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Self-organized lasers from reconfigurable colloidal assemblies

Abstract

Non-equilibrium assemblies, where units are able to harness available energy to perform tasks, can often self-organize into dynamic materials that uniquely blend structure with functionality and responsiveness to their environment. The integration of similar features in photonic materials remains challenging but is desirable to manufacture active, adaptive and autonomous photonic devices. Here we show the self-organization of programmable random lasers from the reversible out-of-equilibrium self-assembly of colloids. The random lasing originates from the optical amplification of light undergoing multiple scattering within the dissipative colloidal assemblies and therefore depends crucially on their self-organization behaviour. Under external light stimuli, these dynamic random lasers are responsive and present a continuously tuneable laser threshold. They can therefore reconfigure and cooperate by emulating the ever-evolving spatiotemporal relationship between structure and functionality that is typical of many non-equilibrium assemblies.

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Fig. 1: Reversible self-organization of colloids in a programmable random laser.
Fig. 2: Dynamics of dissipative colloidal accumulation and random lasing.
Fig. 3: Reconfiguring random lasers by load transfer.
Fig. 4: Cooperative random lasing.

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Data availability

Source data are available for this paper in Figshare with the digital object identifier 10.6084/m9.figshare.19745293 (https://doi.org/10.6084/m9.figshare.19745293)57. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

Code availability

The code that supports the findings of this study is available from the corresponding authors upon reasonable request.

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Acknowledgements

We are grateful to S. Rueber, M. Blunt and V. Barbieri for initial training on experimental techniques. G.V. acknowledges sponsorship for this work by the US Office of Naval Research Global (award no. N62909-18-1-2170). W.K.N. acknowledges the research support funded by the President’s PhD Scholarships from Imperial College London. R.S. and D.S. acknowledge support from The Engineering and Physical Sciences Research Council (EPSRC), grant no. EP/T027258, and the European Community.

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Authors

Contributions

Author contributions are defined based on the CRediT (Contributor Roles Taxonomy) and listed alphabetically. Conceptualization: R.S. and G.V. Data curation: W.K.N. and M.T. Formal analysis: W.K.N., D.S., M.T. and G.V. Funding acquisition: R.S. and G.V. Investigation: W.K.N., R.S., D.S., M.T. and G.V. Methodology: W.K.N., R.S., M.T. and G.V. Project administration: R.S., D.S., M.T. and G.V. Software: W.K.N., D.S. and G.V. Supervision: R.S. and G.V. Validation: W.K.N., D.S. and M.T. Visualization: All. Writing–original draft: All. Writing–review and editing: All.

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Correspondence to Riccardo Sapienza or Giorgio Volpe.

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Nature Physics thanks Neda Ghofraniha and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Diffusion of TiO2 colloids in ethanol solutions of rhodamine dyes.

In our experiments, due to their size and non-negligible density (\({\rho }_{{{{{\rm{TiO}}}}}_{2}}=4.24\) g cm−3), TiO2 colloids quickly sediment at the bottom surface of the experimental chamber, where, in the absence of a heat source, they primarily diffuse in 1% w/v ethanol solutions of rhodamine dyes near the plane defined by this interface. The diffusive behaviour is confirmed by the ensemble-averaged mean squared displacements (MSD(τ) τ) for both rhodamine 6G (circles) and rhodamine B (triangles). Each MSD is calculated from the trajectories of at least 6 colloids. The experimentally measured diffusion coefficients are D = 0.071 ± 0.002 μm2 s−1 for colloids in rhodamine 6G and D = 0.069 ± 0.001μm2 s−1 for colloids in rhodamine B.

Extended Data Fig. 2 Functionalisation of TiO2 colloids.

Fourier-transform infrared spectroscopy (FTIR) measurements of polyethylenimine polymer (PEI), pristine titania colloids (TiO2), and PEI-functionalised titania colloids (PEI@TiO2). Notable peaks at 1740 cm−1, 1365 cm−1 and 1217 cm−1 (dashed lines) corresponding to the presence of PEI are found on the functionalised TiO2 colloids, but not on the pristine particles. Spectra (except that of PEI) are enhanced by a factor of 10 for an improved comparison.

Extended Data Fig. 3 Experimental setup.

Two lasers (Nd:YAG and HeNe) are incorporated into a microscope where the sample with the colloidal particles is held (inset). The HeNe laser is used as an illumination source for the Janus particles, while the pulsed laser is used for lasing measurements. The pump power is controlled by an acoustic optical modulator (AOM), and a digital micro-mirror device (DMD) in the optical path is used to shape its excitation spot. The fibre-coupled HeNe laser is mounted on a separate stage and placed at the top of the sample. The lasing emission from the sample is collected and filtered by a 532 nm dichroic mirror (DM) and two filters (532 nm long-pass and 600 nm short-pass), then spectrally analysed by a spectrometer. The lamp shown in the inset illuminates the sample for bright-field imaging. The sample image is then sent to a camera through a 30:70 beam splitter (BS). M: mirror; CL: cylindrical lens.

Extended Data Fig. 4 Orientation of Janus particles within colloidal assemblies.

Janus particles fabricated from fluorescent SiO2 colloids ( ≈ 10 μm in diameter, excitation peak at 602 nm; emission peak at 623 nm) were used to confirm the orientation of the Janus particles in our experiments after accumulation of TiO2 colloids. (a-c) Schematics (top) and representative bright-field (middle) and fluorescence (bottom) images of the orientation of Janus particles under different conditions. (a) A Janus particle is initially found in a cap-up configuration near the bottom surface of the sample chamber. When excited at 620 nm from the same side of the image detection, it appears bright under fluorescence imaging. (b) After illuminating the particle in a with a continuous-wave laser at 532 nm to induce significant accumulation of TiO2 colloids, the particle is found to assume a cap-down configuration. In fact, when its translational motion is hampered by the surrounding cluster, the particle’s diffusive rotational dynamics lead to a cap-down equilibrium orientation dictated by gravity, due to the higher density of carbon (ρC = 3.52 g cm−3) with respect to silica (\({\rho }_{{{{{\rm{SiO}}}}}_{2}}=2.65\)g cm −3). After having switched off the external illumination by laser light, the detected fluorescence for this particle is indeed visibly lower than in a. The difference in brightness is due to the light screening effect introduced when the carbon cap is facing downwards. (c) This is confirmed by another Janus particle which has sedimented at the bottom surface of the sample chamber and is observed to diffuse with the cap-down equilibrium orientation dictated by gravity. Similar to b, fluorescence light is screened by the cap, hence the particle appears darker under fluorescence microscopy. Imaging and illumination settings were kept constant for all measurements.

Extended Data Fig. 5 Re-accumulation of TiO2 colloids after dispersal.

After dispersal (Fig. 1c), TiO2 colloids can be re-accumulated around the Janus particle and lasing action restored (Fig. 1d). A much shorter time ( ~ 10 minutes) is needed to re-accumulate particles to the same level as at the end of the accumulation phase due to the increased colloidal density after the first round of accumulation and dispersal. For the same reason, lasing action can also be reinstated much faster ( ~ 10 times): lasing is first observed after ~ 100 s of re-accumulation versus ~ 1200 s during accumulation. A few 275 second-long trajectories highlight the colloids’ motion.

Extended Data Fig. 6 Temperature increase measurement around a Janus particle.

All our experiments were performed by illuminating a Janus particles at a fixed HeNe laser power density (0.14 mW μm−2) corresponding to a local temperature increase ΔT = 57 ± 1. 6C (cross), just below the boiling point of ethanol (Tb = 78.37C). Above this power density, a cavitation bubble forms around the cap of the Janus particle (inset). To confirm this temperature increase, we calibrated the relationship between laser power density and ΔT by detecting the onset of the demixing of a critical mixture (2,6-lutidine and water) with respect to a set temperature as a function of laser power (circles). The sample containing the Janus particles for the measurements was placed on a homemade temperature stage with a precision of 0.1 K and allowed to equilibrate for 10 min at a range of different temperatures, before illuminating the particle with gradually increasing laser powers. Each of these temperatures correspond to a well-defined ΔT with respect to the critical temperature of the mixture (Tc = 307.25 K), thus allowing to univocally identify the corresponding power density at which demixing of the critical mixture is clearly observed. Fitting a linear trend to the whole set of data (dashed line) allows us to verify the reliability of our initial temperature estimation due to boiling in ethanol (cross). The error bars around each data point represent one standard deviation around the mean values.

Extended Data Fig. 7 Absence of lasing in assemblies of low refractive index colloids.

(a-b) A light-absorbing Janus particle in a laser dye solution with polymer (polystyrene, PS) microparticles attracts the diffusing colloids (accumulation) when illuminated by a HeNe laser (CW, 632.8 nm). (b) The colloids assemble in a dense cluster as in Fig. 1 for TiO2 particles. The polystyrene colloids have similar size and initial concentration as the TiO2 particles in Fig. 1. The dashed area in a-b represents the pump region (52 μm in diameter). (c) As scattering from the polystyrene particles is weaker than that from TiO2 particles due to their lower refractive index, the spectra for the polymer colloids before and after accumulation show no lasing action. Nonetheless, a similar size cluster of TiO2 particles is lasing (black dashed line). All spectra are obtained at the pump fluence of 130 mJ cm−2. (d-e) The absence of lasing action from the polystyrene cluster is confirmed by the linear (rather than superlinear) increase of the peak intensity as a function of pump fluence in d and by the fact that the emission linewidth does not reduce below 13.5 nm (lasing threshold) in e.

Extended Data Fig. 8 Characterisation of critical radius in TiO2 colloidal samples with rhodamine B dye.

We have performed experiments with both rhodamine 6G and rhodamine B (Methods). The measurement of the critical radius and its modelling has been performed for both dyes. Fig. 2d-e is done with rhodamine 6G, while this figure is done with rhodamine B. In both cases the colloidal samples are similar, and fabricated with the same procedure. The dots in a and b highlight experimental values obtained (a) at threshold and (b) at different linewidths (values in nm in the plot) for different pump radii under a fixed pump fluence (140 mJ cm−2). The lasing threshold (white) is defined when the full width at half maximum is 13.5 nm. The RTE model in a uses a gain length of 11.09 μm as the only free parameter to fit the experimental data (Methods). Theory and experiments show good agreement.

Source data

Source Data Fig. 1

Spectrum versus pump power, intensity and full-width at half maximum.

Source Data Fig. 2

Experimental and modelling data of colloids’ velocity and density versus time. Random laser model and experimental data of critical radius.

Source Data Fig. 3

Lasing spectra at fixed pump power

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Trivedi, M., Saxena, D., Ng, W.K. et al. Self-organized lasers from reconfigurable colloidal assemblies. Nat. Phys. 18, 939–944 (2022). https://doi.org/10.1038/s41567-022-01656-2

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