Through applied voltage (VAC), the characteristic of dye-doped liquid crystal random lasers (DDLC-RLs) inside capillary fiber (CF) has been readily and efficiently modulated. As VAC rose, the intensity of the emission spike increased dramatically at a fixed excited energy, and the slope efficiency of DDLC-RL increased obviously. By means of the white light scattering spectrum, the increase in the output from DDLC-RL is attributed to the enhancement of recurrent light scattering within the liquid crystals (LCs) to strengthen the light localization. In order to distinguish the characteristic of DDLC-RL with VAC = 0 V and 60 V, the α-stable distribution was adopted to show the Lévy distribution of intensity fluctuation with a reduction in value from α = 1.86 to α = 1.59.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Since the first theoretical studies on non-resonant feedback made by Letokhov  in 1968, random lasers (RLs) have attracted considerable attention owing to their unique properties and practical applications. RLs have several peculiar characteristics, including low spatial coherence, multiple emission spikes with narrow linewidths, and broad solid angle output. To date, RLs have been widely used in practical applications including photonic barcodes, optical batteries, low speckle noise imaging , and biomedical diagnostics . Unlike conventional lasers, which have mirrors, mirrorless RLs utilize recurrent light scattering within disordered nanostructures to produce photon localization, i.e., weak localization [4,5], and to provide optical feedback.
In previous studies, semiconductor materials such as ZnO powder , CdSe/CdS nanocrystals  and organic-inorganic halide perovskite , play the role of both the gain medium and scattering material for the generation of RLs. In addition, RLs have been demonstrated by doping lasing dyes as an active medium within a variety of disordering nanostructures, including dielectric particles , polymers , metallic particles , electrospun fibers , and biological tissues such as the wings of butterflies  or cicadas . In this case, the strength of light scattering can be altered independently to manipulate the properties of RLs by varying the morphology and the concentration of the scattering nano-subject.
To date, LCs have become indispensable elements in the display industry because they can be fast-modulated by electric fields. LCs have also been widely used in photonic and optoelectronic applications such as amplitude or phase modulation, speckle noise image suppression , and biomedical diagnosis. By mixing LCs with the chiral molecule, cholesteric LCs (CLCs) have been fabricated as one-dimensional photonic crystals to generate band edge lasing . Unlike other laser systems, the output properties of dye-doped CLC (DDCLC) lasers can be readily controlled by external modulation such as an electric field [17–19] or magnetic field, mechanical stress, or temperature .
Resulting from the intrinsic birefringence characteristic, LCs are also superior light scattering media that have been filled in glass cells [21, 22], capillary tubes , and capillary fibers (CFs)  to fabricate dye-doped liquid crystal RLs (DDLC-RLs) . The characteristics of DDLC-RLs, including the emission spectra, polarization, and lasing threshold, can be alternated by the doping concentration of the polymer, the rubbing direction of coated polyimide (PI) on a glass substrate, and the size of the core diameter . In order to instantaneously manipulate the output behavior of DDLC-RLs, the produced cell is thermally controlled to vary the refractive index of the LCs . However, the modulation of LCs by the variation of temperature is slow, owing to its low thermal conductivity. In this work, we offer insight the readily modulation of the alignment of LCs inside CF by the electric field to change the light scattering; then, the conversion and slope efficiency of RLs can be controlled.
2. Sample preparation and experimental setup
The DDLC mixtures were prepared by doping 0.5 wt% of lasing dye, Pyrromethene 597 (PM597), into 99.5 wt% nematic LC (E7, ne=1.7462, no=1.5216, clearing point approximately 70°C). The LC mixtures were heated and stirred in a small vessel on a hot plate to assure the uniform dispersion of fluorescent molecules within the LCs. The 5-cm long CFs, having hollow core diameters of 20 and 30 μm, were immersed into the admixture. By the capillary effect, the DDLCs were filled into the hole area of the CF. Then, the produced CF with infilling of LC mixtures was sandwiched between two ITO-coated glasses, as shown in Fig. 1(a). The 1-kHz sinusoidal-formed ac voltage (VAC) was applied to the ITO glasses to ensure uniform distribution of the electric field inside the CF.
The schematic setup to excite a DDLCs-RL inside the CF is illustrated in Fig. 1(a). A 532 nm Q-switched laser was used as an excitation source with output pulses having a 10-Hz repetition rate and 2.4-ns duration. The pump beam was focused onto the core area of the CF with a long line stripe (5 mm × 12 μm) through a cylindrical lens (CL) having a focal length f1 of approximately 7.5 cm. To optimize the overlap between the pump area with the central hole of the CF, the produced sample was mounted and adjusted by a 3-axis translation stage. In addition, we combined a half-wave plate (λ/2) and polarization beam splitter (PBS) to control the pump energy. The emission spectra from the CF were coupled into a fiber tip by a convex lens and then measured by a spectrometer (HR4000). Lower Left of Fig. 1(a) shows a picture of the produced DDLC sample pumped by the Q-switched laser.
In previous work, the image of polarization optical microscopy (POM) has been used to confirm the alignment regularity of LCs inside CF with different core diameters . In this investigation, we combined POM with CCD (pixel size approximately 3328×2548) and a spectrometer (HR4000, resolution approximately 0.3 nm, Ocean Optics Inc.) to obtain the image and light scattering spectrum at different applied voltages, as shown in Fig. 1(b). The produced sample was inserted between two crossed polarizers (i.e., polarizer (PL) and an analyzer (AL)). A white light source from a halogen lamp was illuminated onto the produced sample to generate the scattering light owing to the disordering alignment of LCs inside the CF. The scattering light was collected and collimated by an objective lens (20X) and injected into a fiber (P400-2-VIS-NIR, Ocean Optics Inc.). Finally, the light scattering spectrum and POM images of the produced samples were measured by the spectrometer and a CCD. The POM image of CFs without LCs reveals a dark area in the core region (upper right of Fig. 1(b)) and becomes bright after infilling the birefringent LC (lower right of Fig. 1(b)), which causes the enhancement of light scattering.
3. Results and discussion
By the axial pump of the Q-switched laser, the characteristic of DDLC-RL inside CF has been experimentally demonstrated in previous work, which depends on the core diameter . With the side pump configuration in Fig. 1(a), we control the output behavior of DDLC-RL through applied voltage at a fixed pump energy (Ep) of approximately 8.35 μJ. As the applied voltage VAC increases from 0 V to 100 V, the emission spectra from the two produced samples, with core diameter of 20 (DDLC-CF(I)) and 30 μm (DDLC-CF(II)), are shown in Figs. 2(a) and (b). The corresponding SEM images, shown in the insets of Figs. 2(a) and (b), reveal the cross section of CF. There are a number of emission spikes on the top of the broad pedestal, even without the applied voltage (VAC =0 V, black line), which is a characteristic of RLs.
As VAC increased from 0 V to 80 V, the intensity of emission spikes from both samples enlarged apparently, as shown in Figs. 2(a) and (b). The baseline of each spectral curves in these two figures were properly shifted intentionally to avoid overlap. The evolution of the emission spectrum from DDLC-CF(II) (D =30 μm) with the increase in applied voltage in Fig. 2(b) is similar to that from DDLC-CF(I) (D =20 μm). However, the ratio of coherent spike intensity relative to the pedestal intensity declines for the DDLC-CF(II). In addition, less lasing spikes were excited from the DDLC-RL inside a CF with 30 μm core diameters in compared to that inside a CF with 20 μm core diameter. This indicates that coherent feedback became less apparent for the DDLCs inside the CF with a large core diameter than that with a small core diameter. As VAC increased from 80 V to 100 V, the spike intensity of RL did not reveal an obvious increase.
Using the experimental setup in Fig. 1(b), the CCD images (upper side) of the DDLC-CF(I) and light scattering spectrum (lower side) with different applied sinusoidal voltage VAC are shown in Figs. 3(a)–(f). The red region around the core area is caused by the scattering of fluorescence from the lasing dye. It is obvious that there is an increase in bright areas in the central core of the CF and enhancement of light scattering intensity as VAC increases from 0 V to 80 V (Figs. 3(a)–(d)). However, the light scattering intensity does not reveal an apparent increase as VAC rises from 80 V to 140 V (Figs. 3(d)–(f)).
Although no rubbing PI was coated inside the core area of the CF, most LC molecules were aligned along the axis direction of the core . However, multiple light scattering occurred because of the slightly disordered alignment of birefringence LCs. Owing to the intense multiple light scattering, light can be trapped, a phenomenon termed light localization, to form a number of closed loops, as illustrated in Fig. 4(a). Thus, the constructive interference occurs in the closed loop to generate several emission spikes in the spectrum, which is the main characteristic of the coherent feedback. The recurrent light scattering is efficiently amplified when the mean free path, ls, is greater than the gain length, lg, i.e., ls ≥ lg. Here, the mean free path is expressed as ls = 1/(ρσs), where ρ and σs are the number density of the scattering particles and scattering cross section, respectively.
After applying a sinusoidal ac voltage (VAC, frequency f = 1kHz) above a certain threshold, LC molecules were driven by the external electric field and rotated along the electric field. In addition, the alignment of fluorescent dyes will follow the arrangement of the local nematic order of nematic liquid crystals (NLCs). Thus, the alignment of the LC mixture inside the hole area becomes even irregular, causing more intense light scattering (as shown in Fig. 4(b)) and resulting the enhancement of the lasing peak intensity in the emission spectrum.
The peak intensities (IRan, navy squares) of spikes and corresponding deviations (navy error bar) obtained from the emission spectra of the DDLC-CF(I) as a function of VAC are shown in Fig. 4(c). The quick rise in intensity can be seen as VAC increases above 20 V. This demonstrates that high enough VAC is needed to drive the LCs, i.e., the threshold of the driving voltage. As VAC increased further, the alignment of LCs became more disorderly, enhancing the light scattering and increasing the coherent spike intensity. However, the amplitude of lasing spikes did not increase and even saturated with a further increase in applied voltage VAC above 60 V. The integrated intensity (IScat) from the light scattering spectra (Figs. 3(a)–(f)) is also revealed by the red circles in Fig. 4(c). Note that the variation (or trend) of the two curves IRan and IScat versus VAC, is similar. This result demonstrates that the increase in emission spikes from the DDLC-RL as VAC increases is mainly attributed to the enhancement of light scattering.
Figures 5(a) and (b) depict the emission spectra of the DDLC-CF(I) as the pump energy increases from 1.12 μJ to 8.01 μJ without (VAC =0 V) and with (VAC =60 V) applied voltage, respectively. When the pump energy is above 2.41 μJ, several discrete emission spikes can be excited above the pedestal. In both situations (VAC =0 V and 60 V), the emission intensity of the coherent spike from the CF appears to increase as the pump energy increases. In contrast to the state without voltage (VAC =0 V in Fig. 5(a)) at the same excited pump energy, the intensity enhancement of the pedestal and coherent spike becomes clearer with the applied voltage (VAC =60 V in Fig. 5(b)) on the produced sample.
The peak intensities (IRan) of the largest emission spikes from the emission spectra of the DDLC-CF(I) as a function of pulse energy at different applied voltages (0 V to 100 V) are shown in Fig. 5(c). The peak intensity of the DDLC-RL increased slowly at the lower excited pulse energy Ep, but increased dramatically when the Ep exceeded a certain value. After linear fitting, two straight lines with low and high slopes were obtained, respectively. This shows the spontaneous emission at lower excitation and the stimulated emission when the pump energy is above a threshold value of approximately 1.7 μJ/pulse. In addition, the slope efficiency of the RL increases as VAC increases from 0 V to 60 V. Because the light scattering (IScat) inside the DDLCs did not increase at high voltage, as shown in the red circle in Fig. 4(c), the increased rate of slope efficiency slowed down as VAC exceeded 60 V. In addition, the slope and conversion efficiency of DDLC-RL with VAC = 100 V is smaller than that for VAC = 80 V, as shown in Fig. 5(c).
The power Fourier transform (PFT) of the emission spectra from DDLC-RL at different VAC with Ep = 8.2 μJ is shown in Fig. 5(d). Unlike the narrow and regular peaks from the Fabry-Pérot cavity, the PFT in Fig. 5(d) contains a series of nonperiodic and broad spectral components that illustrate a number of specific oscillation modes. Theoretically, the frequencies of harmonics from the PFT occur at multiples of neff Lc/π, where neff =(2no+ne)/3 is the effective refractive index of the LCs and Lc is the cavity path length. From the PFT of the RL without applied voltage (VAC = 0 V, black line in Fig. 5(d)), we estimate the cavity path length of RL to be approximately 207 μm. With the applied voltage, the PFT of emission spectra from the DDLC-RL in Fig. 5(b) reveals broader bandwidth owing to the increase in the number of resonant modes. This is also because the alignment of NLCs inside the CF becomes more disordered so that light scattering increases intensely with the applied voltage. Thus, the cavity path length of RL, estimated from the harmonics of the power spectrum, reduces to approximately 173 μm at VAC = 60 V.
To quantitatively define the threshold of an RL, the α-stable distribution, which is an econophysical function used by Uppu et al.  is applied. By statistical measurements of intensity fluctuations of dynamic systems, Lévy fluctuations (power-law tailed) have been developed to represent the Gaussian or Lévy statistics. Generally, the α-stable distribution [27,28] utilizes four parameters, including α, μ, β, and σ, to fit the statistical data, which is constructed by the intensity distribution of the scattering system, and can completely illustrate the heavy-tail distribution. The parameter α describes the exponential tail of the distribution, which displays Gaussian behavior for α = 2 and Levy behavior for α < 2. The other parameters μ, β, and σ describe the location, skewness, and width of the distribution, respectively.
To confirm the characteristics of the RL from DDLCs inside the CF without (VAC =0 V) and with (VAC =60 V) applied voltage, the α-stable distribution is adopted by grabbing one thousand spectrum slots to obtain the time-varying intensity evolution with emission wavelength λ = 593 nm, as shown in the inset of Figs. 6(a) and (b). The probability of the intensity distribution is shown by the histogram that can be fitted by the α-stable distribution (red solid curve). The larger intensity fluctuation and wider intensity distribution can be seen in Fig. 6(b) with VAC = 60 V in comparison to Fig. 6(a) with VAC = 0 V. A more fat-tailed distribution is achieved in Fig. 6(a) with α = 1.86 than that in Fig. 6(b) with α = 1.59, showing more obvious light scattering inside the CF.
Through applied voltage, the characteristics of a DDLC-RL inside a CF, using the side pump of a Q-switched Nd:YAG laser, were efficiently and quickly controlled. Similar to the trend of light scattering intensity by means of DDLCs inside a CF, an obvious increase in emission spike intensity from the RL was revealed when VAC increased above 20 V and started to saturate when VAC increased above 60 V. In addition, the conversion and slope efficiency of an RL enhanced dramatically with applied voltage, when VAC fell 60 V. The characteristic of an RL versus applied voltage was verified by the PFT of emission spectra of a DDLC-RL to illustrate the nonperiodic and broad peaks. The α-stable distribution was adopted to show the Lévy distribution of the DDLC-RL inside the CF with a reduction in value from α = 1.86 to α = 1.59. The investigations offer insights the manipulative characteristics of the DDLC-RLs through applied voltage with direct implication for intriguing physical phenomenon and posses potential optoelectronics applications and biomedical diagnostics.
Ministry of Science and Technology of Taiwan (MOST 105-2112-M-027-001-MY3).
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