Open Access
Add to BibSonomy
Abstract
Control of lasing properties through tailorable and dynamically tunable materials and reconfigurable compositions can augment the performance of random lasers for a wide range of applications. Here, a colloid of randomly dispersed weakly scattering single-layer titanium carbide (Ti3C2Tx) MXene flakes embedded within rhodamine 101 gain medium is experimentally shown to provide feedback for random lasing. Additionally, in contrast to previously reported random laser systems where the optical properties of scatterers are static, the relative permittivity of Ti3C2Tx MXene flakes can be varied under optical pumping due to the saturable absorption properties. Numerical simulations indicate that the observed nonlinear response of Ti3C2Tx MXene flakes enables dynamically tunable random lasing. Thus, pumping the Ti3C2Tx MXene flakes with a second optical source decreases the gain threshold required to obtain random lasing. Also, using numerical simulations, it is shown that the control over the intensity of the second pump enables tuning the field distribution of the random lasing modes. Considering the diversity of the MXenes family, the proposed MXene colloidal metamaterial design opens up a new avenue to advanced control of lasing properties for photonic applications.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Random lasers (RLs) represent one of the most intriguing classes of coherent optical sources where the optical feedback is usually provided by multiple scattering of light caused by refractive index inhomogeneities [1,2]. Various novel optical phenomena have been observed in RLs with different scattering strength, such as Anderson localization of light in strongly scattering regime [3–5] and directional emission in weakly scattering media [6,7]. RLs have also brought new opportunities in the fields of optical imaging [8], biological probes [9], and light-emitting diodes [10]. Moreover, the dynamic control of lasing properties is of great importance to enable new capabilities and functionalities of RLs. Therefore, significant efforts have been devoted to developing new materials and structures suited for dynamic tuning [11–13]. For instance, the RL emission intensity can be engineered by exciting anisotropic plasmonic resonances with polarized pump light in a plasmonic metamaterial device [14]. However, conventional RLs lack external real-time tunability and control over the spatial pattern of the lasing emission, since it is difficult to tame the scattering strength of the dielectric and metallic scatterers directly.
A promising strategy for allowing external real-time control over the RLs has been proposed by replacing the scattering particles with subwavelength highly nonlinear inclusions [15]. In such a structure, the lasing modes are not formed by the multiple scatterings of light as in conventional RLs. Instead, the subwavelength nonlinear inclusions and the gain material create a system whose collective response can produce self-organizing light modes that support the lasing action. The response of such a system can be tuned by controlling the nonlinearity of the inclusions using optical pumping, for instance. It has been shown theoretically that the optical modes of the collective lasing system can be tuned from single-mode RL operation to chaotic response relying on the external optical pumping. However, so far, an experimental realization of RLs based on highly nonlinear sub-wavelength inclusions has not been reported to the best of our knowledge.
The extraordinary optical properties of two-dimensional (2D) materials could offer new avenues to control stimulated emission and achieve dynamically tunable random lasing [15,16]. Practically, 2D materials have demonstrated saturable absorption at rather modest light intensities [17]. Compared to single-walled carbon nanotubes and semiconductor saturable absorber mirrors, the saturable absorption intensity of 2D materials could be one order of magnitude lower while the modulation depth is 2-3 times larger [17]. Therefore, ultrathin 2D materials have been exploited extensively in the diverse application of nonlinear optics [18,19], such as broadband optical modulation [20], optical frequency mixing [21], and ultrafast laser generation [17]. The extremely low threshold for saturable absorption allows one to tame the optical properties of 2D materials by external pumping under the damage threshold of 2D flakes. Consequently, the fluctuation of the dielectric constant in the space of an RL device composed of 2D material flakes can be mediated by pumping the flakes with an external optical source, leading to tunable optical responses and feedbacks for random lasing [15]. However, 2D materials are generally fabricated by CVD (chemical vapor deposition) technique or exfoliated from bulk counterparts, where it may be difficult to compose such random laser systems.
Here, the experimental demonstration of RLs utilizing 2D materials is demonstrated by an emerging 2D material family, namely transition metal carbides, nitrides, and carbonitrides (MXenes) [22]. MXenes have drawn attention due to their tunable electrical and optical properties and a wide range of applications [22–24]. The MXene chemical formula is M$_{n+1}$X$_n$T$_x$ (n = 1–4) where M is the transition metal (e.g., Ti, Ta, Nb, Zr, Hf, Cr, Mo, etc.), X is C and/or N, and T represents surface terminations [25]. Millions of MXenes have been predicted when alloying is considered, and about 30 stoichiometric MXenes and more than 20 solid solutions have been experimentally synthesized, making them among the fastest growing and the most diverse 2D material families [22]. These materials have exhibited promising performance in many areas such as supercapacitors [26], electromagnetic interference shielding [27], catalysis [28], biosensing [29], photothermal therapy [30], surface-enhanced Raman scattering [31,32], light-to-heat conversion for energy harvesting [33], and plasmonics [34]. In contrast to other 2D materials fabricated by either mechanical exfoliation of their bulk counterparts or chemical vapor deposition, single to few-layer flakes of MXene are isolated through wet chemical etching of bulk ternary carbides and nitrides [22,35], and the lateral dimensions and quality of materials produced can be controlled through the synthesis and processing approaches. In addition, 2D titanium carbide and carbonitride MXenes exhibit a low threshold of saturable absorption and large nonlinear absorption coefficients with values comparable to those of other 2D materials such as graphene, satisfying the RL design requirements [36,37].
In this study, a random weakly scattering colloidal metamaterial composed of delaminated Ti$_3$C$_2$T$_{\textrm {x}}$ MXene flakes and rhodamine 101 (R101) dye molecules is used to construct a random laser device where lasing action is experimentally demonstrated. The demonstrated random laser operates in the weakly scattering regime or quasistatic, where the system behaves as a collective random highly-nonlinear medium [15,38,39]. We detected coherent random lasing emission in the visible with spectra showing strong shot-to-shot variance. The optical feedback and emission features are highly dependent on the concentration of Ti$_3$C$_2$T$_{\textrm {x}}$ flakes, where the lowest pump threshold is observed at 0.21 mg/ml flake density. To the best of our knowledge, this is the first experimental demonstration of RL based on highly nonlinear subwavelength inclusions. Furthermore, numerical simulations demonstrate that the random lasing action can be tuned when an additional optical source is introduced to pump the Ti$_3$C$_2$T$_{\textrm {x}}$ flakes by forming coherent random lasing modes below the pump threshold of the dye.
2. Results and discussion
The colloidal system is comprised of randomly dispersed Ti$_3$C$_2$T$_{\textrm {x}}$ flakes (mainly, single layer) with a lateral size of 100 nm, immersed in a rhodamine 101 (R101, 3.3 mM) solution (Fig. 1(a)). R101 is an organic laser dye with a high quantum yield, which allows for efficient pumping with the second-harmonic output from an Nd:YAG laser (532 nm, 1Hz repetition rate, and 400 ps pulse duration). Also, the negative charge on the MXene surface leads to adsorption of rhodamine dye molecules via amine groups on MXene [32]. To evaluate the lasing properties of the colloid, the pump laser was focused on the samples through a lens, forming a pump spot with a diameter of 80 $\mu$m. The emitted light was collected from the same lens and directed into a spectrometer (SP-2150i, Princeton Instruments) equipped with a charge-coupled device (CCD) through an optical fiber. All the measurements were performed at room temperature.
Fig. 1. (a) Schematic illustration (not to scale) of the proposed RL colloidal system, which consists of a mixture of Ti$_3$C$_2$T$_{\textrm {x}}$ MXene flakes with 0.21 mg/ml flake density and rhodamine 101 (R101, 3.3 mM) dye molecules. (b) Emission spectra recorded at various pump energies of a picosecond pulsed pump laser ($\lambda$ = 532 nm). An offset of a 1000 a. u. is applied when plotting the spectra. (c) Integrated emission intensity versus pump energy from 0.1 to 2.0 $\mu$J.
Figure 1(b) depicts the evolution of the emission spectrum with the pump energy. At a critical pump energy of 0.70 $\mu$J, a single sharp peak centered at $\lambda$ = 602 nm emerges over the broad background spectrum with a spectral linewidth as narrow as 0.40 nm. As the pump energy increases, additional sharp peaks subsequently appear, and the emission intensity increases dramatically. The pump-dependence of spectrally integrated emission intensity is plotted in Fig. 1(c), which shows a clear kink around 0.70 $\mu$J indicating the threshold behavior. The above results are consistent with the behavior of random lasing achieved through coherent feedback [14].
The single-shot emission spectra recorded under a single pulse excitation indicates strongly chaotic behavior (Fig. 2), originating from the continuous movement of the Ti$_3$C$_2$T$_{\textrm {x}}$ flakes in solution leading to a dynamic sample configuration [38]. Generally, the amplifying random media can be classified as either static or dynamic, depending on the time variance of the configuration of scattering elements [40,41]. For static random laser systems (e.g., solid systems with fixed scattering element positions), the wavelengths of lasing modes should be maintained from pulse to pulse since the static configuration of particles provides fixed feedback cavities [14]. In contrast, shot-to-shot variation or chaotic behavior in emission spectra is usually observed in an RL with varying geometry (e.g., suspension of particles in dye solutions) [38]. The movement of the particles results in the transient variation in the oscillation cavities for random lasing. The above mentioned RL behavior well explains our observation in Fig. 2. Due to mode competition, and the motion of the Ti$_3$C$_2$T$_{\textrm {x}}$ flakes in the solution, the emission spectrum is also dynamically changing with each excitation pulse.
Fig. 2. Pseudo color map of single-shot emission spectra obtained upon different pump pulses. The pump energy is fixed at 1.98 $\mu$J.
The lasing behavior in this system can be controlled by varying the density of the Ti$_3$C$_2$T$_{\textrm {x}}$ flakes in solution, as shown in Fig. 3. With increasing density of Ti$_3$C$_2$T$_{\textrm {x}}$ flakes (from 0.02 to 0.21 mg/ml), the scattering inside the colloidal metamaterial is enhanced, resulting in an easier formation of lasing modes and a decrease in the pump threshold (Fig. 3(a)). For example, the pump threshold for the sample with 0.21 mg/ml Ti$_3$C$_2$T$_{\textrm {x}}$ flakes reaches as low as 0.72 $\mu$J, which is reduced compared to the sample with 0.02 mg/ml Ti$_3$C$_2$T$_{\textrm {x}}$ flakes with a threshold of 1.27 $\mu$J. The enhanced lasing feedback can also be inferred in the emission spectrum (Figs. 3(b)-d). For pure dye solution, only spontaneous emission is observed at pump energy of 1.98 $\mu$J due to the lack of feedback cavities (Fig. 3(b)). Coherent random lasing modes start to form in the sample solution when Ti$_3$C$_2$T$_{\textrm {x}}$ flakes are added (even at the lowest concentration tested at 0.02 mg/ml). The spontaneous emission background is reduced, and coherent random lasing modes are dominant in the emission spectrum when the concentration of Ti$_3$C$_2$T$_{\textrm {x}}$ flakes is increased to 0.21 mg/ml (Fig. 3(d)). These observations indicate that a more profound lasing behavior can be obtained by just increasing the concentration of Ti$_3$C$_2$T$_{\textrm {x}}$ flakes.
Fig. 3. Dependence of random lasing on the concentration of Ti$_3$C$_2$T$_{\textrm {x}}$ flakes. (a) Pump threshold as a function of the concentration of Ti$_3$C$_2$T$_{\textrm {x}}$. (b-d) Emission spectra of samples with pure dye, 0.11 mg/ml Ti$_3$C$_2$T$_{\textrm {x}}$ and 0.21 mg/ml Ti$_3$C$_2$T$_{\textrm {x}}$, respectively.
In contrast to previously reported RLs where the refractive index of scatterers is constant, the optical properties of the Ti$_3$C$_2$T$_{\textrm {x}}$ flakes in this system could vary upon external optical pump due to the saturable absorption properties of this 2D material. When the ground state absorption coefficient of a material is higher than that of its excited states, bleaching of the ground state electron population occurs at high pump intensities and rates, leading to saturable absorption behavior [42]. The light-intensity (I) dependence of the absorption coefficient follows Beer’s law , where is the linear absorption coefficient and is the saturation intensity. Saturable absorption behavior in 2D materials has been demonstrated to be vital for the development of next-generation passive mode-locking lasers [43] with ultrafast laser operation, broadband tunability, and quality-factor switching. Recent studies have shown that 2D titanium carbide and carbonnitride MXenes exhibit robust nonlinear optical properties with higher optical damage threshold than other 2D materials, which are essential for photonic applications [33]. Therefore, it should be possible to engineer the optical response of the RLs system by pumping the Ti$_3$C$_2$T$_{\textrm {x}}$ flakes, leading to a tunable random lasing behavior.
To achieve dynamic tuning of laser emission, we numerically simulate the excitation of the system with two-color pumps. A 532-nm laser source (U1) is used to pump the dye molecules, and a 700-nm pump source (U2) is adapted to pump the Ti$_3$C$_2$T$_{\textrm {x}}$ flakes (Fig. 4(a)). For simplicity of the numerical model, the absorption spectrum of the Ti$_3$C$_2$T$_{\textrm {x}}$ flakes is assumed to be narrow enough not to allow the 532-nm source to pump the Ti$_3$C$_2$T$_{\textrm {x}}$ flakes. Similarly, the second pump laser wavelength (700 nm) is assumed to be far away from the absorption band of R101, to avoid interaction with the dye molecules (details of the numerical simulation technique can be found in our earlier publications [44–47]). When the system is solely pumped by U1, the intensity of the electric field at the lasing wavelength (604 nm) decays very fast along x-direction at low energy U1 (Fig. 4(a)). This fast decay indicates that the level of optical gain is insufficient to compensate for the loss and support random modes inside the device. However, when the energy of U1 is above the threshold (i.e., 2 $\mu$J), random lasing modes start to form inside the system (Fig. 4(c)). This threshold behavior agrees well with our experimental observations.
Fig. 4. Tunable random lasing with a two-color pump. (a) Schematic of numerical simulation. The blue and red dots represent Ti$_3$C$_2$T$_{\textrm {x}}$ flakes and R101 molecules, respectively. (b, c) Field distributions below and above the pump threshold of U1 without the second pump U2. (c, d) Field distributions above the pump threshold of U1 (0.6 $\mu$J) with different intensities of U2. The field distributions in (b-e) are plotted at the lasing wavelength, 604 nm.
However, when the Ti$_3$C$_2$T$_{\textrm {x}}$ flakes are pumped with both sources U1 and U2, there are two significant effects observed in the simulation. First, due to the strong saturable absorption of the Ti$_3$C$_2$T$_{\textrm {x}}$ flakes, the absorption of the material decreases at higher intensities, which in turn leads to the decrease of the loss in the flakes causing the gain threshold to drop. The random lasing modes start to form at U1 = 0.6 $\mu$J in the presence of the additional pump U2 = 0.5 $\mu$J. A 70% decrease in the gain threshold of U1 is observed when the second pump is added. Figures 4(c) and (d) depict the field distributions of random lasing modes above the gain thresholds of U1 with and without pump U2, respectively. These results suggest that pumping the flakes with U2 could significantly reduce the pump energy of U1 to achieve coherent random lasing modes in the RL device. Second, the random lasing modes vary while changing the optical properties of the flakes with optical excitation U2. The electrical field distributions of random lasing modes above the pump threshold of U1 with U2 values of 0.5 and 0.6 $\mu$J are depicted in Fig. 4(d)-e. The variation of pump intensity of U2 can significantly modify the mode distributions, enabling control of the spatial pattern of random lasing emission. In the simulation, a 20% increase in the emission intensity was observed when the energy of U2 increases from 0.5 to 0.6 $\mu$J while U1 stays constant at 1$\mu$J (Fig. 4(d)-e). These simulation results predict that we could achieve dynamically tunable random lasing emission in the RL device by introducing the second pump beam U2 to tune the optical properties of Ti$_3$C$_2$T$_{\textrm {x}}$ flakes where the gain threshold and mode distribution both show a strong dependence on the energy of U2.
3. Conclusion
We have experimentally demonstrated that an active colloidal metamaterial system consisting of randomly dispersed 2D Ti$_3$C$_2$T$_{\textrm {x}}$ MXene flakes embedded within rhodamine R101 gain medium can act as a random laser. Coherent random lasing emission was detected with spectra showing strong shot-to-shot variance typical for RLs. The optical feedback and emission features depend highly on the concentration of Ti$_3$C$_2$T$_{\textrm {x}}$ flakes, where the lowest pump threshold of 0.72 $\mu$J is obtained at 0.21 mg/ml flake density. In contrast to previously reported random laser systems where the optical properties of scatterers remain static, the relative permittivity of Ti$_3$C$_2$T$_{\textrm {x}}$ MXene flakes can be engineered through external optical pumping due to the flexible nonlinear effect of saturable absorption similar to other 2D materials such as graphene. Furthermore, numerical simulations indicate that the nonlinear response of Ti$_3$C$_2$T$_{\textrm {x}}$ MXene flakes enables dynamical tunable random lasing. The gain threshold required to achieve random lasing mode could be greatly reduced by adding another optical source to pump the Ti$_3$C$_2$T$_{\textrm {x}}$ MXene flakes. The lasing modes could also be modified by changing the intensity of the second pump source. Such an all-optical spatio-temporal colloidal metamaterial control opens a new avenue to dynamically tailor the properties of random lasers for advanced photonic applications. Considering the diversity of the MXene family, this work can be extended to other active colloidal and solid-state systems and laser designs to enable improved and tunable nanophotonic devices.
Funding
U.S. Department of Energy (DE-SC0017717); Air Force Office of Scientific Research (FA9550-20-1-0124); Defense Advanced Research Projects Agency (HR00111720032); Mountain Tai Young Scholarship (23170504); Incubation Program of Universities' Preponderant Discipline of Shandong Province (03010304); National Natural Science Foundation of China (11774188); Office of Naval Research (N00014-17-1-2588).
Acknowledgment
Zhuoxian Wang and Shaimaa I. Azzam contributed equally to this work. The authors would like to acknowledge valuable discussions with Prof. Alexey Yamilov, Prof. Hui Cao, and Dr. Seung Ho Choi. The authors acknowledge the financial support by the U.S. Department of Energy (DOE), the Office of Basic Energy Sciences (BES), and the Division of Materials Sciences and Engineering under Award No. DE-SC0017717 (K.C.), the support from the Air Force Office of Scientific Research under Award No. FA9550-20-1-0124, and the funding from the DARPA/DSO Extreme Optics and Imaging Program (EXTREME) under Award HR00111720032 (numerical simulations). X. M. is grateful to the financial support by the National Natural Science Foundation of China (No. 11774188), the Incubation Program of Universities’ Preponderant Discipline of Shandong Province, China (No. 03010304) and Mountain Tai Young Scholarship (No. 23170504). The authors acknowledge the funds from Office of Naval Research under award number MURI N00014-17-1-2588.
Disclosures
The authors declare no conflicts of interest.
References
1. V. Letokhov, “Generation of light by a scattering medium with negative resonance absorption,” Sov. Phys. JETP 26, 835–840 (1968).
2. M. Noginov, Solid-state Random Lasers, vol. 105 (Springer, 2006).
3. V. Milner and A. Z. Genack, “Photon localization laser: low-threshold lasing in a random amplifying layered medium via wave localization,” Phys. Rev. Lett. 94(7), 073901 (2005). [CrossRef]
4. J. Liu, P. Garcia, S. Ek, N. Gregersen, T. Suhr, M. Schubert, J. Mørk, S. Stobbe, and P. Lodahl, “Random nanolasing in the Anderson localized regime,” Nat. Nanotechnol. 9(4), 285–289 (2014). [CrossRef]
5. S. H. Choi, S.-W. Kim, Z. Ku, M. A. Visbal-Onufrak, S.-R. Kim, K.-H. Choi, H. Ko, W. Choi, A. M. Urbas, T.-W. Goo, and Y. L. Kim, “Anderson light localization in biological nanostructures of native silk,” Nat. Commun. 9(1), 452 (2018). [CrossRef]
6. X. Wu, W. Fang, A. Yamilov, A. Chabanov, A. Asatryan, L. Botten, and H. Cao, “Random lasing in weakly scattering systems,” Phys. Rev. A 74(5), 053812 (2006). [CrossRef]
7. S. Perumbilavil, A. Piccardi, R. Barboza, O. Buchnev, M. Kauranen, G. Strangi, and G. Assanto, “Beaming random lasers with soliton control,” Nat. Commun. 9(1), 3863 (2018). [CrossRef]
8. B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6(6), 355–359 (2012). [CrossRef]
9. R. C. Polson and Z. V. Vardeny, “Random lasing in human tissues,” Appl. Phys. Lett. 85(7), 1289–1291 (2004). [CrossRef]
10. X. Ma, P. Chen, D. Li, Y. Zhang, and D. Yang, “Electrically pumped ZnO film ultraviolet random lasers on silicon substrate,” Appl. Phys. Lett. 91(25), 251109 (2007). [CrossRef]
11. T. Hisch, M. Liertzer, D. Pogany, F. Mintert, and S. Rotter, “Pump-controlled directional light emission from random lasers,” Phys. Rev. Lett. 111(2), 023902 (2013). [CrossRef]
12. M. Leonetti, C. Conti, and C. Lopez, “The mode-locking transition of random lasers,” Nat. Photonics 5(10), 615–617 (2011). [CrossRef]
13. N. Bachelard, S. Gigan, X. Noblin, and P. Sebbah, “Adaptive pumping for spectral control of random lasers,” Nat. Phys. 10(6), 426–431 (2014). [CrossRef]
14. Z. Wang, X. Meng, S. H. Choi, S. Knitter, Y. L. Kim, H. Cao, V. M. Shalaev, and A. Boltasseva, “Controlling random lasing with three-dimensional plasmonic nanorod metamaterials,” Nano Lett. 16(4), 2471–2477 (2016). [CrossRef]
15. A. Marini and F. G. de Abajo, “Graphene-based active random metamaterials for cavity-free lasing,” Phys. Rev. Lett. 116(21), 217401 (2016). [CrossRef]
16. H.-W. Hu, G. Haider, Y.-M. Liao, P. K. Roy, R. Ravindranath, H.-T. Chang, C.-H. Lu, C.-Y. Tseng, T.-Y. Lin, W.-H. Shih, and Y. Chen, “Wrinkled 2D materials: A versatile platform for low-threshold stretchable random lasers,” Adv. Mater. 29(43), 1703549 (2017). [CrossRef]
17. Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009). [CrossRef]
18. Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016). [CrossRef]
19. Q. Wu, S. Chen, Y. Wang, L. Wu, X. Jiang, F. Zhang, X. Jin, Q. Jiang, Z. Zheng, J. Li, M. Zhang, and H. Zhang, “MZI-Based All-Optical Modulator Using MXene Ti3C2Tx (T= F, O, or OH) Deposited Microfiber,” Adv. Mater. Technol. 4(4), 1800532 (2019). [CrossRef]
20. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011). [CrossRef]
21. T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G.-Q. Lo, D.-L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012). [CrossRef]
22. B. Anasori and Y. Gogotsi, 2D Metal Carbides and Nitrides (MXenes) (Springer, 2019).
23. M. Naguib, O. Mashtalir, J. Carle, V. Presser, J. Lu, L. Hultman, Y. Gogotsi, and M. W. Barsoum, “Two-dimensional transition metal carbides,” ACS Nano 6(2), 1322–1331 (2012). [CrossRef]
24. X. Jiang, A. V. Kuklin, A. Baev, Y. Ge, H. Ågren, H. Zhang, and P. N. Prasad, “Two-dimensional mxenes: From morphological to optical, electric, and magnetic properties and applications,” Phys. Rep. 848, 1–58 (2020). [CrossRef]
25. M. A. Hope, A. C. Forse, K. J. Griffith, M. R. Lukatskaya, M. Ghidiu, Y. Gogotsi, and C. P. Grey, “NMR reveals the surface functionalisation of Ti3C2 mxene,” Phys. Chem. Chem. Phys. 18(7), 5099–5102 (2016). [CrossRef]
26. O. Mashtalir, M. R. Lukatskaya, M.-Q. Zhao, M. W. Barsoum, and Y. Gogotsi, “Amine-assisted delamination of Nb2C mxene for li-ion energy storage devices,” Adv. Mater. 27(23), 3501–3506 (2015). [CrossRef]
27. F. Shahzad, M. Alhabeb, C. B. Hatter, B. Anasori, S. M. Hong, C. M. Koo, and Y. Gogotsi, “Electromagnetic interference shielding with 2D transition metal carbides (mxenes),” Science 353(6304), 1137–1140 (2016). [CrossRef]
28. X. Xie, Y. Xue, L. Li, S. Chen, Y. Nie, W. Ding, and Z. Wei, “Surface Al leached Ti3AlC2 as a substitute for carbon for use as a catalyst support in a harsh corrosive electrochemical system,” Nanoscale 6(19), 11035–11040 (2014). [CrossRef]
29. H. Liu, C. Duan, C. Yang, W. Shen, F. Wang, and Z. Zhu, “A novel nitrite biosensor based on the direct electrochemistry of hemoglobin immobilized on MXene-Ti3C2,” Sens. Actuators, B 218, 60–66 (2015). [CrossRef]
30. J. Xuan, Z. Wang, Y. Chen, D. Liang, L. Cheng, X. Yang, Z. Liu, R. Ma, T. Sasaki, and F. Geng, “Organic-base-driven intercalation and delamination for the production of functionalized titanium carbide nanosheets with superior photothermal therapeutic performance,” Angew. Chem. 128(47), 14789–14794 (2016). [CrossRef]
31. E. Satheeshkumar, T. Makaryan, A. Melikyan, H. Minassian, Y. Gogotsi, and M. Yoshimura, “One-step solution processing of Ag, Au and Pd@ MXene hybrids for SERS,” Sci. Rep. 6(1), 32049 (2016). [CrossRef]
32. A. Sarycheva, T. Makaryan, K. Maleski, E. Satheeshkumar, A. Melikyan, H. Minassian, M. Yoshimura, and Y. Gogotsi, “Two-dimensional titanium carbide (MXene) as surface-enhanced raman scattering substrate,” J. Phys. Chem. C 121(36), 19983–19988 (2017). [CrossRef]
33. R. Li, L. Zhang, L. Shi, and P. Wang, “MXene Ti3C2: an effective 2D light-to-heat conversion material,” ACS Nano 11(4), 3752–3759 (2017). [CrossRef]
34. K. Chaudhuri, M. Alhabeb, Z. Wang, V. M. Shalaev, Y. Gogotsi, and A. Boltasseva, “Highly broadband absorber using plasmonic titanium carbide (MXene),” ACS Photonics 5(3), 1115–1122 (2018). [CrossRef]
35. M. Naguib and Y. Gogotsi, “Synthesis of two-dimensional materials by selective extraction,” Acc. Chem. Res. 48(1), 128–135 (2015). [CrossRef]
36. Y. I. Jhon, J. Koo, B. Anasori, M. Seo, J. H. Lee, Y. Gogotsi, and Y. M. Jhon, “Metallic MXene saturable absorber for femtosecond mode-locked lasers,” Adv. Mater. 29(40), 1702496 (2017). [CrossRef]
37. X. Jiang, S. Liu, W. Liang, S. Luo, Z. He, Y. Ge, H. Wang, R. Cao, F. Zhang, Q. Wen, J. Li, Q. Bao, D. Fan, and H. Zhang, “Broadband nonlinear photonics in few-layer mxene Ti3C2Tx (T= F, O, or OH),” Laser Photonics Rev. 12(2), 1700229 (2018). [CrossRef]
38. R. Polson and Z. Vardeny, “Organic random lasers in the weak-scattering regime,” Phys. Rev. B 71(4), 045205 (2005). [CrossRef]
39. A. Sarkar, B. S. Bhaktha, and J. Andreasen, “Replica symmetry breaking in a weakly scattering optofluidic random laser,” Sci. Rep. 10(1), 2628 (2020). [CrossRef]
40. S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007). [CrossRef]
41. X. Meng, K. Fujita, S. Murai, and K. Tanaka, “Coherent random lasers in weakly scattering polymer films containing silver nanoparticles,” Phys. Rev. A 79(5), 053817 (2009). [CrossRef]
42. Y. Dong, S. Chertopalov, K. Maleski, B. Anasori, L. Hu, S. Bhattacharya, A. M. Rao, Y. Gogotsi, V. N. Mochalin, and R. Podila, “Saturable absorption in 2D Ti3C2 MXene thin films for passive photonic diodes,” Adv. Mater. 30(10), 1705714 (2018). [CrossRef]
43. Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. J. Kelleher, J. C. Travers, V. Nicolosi, and A. C. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3(9), 653–660 (2010). [CrossRef]
44. S. I. Azzam, J. Fang, J. Liu, Z. Wang, N. Arnold, T. A. Klar, L. J. Prokopeva, X. Meng, V. M. Shalaev, and A. V. Kildishev, “Exploring time-resolved multiphysics of active plasmonic systems with experiment-based gain models,” Laser Photonics Rev. 13(1), 1800071 (2019). [CrossRef]
45. S. I. Azzam and A. V. Kildishev, “Time-domain dynamics of saturation of absorption using multilevel atomic systems,” Opt. Mater. Express 8(12), 3829–3834 (2018). [CrossRef]
46. S. I. Azzam and A. V. Kildishev, “Time-domain dynamics of reverse saturable absorbers with application to plasmon-enhanced optical limiters,” Nanophotonics 8(1), 145–151 (2018). [CrossRef]
47. J. Trieschmann, S. Xiao, L. J. Prokopeva, V. P. Drachev, and A. V. Kildishev, “Experimental retrieval of the kinetic parameters of a dye in a solid film,” Opt. Express 19(19), 18253–18259 (2011). [CrossRef]
