2.1.

Fabrication of Droplet Resonators

For all the results shown in Figs. 2–4, the droplets were prepared by mixing DI water/glycerol (volume ratio = 1:1). The purpose of mixing water and glycerol is to prevent droplets from evaporation. To confirm this effect, we compared the size changes of a droplet over periods of time with and without adding glycerol in Fig. S1 in the Supplementary Material. No obvious changes of the water/glycerol droplets were observed in 7 h; in contrast, the size of the water droplets shrank dramatically in 20 min due to evaporation. The slow evaporation of the water/glycerol mixture can be atttributed to the hydroscopic nature of glycerol.³⁷ For the preparation of lasing droplets, 2 mM (1 mM = 1 mmol/L) fluorescein sodium salt (FITC, Sigma-Aldrich #F6377) solution was prepared and printed on a dielectric mirror (customized by Evaporation Coatings Inc.) or a glass slide using an inkjet printer (Fig. S2 in the Supplementary Material). The hydrophobicity of the mirror in Fig. 4 was tuned by treating the mirror with different ratios of hydrophobic reagent/ethanol solutions. For the recording of molecular hydrophobicity in Fig. 5, the droplet resonators with different biomolecular concentrations were fabricated on a dielectric mirror using an inkjet printer (Fig. S2 in the Supplementary Material). First, molecular solutions with varying concentrations of bovine serum albumin (BSA) (Supelco #P5369), insulin (Sigma Aldrich #I0908), and V5 peptide (Sigma Aldrich #V7754) were prepared by dissolving specific amounts of biomolecules into buffer solutions. For the BSA and V5, phosphate-buffered saline (PBS) buffer was used as the solvent. For the insulin, triethylammonium bicarbonate buffer (Sigma Aldrich #T7408) was used as the solvent. Then the protein/peptide solution was mixed with glycerol (volume ratio = 3:1) and FITC to prepare a final solution with 4 mM FITC. The purpose of decreasing the volume ratio of glycerol is to reduce the hindrance of contact angle changes induced by the droplet viscosity. In Figs. 4 and 5, the droplets were fabricated using the same printer and program, thus the volumes of the droplets with different contact angles were close (about 68.5 pL). The dielectric mirror used in Fig. 5 was previously treated by octadecyl trichlorosilane (Sigma-Aldrich #104817) to form a hydrophobic surface.

Fig. 2

Demonstration of lasing action. (a) Schematic of a round droplet on a glass slide. (b) The optical spectrum of the droplet on a glass slide showing no laser emission. Inset: top-view profile of a round droplet on a glass slide (top) and the optical image after pumping (below). (c) Schematic of a round droplet on a highly reflective mirror. (d) The optical spectrum of the round droplet on the mirror showing laser emission. Inset: top-view profile of a round droplet on a mirror (top) and the optical image after pumping (below). (e) Schematic of a “deformed” droplet on a highly reflective mirror. (f) The optical spectrum of the “deformed” droplet showing laser emission. Insets: top-view profile of the “deformed” droplet (top) and the optical image after pumping (below). Scale bars in insets: $20\mu \mathrm{m}$. (g) Optical spectra of a droplet resonator with increasing pump energy densities. Inset: optical image of the droplet laser. (h) Enlarged spectra of the droplet resonator under the pump energy of $72.6\mu \mathrm{J}/{\mathrm{mm}}^2$ (below threshold) and $108.1\mu \mathrm{J}/{\mathrm{mm}}^2$ (above threshold). FWHM: full width at half-maximum. (i) Spectrally integrated output intensity and linewidth as a function of pump energy density [extracted from (g)]. FITC concentration: 2 mM.

Fig. 3

Characterization of the AL modes through FSRs. (a) Side-view profile of a droplet. $\alpha$, contact angle. $D$, diameter. Black dot circle, the complete circle containing the droplet profile. Blue line, an $N$-sided polygon containing the AL mode oscillation path (solid blue line). $l$, side length of an $N$-sided polygon. $h$, length of the two vertical short sides. (b) Measured FSRs (blue triangles) and the theoretical lines calculated by considering WGM (black line) and AL modes (colored lines). (c)–(e) The optical spectra of droplet resonators with the contact angles of (c) 69 deg, (d) 79 deg, and (e) 85 deg, respectively. Insets: CCD images of lasing emissions from individual droplets. (f) Simulated electric field distribution of the AL mode with $N=4$ calculated through the FSR in (c). (g) Simulated electric field distributions of the AL modes with $N=4$ and $N=6$ calculated through the FSRs in (d). (h) Simulated electric field distributions of the AL modes with $N=6$, $N=8$, $N=10$, and $N=20$ calculated through the FSRs in (e). FITC concentration: 2 mM. Pump energy density: $78\mu \mathrm{J}/{\mathrm{mm}}^2$.

Fig. 4

Lasing action of droplet lasers under different hydrophobicity. (a) Top: side-view profiles of droplets with varying contact angles. Below: optical images of the droplets after pumping. Yellow boxes, the laser emission regions. Red dashed circle in the CCD images represents excitation pump regions. Scale bar: $20\mu \mathrm{m}$. (b) Statistics of spectrally integrated laser outputs at different interfacial tensions and contact angles under the same pump energy density. Inset: spectrally integrated laser outputs as a function of pump energy density at contact angles of 75 deg, 79 deg, 85 deg, and 90 deg. (c) Optical spectra of droplet resonators with different interfacial tensions. Inset: laser linewidths under different contact angles. (d) Calculated $Q$-factors and the maximum number of AL oscillation paths as a function of contact angle. (e) Simulated electric field distributions and $Q$-factors of the AL modes with $N=4$, 6, and 8 under the same contact angle of 83 deg. (f) Simulated electric field distributions and $Q$-factors of the AL modes with $N=4$, 12, and $\infty$ for respective contact angles of 67 deg, 83 deg, and 90 deg. FITC concentration: 2 mM. Pump energy density: $78\mu \mathrm{J}/{\mathrm{mm}}^2$. Calculation parameters: volume of $\text{droplets}=68.5\mathrm{pL}$; refractive $\text{index}=1.41$. Interfacial tension calculations:^34–36 refer to Sec. 2 in the Supplementary Material.

Fig. 5

Modulating laser emission with intermolecular forces at the biointerface. (a) Schematic of biointerface modulating laser emissions based on biomolecular adsorptions with different concentrations. Higher concentration of biomolecules leads to smaller interfacial tension ${\gamma }_i$ and lower laser intensity. (b) Interfacial tensions (top), contact angles (top), and spectrally integrated laser outputs (bottom) as a function of BSA concentration. (c), (d) Contact angles and spectrally integrated laser outputs as a function of different biomolecular concentration, including (c) insulin and (d) V5 peptide. Insets in (b) (top), (c), and (d): side views of droplets with different biomolecular concentrations. Inset in (b) (bottom): CCD images of lasing emissions under different concentrations, where the emission regions are marked with yellow boxes. FITC concentration: 4 mM. Pump energy density: $36\mu \mathrm{J}/{\mathrm{mm}}^2$. Interfacial tension calculations:^38,39 refer to Sec. 2 in the Supplementary Material.

2.2.

Optical System Setup

The schematic of the optical system can be seen in Fig. S2(b) in the Supplementary Material. Optical pumping was achieved by a pulsed ns-laser (EKSPLA PS8001DR) integrated with an optical parametric oscillator (repetition rate: 50 Hz; pulse duration: 5 ns). According to the absorption spectrum of FITC, 479 nm was selected as the pumping wavelength. An upright microscopic system (Nikon Ni2) with a $10\times$ 0.3 NA objective was used to focus the pump light onto the droplets and was also used to collect the emissions from the droplets. The beam diameter at the objective focal plane was measured to be $40\mu \mathrm{m}$. The collected emissions from droplets were separated by a beam splitter and incident into a charge-coupled device (CCD) camera (Newton 970 EMCCD) and imaging spectrometer (Andor Kymera 328i). The side-view droplet profiles were recorded by a color CCD (Andor Zyla SCMOS) mounted on an inverted microscopic system (Nikon Ti2) with $20\times$ 0.4 NA objective.

2.3.

Simulations

The electric field distributions of AL modes and WGM and their $Q$-factors were calculated with the finite element method using COMSOL Multiphysics software. The eigenfrequency study was applied in the electromagnetic waves, frequency-domain interface within the wave optics modules. For AL modes, a 2D model was employed. For WGM, a 2D axisymmetric model was employed. The geometries of the droplet resonators were set to be parts of perfect rounds, and the refractive index (RI) was 1.41. For the $Q$-factor calculations, a bottom mirror with a reflectivity of $\sim 99.995\%$ was considered, which introduced $\sim 0.01\%$ losses for AL modes and thereby limited the $Q$-factors of AL modes up to the $\sim {10}^7$ level. A bottom distributed Bragg reflector (DBR) was composed of 24 dielectric layers alternating between high-RI (2.32) and low-RI (1.38) layers. The thickness of the high-RI layers was 58.2 nm; and the thickness of the low-RI layers was 97.8 nm. The $Q$-factors under each contact angle were the maximum values selected from 100 solutions around 540-nm wavelength obtained by COMSOL Multiphysics software.

3.1.

Concept and Principle of Droplet Resonators Hosting AL Modes

Figure 1 presents the fundamental concept and principle of droplet resonators hosting AL modes based on different hydrophobic forces at droplet–solid interfaces. A droplet doped with a fluorescent dye is formed on a highly reflective mirror corresponding to the fluorescent emission wavelength. The volumes of droplets were fixed using a commercial inkjet printer (Fig. S2 in the Supplementary Material). Owing to the strong reflections of the mirror at two ends of the droplet and the internal reflections along the droplet–air interface between the two ends, a unique oscillation pathway of AL modes is formed [Fig. 1(a)]. An active layer of molecules is deposited at the interface between the droplet and mirror, where the hydrophobic forces govern the cavity geometry of a droplet laser [Fig. 1(b)]. Explicitly, the contact angle $\alpha$ that characterizes the cavity geometry is the result of balance among the droplet–solid interfacial tension ${\gamma }_i$, solid surface tension ${\gamma }_s$, and droplet surface tension ${\gamma }_l$. In principle, the AL modes that follow the oscillation paths corresponding to segments of “$N$-sided polygons” are highly correlated with the contact angles of droplet lasers. As the contact angle increases, AL modes with higher orders of $N$-sided polygon paths can be supported in the droplet, as shown in Fig. 1(c). The corresponding electric field distributions are simulated in Fig. 1(d) under different $N$. Consequently, more AL modes can be excited with the increase of contact angles, resulting in increased laser intensities.

3.2.

Demonstration of Lasing Action

To demonstrate that “AL mode oscillations” are the result of strong reflections between the mirror and the droplet–air interface, two types of bottom substrates with different reflectivity and identical hydrophobicity (Fig. S3 in the Supplementary Material) were prepared. As compared in Figs. 2(a) and 2(c), FITC water/glycerol droplets were prepared on a glass slide (reflection $R<1\%$) and a highly reflective DBR mirror ($R>99.99\%$ at FITC emission wavelength). Without highly reflective mirrors, no lasing mode was observed in the CCD image of the optically pumped droplet [inset in Fig. 2(b)], indicating no laser oscillations in the droplet. Similarly, no lasing spectrum was seen in Fig. 2(b); only a typical broad fluorescence emission profile was present. In contrast, lasing was observed under the same pump energy density with the addition of a highly reflective mirror. Strong laser modes were symmetrically emitted from the two opposite ends of the droplet [inset in Fig. 2(d)]. The corresponding emission spectrum shows typical lasing peaks of microlasers [Fig. 2(d)], which further indicates laser oscillations in the droplet. The results imply that the reflectivity of the bottom mirror substrate plays a vital role in the oscillations of droplet laser resonators.

To further demonstrate that internal reflections along the droplet–air interface also participate in laser oscillations, a “deformed” droplet was formed on a highly reflective mirror [Fig. 2(e)]. It is noteworthy that the random-shaped configuration definitely cannot support WGM that oscillates in the droplet bottom plane. Surprisingly, laser emissions were also observed under the same pump conditions [Fig. 2(f)]. Similar to the laser emission from a regular droplet resonator [inset in Fig. 2(d)], the laser signals were also emitted symmetrically from the two ends of the droplet [inset in Fig. 2(f)]. This finding indicates that internal reflections along the droplet surface between the two ends still participated in the laser oscillations, forming the proposed vertically orientated oscillation paths.

We further measured the output intensities and linewidths of a droplet resonator by increasing the pump energy densities to demonstrate lasing action. Spectrally integrated output intensities and linewidths were subsequently measured based on the spectra in Fig. 2(g), where the linewidth of a peak is defined by its full width at half-maximum [Fig. 2(h)]. As shown in Fig. 2(i), a clear threshold was observed for both the output intensities and linewidths. For instance, a relatively broader linewidth was measured when the pump energy density is below the threshold [Fig. 2(h)], which is contributed by enhanced spontaneous emissions. In contrast, linewidth narrowing was obtained when the pump energy density reached above the lasing threshold.

To investigate the properties of a laser output beam, an imaging spectrometer was used to observe the corresponding laser modes. As presented in Fig. S4 in the Supplementary Material, distinctive transverse modes with symmetrical sector shapes and nodal lines were observed from both ends of the microdroplet. The laser beams were found to possess a strong lasing polarization that is perpendicular to the direction along two opposite ends, indicating TE mode lasing in a droplet. Additionally, we investigated how different dye concentrations influence the lasing performance. Under a fixed contact angle, the output laser intensities increase with the increase of dye concentrations; meanwhile, the lasing thresholds decrease (Fig. S5 in the Supplementary Material). We further calculated the lasing thresholds by solving rate equations (Sec. 1 in the Supplementary Material). The calculation results have a good agreement with the experiment, which indicate that the lasing thresholds are consistent with the magnitudes of the gain and resonator losses^40,41 [Sec. 1, Fig. S5(b) in the Supplementary Material].

3.3.

Characterization of Arc-Like Modes in Droplet Resonators

Considering the fact that all the microdroplets used in this study are smaller than the capillary length, all the droplets can be regarded as parts of ideal spheres^42–44 (Sec. 2 in the Supplementary Material). As such, it can support a series of laser oscillation modes propagating along pathways representing segments of $N$-sided polygons, as shown in Figs. 1(c) and 1(d). By following such pathways, the laser can be efficiently confined through the strong vertical reflections by the mirror and near-total reflections along the droplet–air interface. Considering the geometric characteristics of the AL oscillation paths, the number $N$ representing the side number of the $N$-sided polygon can be specified to characterize the AL mode. Determined by the axial symmetry of the AL oscillation path, $N$ is an even number. In practice, the AL oscillation paths cannot be directly observed due to a lack of scatterings in droplets. Nonetheless, AL modes with a specific $N$ can still be characterized by measuring their free spectrum ranges (FSRs). In a droplet resonator with a diameter of $D$ and a contact angle of $\alpha$ [Fig. 3(a)], the optical path length of the AL mode with a specific $N$ in a round trip can be calculated as (Sec. 3, Fig. S6 in the Supplementary Material)

To be more explicit, we demonstrate the lasing profiles of three individual droplet resonators with different contact angles (69 deg, 79 deg, and 85 deg). As shown in Figs. 3(c)–3(e), lasing spectra from the three droplets presented unique sets of FSRs as well as different numbers of AL modes. For instance, only one set of FSRs can be found in the droplet with a contact angle of 69 deg. According to Eq. (2), the calculated FSR corresponds to the AL mode with $N=4$ [Fig. 3(c)], while the simulated electric field with $N=4$ is also shown in Fig. 3(f). As the contact angle increased to 79 deg, two sets of FSRs corresponding to the AL modes with $N=4$ and $N=6$ were observed [Fig. 3(d)]. The simulated electric fields also support the AL modes with $N=4$ and $N=6$ [Fig. 3(g)]. For an even larger contact angle (85 deg), complicated lasing peaks were observed, including four sets of FSRs corresponding to AL modes with $N=6$, $N=8$, $N=10$, and $N=20$, respectively [Fig. 3(e)]. The simulated electric fields with $N=6$, $N=8$, $N=10$, and $N=20$ are also presented in Fig. 3(h), respectively. As such, the lasing spectra shown in Figs. 3(c)–3(e) present the tendency that more AL laser modes can be excited with the increase of contact angles.

3.4.

Lasing Action under Different Hydrophobic Forces

Next, we attempt to investigate how hydrophobic forces interplay with the droplet resonator and influence the lasing output. For this purpose, mirrors with different surface hydrophobicity were prepared. The interfacial tension increases with the increasing hydrophobic forces at the droplet–solid interface, resulting in the increase of droplet contact angles. The resultant side-view images of the droplet lasers with various contact angles (58 deg to 90 deg) are shown in Fig. 4(a) (top row). Under the same FITC dye concentration and pump energy density, the lasing actions of the droplet lasers were studied as a function of interfacial tension as well as contact angle. The laser modes for the respective contact angles were recorded with a CCD in Fig. 4(a) (bottom row). At a relatively small contact angle (58 deg), no laser emission was observed. When the contact angle reached 67 deg, sharp laser emissions started to emerge. As the contact angles continued to rise, more intense laser modes with broader emission regions were observed. The statistics of spectrally integrated laser output intensities based on different interfacial tensions as well as contact angles are compared in Fig. 4(b). With the increase of interfacial tension and contact angles, a significant enhancement of laser output intensities was obtained, as shown in Fig. 4(b). The spectrally integrated laser outputs as a function of pump energy density under different contact angles were also investigated [inset in Fig. 4(b)], showing lower pump thresholds and higher slope efficiencies with the increase of interfacial tensions. Figure 4(c) shows the representative lasing spectra recorded under different interfacial tensions. The lasing intensity and number of lasing modes increased accordingly with the interfacial tension and contact angle, which can be attributed to an increased number ($N$) of AL modes supported within the droplet. The linewidths of the lasing peaks are in the range of 0.13 to 0.2 nm, which present a decreasing tendency as the contact angle increases [inset in Fig. 4(c)].

To understand the modulating mechanism, theoretical calculations of the $Q$-factor were carried out under different contact angles (based on fixed droplet volume). By increasing the contact angles from 58 deg to 90 deg, a dramatic increase of $Q$-factors from $\sim {10}^3$ to ${10}^7$ was achieved [red squares in Fig. 4(d)]. Note that under a specific contact angle, AL modes with different $N$ possess different $Q$-factors. However, only the maximum calculated $Q$-factors are plotted here in order to reflect the maximum capability of laser confinement. The maximum number of AL oscillation paths in a droplet that follow segments of $N$-sided polygons was also calculated based on reflection law (Sec. 3 in the Supplementary Material). For example, only AL oscillation paths that follow 4-sided and 6-sided polygons can be hosted in a droplet when the contact angle is fixed at 67 deg; therefore, the corresponding maximum number of AL oscillation paths is 2. As shown in Fig. 4(d), the blue line shows a significant increase of the maximum number of AL oscillation paths with the increasing contact angles. Based on the above theoretical results, the higher $Q$-factors at larger contact angles indicate lower optical losses. Additionally, the increasing maximum number of AL oscillation paths will result in more AL modes excited at larger contact angles. These two key factors co-determine the laser output intensities as well as lasing mode profiles as the contact angle changes. We also calculated the $Q$-factors of AL modes with different $N$ values under the same contact angle. In general, the AL mode with a larger $N$ possesses a higher $Q$-factor under the same contact angle [Fig. 4(e)]. The results are reasonable because the AL mode with a larger $N$ possesses larger internal reflection angles on the droplet–air interface, resulting in a lower loss and a higher $Q$-factor. Therefore, the AL laser modes with a larger $N$ and higher $Q$-factors will be excited as the contact angle increases [Fig. 4(f)].

3.5.

Modulating Laser Emission with Intermolecular Forces at the Biointerface

Based on the above experimental and theoretical findings, we have explicitly demonstrated the correlation between laser emission intensities and hydrophobic forces at the droplet–solid interface. Herein, we investigated the possibility of modulating laser emissions of droplet resonators at the biointerface with different hydrophobic forces. Biointerface refers to the region where a biomolecule contacts an inorganic/organic surface, providing the basis for studying biomolecular interactions.^28,45–48 As such, different concentrations of protein and peptide solutions were prepared in droplet resonators via inkjet printing in which biointerfaces were formed by biomolecular adsorptions on mirrors and the interfacial hydrophobicity was altered by biomolecular concentrations. The laser emission intensities of droplet resonators were subsequently recorded, as shown in Fig. 5(a). In the process of interface adsorption, non-polar side chains of biomolecules tend to be adsorbed on the hydrophobic surface, forming an interface with a higher hydrophilicity.⁴⁹ The higher concentration of biomolecules adsorbed on the mirror surface, the lower the interfacial tension and contact angle will become. We first performed the statistics of interfacial tensions, contact angles, and laser output intensities as a function of BSA concentration. As shown in Fig. 5(b), the interfacial tension and contact angle decrease with the increase of BSA concentration, indicating a decrease of interfacial hydrophobicity. Meanwhile, the laser output intensities also decrease with the increase of BSA concentration. In particular, the hydrophobicity change induced by a 15 nM concentration of BSA could be identified through droplet lasers. In addition to BSA, insulin and V5 peptide with different concentrations were also employed to modulate laser emissions of droplet resonators by tuning the interfacial hydrophobicity [Figs. 5(c) and 5(d)]. Figure 5 shows the significant changes in laser intensity under different molecular hydrophobicity (or molecular concentrations), showcasing the potential of modulating laser emissions with tiny interfacial molecular forces and hydrophobic interactions at the biointerface.