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Abstract
This study introduces design and coupling techniques, which bridge an opaque liquid metal, optical WGM mode, and mechanical mode into an opto-mechano-fluidic microbubble resonator (MBR) consisting of a dielectric silica shell and liquid metal core. Benefiting from the conductivity of the liquid metal, Ohmic heating was carried out for the MBR by applying current to the liquid metal to change the temperature of the MBR by more than 300 °C. The optical mode was thermally tuned (>3 nm) over a full free spectral range because the Ohmic heating changed the refractive index of the silica and dimeter of the MBR. The mechanical mode was thermally tuned with a relative tuning range of 9% because the Ohmic heating changed the velocity and density of the liquid metal.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Droplet microresonators, made of materials such as carbon disulfide [1], water [2], octane [3], silicon oil [4,5], paraffin, [6] and biological lipids [7], in the liquid phase have recently drawn considerable attention with regard to many applications, owing to the enhanced direct interaction of light with the liquid. In contrast to solid microresonators [8–11], which interact with the external environment by using the evanescent wave, the optical mode is directly formed in the intra-droplet with a greatly enhanced electric field, which contributes to the development of nonlinear optics [1,3,5] and sensing applications [2,6,12]. Droplet microresonators are also biocompatible with cells and tissues. By injecting biolipid droplets into the cells [7], intracellular microlasers can be formed in vitro for biosensing and imaging.
Particularly, the optomechanical coupling effect [4,5] in soft liquid microresonators with low viscosities will be more pronounced compared with that in solid microresonators. The mechanical mode in transparent liquid microresonators, that are optically tweezed [3] or held by a silica stem [4], can be triggered by exciting the optical mode through a tapered fiber [4] or free-space light coupling [5,13]. However, these coupling schemes do not apply to opaque droplet (for example, liquid metal) microresonators because they do not support the high Q resonant mode. Additionally, the stability of the liquid microresonator is limited owing to the fast evaporation of the liquid [2].
In previous studies [14–17], a bridge between optofluidics and optomechanics was established in a microbubble resonator (MBR) with a liquid inside by coupling the light from the outer dry silica shell. Compared with optomechanical resonators directly submerged in liquid, the optical absorption and acoustic loss can be suppressed in optofluidic MBR with a silica shell [18]. Additionally, MBR [19] with a hollow structure and two stems is highly tunable. Several tuning methods for the optical mode and mechanical mode have been reported, such as strain tuning [20–23], aerostatic pressure tuning [24,25], thermal tuning [26–28], fluidic tuning [14,15], and all-optical tuning [29].
This study experimentally investigated the optical mode and mechanical mode in a novel optofluidic MBR with a liquid metal core (Fig. 1(b)). A bridge was established between the liquid metal optofluidics and optomechanics by launching light into the silica shell to excite the optical and mechanical modes. Thus, the opto-mechano-fluidic MBR with a liquid metal core was experimentally investigated for the first time. In particular, liquid metals (mercury in this study) are an excellent conductive material. By applying current to the liquid metal core, the Ohmic heating of the microcavity was investigated and the microcavity temperature increased to over 300 °C. Owing to the refractive index of the silica shell, the diameter of the cavity, the velocity and density of the liquid metal are depended on the temperature, the ultra-broadband tuning of both the optical and mechanical modes was realized.
Fig. 1. (a) Schematic of experimental setup. The bubble stems are connected with Au microwire electrodes to control the current of the liquid metal core. VOA: variable optical attenuator; FPC: fiber polarization controller; PD: photoelectric detector; OSC: oscilloscope; RTSA: real-time spectrum analyzer; DAQ: data acquisition. The current of the liquid metal core is controlled by a current source. The liquid is pumped into the microchannel of the MBR using a syringe pump. (b) Schematic of liquid metal MBR. (c) Optical photograph of liquid metal MBR coupled with tapered fiber.
2. Experimental results
The schematics of the experimental setup are shown in Fig. 1(a). To investigate the optical and mechanical mode properties of the liquid metal core MBR, an optical tapered fiber was used for microcavity coupling (Fig. 1(c)). The laser was swept back and forth by a function generator or data acquisition (DAQ) card across the cavity resonance. The laser’s intensity and polarization were controlled by a variable optical attenuator and fiber polarization controller, respectively. The cavity transmission spectrum and mechanical spectrum were recorded by an oscilloscope (or DAQ card) and real-time spectrum analyzer, respectively. The dielectric MBR was fabricated using the fuse-and-blow technique [30]. The thickness of the silica shell varied from 2 to 25 µm, and the diameter of the MBR varied from 125 to 400 µm in our fabrication [31]. Mercury was poured through the bubble microchannel using a microsyringe. Two Au microwire electrodes (Fig. 1(b)) were fixed to the microchannel of the bubble stem to apply current to the mercury from a current source.
A typical transmission spectrum of an empty MBR with a radius (Rb) of 123 µm and shell thickness (t) of 5 µm is shown in Fig. 2(a). Because the MBR supported highly non-degenerate WGMs [19,20,32], very dense and rich WGM resonances were efficiently excited and the azimuthal free spectral range (FSR) was hardly distinguishable. The optical Q factor in the empty MBR was typically above 107. The dense modes were very suitable for a cavity quantum electrodynamics (QED) experiment [33]. However, they were also harmful for the wavelength tuning or a biosensing experiment because a dense spectrum presents difficulty in identifying and tracing the desired mode. After mercury filling with a microchannel, a cleaner transmission spectrum with an identifiable FSR of 2.19 nm was obtained (Fig. 2(b)). Thus, this approach is equivalent to the spectrum clean-up method [34]. The Q factor reduction (Fig. 2(b)) in this thin shell sample was caused by the absorption of mercury. The Q factor of the fundamental and lower order WGMs in the thick shell sample (t > 10 µm) was maintained at 107 because the WGM was localized in the shell and did not interact with the mercury. Therefore, a thin shell sample was used in the optical mode tuning experiment to easily track the optical mode, while a thick shell sample was used in the mechanical mode tuning experiment to efficiently excite the mechanical mode.
Fig. 2. (a) Typical transmission spectrum of empty MBR. (b) Transmission spectrum of liquid metal MBR.
2.1 Tuning optical resonance wavelength
Tunable optical resonance is beneficial in many microcavity applications, such as optical filters, nonlinear optics, and cavity QED experiments. Because the mercury is a good conductor, two Au microwires were bounded to the optofluidic core as electrodes to feed current from a current source to the mercury. The Ohmic heating induced by the mercury changed the temperature of the resonator and hence tuned the optical resonance wavelength. The electrical resistance R of the mercury between the two electrodes was measured as approximately 6 Ω using a multimeter. The Ohmic heating W of the mercury between the two electrodes can be expressed as: W = I2Rt, where I is the current applied to the mercury and t is the heating time. After a certain heating time, the temperature of the microcavity will become stable when thermal equilibrium is established. The temperature change of the microcavity can be expressed as δT = W/K, where K is the thermal conductivity coefficient. The temperature change of the microcavity alters the refractive index and radius of the microcavity; thus, the optical path and resonance wavelength λ of the WGM is modified. The resonance wavelength shift can be calculated as follows:
where λ0 and n0 are the initial wavelength and refractive index of the silica, respectively; dn/dT is the thermo-optic coefficient. Note that the thermal expansion coefficient is at least one order lower than the thermo-optic coefficient, and the thermal expansion effect is ignored in Eq. (1). Finally, we conclude that the resonance wavelength shift is proportional to the square of the current applied to the mercury, that is, δλ ${\propto}$ I2.The WGM measured in Fig. 2(b) was experimentally tested by applying Ohmic heating to determine the tuning ability. By increasing the current applied to the mercury with a step of 50 mA, the resonant wavelength red-shifted as shown in Fig. 3(a). The optical resonance wavelength was tuned over 3 nm (Fig. 3(b)), which is larger than the FSR of 2.19 nm (Fig. 2(b)). This indicates that the optofluidic liquid metal core MBR was fully tunable. The relationship of δλ versus I is plotted in Fig. 3(b). The measured data match very well with the quadratic fit (red line) δλ(I)=AI2=2.35×10−5I2. Moreover, the coupling depth (Fig. 3(a)) decreased as the current increased. This resulted from the fact that the Ohmic heating increased the effective mode index of the WGM, and from the fact that the effective mode index mismatch between the tapered fiber and the WGM increased. Additionally, the Q factor slightly decreased as shown in the inset of Fig. 3(b). According to Eq. (1), the temperature change δT of the microcavity can be estimated under different currents [35]. Alternatively, a more accurate prediction of δT can be calculated by δT=δλ/S, where S is the thermal sensitivity. This study used the experimentally determined value of S = 10.82 pm/K for the silica microcavity [36]. The temperature change of the microcavity can be seen in the right Y-axis in Fig. 3(b); the maximum δT value reached up to 280 °C, and the microcavity temperature reached 303 °C (the clean room temperature stabilized at 23 °C).
Fig. 3. Broadband tuning resonant wavelength by Ohmic heating liquid metal core. (a) Resonant mode spectrum changes as current of mercury increased by step of 50 mA. Inset shows sample emitting blue-green light when the current was 420 mA. (b) Resonant wavelength shift (inset shows Q change) as function of current.
An interesting phenomenon occurred when the current applied to the mercury was 420 mA. According to the relationship of δT and I (Fig. 3(b)), the entire microcavity temperature reached approximately 400 °C. This temperature is higher than the evaporation temperature of the mercury (356.58 °C). Hence, the mercury liquid transitioned to mercury vapor. When the current flowed through the mercury vapor, the electrical energy transformed into the mercury’s resonant emission line at 254 nm, which corresponds to a transition from 23P1 to the ground state [37]. The other weaker emission lines were 436 nm and 546 nm. The charge coupled device (CCD) used in this experiment could not detect ultraviolet (UV) light and only 436 nm and 546 nm emitting light is captured by the CCD. As a result, the microbubble only exhibited a blue-green color (inset of Fig. 3(a) and Visualization 1). At this stage, the microcavity is unstable and the WGM wavelength changes dramatically. Therefore, for stable thermal tuning the WGM, the current applied to the mercury must be below 370 mA to avoid phase transition of the mercury.
2.2 Tuning mechanical frequency
The analytical solution for the mechanical frequency fm of the liquid droplet microresonator [4] revealed the following: (i) fm is proportional to the bulk modulus of medium B, which is proportional to the square of the sound speed of liquid c2, and thus fm is proportional to c; (ii) fm is inversely proportional to the root of the liquid density ρ. Hence, the mechanical frequency can be tuned by changing c or ρ for a fixed-size droplet microcavity. Moreover, the mercury’s c and ρ are related to the temperature T as follows [38,39]:
In accordance with the abovementioned experimental results, the temperature of the entire microcavity can be tuned by changing the current applied to the mercury, which means changing c and ρ of the mercury (Eqs. (2) and (3)). Thus, fm can be tuned accordingly. Because, δc/c is much larger than δρ/ρ, δfm was assumed to be proportional to δc and δT. However, δT is proportional to I2, hence δfm is also proportional to I2. To verify this deduction, we conducted a finite element method (FEM) simulation (solid mechanics and acoustics module in COMSOL MULTIPHYSICS) to calculate the mechanical eigenfrequency fm. The solid-domain displacement fields associated with the fluid domain were considered to analyze the hybrid shell-fluid mechanical mode [40] in MBR with Rb=120 µm and t = 25 µm, and truncated harmonic oscillator profile curvature Δk = 0.005 µm−1 [30].The fundamental first order breathing mode (1,1,0) profile of the liquid metal core MBR is shown in Figs. 4(a)–4(c) with fm=7.15 MHz; the frequency of the fundamental first order breathing mode (1,1,0) of the air core MBR fm=9.85 MHz. The decrease of fm by replacing the air with mercury increased the effective mass of the mechanical mode meff, which is proportional to density ρ [15,40]. The current applied to the mercury was assumed to range from 0 to 320 mA; the microcavity temperature ranged from 23 °C to 246.2 °C according to the relationship of δT versus I shown in Fig. 3(b); c and ρ ranged between 1458.9-1302.6 m/s and 13539.2-12996.8 kg/m3 according to Eqs. (2) and (3), respectively. The results for fm were obtained as functions of c (at constant ρ=13539.2 kg/m3) and ρ (at constant c = 1458.9 m/s) for the fundamental first order breathing mode, as shown in Figs. 4(d) and 4(e), wherein approximately linear relationships can be observed. The absolute variation of fm (−0.65 MHz, Fig. 4(d)) induced by the c variation was much larger than that (0.01 MHz, Fig. 4(e)) induced by the ρ variation. The c-related sensitivity of fm versus T was -1896.8 Hz/°C, whereas the ρ-related sensitivity of fm versus T was only 41.8 Hz/°C. Thus, c was the main factor influencing fm. Additionally, fm decreased when the microcavity temperature increased. We linked c, ρ, and T with I in COMSOL’s material settings to calculate Δfm versus I, as plotted in Fig. 5(d) (blue dotted line). From the above theoretical analysis, it is understood that Δfm is proportional to I2.
Fig. 4. Simulated result for (a) 3-D and (b) 2-D shell displacement field distribution of fundamental mechanical mode of optofluidic liquid metal core MBR; (c) 2-D fluid pressure field distribution of fundamental mechanical mode of optofluidic liquid metal core MBR. Black solid lines indicate boundary of MBR shell. Mechanical frequency versus (d) sound speed (mercury density was fixed at 13539.2 kg/m3) and (e) density of mercury (sound speed was fixed at 1458.9 m/s) were calculated.
Fig. 5. Mechanical power spectrum when optofluidic core is filled with (a) air and (b) mercury. (c) Mechanical power spectrum changes caused by increasing the current of mercury with a step of 40 mA. (d) Experimentally measured data (※) versus different currents; red line indicates quadratic fitting of measured data, and blue dotted line indicates calculated result of relative mechanical frequency shift as function of current applied to liquid metal core.
For the experiment, a thick shell MBR with Rb=120 µm, t = 25 µm, and Δk = 0.005 µm−1 was fabricated to avoid liquid metal absorption and obtain a high Q (>107) optical mode. The transmitted power spectrum of the air core and liquid metal core MBR are shown in Figs. 5(a) and 5(b), respectively. As expected, the mechanical mode frequency decreased from 10.76 MHz to 6.73 MHz when the air microchannel was replaced by the liquid metal with a higher ρ. The decrease of the mechanical mode frequency was observed (Fig. 5(c)) as the current applied to the liquid metal increased from 0 to 320 mA with a step of 40 mA. The relative mechanical frequency shift Δfm at different currents is plotted in Fig. 5(d), and the measured data were quadratically fitted (red line), which verifies that Δfm is proportional to I2, according to the abovementioned theoretical prediction. The maximum Δfm value was approximately 0.6 MHz; the relative tuning range of the mechanical mode reached 9%, which is larger than that of the aerostatic tuning [24], strain tuning [22], and thermal tuning [41] methods. The measured Δfm data match very well with the calculated data (blue dotted line in Fig. 5(d)). The long-time data acquisition of the mechanical oscillation spectrogram is shown in Fig. 6. The standard deviations of the mechanical oscillation peak over a time span of 260 s were 782 Hz and 652 Hz for I = 0 (Fig. 6(a)) and I = 320 mA (Fig. 6(b)), respectively. This indicates that applying current to the liquid metal core will not cause noise in the mechanical oscillation peak.
Fig. 6. Long time data acquisition of mechanical oscillation spectrogram (a) when current was not applied to liquid-meal core and (b) when current I = 120 mA was applied to liquid metal core.
Finally, the intrinsic mechanical mode quality factor Qm was estimated by exploiting the effect of pump power on the mechanical power spectrum and linewidth of the mechanical mode [42,43], because the optomechanical coupling is proportional to the intracavity photons [44]. The input pump power was tuned below the phonon lasing threshold, and the transmitted power spectra are shown in Fig. 7(a). The peak of the mechanical oscillation spectra increased as the pump power increased. The linewidth (3-dB bandwidth) of the mechanical mode δfm as a function of input power is plotted in Fig. 7(b), where it can be seen that δfm linearly decreased as the pump power increased. The intrinsic linewidth of the mechanical mode corresponds to the extrapolation of δfm at zero pump power. Through the linear fitting shown in Fig. 7(b), the intrinsic δfm was estimated as 17 kHz, which corresponds to a Qm of approximately 395 for the liquid metal core MBR.
Fig. 7. (a) Mechanical power spectrum with different input pump laser power. (b) 3-dB bandwidth δfm as function of input pump laser power.
3. Summary
This study experimentally demonstrated an opto-mechano-fluidic microcavity consisting of a liquid metal core and silica shell by bridging the optical mode, mechanical mode, and liquid metal optofluidics. The ultra-broadband tuning of the optical and mechanical mode was realized by Ohmic-heating the microcavity through the application of current to liquid metal. The optical mode wavelength was tuned to over 3 nm, which exceeds the FSR, and the frequency of the mechanical mode was tuned with a relative tuning range of 9%. This study lays the foundation for investigating the optical and acoustic properties of opaque or highly absorbable liquid materials. Liquid metal is a unique material because it can dissolve other inorganic materials, such as metals. This facilitates the investigation of a solute that is not applicable in water. Thus, the optomechanical platform introduced by this study can be useful for further fundamental scientific and application studies on liquid metals.
Funding
National Natural Science Foundation of China (61705039); National Basic Research Program of China (973 Program) (2015CB352006); China Postdoctoral Science Foundation (2019T120553, 2017M610389); Distinguished Young Scientific Research Talents Plan in Universities of Fujian Province; Fujian Provincial Key Project of Natural Science Foundation for Young Scientists in University (JZ160423); Changjiang Scholar Program of Chinese Ministry of Education (IRT_15R10); Special Funds of the Central Government Guiding Local Science and Technology Development (2017L3009); Anhui Initiative in Quantum Information Technologies (AHY130200).
Disclosures
The authors declare that there is no conflict of interest.
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