This paper reports for the first time an electrically and thermally controllable nanoparticle (NP) random laser in a well-aligned dye-doped liquid crystal (DDLC) cell. Experimental results show that the random lasing emission is attributed to the amplification of the fluorescence via the multiple scattering of the randomly distributed NPs in the diffusion rout of the well-aligned DDLC cell. The random laser can be electrically and thermally controlled by varying the applied voltage and cell temperature, respectively. As the applied voltage is increased, the orientational change of the LCs from homogeneous to homeotropic texture decreases the dye absorption and thus the spontaneous fluorescence emission, resulting in the decrease of the random lasing emission. The random lasing intensity decreases with increasing temperature at the nematic phase and dramatically increases after the nematic→isotropic (N→I) phase transition. The result in the former stage is attributed to the decreases in the absorption and thus in the spontaneous fluorescence emission for the laser dyes because of the decrease in the order of the laser dyes with increasing temperature at the nematic phase. The result in the latter stage results from the significant decrease of the loss because of the disappearance for the strong leakage of the scattering fluorescence light through the boundaries of the LCs and the glass substrates after the N→I phase transition. Moreover, the anisotropy of the random lasing is crucially determined by two factors: the anisotropies in the spontaneous emission and the leakage of the scattering fluorescence light.
© 2015 Optical Society of America
In recent years, random lasers have attracted considerable attention not only because of their unusual lasing mechanisms and properties but also because of their potential applications in photonics and biomedicine [1–22 ]. Many randomly dispersive materials, such as TiO2, ZnO, and SiO2 powders [2, 4, 6, 7 ], human tissue , polymers , silver nanopowders , liquid crystals [11–18 ], and polymer-dispersed LCs (DDPDLCs) [19, 20 ], can be exploited to generate random lasing. A random laser can be obtained through either extended or localized modes via a multi-scattering mechanism. The travel time for the photons in the multi-scattering process in a disorder active medium is sufficient; the gain for the fluorescence can exceed optical loss results in random lasing emissions [1, 6, 23 ]. In the aforementioned media, only optically anisotropic LC-based random lasers can be used to control lasing characteristics with the externally flexible controllability of LC orientation, and therefore of either the refractive index or dielectric property of LCs [13, 16–22 ]. Electrical and thermal methods are the simplest ways to achieve the applications of controllable or tunable LC-based photonic devices, including random lasers [11, 12, 14–16, 18 ].
In this paper, we report for the first time an electrically and thermally controllable random laser in a well-aligned nanoparticle-added DDLC (NPDDLC) cell. Experimental results indicate that the random lasing is generated by the amplification of the fluorescence via the multi-scattering of the randomly-dispersed NPs in the diffusion rout of the NPDDLC. The electrical controllability of the random laser can be attributed to the decrease of the dye absorption and thus of the spontaneous emission. This is because the reorientation of the dye guest follows with the LC host from homogenous to homeotropic alignment by increasing the applied voltage. The lasing intensity decreases with increasing temperature at nematic phase and then dramatically increases after the nematic→isotropic (N→I) phase transition. The former stage is attributed to the decrease of the dye absorption (and thus of the spontaneous emission) due to the decrease of the dye order by increasing temperature at nematic phase. The latter is attributed to the large decrease of the loss due to the disappearance of the strong leakage of the scattering fluorescence light through the boundaries of the LCs and the substrates after the N→I phase transition. Additionally, two factors significantly influence the anisotropy of the random lasing: anisotropies of the spontaneous emission and the leakage of the scattering fluorescence light.
2. Sample preparation and experimental setup
This work employs materials of nematics E7 (refractive indices n o = 1.5216 and n e = 1.7462 at 20 °C and 589 nm, dielectric constants ε|| = 19.0 and ε⊥ = 5.2 at 20 °C and 1 kHz), laser-dye DCM (4-dicyanmethylene-2-methyl-6-(p-dimethylaminostyryl)-4-H-pyran, from Exciton), and BaTiO3 NPs (barium titanate nanoparticles, particle size ≅ 100 nm, refractive index ≅ 2.2, from Inframat Advanced Materials). BaTiO3 NP is not ferroelectric because its structure is cubic. Seven uniform mixtures with the same 0.6 wt% laser dye and different ratios of LC:NP in weight (99.4:0, 99.3:0.1, 99.1:0.3, 89.9:0.5, 89.7:0.7, 89.5:0.9, and 89.3:1.1) are prepared and then injected into empty cells. The volume fractions of BaTiO3 NP in the seven mixtures are 0, 0.016%, 0.048%, 0.089%, 0.124%, 0.160%, and 0.196%, respectively. Each empty cell is fabricated with the same condition as when two PVA-coated ITO glass slides are stacked and separated by two 23 μm-thick plastic spacers. The two slides are pre-rubbed in anti-parallel directions. Then, the cells are filled with mixtures via the capillary effect to form NP-added DDLC (NPDDLC) cells with well-aligned homogeneous textures. The long axes of the dyes in the cells are confirmed to be parallel to those of LCs because of the guest-host effect using the polarizing optical microscope.
Figure 1 shows the experimental setup for investigating electrically and thermally controllable NP random lasers based on a NPDDLC cell. A pumped laser beam, derived from a Q-switched Nd:YAG second harmonic generation pulse laser (λ = 532 nm) with a pulse duration of 8 ns, repetition rate of 10 Hz, and pumped energy U, propagates along the x direction and focused by a cylindrical lens (with focal length of 15 cm) on a stripe region of the cell. The excited stripe region is approximately 3 mm long and 0.3 mm wide. A fiber-optic probe of a fiber-based spectrometer (Jaz-Combo-2, Ocean Optics, resolution of ~0.9 nm) is placed such that it faces one of the edges of the cell to record the lateral fluorescence emission output of the random laser laterally emitted along the + z direction for the polarization components of the x and y directions, Ex and Ey, respectively (see Fig. 1). The combination with a half-wave plate (λ/2 WP, for 532 nm), a polarizer (P), and a nonpolarizing beam splitter (NBS) is placed in front of the cylindrical lens to vary the incident energy of the pumped pulses. The NBS can split the incident pulse beam with half the energy into the detector of the energy meter to measure the energy of the incident pulses. The transmission axis of the polarizer is set parallel to the rubbing direction R (along the y axis) such that the polarization of the incident pulses is parallel to the y axis. Thus, the dye in the cells has maximum absorption. An external AC voltage (1 kHz) and a temperature controller are applied on the NP-added DDLC cell to examine the electrical and thermal controllabilities of the random laser, respectively. In addition, a non-polarized white light from a tungsten halogen light source (LS-1, Ocean Optics) is utilized to normally pass through the sample. The fiber-based spectrometer is placed behind the sample to record the transmitted intensity spectrum I(λ). The transmittance spectrum T(λ) is then obtained by using the ratio of I(λ)/I 0(λ), where I 0(λ) is the incident intensity spectrum of the white light source. In accordance with Beer–Lambert law, the absorption (absorbance) spectrum A(λ) of the sample can be obtained by the following formula:
3. Results and discussion
3.1 Obtained intensity spectra of the fluorescence emission output from the NPDDLC cells with various NP concentrations
Figure 2 presents the variation of the measured intensity spectra of fluorescence emission output (along + z direction) from the NPDDLC cells with the NP concentrations of 0, 0.1, 0.3, 0.5, 0.7, 0.9, and 1.1 wt% at U = 10 μJ/pulse. Obviously, the performance of the NP random laser is related to the concentration of the added NPs. An optimum random lasing output with multiple narrow spikes can be obtained when the added NP concentration is an intermediate value of 0.3 wt%. The experimental results in Fig. 2 demonstrate that the obtained random lasing emission in the NPDDLC is mainly based on the amplification of the fluorescence via the multiple scattering of the fluorescence photons from the disorderly-distributed NPs in the diffusive rout in the DDLC. The dwelling time of the photons in the active NPDDLC medium can be sufficiently prolonged via the process of the multiple scattering so that the gain of the fluorescence can exceed the loss, which results in the random lasing emission. The increase of the NP concentration in the cell may decrease the diffusion constant and increase the scattering strength of the fluorescence in their multiple scattering and, as a result, increase the performance of the random laser. Excessive NP doping in the cell (>0.5 wt%) can instead induce significant aggregation of the NPs and therefore the decay of the random lasing. The inset in Fig. 2 shows the photograph of the lateral random lasing pattern on the screen for 0.3 wt% NPDDLC cell. Notably, the random lasing output appearing as a bright-white stripe-like pattern lies in the xz plane. This implies that the fluorescence photons undergo multiple scattering events from the NPs effectively in the xz plane for the generation of the lateral random lasing. The following experiments performing electrical and thermal controllabilities of the NP random laser use the NPDDLC cells with the optimum NP concentration of 0.3 wt% (0.3 wt% NPDDLC cells).
3.2 Lasing features of the NPDDLC random laser
Figure 3(a) presents the variation of the measured intensity spectra of fluorescence emission output from the 0.3 wt% NPDDLC cell with a pumped energy U = 2.5–10 μJ/pulse. Figure 3(b) summarizes the experimental results in Fig. 3(a), in which the variations of the peak intensity of the fluorescence emission output and the corresponding full widths at half-maximum (FWHM) with the pumped energy are given. Perceivably, the peak intensity of the emission output nonlinearly increases with the increase of the pumped energy, and an energy threshold (Uth) of ~3 μJ/pulse can be obtained. In addition, several narrow random spikes with a width of ~1 nm at U > Uth present at the same time. All these features imply the generation of a random lasing. The spontaneous fluorescence emission curve (shown later in the inset of Fig. 5) for the 0.3 wt% NPDDLC cell between 590 nm and 650 nm shows its peak at roughly 610 nm. The discrete spikes of the random lasing are distributed roughly within the range of 607 nm–613 nm, which is near the peak wavelength of the spontaneous fluorescence emission. Figure 3(b) also shows that the relative efficiency slope of the random lasing emission drops and its FWHM rises at a higher pumped energy U > 7 μJ/pulse. This result is possibly due to the decrease of absorption and thus of the spontaneous emission of the dye from the pulse-induced thermal effect. Further results regarding the influence of thermal effect on the performance of random NPDDLC lasing of cells at different temperatures is displayed in Section 3.4.
To identify the multi-scattering source that dominates the occurrence of the random lasing shown in Fig. 3, the emission characteristics of the NP-free DDLC cell should also be examined under the same experimental conditions used for the NPDDLC cell. Figure 4 shows the variation in the obtained emission spectra with incident pumped energy for a well-aligned NP-free DDLC cell. The experimental results in Figs. 4(a) and 4(b) show that both the amplification and gain narrowing effects of the fluorescence emission based on the NP-free DDLC cell are significantly weaker than those based on the 0.3 wt% NP-added DDLC cell. Moreover, no obvious lasing spikes appear based on the NP-free DDLC system. These results are attributed to the well-aligned LC molecules in the NP-free DDLC cell that results in the weak fluctuations of the local dielectric tensor of LCs and thus in the very weak scattering strength for the fluorescence photons [13–15 ]. Therefore, the multi-scattering source that dominates the occurrence of the random lasing shown in Fig. 3 is not the LCs but the NPs that randomly distribute in the DDLC.
The transport mean free path of the fluorescence photons in the scattering of the NPDDLC cell must be measured to identify the mechanism for the formation of the random lasing based on the NPDDLC cell presented in Fig. 3. This procedure can be performed with a coherent backscattering experiment by probing the 0.3 wt% NP doped LC cell with the use of a weak 633 nm laser beam [24–27 ]. The measured cone width of the coherent backscattering light is ~7.7 mrad. Based on the obtained results in Refs. 22–25 , scattering cone θ is related to the transport mean free path ℓ* (defined as the average distance a photon travels before its propagation direction is completely randomized) using the following approximate equation:Eq. (2), we calculate the transport mean free path as approximately ℓ* ≅ 13.1 μm. Given the satisfaction of the condition kℓ* = 2πℓ*/λ ≅ 101 > 1, the random lasing in the present study must result from the diffusion of the fluorescence photons via the multi-scattering from the NPs added in the DDLC cell [1, 4, 5, 13–15, 22 ].
Figure 5 shows the emission spectra of the fluorescence outputs of the NPDDLC cell in the orthogonal Ex- and Ey-components at U = 6–10 μJ/pulse. Apparently, the random lasing emission is anisotropic, in which the fluorescence emission of the Ey-component is significantly stronger than that of the Ex-component. The refractive index contrast between the host and the scattering sources crucially determines the diffusion constant and thus the scattering strength as the fluorescence photons undergo multiple scattering. In the present NPDDLC system, the refractive indices for the LC host range from no = 1.5216 to ne = 1.7462 at room temperature and for NPs is nNP ≅ 2.2. When the fluorescence photons propagate roughly along the z direction and undergo multi-scattering in the xz plane at 23 °C, the extraordinary wave with y polarization experiences a smaller refractive index contrast between the LCs and the NPs (about |ne – nNP|) than that experienced by the ordinary wave with x polarization (about |no – nNP|). This phenomenon should cause an anisotropic diffusion constant that the x-polarized component is shorter than the y-polarized one, such that the scattering strength for the x-polarized component is stronger than that for the y-polarized one. However, such an occurrence will not lead to the experimental outcome of the anisotropy of the random lasing, in which the y-polarized component is significantly stronger than the x-polarized one shown in Fig. 5. Thus, the anisotropy of the refractive index contrast between the LCs and NPs is not crucial in determining the anisotropy of the random lasing output. Instead, a noticeable factor to cause the anisotropy of the random lasing is the anisotropy of the spontaneous fluorescence emission because the cell is pumped by the y-polarized pumped pulses. The inset in Fig. 5 shows the fluorescence emission spectra for x- and y-polarized components after the excitation of the NPDDLC cell by a CW diode-pumped solid-state (DPSS) green laser beam (532 nm, 5 mW/cm2) with a linear polarization along the y axis. Apparently, the measured fluorescence intensity via the spontaneous emission of the excited dyes in the y-component is stronger than that in the x-component. After the dye molecules absorb the incident pumped pulses with a polarization at the y direction, the oscillation of the dipoles along the y axis can emit a fluorescence emission with a polarization roughly parallel to the transition dipole moments of the dyes (at the y direction). The stronger y-component fluorescence emission can be significantly amplified in their diffusive routes through a multiple scattering mechanism of the randomly-distributed NPs so as to generate the anisotropic random lasing shown in Fig. 5.
3.3 Electrical controllability of the NPDDLC random laser
Figure 6(a) shows the experimental results associated with the electrical controllability of the total fluorescence emission output of the NPDDLC random laser, in which the intensity spectra of the fluorescence emission outputs at various voltages at U = 10 μJ/pulse are measured. The peak intensities for the x- and y-polarized fluorescence emission outputs at various voltages at U = 14 μJ/pulse are also obtained and summarized in Fig. 6(b). The lasing output of the NPDDLC random laser apparently decreases as the applied voltage increases from 0 V to 2.5 V regardless of the x- or y-polarized components. To explain the electrical controllability of the random lasing, we further measured the absorption and fluorescence emission spectra of the 0.3 wt% NP-added DDLC and NP-free DDLC cell. Figures 7(a), [7(c)] and 7(b) [7(d)] show the measured absorption and fluorescence emission spectra, respectively, at 0, 0.5, 1.0, 1.5, 2.0, and 2.5 V based on the DDLC (NPDDLC) cell. Apparently, the absorption and fluorescence emissions of either the DDLC or NPDDLC cell decrease when the voltage increases from 0 V to 2.5 V because the direction of the transition dipole moments of the dyes may follow that of the LC director when the LC molecules reorient away from the y direction to the x direction from 0 V to 2.5 V. This occurrence causes that the absorption of the dyes and thus the spontaneously emitted fluorescence decreases with increasing voltage after the excitation of the pumped pulses. This phenomenon leads to the decrease of the intensity of the scattering fluorescence light via the multi-scattering of NPs and thus the decay of the obtained random lasing strength.
The contrast between the refractive indices of LCs and NPs experienced by the y-polarized component of fluorescence light propagating roughly along z direction in the xz plane at 23 °C increases from |n e–nNP| to |n o–nNP| with increasing voltage from 0 V to 2.5 V. This phenomenon decreases the diffusion constant, increases the scattering strength, and thus increases the random lasing intensity for the y-polarized component. However, the experimental result shown in Fig. 6(b) is not consistent with this prediction. Moreover, the refractive indices experienced by the x-(y-)polarized component of the scattering fluorescence will increase (decrease) from n o to n e (from n e to n o) with increasing voltage from 0 V to 2.5 V at 23 °C. This will cause the result that the contrast between the refractive indices of LCs and substrates for the x-(y-)polarized component increases from |n o–ng| to |n e–ng| (decreases from |n e–ng| to |n o–ng|) with increasing voltage from 0 V to 2.5 V, where n g = 1.52. This result indicates that the confinement strength for the x-(y-)polarized in the LC layer will increase (decrease), respectively, with increasing voltage from 0 V to 2.5 V. However, the experimental result shown in Fig. 6(b) is also not consistent with this prediction. The above-mentioned findings suggest that both the index contrasts between the LCs and NPs and between the LCs and the substrates are not crucial in determining the relation of the random lasing output and the applied voltage. The contribution levels of the elements influencing the electrical control of the random laser, including the strength of scattering due to the index contrast between LCs and NPs, the strength of spontaneous emission due to the orientation of dye molecules, and the strength of confinement due to the index contrast between LCs and substrates, are summarized in Table 1 .
3.4 Thermal controllability of the NPDDLC random laser
Fig. 8 shows the experimental results associated with the thermal controllability of the NPDDLC random laser. The lasing intensity of the random laser decreases as the temperature increases from T = 23 °C to 50 °C. This temperature dependence of random lasing intensity should be related to the temperature-dependent absorption and spontaneous fluorescence emission of the cell. Figures 9(a) and 9(b) show the variations of the absorption and the spontaneous fluorescence emission with temperature, respectively. Both the absorption and the spontaneous fluorescence emission decrease with increasing temperature. This result is reasonable because the transition dipole moments of the dyes may follow that of the LC director when the LC molecules reorient from a more ordered state (at y direction) to a less ordered state from 23 °C to 50 °C, such that the absorption of the dyes and thus the spontaneously emitted fluorescence decreases. This phenomenon may decrease the intensity of the scattering fluorescence light via the multi-scattering of the randomly distributed NPs in the DDLC, such that the strength of the random lasing output decreases.”
As displayed in Fig. 8, the random lasing almost vanishes when the temperature increases to 50 °C. Nevertheless, the random lasing reappears at T = 55 °C (> clearing temperature), and its strength is even stronger than that at T = 23 °C. The dramatic reappearance of the strong random lasing after the N→I phase transition cannot be completely explained on the basis of the aforementioned absorption (or spontaneous fluorescence emission) mechanism. The reason is that the absorption and fluorescence emission of the cell at 55 °C are lower than the halves of those at 23 °C [Figs. 9(a) and 9(b)]. We observed the lateral fluorescence emission pattern at various temperatures during the excitation of pumped pulses to determine the stimulus of the abovementioned phenomenon. Figures 10(a)-10(d) present the images of the NPDDLC cell under a polarizing optical microscope (POM) with crossed polarizers (on the top of the figures) and the lateral fluorescence emission patterns of the cell pumped at U = 10 μJ/pulse (on the bottom of the figures) at T = 23 °C, 40 °C, 50 °C, and 55 °C. The included angle between the rubbing direction of the cell and the polarizer is 45°. The bright and dark POM images appearing at T < 50 °C and T = 55 °C, respectively, show that the LCs are at the nematic and isotropic phases, respectively. The formation of droplets at 50 °C [Fig. 10(c)] indicates that the LCs begin to undergo an N→I transition at this temperature. Figure 10 displays the butterfly-shaped fluorescence emission pattern on the screen at 23 °C after the excitation of the pumped pulses on the cell. This brightness pattern gradually decays when the temperature increases from 23 °C to 50 °C. When the temperature further increases to 55 °C, the bright stripe in the center of the pattern reappears and the two wing-like parts out of the center vanish. For convenience, we divided the splendid butterfly-shaped emission pattern into two regions: the lasing and nonlasing output regions. In the lasing output region, the strong random lasing output can be observed as a bright-white stripe-like pattern on the center of the emission pattern, e.g., at 23 °C and 55 °C [Figs. 10(a) and 10(d), respectively]. The butterfly-shaped emission appearing in the nonlasing output region (beyond the lasing output region) at T = 23–50 °C must be attributed to the scattering fluorescence photons that are not well-confined in the LC layer and significantly leak out of the layer. This strong leakage can cause a large loss and significantly raise the lasing threshold for the generation of the random laser. To understand whether or not this leakage of the scattering fluorescence is also related to the anisotropy of the random lasing output, we detected the leaky fluorescence intensities at x and y polarizations [i.e., the ordinary and extraordinary (o- and e-, respectively) components, respectively] in the nonlasing output regions. Figures 10(e) and 10(f) show the spectra of the leaky scattering fluorescence for the o- and e-components in the xz-plane in a certain nonlasing output region [on the left of the lasing output region, indicated with the white dotted circles shown in Figs. 10(a)–10(d)] at various temperatures. Apparently, the intensity of the leaky scattering fluorescence light for the o-component is apparently stronger than that for the e-component at the nematic phase (at T < 50 °C), and the leakage of the fluorescence emission after the N→I phase transition (at 55 °C) is weaker than that at the nematic phase. Similar results can be obtained at other nonlasing output regions in the butterfly-shaped emission pattern (not shown). The following analysis will demonstrate two points:
- (i) The anisotropy of the leaky scattering fluorescence light may partially influence the anisotropy of the random lasing output.
- (ii) The dramatic reappearance of the random lasing after the N→I phase transition is strongly related to the large discrepancy in the leaky scattering fluorescence light and thus the loss at the nematic and isotropic phases.
At 23 °C, the difference between the refractive index of the glass substrates (ng = 1.52) and the ordinary refractive index (no = 1.5216) experienced by the o-component scattering fluorescence light is significantly smaller than that between ng and the extraordinary refractive index (ne = 1.7462) experienced by the e-component scattering fluorescence light. The critical angles for the total internal reflection of the o- and e-component scattering fluorescence light on the boundaries of the glass substrates and the LCs are 87.4° and 60.5°, respectively. This result indicates that the confinement for the e-component scattering fluorescence light in the LC layer is significantly better than that for the o-component. Most o-component scattering fluorescence light can leak out the boundary of the LCs and glass substrates in the multi-scattering diffusive rout because of the matching of no and ng. In addition to the aforementioned mechanism of the anisotropy in the spontaneous emission of the dyes, this anisotropy of loss caused by the anisotropy in the leakage of the scattering fluorescence light at the nematic phase is another considerable mechanism that may induce the anisotropy of the random lasing emission. That is, the y-polarized random lasing component is significantly stronger than the x-polarized one. In addition to the serious leak of the o-component scattering fluorescence light in the xz-plane, the leakage of that component not emitting in the xz-plane [Figs. 10(a) and 10(b)] is also serious because of the identical match between n o and n g.
Moreover, the variation in the ordinary refractive index of E7 is very small (between 1.52 and 1.53) between 23 °C and <50 °C . This variation leads to a strong leakage loss of the o-component scattering fluorescence light at the entire nematic phase. The leakage of the scattering fluorescence wave is significantly weaker at the isotropic phase than at the nematic phase because of the high and isotropic contrast of the refractive indices between the isotropic LCs (n i ≅1.6) and glass substrates (ng ≅ 1.52) at all directions. This significantly smaller loss of the scattering fluorescence photons at the isotropic phase than at the nematic phase may cause the dramatic reappearance of the strong random lasing after the N→I phase transition, even though the spontaneous fluorescence emission at the isotropic phase is lower than that at the nematic phase [Fig. 9(b)]. The contribution levels of the strengths of scattering, spontaneous emission, and confinement to the thermal control of the random laser are summarized in Table 2 .
This study is the first to investigate an electrically and thermally controllable random laser on the basis of a NPDDLC cell. Experimental results indicate that the random lasing is attributable to the enhancement of the fluorescence via the multi-scattering of NPs in the diffusion rout of the NPDDLC. The lasing intensity of the obtained random laser can be controlled by varying the applied voltage or temperature of the cell. The electrical controllability of the random laser is attributable to the decreases of the absorption and thus of the spontaneous fluorescence emission for the dyes when the LC host and thus the dye guest reorient from a homogenous to a homeotropic texture as the applied voltage increases. The random lasing intensity decreases below the clearing point with increasing temperature and then dramatically increases via the N→I phase transition. The result in the former stage is credited to the decrease of the dye absorption and thus of the spontaneously emitted fluorescence because of the decrease in the dye order as the temperature increases below the clearing point. In the latter stage, the result is attributed to the large decrease in the loss because of the disappearance of the strong leakage of the scattering fluorescence light through the boundaries between the LCs and the glass substrates after the N→I phase transition. Moreover, both the anisotropies in the spontaneous emission and the leakage of the scattering fluorescence light are crucial in determining the anisotropy of the random lasing.
The authors would like to acknowledge the financial supports provided by the Ministry of Science and Technology of Taiwan (Contract number: MOST 103-2112-M-006-012-MY3) and the Advanced Optoelectronic Technology Center in National Cheng Kung University under the projects of the Ministry of Education, and the Chung Shan Medical University (Contract number: CSMU-INT-102-09). The authors are also grateful to KGSupport for their editorial assistance.
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