) host BL006. The solubility of ZLI-811 in BL006 at room temperature is ~24 wt%, but can be enhanced by increasing the temperature. Consequently, the photonic band gap of the cholesteric liquid crystal (CLC) mixed with more than 24 wt% chiral dopant ZLI-811 is blue shifted as the temperature increases. Based on this property, we demonstrate two applications in thermally tunable band-pass filters and dye-doped CLC lasers.
Low-threshold lasing is observed at the edge of the stop band of a one-dimensional structure-a dye-doped cholesteric liquid-crystal film. The mode closest to the edge has the lowest lasing threshold. The rates of spontaneous and stimulated emission are suppressed within the stop band and enhanced at the band edge. The ratio of right to left circularly polarized spontaneous emission is in good agreement with calculated density of photon states.
IntroductionTypes of LasersLowering ThresholdTunability3D LC LasersConclusions
References
The paper presents the results of calculating the threshold pumping power necessary for laser generation in cholesteric liquid crystals doped with fluorescent dyes. Calculations have been performed with allowance for (i) specific spectral properties of the chiral cholesteric medium as a photonic structure and (ii) the spatially distributed character of feedback in the active medium. The dependences of the threshold pumping power on the sample thickness, dye concentration, and leading front widths of long pumping pulses have been studied.
We report on the results of calculating the conditions for light generation in cholesteric liquid crystals doped with fluorescent dyes using kinetic equations. Specific features of spectral properties of the chiral cholesteric medium as a photonic structure and spatially distributed type of the feedback in the active medium are taken into account. The expression is derived for the threshold pump radiation intensity as a function of the dye concentration and sample thickness. The importance of taking into account the distributed loss level in the active medium for calculating the optimal parameters of the medium and for matching the calculated values with the results of experiments is demonstrated.
Cholesteric liquid crystals (CLCs) and cholesteric blue phases (BPs) are one-dimensional and three-dimensional photonic bandgap (PGB) materials. In this work, fluorescence and lasing are experimentally studied in dye-doped CLC films and BPs, together with the calculations of density of states rho in CLC films. The normal modes of light propagation in a CLC film in the direction along the helical axis have been obtained analytically, using transfer matrix method. Two normal modes are elliptically polarized and their rho differ greatly. The value and wavelength of the largest rho depend on the CLC film thickness. The fluorescence spectra of dye DCM in CLC films are greatly altered: suppressed in the stop band and enhanced at band edges with intensity oscillations. The altered fluorescence spectra are in good agreement with the calculated spectra from rho. The fluorescence lifetimes, however, have no measurable difference. At high dye concentration, the fluorescence intensity is quenched by the formation of dye excimers. Mirrorless lasing in CLC films has been studied systematically. The lasing wavelengths and thresholds are in good agreement with the calculated values from rho. The threshold is optimized over CLC film thickness and dye concentration. Lasing at defect modes has been observed in CLC composite structures. Photon-counting statistics confirms the transition from the incoherent fluorescence to coherent laser emission with increasing pump energy. The totally coherent emitting area is estimated from the diffraction pattern of the CLC laser emission. The structures of BPs are characterized through textures and reflection measurements. In BP I, the stimulated emission is due to the multiple reflection of the fluorescence by small BP I crystals. In large BP II single crystals, the fluorescence is altered and lasing occurs at edges of the reflection peak or at defect modes. Lasing in three dimensions has been observed for the first time in PGB materials, and understood in terms of coupling of orthogonal lasing modes by reciprocal lattice vector.
The laser action in a dye-doped cholesteric liquid crystal has been investigated as a function of temperature. The discontinuous shift of the lasing wavelength has been observed. It has also been found that the shift of the stop band in the cholesteric liquid crystal is discontinuous when the size of the measured area for the spectrum is small. These results have been interpreted to originate from the disappearance of every half period of the cholesteric liquid crystal helix in the unwinding process as the temperature decreases.
The syntheses of derivatives of isosorbide and cinnamic acid are described. These chiral compounds are photoisomerizable. The Z‐isomers could also be obtained after irradiation of these E‐isomeric cinnamic derivatives. The Z‐isomers were found to have a much lower helical twisting power than the E‐isomers. These compounds are very suitable for use in cholesteric colour filters for liquid crystal displays. This was investigated by functionalizing the E‐isomeric derivatives with two acrylate groups. The reflection wavelength of cholesteric layers made with these diacrylates can be tuned by means of UV irradiation because the pitch of the cholesteric layer increases on isomerization to the Z‐isomer. Subsequent photopolymerization results in cholesteric films with excellent thermal stability.
Electrically controllable omnidirectional propagation of laser emission from a photonic composite film that contains conventional non-reactive nematic liquid crystals (NLC) embedded in helical-polymer networks of photopolymerized cholesteric liquid crystals (CLC) was reported. The results show that with an increase in the concentration of CLC component, the photonic bandgap (PBG) of the composite film shifts to shorter wavelengths. The observed full width at half maximum (FWHM) of the emission peak is approximately 3 nm. The emission peak intensity plotted against the pumping power for several concentrations of fluorescent dye shows that the lasing threshold decreases with an increase in dye concentration. Investigation of the possibility of controlling the direction of propagation of the laser emission by applying an electric field shows a strong laser emission at viewing angles near 0° when no electric field is applied.
Two types of lasing in cholesteric liquid crystals (LCs) in the range of luminescence of laser dye molecules have been investigated.
The first type belongs to the Bragg modes at the photonic band edge, which propagate along the normal to the LC layer. The
second type of lasing is related to the modes leaking into the substrate and propagating at small angles to the LC layer.
It is shown that the Bragg lasing efficiency can be significantly increased under wide-aperture optical pumping. The method
proposed for increasing the lasing efficiency is based on suppressing the excitation of leaky laser modes using partially
absorbing thin films as the coatings for LC-orienting substrates. Both experimental results and the theoretical model of the
effect using the numerical simulation data are discussed.
Due to the sinusoidal modulation of the dielectric properties along the helical axis, cholesteric liquid crystals exhibit
a photonic stop band for circularly polarized light, which strongly affects the emission of fluorescent guest molecules. In
this paper, we discuss the resulting changes in the emission spectrum. In an analytical treatment, we first derive the photonic
densities of states of the two normal light modes for propagation parallel to the helical axis, taking into account multiple
reflections due to the finite film thickness. Then we discuss the influence of the degree of order of the dye's transition
dipole moment on the emission characteristics. Finally, we present experimental results, which show excellent quantitative
agreement with our theoretical description.
The original results of studies of the electro-optical and laser effects which have been performed at the Laboratory of Liquid
Crystals of the Institute of Crystallography, Russian Academy of Sciences, over the last few years are reviewed. Cholesteric
liquid crystals as vivid representatives of photonic structures and their behavior in an electric field are considered in
detail. The formation of higher harmonics in the periodic distribution of the director field in a helical liquid crystal structure
and, correspondingly, the new (anharmonic) mode of electro-optical effects are discussed. Another group of studies is devoted
to bistable light switching by an electric field in chiral nematics. Polarization diffraction gratings controlled by an electric
field are also considered. The results of studies devoted to microlasers on various photonic structures with cholesteric and
nematic liquid crystals are considered in detail. Particular attention is given to the new regime: leaky-mode lasing. Designs
of liquid crystal light amplifiers and their polarization, field, and spectral characteristics are considered in the last
section.
The density of states approach [J. Bendickson et al., Phys. Rev. E 53, 4107 (1996)] was applied to a simple dielectric plate and a formula was found for the spectrum of the threshold gain for
lasing. Then the validity of the same approach was verified for cholesteric liquid crystals (CLC) having helical structure.
For non-absorbing CLC, the dependences were found of the minimum threshold gain on the layer thickness and the optical anisotropy
of the material. The contribution of the dye absorption was discussed separately. The experimental data presented are in good
agreement with threshold gain calculations.
This article presents a review of the lasing and photonic properties of periodic one-dimensional anisotropic structures with the symmetry of a double helix. Examples are self-organized cholesteric liquid crystals (CLCs) and sculptured thin films created by vapor deposition. A reflection band with sharp, closely spaced transmission peaks at its edges occurs for circularly polarized light with the same handedness as the helical structure. Within the reflection band, this wave is evanescent, corresponding to a vanishing density of states (DOS). Oppositely polarized light is uniformly transmitted. Since optical emission is proportional to the DOS, it is suppressed within the reflection band. However, it is enhanced at the band edge, where a series of narrow long-lived transmission modes are found. For this reason lasing in dye-doped CLCs occurs at the edge of the stop band rather than at its center, where reflection is highest. Introducing an additional rotation or an isotropic layer within a chiral structure creates a single circularly polarized localized mode with the same handedness as the structure. A resonance appears in the transmission of light of this polarization in thin samples. In thicker samples, the resonance appears instead in the reflection for oppositely polarized light. In contrast to strong modulation of the intensity within the sample on a wavelength scale, a characteristic of layered dielectric medium, the intensity within a chiral medium varies slowly when the sample is excited either at the band edge or at a localized mode. A transverse coherence is created in emission over a length scale proportional to the square root of the photon dwell time at resonance with long-lived modes. This makes possible spatially coherent lasing over a large area in thin films. The photonic properties of chiral thin films make them promising candidates for a variety of filter and laser applications.
External cavity-free and electrically tunable laser made from photonics band gap (PBG) materials with electrically tunable stop band is reported. The tunable PBG materials are developed from a family of novel cholesteric liquid crystals (CLC) with electrically variable pitch that adopts a non-constant distribution in space across the CLC film. The CLC exhibits a distributed feedback cavity whose resonant frequency can be electrically varied over a spectral range wider than 300 nm. Under an optical pumping and subject to a variable electric field, a tunable laser has been demonstrated in experiment that shows a wavelength tuning over 33 nm.
In order to understand how the performance of a liquid-crystal laser depends on the physical properties of the low molar mass nematic host, we have studied the energy threshold and slope efficiency of ten optically pumped liquid-crystal lasers based on different hosts. Specifically, this leads to a variation in the birefringence, the orientational order parameter, and the order parameter of the transition dipole moment of the dye. It is found that low threshold energies and high slope efficiencies correlate with high order parameters and large birefringences. To a first approximation this can be understood by considering analytical expressions for the threshold and slope efficiency, which are derived from the space-independent rate equations for a two-level system, in terms of the macroscopic liquid crystal properties.
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