Significance A random laser necessitates not a physical resonator, but multiple scattering of photons in an active random medium to bring optical feedback to reach the threshold. This unique principle signifies that random lasers have several characteristics to distinguish them from conventional lasers. Firstly, without a resonant feedback, random lasers can be any geometries, which indicates it reduced greatly manufacturing difficulty and cost. Secondly, the emission spectrum has mutiple narrow spikes, which can be tuned by changing the pump conditions or environment. Thirdly, random lasers have low spatial coherence and large emission angle. Endowing with these superior features, random lasers have been widely used in speckle-free imaging, temperature sensing, medical diagnosis and super-resolution spectrum.

After decades of development, scientists have explored a variety of materials as scattering media. Among them, liquid crystals are ideal scattering medium with a tunable disordered degree of the system and orientation of dye molecules. As a result, the laser characteristics of liquid crystal random laser, including threshold, intensity, and polarization, can be well controlled, which provides many potential opportunities for various applications of random lasers.

Progress In 1968, Letokhov predicted the existence of random laser theoretically. Scattering of particles increases the distance that photons travel through the medium. The energy density of photons will increase exponentially with time as the strength of scattering and pumping energy increases. If the gain depends on wavelength, the light at this wavelength has a competitive advantage and can be further amplified to form a narrow-band spectrum, which is called spontaneous emission amplification. Meanwhile, the threshold of spontaneous emission amplification in random scattering medium is similar to that of traditional laser. Until 1994, Lawandy confirmed Letokhov's prediction by observing narrow-band emission peaks in amplifying random medium. In 1999, the Cao's group observed several discrete radiation peaks with very narrow spectral linewidth. The results proved the existence of coherent feedback in the random laser.

Since the interference effect caused by strong scattering is not considered in Letokhov's theory, the mechanism of the random laser cannot be well explained. In 1999, Cao used ring resonator theory to explain the localization of the random laser. She proposed that in the case of strong scattering, the photon may return to the scatterer from which it was scattered before, creating a closed loop, which plays the role of laser resonator. When the gain of the photon in the closed loop becomes larger than the loss, laser oscillation occurs. Due to the complexity of random laser, up to now there is not an accepted and complete theory that can fully explain the various characteristics of random lasers.

In 2006, Liu Jinsong's group used FDTD simulation to study the influence of the degree of orientational disorder of uniaxial scattering medium on the random laser mode in one-dimensional and two-dimensional systems. The results showed that with the increase of the orientational disorder of the liquid crystals, the scattering degree of the system increases gradually, leading to the occurrence of a random laser. Since the orientation of liquid crystal molecules can be adjusted in a variety of ways, we can use liquid crystals to regulate the disorder of the system, and thus improve the laser's Q-value.

For nematic liquid crystals random lasers, Ye et al. studied the influence of the liquid crystal cell thickness on the random laser action in the dye-doped nematic liquid crystals system (Fig. 1). Subsequently, Lin et al. investigated the polarization properties of dye-doped twisted nematic liquid crystals in a wedge-shaped cell. In 2019, Naruta et al. prepared a dye-doped random laser with ferromagnetic nematic liquid crystal, which could be tuned by the magnetic force. In 2006, Liu et al. studied the characteristics of dye-doped polymer-dispersed liquid crystals (DD-PDLC) random laser (Fig. 6). In 2019, Dai et al. realized the magnetically tunable DD-PDLC random laser by doping magnetic nanoparticle. Lee et al. previously proposed an optically controlled method of DD-PDLC random laser by doping the azo dye.

For cholesteric liquid crystal (CLC) random laser, in 2012, Morris et al. realized selective emission of random lasers and band-edge laser by changing the frequency of the applied electric field (Fig. 9). In addition, Huang et al. proposed a CLC finger texture reconstruction method based on electric field induction, resulting in flexible modulation of laser wavelength and multiple modes (Fig. 10). In 2018, Hu et al. utilized liquid crystal multiple scattering and near-infrared controlled photothermally band gap tuning to achieve a random laser. In 2020, the group also constructed polymer-stabilized CLC to achieve random laser emission with low coherence and wide tuning range (100 nm) at the band edge.

For blue phase liquid crystal (BPLC) and polymer-stabilized blue phase liquid crystal (PS-BPLC), Lin et al. studied random lasers based on coherent feedback in BPLC and PS-BPLC in 2012 (Fig. 11). In 2020, Luo's group demonstrated a spatially and electrically tunable random lasing based on PS-BPLC-wedged cell (Fig. 12). In 2020, Chauhan et al. proposed a random laser based on spatially-assembled dye-doped BPLC microdroplets (Fig. 14). Wang et al. studied bichromatic coherent random laser from dye-doped PS-BPLC controlled by pump light polarization.

When metal nanoparticles are combined with a disordered active medium, the scattering intensity can be significantly increased. In addition, it can increase the laser gain and reduce the random laser threshold through localized surface plasmon resonances (LSPR). Deng's group has done a lot of research on the plasmon-enhanced liquid crystal random laser.

Conclusion and Prospect Though there is significant progress on the liquid crystal random lasers, their mechanisms remain to be further explored. Future development can be made in the following aspects including further reduced threshold, directionality and polarizations, electrical pumping, miscibility between liquid crystals and novel gain media, etc. Significant performance improvement of liquid crystal random lasers is of great importance for the practical applications and commercialization.