Continuous-wave upconversion lasing with a sub-10 W cm−2 threshold enabled by atomic disorder in the host matrix

Microscale lasers efficiently deliver coherent photons into small volumes for intracellular biosensors and all-photonic microprocessors. Such technologies have given rise to a compelling pursuit of ever-smaller and ever-more-efficient microlasers. Upconversion microlasers have great potential owing to their large anti-Stokes shifts but have lagged behind other microlasers due to their high pump power requirement for population inversion of multiphoton-excited states. Here, we demonstrate continuous-wave upconversion lasing at an ultralow lasing threshold (4.7 W cm−2) by adopting monolithic whispering-gallery-mode microspheres synthesized by laser-induced liquefaction of upconversion nanoparticles and subsequent rapid quenching (“liquid-quenching”). Liquid-quenching completely integrates upconversion nanoparticles to provide high pump-to-gain interaction with low intracavity losses for efficient lasing. Atomic-scale disorder in the liquid-quenched host matrix suppresses phonon-assisted energy back transfer to achieve efficient population inversion. Narrow laser lines were spectrally tuned by up to 3.56 nm by injection pump power and operation temperature adjustments. Our low-threshold, wavelength-tunable, and continuous-wave upconversion microlaser with a narrow linewidth represents the anti-Stokes-shift microlaser that is competitive against state-of-the-art Stokes-shift microlasers, which paves the way for high-resolution atomic spectroscopy, biomedical quantitative phase imaging, and high-speed optical communication via wavelength-division-multiplexing.

Emission spectrum of upconversion lasing from LQUMs of various diameters. An LQUM of 1.46 μm in diameter (a) exhibits a low Q factor due to high curvature loss 2 . An LQUM of 2.14 μm in diameter (b) does not exhibit resonance with the red emission band of Er 3+ ; therefore, upconverted photons of the red emission band could not participate in the laser process. To maximize the laser efficiency, we concluded that 2.44 μm is the optimal LQUM diameter in the present study, which is in line with a theoretical calculation 3 .

Supplementary Note 1
We find that the efficiency of the upconversion microlaser is determined by three factors: (1) heat generation in the microcavity, (2) Figure 5b). First, the heat generation for the rim and the center pumping was significantly higher than that for the edge pumping, which was supported by the laser line shifts (which originated from the increased temperature of the microsphere) (Supplementary Figure 5c). On the other hand, compared with the other pumping positions, the edge pumping results in severe pump power loss due to its minimal overlap with the pump beam, indicated by the weakest upconversion luminescence coming from edge pumping (Supplementary Figure 5d). Additionally, the low intensity ratio of 2 H 11/2 → 4 I 15/2 to 4 F 9/2 → 4 I 15/2 transitions supports that the pump power loss is more significant in edge pumping than in the other pumpings 1 . The pump power loss for the edge pumping is also 7 responsible for the low intensity ratio of Peak H to Peak F (Supplementary Figure 5e). Nevertheless, the highest laser peak integrated intensity was found for the edge pumping. Therefore, at high pumping power, detrimental heat generation is more crucial than the loss of pump power for intense upconversion lasing. However, as we decreased the pumping power to less than 1.0 MW cm -2 , where the 8 heat effects are less significant, rim pumping showed the most sustainable lasing, which led to a lower lasing threshold than the edge and center pumping by a factor of 28 (Supplementary Figure 6). This is an unexpected result because most papers have reported edge pumping for optimal laser performance. As the pump power density decreases, the integrated lasing intensity of the edge and the center pumping systems collapsed faster than that of the rim pumping system (Supplementary Figure 6a). As a result, the most sustained lasing was produced by rim pumping (Supplementary Figure 6b To support the fact that our monolithically designed WGM resonator yields sufficient pump-to-gain interactions with a free-space beam at the rim pumping, the pump-to-gain interactions have been carefully studied in terms of the pump position through numerically simulated spatial overlaps between the optical field distributions of the transverse magnetic 1) A Gaussian-type pump beam irradiates the microsphere along the z-axis.
2) The pump beam moves on the focal plane (xy plane), which includes the maximum intensity point of the pump beam and the edge and the center of the simulated microsphere.
3) The overlap area of the pump beam and the optical mode in the cross-section (xz plane) represents the pump-to-gain coupling effect in the microsphere.
In a real situation, the pump beam intensity does not follow a perfect Gaussian beam profile because diode lasers are not a point light source. The distributed emitting points in the active area of several micrometers across broaden the focusing spot size to be larger than the ideal Gaussian beam waist, which is determined by the numerical aperture of the focusing lens 5 . Furthermore, astigmatism, which refers to the difference in the focusing distance between the fast and slow axes of the active area, produces the larger focusing spot size at the focal plane 6 . For these reasons, the focused spot of our optical setup is approximated to be 3 μm in diameter. Nevertheless, because the pump beam profile in real situations can be considered the sum of coherent lights from multiple point sources, we were able to investigate the pump-to-gain coupling effect using the ideal Gaussian-type beam profile of our optical pumping setup (2ω 0 =720 nm for λ=980 nm, N.A.=1.3). As a side note, we considered only the two-dimensional pump-to-gain coupling effect rather than the threedimensional case because most coupling effects occur on the circumferential plane where the resonance occurs 4 , in our case, the xz plane.
To determine the optical mode of the upconversion lasing at 660 nm (TM mode, m=15, n=1.719), we computed the TM mode optical field distribution in the microsphere using MATLAB software following methods in the literature 7 , as shown in Supplementary   Figure 7b. To quantify the pump-to-gain interaction, we newly defined the effective pump-togain coupling distance, which is defined as the full-width-half-maximum of the optical fields from the WGM resonator's surface for effective coupling of gain with pump laser beam, was determined to be 370 nm. Next, we defined the pump-to-gain coupling effect as the magnitude of the effective pump power that is converted into upconversion lasing. Since the upconversion at 660 nm (two photon excitation) is proportional to the pump power intensity to the second power (∝I 2 ), we calculated the pump-to-gain coupling effect as the sum of the square of the pump intensity that overlaps with the effective pump-to-gain coupling distance.
With these conditions, we plotted the normalized pump-to-gain coupling effect depending on the pumping positions from the edge to the center (Supplementary Figure 7c). A considerable 11 magnitude of the pump-to-gain coupling effect is observed at the very edge (Supplementary Figure 7d). As the pump moves toward the center, the maximum coupling effect was found at 21% of the radius from the edge (Supplementary Figure 7e), strongly supporting our experimental observations (Supplementary Figure 6). Exceeding the maximum point, the pump-to-gain coupling effect continued to dramatically decrease, reaching a value smaller than one-seventh of the maximum for center pumping (Supplementary Figure 7f).   After performing the AAMD simulation, density functional theory (DFT)-based ab initio molecular dynamics (AIMD) simulations were performed to construct a more valid amorphous system. To perform the AIMD simulation, amorphous configurations of NaYF 4 +SiO 2 were randomly extracted from the bulk model system obtained by the AAMD simulation (Supplementary Figure 10) based on the interatomic distances of each pair from the radial distribution function (RDF). Ten types of amorphous NaYF 4 +SiO 2 model systems were constructed with a 1:1 volume ratio, which was the ratio for the experimental LQUM (Supplementary Figure 11). The Yb 3+ -, Er 3+ -and Tm 3+ -doped systems were constructed by substitution of one Y atom in each model system (Figures S12, S13, and S14). All AIMD simulations were carried out using the CASTEP program 10,11 . The Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) 12  The k-points used for the phonon DOS were 2 × 2 × 2.