Lasers with high spatial coherence and brightness are used extensively in various industries, medical fields, and other aspects of modern life. However, their high spatial coherence can make them vulnerable to environmental interference, resulting in issues, such as spot diffusion, drift, and light intensity flicker in optical imaging^[1–3]. In contrast, incoherent light sources such as LEDs have a broad spectrum and low photon degeneracy, leading to inadequate transmission in complex environments and loss of high-frequency image information^[4,5]. Optical coherence refers to the degree of correlation between the electric field fluctuations of random light fields at two distinct points in space or time. It is typically categorized as spatial and temporal coherence, which describe the correlation of electric field fluctuations at different times within the same position or at different locations at the same time, respectively.

This Letter primarily focuses on spatial coherence, which represents the correlation between light fields at different positions of two points in space at the same time. Spatial coherence is quantitatively described by the transverse coherence length. A beam with a coherent length approaching infinity is termed a completely coherent beam, while a beam with a coherence length approaching zero is referred to as a completely incoherent beam. Beams that fall between these two extremes are classified as partially coherent beams.

Research indicates that partially coherent beams exhibit strong resistance to environmental interference and offer unique benefits in speckle-free imaging, atmospheric turbulence suppression, classical “ghost imaging,” laser fusion, and other applications^[6–10]. The experimental generation of partially coherent light typically involves two main approaches: reducing the spatial coherence of fully coherent light sources by introducing dynamic elements like spatial light modulators and rotating ground glass outside the laser resonator^[11–13] or enhancing the spatial coherence of incoherent light sources like LEDs through spatial filtering^[14,15]. However, these methods often increase optical path complexity and result in substantial energy loss. Fortunately, advancements in laser technology have opened up new possibilities for generating partially coherent light.

Random lasers are a novel type of laser that does not require a strict optical resonator, instead relying on multiple scattering in a disordered medium for optical feedback^[16–20]. So far, random lasers have been achieved in diverse materials, especially liquid crystals^[21,22]. Liquid crystal is a perfect soft matter photonic crystal with multidimensional tunabilities, such as changing the pitch and lattice constant, which orients the helical axis^[23,24]. Compared to traditional lasers, random lasers are characterized by their small size, flexible shape, and low spatial coherence. Random lasers offer the advantages, such as a narrow line width and high photon degeneracy, over incoherent light sources like LEDs. Serving as a bridge between traditional lasers and incoherent light sources, random lasers are promising for generating high-power partially coherent light^[25]. They have a wide range of applications in areas such as biological monitoring, speckle-free imaging, flat panel displays, and integrated opto-electronics^[6,26–31].

Notably, recent studies have shown the effectiveness of random lasers in speckle-free imaging, with advancements in surface-emitting perovskite random lasers and two-color random laser sources^[28,29]. Spectral super-resolution spectroscope using a random laser has been demonstrated^[32]. An electrically driven low spatial coherence random laser based on modified diodes has been proposed^[33], which holds potential for integrated imaging applications. Researchers have also demonstrated speckle-free holographic imaging and high-definition speckle-free imaging in complex scattering environments using random lasers enhanced by titanium nitride nanoparticles^[30,31]. In addition, other partially coherent light sources, such as broadband superluminescent diodes (SLD), vertical-cavity surface-emitting lasers (VCSELs), and multimode random fiber lasers have been demonstrated to be effective in high-resolution and speckle-free imaging^[34–39]. Given the importance of spatial coherence in determining optical image resolution, speckle degree, and edge contrast, there is a need for precise and dynamic regulation of the spatial coherence of random lasers.

This Letter presents the design of a random laser with dynamically adjustable spatial coherence through the application of an electric voltage. The results demonstrate that, along with controlling the spectral intensity and wavelength, the spatial coherence of the random laser can also be influenced by the applied voltage. This adjustment reduces interference from the scattering environment on the random laser beam and suppresses the formation of speckle. Furthermore, by varying the applied voltage, we can optimize the quality of optical imaging. Overall, our study offers a new method for dynamically controlling the spatial coherence of random lasers and enhancing optical imaging quality in scattering environments.

The random laser sample was prepared by dissolving PM597 (from Exciton) with a mass ratio of 0.5% (mass fraction) in a nematic liquid crystal (NLC) solution (P0616A, from Slichem). Titanium nitride (TiN) nanoparticles with the number density of $3.36\times {10}^{10}/\mathrm{mL}$ were then added to improve the quality of the random lasers. TiN nanoparticles (Beijing Deke Island Gold Technology Co., Ltd.) are spherical with a diameter of 40 nm. To ensure uniform mixing, the solution was first vortexed for 10 min and then ultrasonicated for 30 min. The resulting mixture was filled into cells with a thickness of 100 µm, with the liquid crystal cell in anti-parallel orientation.

Figure 1 illustrates the experimental setup used in this study. A frequency-doubled Q-switched Nd:YAG pulsed laser operating at a wavelength of 532 nm, with a repetition rate of 10 Hz and a pulse duration of 20 ps, serves as the pump laser. To manipulate the pump energy and establish the polarization direction of the pump light in the horizontal plane, we employ a half-wave plate (HWP) and a polarizer (POL). Subsequently, the laser beam is split into two equal-energy beams using a neutral beam splitter (${\mathrm{NBS}}_1$). One beam is directed toward an energy meter to monitor the real-time pump energy while the other beam passes through a cylindrical lens (CL) to create a long stripe for pumping the random laser sample positioned at the focal point of the CL. A DC voltage source is applied to the sample. The emitted light is split into two beams after passing through a convergent lens (${\mathrm{L}}_1$) and a filter (F). The filter is utilized to eliminate the pump light scattered by the sample. One of these beams is further split by a neutral beam splitter (${\mathrm{NBS}}_3$) into two sub-beams. One sub-beam is analyzed by a fiber spectrometer with a resolution of 0.07 nm, while the other is used for Yong’s double slit experiment, with the interference fringes being captured by a CCD camera (${\mathrm{CCD}}_1$). The remaining beam is once again split by a neutral beam splitter (${\mathrm{NBS}}_4$) into two sub-beams. After one sub-beam passes through a scatterer (${\mathrm{S}}_1$), the resulting speckle pattern is recorded by a CCD camera (${\mathrm{CCD}}_2$). The other sub-beam is directed through a scatterer (${\mathrm{S}}_2$) toward the 1951 US Air Force resolution test chart (AF), with the imaging information being recorded by a CCD camera (${\mathrm{CCD}}_3$).

The emission characteristics of the random laser were measured at room temperature, as illustrated in Fig. 2. When the pump energy is low, such as 2.59 µJ/pulse, the emission spectrum appears as a spontaneous radiation spectrum with a wide linewidth and low intensity, indicating the absence of a random laser. However, at a higher pump energy of 4.35 µJ/pulse, the emission spectrum displays discrete spikes with a linewidth of less than 1 nm, as depicted in the inset of Fig. 2(a), suggesting the potential generation of random lasers. As the energy further increases, numerous discrete spikes with a linewidth of less than 1 nm consistently appear in the emission spectrum, with their intensity progressively strengthening. The absence of a predefined resonator results in the laser behavior being attributed to multiple scattering from liquid crystal molecules and TiN NPs, leading to the characteristic presence of multiple modes in the lasing spectrum instead of a single laser mode.

The peak intensity of the emission spectrum exhibits two distinct stages of variation with pump energy, as shown in Fig. 2(b). In the first stage, the peak intensity increases gradually with the pump energy, while in the second stage, the increase in peak intensity becomes more rapid. By fitting the emission intensity to the pump energy in these two regions, the two fitting lines intersect at approximately 3.9 µJ/pulse, which is commonly recognized as the pump threshold. Figure 2(c) shows the emission spectrum of the random laser as a function of the number density of the TiN nanoparticles when the pump energy is 14.7 µJ/pluse. According to the variation curve of the emission intensity of the random laser with the concentration of TiN nanoparticles, we prepared the random laser with a TiN nanoparticle density of $3.36\times {10}^{10}/\mathrm{mL}$, which is close to the optimal value.

The controllable direction vector of the liquid crystal molecules by the applied voltage enables changes in the scattering intensity of a random system, allowing for dynamic control of a random laser. In Fig. 2(d), the emission spectrum of the random laser is depicted as a function of the applied voltage. The peak intensity of the emission spectrum in relation to the voltage is illustrated in Fig. 2(e). Notably, the emission spectrum experiences minimal change when the voltage is increased from 0 to 2.6 V. This is attributed to the insignificant alteration in the orientation of liquid crystal molecules at voltages below 2.6 V, which does not sufficiently impact the scattering intensity of the random system to significantly alter the emission spectral characteristics of the random laser. However, a further increase in voltage leads to a deterioration in the emission spectrum of the random laser. Specifically, the peak intensity of the emission spectrum decreases almost linearly from 55 to 28 a.u. as the voltage escalates from 2.6 to 11 V. Beyond 2.6 V, the electric field’s force overcomes the weak interaction force between the NLC molecules, prompting the reorientation of the NLC molecules toward the electric field direction. Consequently, the effective refractive index of the NLC random system decreases, weakening the scattering intensity and reducing the spectral intensity of the random laser.

With continued voltage increase, more liquid crystal molecules align with the electric field, causing a reduction in the quality of the random laser. When the voltage exceeds 11 V, the emission spectrum stabilizes, indicating orientation saturation as almost all liquid crystals have been reoriented. In addition, the wavelength of the random laser exhibits a red shift with the enhancement of the electric field, as shown in Fig. 2(d). This phenomenon is attributed to the reorientation of the liquid crystal molecules induced by the applied voltage. As the voltage increases, the orientation of the liquid crystal molecules orients away from the cell surface at an angle that can be adjusted from 0 to 90 deg. Consequently, the refractive index of the extraordinary light can be changed by applying a voltage, thereby regulating the emission wavelength of the random laser^[40]. Figure 2(f) shows the transmission spectrum intensity of the nematic liquid crystal at 0, 5, and 9 V, in the absence of the PM597 dye in the sample. As the voltage rises from 0 to 5 and then to 9 V, the transmission spectrum intensity of the sample at the wavelength range of interest increases. This observation confirms that the orientation of the liquid crystal molecules is reoriented by the applied voltage.

This study investigates the spatial coherence of the random laser in relation to the applied voltage, as illustrated in Fig. 3. Spatial coherence is quantified by the visibility ($\gamma$) of interference fringes in the central region, determined using Young’s double slit experiment^[41]. The experiment involves two slits, each 100 µm wide and separated by 300 µm. As a comparison, the spatial coherence of a conventional laser is studied, as shown in Fig. 3(a). The visibility value is larger than 0.9 for the Nd:YAG laser. Figures 3(b)–3(d) show the spatial coherence of the random laser at different voltages. The visibility values are 0.27, 0.11, and 0.05 for 0, 4.5, and 11 V, respectively, which are all obviously lower than those of the Nd:YAG laser. Figure 3(e) displays the variation curve of spatial coherence with the applied voltage. As the voltage increases, the visibility decreases rapidly from 0.27 to 0.05. When the voltage is applied, the emission spectrum of the random laser is transformed from multiple distinct spikes to a smoother emission spectrum, as shown in Fig. 2(d). This transformation leads to a reduction in spatial coherence. This is very convenient for regulating the degree of speckle.

Next, we investigated the speckle pattern of the random laser beam passing through a scattering environment, as illustrated in Fig. 4. The scattering environment is established using a frosted glass sheet with 1500 mesh sourced from LBTEK. As a comparison, the speckle pattern of a conventional laser is studied in the same environment, as shown in Fig. 4(a). Figures 4(b)–4(d) show the speckle patterns for the random laser at different voltages. The degree of speckle can be quantified by the speckle contrast $C=\text{σ/}⟨I⟩$^[31,42], where σ represents the standard deviation of intensity and $⟨I⟩$ denotes the average intensity. Specifically, when no voltage is applied, the speckle contrast $C$ is approximately 0.167, which is already weaker than the speckle (about 0.64) produced by the Nd:YAG laser. With the application of voltage, the speckle is further suppressed, resulting in speckle contrasts of 0.085 and 0.06 for 4.5 and 11 V voltages, respectively. By adjusting the applied voltage, we can modulate the speckle contrast within the range of 0.060 to 0.167, as depicted in Fig. 4(e).

In order to compare with random laser sources, we investigated the imaging quality using a Nd:YAG laser in the same scattering environment. Figure 5(a) presents the image of the 1951 US Air Force resolution test chart illuminated by the Nd:YAG laser. There are a lot of speckles in the image, which seriously damage the image quality. It is worth noting that the speckle in the image is obviously suppressed when the random laser is used as the light source, as shown in Figs. 5(b)–5(d). Results show that increasing the voltage enhances the image definition. Image quality can be assessed using the signal-to-noise ratio (SNR), which is defined as $\mathrm{SNR}=(1-⟨I_n⟩/⟨I_s⟩)/({\sigma }_s/⟨I_s⟩)$^[43,44], where $I_s$, $I_n$, and ${\sigma }_s$ express the intensities of the signal (bright), the intensity of the noise (dark), and the standard deviation of the intensity fluctuation in the signal (bright), respectively. $⟨·⟩$ expresses the average value. The SNR improves with increasing voltage, measuring about 1.552, 2.449, and 3.019 for 0, 4.5, and 11 V, respectively, as shown in Figs. 5(f)–5(h), which is all higher than that (1.477) of the Nd:YAG laser as the light source, as shown in Fig. 5(e). From Figs. 5(j)–5(l), we can obtain that the speckle contrast decreases with increasing voltage and about 0.24, 0.18, and 0.15 for 0, 4.5, and 11 V, respectively, which is all significantly lower than that (0.69) of the Nd:YAG laser as the light source, as shown in Fig. 5(i). Figures 5(n)–5(p) show the edge sharpness of the image illuminated by the random laser with different voltages, which can be expressed by $\mathrm{ES}=(I_s-I_n)/({\lambda }_n-{\lambda }_s)$. The edge sharpness values are around 0.056, 0.035, and 0.031 for 0, 4.5, and 11 V, respectively, which is lower than that (0.209) of the Nd:YAG laser as the light source, as shown in Fig. 5(m). Figure 6 presents how the SNR, speckle contrast, and edge sharpness of the images change with the applied voltage when the random laser is used as the light source. The speckle contrast decreases with increasing voltage, while edge sharpness also diminishes. Notably, SNR always improves with increasing voltage until it reaches relative stability. Therefore, the choice of voltage needs to balance speckle contrast and edge sharpness based on specific requirements.

This study presents the design of a random laser with dynamically regulated spatial coherence through the application of an electric voltage. The results demonstrate that, in addition to spectral intensity and wavelength, the spatial coherence of the random laser is also affected by the applied voltage. Specifically, the visibility decreases from 0.27 to 0.05 as the voltage increases from 0 to 11 V. Increasing the voltage reduces the interference of the scattering environment on the random laser beam and then suppresses the formation of speckle. For a scattering plate with 1500 mesh, the speckle constant decreases from 0.167 to 0.06 as the voltage increases from 0 to 11 V. The spatial coherence of the random laser influences both speckle and edge sharpness in imaging. Therefore, by adjusting the applied voltage, the balance between image uniformity (speckle-free) and edge sharpness can be optimized quantitatively. This study introduces a novel approach to generate and control partially coherent light and enhance the quality of optical imaging in scattering environments. These results have guiding significance in the application fields of free-space optical communication, optical imaging, photonic computing, and so on^[45].