1. Introduction

Random lasers represent a unique class of laser sources, whose structures are characterized by the presence of scatterers, such as microparticles, randomly dispersed within a gain medium [1–10]. These lasers operate by pumping the random gain medium, which causes the light generated within the medium to undergo multiple scattering, traverse along an extended optical path, and get amplified through stimulated emission. Eventually, the light is emitted as a laser oscillation due to the pseudo-cavity structure formed by the scatterer distribution. Random lasers exhibit relatively high monochromaticity, but have lower directivity compared to conventional lasers. Such a multidirectional property results from low spatial coherence. Thus, random lasers can emit light with minimal interference, leading to the excellent feature of almost negligible speckle noise [11]. This attribute makes them particularly desirable for applications involving laser displays and measurement devices. However, the practical applicability of random lasers has been hindered by difficulties encountered in controlling their emission properties. These difficulties arise from their inherent randomness and low emission efficiency.

Consequently, numerous methods have been proposed for managing the emission characteristics of random lasers [12]. These approaches are primarily grounded on the fact that the size, shape, refractive index, and spatial distribution of scatterers within the gain media strongly affect the random laser action. One approach to controlling the emission spectrum involves adjusting the diameter and refractive index of monodisperse spheres with Mie resonances [13]. The introduction of inhomogeneities in scatterer distribution improves the random laser mode selection. For example, in a random gain medium featuring homogeneously distributed monodisperse particles, the presence of a defect focuses and amplifies the light, thereby selecting the emission wavelength [14]. Laser ablation-induced defects have been found to change the number of lasing modes [15]. Furthermore, by incorporating plasmonic gold nanostars suspended in laser dyes, it has been possible to extend the range of random lasing from yellow to the infrared spectrum [16]. However, these techniques typically necessitate the reproducing random gain media to change the emission properties, rendering real-time emission control challenging.

To achieve the real-time control of random lasing, several researchers have concentrated on manipulating the spatial distribution of the pumping light. Adjusting the pump intensity pattern allows the tuning of the emission spectrum [17,18] and direction [19], resulting in single sharp spectral peaks or directional control of the laser emission. Changing the pump shape also activates different lasing modes [20]. Spectral control is also achieved through specific near-infrared light patterns [21] or by using helium-neon (He-Ne) laser illumination on light-absorbing Janus particles in a colloidal dispersion of titanium dioxide (TiO₂) particles, creating temperature gradients for particle accumulation [22]. The excitation of surface plasmons is also used to achieve directional control [23].

In this study, we investigated a method for controlling the distribution of scatterers using an optical trapping technique. Optical trapping is a method that employs focused light to trap particles and reposition them to an arbitrary position [24]. This technique finds application in various fields, including nanotechnology, spectroscopy, soft matter, and biology [25]. When a laser beam is focused onto a particulate medium, scatterers near the focused spot are drawn into the waist region of the beam, forming a non-uniform scatterer distribution [26,27]. Previous studies have demonstrated that the presence of spacer particles (nonscattering regions) dispersed within a random gain medium enhances the peak intensity of the emission spectrum [28,29]. The lasing threshold of a random laser with clustered particles decreased as the degree of particle aggregation increased [30]. Optical trapping enables the creation of another form of inhomogeneous scatterer distribution, characterized by localized high-density scatterer regions surrounded by low-density areas. Accordingly, we experimentally investigated the impact of this inhomogeneous scatterer distribution on the emission spectrum of a random laser.

2. Experiments

First, we prepared an aqueous ethanol solution (ethanol: 67.89 wt%) doped with Rhodamine 590 laser dye (density: 6.7 × 10⁻³mol/L), which served as the gain medium. Next, we dispersed spherical-TiO₂ particles (diameter: 250 nm) in the gain medium as scattering particles. The refractive indices of the TiO₂ particles and the ethanol solution were 2.7–3.0 (depending on the wavelength) and 1.36, respectively. To create the sample medium, a droplet of the dye-doped ethanol solution mixed with TiO₂ scatterers was placed on a glass slide. A cover glass was carefully positioned over the droplet to maintain the thickness of the medium at 0.2 mm, which was determined by the thickness of the vinyl tape used for the enclosure. An example of the sample medium is illustrated in Fig. 1(b).

 

Fig. 1. (a) Schematic representation of the experimental setup. (b) A photograph taken from above the sample. The random gain medium was 10 × 10 mm in the center, surrounded by electrical tape with a thickness of 0.2 mm. (c,d) Photographs captured through imaging optics when light trapping is inactivated (c) and activated (d). In (d), the particles were trapped around the two trap spots, with the power of the trapping light being 15 mW.

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The experimental setup is schematically depicted in Fig. 1(a). A continuous-wave (CW) laser with a wavelength of 671 nm illuminated the sample from the bottom and trapped the scattering particles. At this wavelength, there is little absorption of trapping light in the medium. Holographic optical trapping was accomplished by expanding the diameter of the CW laser to 10 mm and then illuminating a liquid crystal on a silicon spatial light modulator (LCOS-SLM, Santec SLM-200). The light reflected from the SLM formed two trap spots set 15.7 µm apart at the focal position of the microscope objective (magnification 40×, NA: 0.5). Two trap spots were used because two particle ensembles in the trap regions were confirmed to provide greater light amplification than one. The position of the beam waist of the trapping light was set at the center of the sample medium along the propagation direction, that is, 0.1 mm above the slide glass and 0.1 mm below the cover glass. The sample was pumped with a frequency-doubled Nd:YAG laser beam with a wavelength of 532 nm and a pulse duration of 10 ns. The pump beam was focused onto the sample surface using a cylindrical lens with a focal length of 50 mm. The width and length of the pump area were 87 µm and 5 mm, respectively. The light emitted from the sample was detected using an optical spectrum analyzer (Ocean Optics HR2000). This was realized through a collector lens (focal length of 60 mm, magnification 1×), a notch filter, and an optical fiber with a core diameter of 400 µm, all at a detection angle of approximately 45°. Therefore, the detection area of the emitted light at the medium surface was an ellipse with a major axis of approximately 570 µm and a minor axis of 400 µm. For each configuration, four sample media were prepared and averaged. The emission spectrum for each sample medium was measured every 300 ms for approximately 5 min, resulting in 1000 spectral data with a spectral resolution of 0.2 nm. Neither photobleaching of the dye nor ethanol evaporation were observed within the measurement time.

3. Results

Figures 1(c) and 1(d) provide an example of the particle distribution when the trapping light was off and on, respectively. The volume fraction of the particles was 0.2% and the total power of the trapping light was 15 mW. Notably, the intensities of the two trap spots are not precisely equal to 7.5 mW because they cannot be made equal. Figure 1(d) illustrates that a substantial number of particles were agglomerated at the two laser spots. The slightly blurring of the image of the trapped particles indicates their location being above the beam waist of the trapping light.

We examined the impact of particle trapping on the characteristics of the emission spectrum. Figure 2 shows examples of the spectra measured for samples with 0.1 and 0.3% volume fractions of the scattering particle. These low particle concentrations were selected to minimize the scattering of the trapping light itself. The pump energy was 30 µJ in all cases. For a 0.1% volume fraction, almost no lasing was observed without trapping. However, in other cases, the emission spectra displayed several distinct and sharp spikes, indicative of the features associated with coherent random lasing.

 

Fig. 2. Emission spectra for two different volume fractions of particles. (a) 0.1% without trapping, (b) 0.1% with trapping, (c) 0.3% without trapping, and (d) 0.3% with trapping. The pump energy and the power of the trapping light were 30 µJ and 15 mW, respectively.

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The emission spectra characteristics were evaluated using three parameters: maximum spike intensity, average spike intensity, and number of spikes. Notably, spike intensity refers to the height from the baseline of each spike in the spectrum, and not from zero intensity. This approach helps minimize the influence of the fluorescence pedestal. Figure 3 presents the average intensity of the maximum spike in each spectrum, the average intensity of all spikes in the spectra, and the average number of spikes in each spectrum when light trapping was activated and deactivated. The maximum and average spike intensities were averaged only over spectra with spikes. In contrast, the number of spikes was averaged over all spectra, including those with no spikes. The spectra were measured for 5 min for each configuration. Figures 3(a) and 3(c) illustrate that both the maximum and average spike intensities increased for a 0.1% particle fraction when the trapping light was incident on the sample. The average number of spikes also increased from 0.79 to 3.14, indicating the onset of random lasing when the trapping light was on. As random lasing did not occur due to weak scattering when the particles were not trapped, this outcome suggests that the trapped particles generate stronger scattering than randomly dispersed particles. Therefore, although the detection area covers a region considerably greater than the trapped particles only, the spatial modes are indicated to be distributed only within each of the trapped clusters or between the two trapped clusters. Further research is needed to understand the interaction between the clusters. This is currently under investigation and will be reported in a separate study.

 

Fig. 3. (a,b) Maximum spike intensity, (c,d) average spike intensity, and (e,f) number of spikes of the emission spectrum with and without trapping for volume fractions of particles of (a,c,e) 0.1% and (b,d,f) 0.3%. The power of the trapping light was 15 mW. The error bars represent the standard error (n = 4).

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Conversely, for 0.3% particle fraction, the increase in both maximum and average spike intensities was relatively small. This implies that particle trapping becomes less effective when the particle fraction increases. This is partly because larger particle fractions cause more light to be scattered, resulting in decreased trapping power. However, the ratio of the maximum intensity of the spikes to their average intensity for a 0.3% fraction increased from 2.41 to 2.58, in the presence of trapping light, while the number of spikes remained approximately constant. An earlier study [29] demonstrated that strong random lasing tends to concentrate on fewer wavelengths, and the spectral intensity of these lasing wavelengths increases for inhomogeneous scatterer distributions (such as bubble structures). Despite a negligible decrease in the number of spikes, the same spectral features were obtained in both previous and current studies, even though different spatial configurations of scatterers were used. This suggests that the inhomogeneous distribution of scatterers limits the number of strong lasing wavelengths and increases the spectral radiance.

We calculated the terminal velocity of a particle settling in the sample medium using Stokes’ law, and the average displacement distance of a Brownian particle in 1 s using the Stokes-Einstein equation. Table 1 summarizes the parameter values employed in this calculation and in the simulation shown later. The terminal settling velocity was 44.4 nm/s, while the average particle displacement due to Brownian motion was 1.17 µm/s. The calculated settling distance at 1 s was smaller than the Brownian displacement at 1 s, implying that, theoretically, the particles did not settle in the medium. However, we observed that the particles did gradually settle. This can be attributed to particle agglomeration, which suppresses Brownian motion.

Table 1. Parameter values used in the simulation

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Consequently, the particle density decreased in the upper layer of the medium, which exhibited a relatively high gain. When the volume fraction of the particles was 0.1%, there were few particles in the upper layer of the medium; therefore, multiple scattering was not strong enough to cause random lasing. However, when illuminated with trapping light, many particles in the lower layer of the medium were trapped and elevated into the upper layer, resulting in random lasing. When the volume fraction of the particles was 0.3%, random lasing occurred even without the trapping-light illumination since not a few particles remained in the upper layer of the medium. The properties of the laser emission were slightly changed by the trapping light because some particles were further positioned in the upper layer.

From the perspective discussed above, we expected that increasing the power of the trapping light would increase the emission intensity of random lasing. Figure 4 shows the maximum spike intensity, average spike intensity, and number of spikes in the emission spectrum for three different trapping light powers. As expected, the spike intensity increased when the power of the trap spots increased from 10 to 15 mW. However, contrary to expectations, the spike intensity was higher for the 15 mW trap spots than for the 30 mW ones, and the number of spikes decreased.

 

Fig. 4. (a) Maximum spike intensity, (b) average spike intensity, and (c) number of spikes of the emission spectrum for different trapping powers. The volume fraction of particles was 0.1%. The error bars represent the standard error (n = 4).

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To elucidate this result, we conducted a numerical simulation to understand how the particles were trapped in the focal region of the trapping light. The parameter values used in the simulations are listed in Table 1. For simplicity, we assumed a Gaussian beam for the trapping light. Details of the simulation method can be found in [27,31]. The results are illustrated in Fig. 5, where the initial positions of the particles and the particle positions after 10 s are indicated by small and large circles, respectively. The intermediate trajectories are indicated by white lines. Initially, thirty particles were randomly placed in a 2 ${\times} $ 2 ${\times} $ 2 µm cube whose center was at the beam-waist center of the trapping light. We used two different diameters of the beam waist. One corresponds to the theoretical value calculated from the equation $1.22\lambda /\textrm{NA}$, where $\lambda $ is the wavelength of light, and $\textrm{NA}$ is the numerical aperture of an objective lens. This value is for a plane wave incident on the lens, and not for a Gaussian beam. Furthermore, the aberration of the objective lens causes the spot diameter of the beam to exceed the theoretical value. Therefore, the calculations were also performed for the case of twice the theoretical value.

 

Fig. 5. Simulation results on the trajectory and final position of 30 trapped particles for different powers and beam waists of the trapping light. The trapping beam was incident from below along the z-axis. The upper and lower figures in (a-f) represent the top and side views, respectively. The beam waist diameter was (a–c) 1.64 µm and (d–f) 3.28 µm. The power of the trapping light at each spot was (a,d) 5 mW, (b,e) 7.5 mW, and (c,f) 15 mW. The ratio of the trapped particles was (a) 0.85, (b,c) 1.0, (d) 0.29 (e) 0.99, and (f) 1.0.

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Figure 5 illustrates that at a trapping power of 5 mW (corresponding to two spots of total 10 mW in the experiment), some particles were not trapped and escaped from the central cube. However, at trapping powers of 7.5, and 15 mW (corresponding to 15 and 30 mW in the experiment), all the particles were trapped near the beam waist. The spread of the trapped particle distribution in the longitudinal direction increased with decreasing trap power. The filling ratio of the trapped particles within the central 1 µm radius sphere was 2.1, 7.1, and 7.2 particles/µm³ at the 5, 7.5, and 15 mW powers, respectively, for a beam waist diameter of 3.28 µm. For 2.5 times the theoretical beam waist diameter (4.10 µm), the filling ratio dropped to 5.1 particles/µm³ with a 7.5 mW power, but it remained constant at 7.2 particles/µm³ with a 15-mW power. Considering that there is an optimal particle-filling ratio that maximizes the emission efficiency of the random laser, it is reasonable to assume an optimal power for trapping light that traps particles at an optimal filling ratio. For this simulation, the number of particles was fixed at 30. In actual situations, the trapping light with higher power gathers more particles in the trap regions and leaves fewer particles around them. Therefore, the experimental results suggest that there is an optimal ratio between the number of trapped and untrapped particles.

Finally, we discuss the temporal response of the emission spectrum when the light trapping illumination is turned on and off. When the light trapping was switched from off to on, the spectral change was confirmed to occur within 3 s. However, when light trapping was switched from on to off after one minute illumination, the spike intensity did not return to the spectrum observed without the trapping light. This is because the change in the distribution of trapped particles is solely due to particle diffusion, and the rate of particle diffusion is much slower than that of particle trapping. Additionally, once the particles agglomerated, they did not separate spontaneously. Therefore, if a reversible change in the emission spectrum is required, one approach would be to move the trapping points in and out of the gain region.

4. Summary

This study investigates the emission characteristics of random lasers in the presence of optically trapped scattering particles. The experimental results showed that the illuminating the trapping light on the particle suspension with gain induced changes in the emission spectrum properties. Notably, for random gain media with a low particle volume fraction of 0.1%, the lasing onset occurred when the trapping light was incident on the medium. Therefore, random lasing can be turned on promptly in seconds using optical trapping. In contrast, for random gain media with larger particle fractions, the effect of optical trapping was less noticeable. However, the intensity of the limited number of spectral spikes increased, suggesting enhanced spectral radiance. The holographic optical tweezers employed in this study allowed for the generation of numerous trap spots at the desired locations. As the next step, we intend to explore the effects of trap patterns, such as regularly aligned and randomly distributed spots, on random laser emission. Thus, this study not only aids in determining more suitable random structures for efficient random lasing but also contributes to the investigation of networked random lasers [32,33] by controlling both the pumping regions and the trap spot positions.