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Abstract
Whispering gallery mode polymer resonators are becoming competitive with devices made of other materials, however, the inherent thermal sensitivity of the materials and the small size limit their applications, such as high-precision optical gyroscope. Here, a method is proposed for fabricating large-scale NOA65 resonators with quality factors greater than 105 on a chip employing superoleophobic. The sandwich structure as the core layer of resonator is used to present the flexible remodeling characteristics, the surface roughness remains below 1 nm when the diameter changes by more than 25%. Importantly, theoretical and experimental results show that under the tuning action of external pressure, the equivalent thermal expansion coefficient of the resonator gradually approaches the glass sheet on both sides with the variation of 2 × 10−4 /°C∼0.9 × 10−4 /°C, and the corresponding temperature response range of 0.12 nm/°C∼−0.056 nm/°C shows the promise of temperature insensitivity resonators on a chip.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Whispering gallery mode (WGM) optical resonators with high quality factor (Q) have been of great interest as a highly sensitive sensor in the last two decades, due to the resonant mode with a narrow linewidth is capable of detecting slight external disturbances [1–5]. Such as angular velocity sensor [6,7], temperature sensor [8,9], magnetic sensor [10,11], biosensor [12,13]. Among them, polymer WGM resonators are becoming more and more competitive with devices made of other materials, thanks to convenient processing, flexible structure, and easy doping of gain materials [14–16]. More importantly, compared with the traditional semiconductor and crystalline materials, the Young's Modulus with the order of kPa is possible to obtain by changing the ration between the base and the curing agent [17]. This feature makes the polymer resonators more flexible to remodel after curing, which provides great operability in the engineering of spectrum or dispersion.
At present, the fabricating methods of high Q factor polymer resonator can be roughly divided into two types. One is to fabricate polymer resonators on-chip by means of exposuring [18,19], imprinting [20,21], femtosecond processing [22,23] or self-assembling [24,25]. These on-chip fabricating methods make it more conducive to integration, and most cured resonators are tens of micrometers in size. The other type mainly uses the surface tension effect to form off-chip resonators on the optical fiber [26,27] or thin-diameter metal wire [28]. The cured polymer resonator has higher Q factor, due to the suppression of surface scattering loss which results from the very smooth boundaries. However, the fluidity of polymer droplets and the effect of gravity restrict the size of the resonator during the curing process. Although resonator tuning based on the flexible properties of polymer materials has been reported, large dynamic range adjustment of cured polymer resonators is rare due to the limitation of size or structure. In addition, for high-precision sensing applications, the inherently large coefficients of thermal-optic and thermal expansion will lead to inevitable thermal noise, which seriously affect the measurement accuracy. These are still challenges for existing fabricating methods.
Here, inspired by the droplet resonator on superhydrophobic interface, a rapid fabricating method of on-chip polymer resonator using UV-curable adhesive NOA65 is proposed. The resonators with controllable dimensions are cured on chips employing superoleophobic, and the flexible advantages of polymer materials are exhibited. The millimeter-scale resonator is remodeled by pressure and more than 25% diameter variation is achieved, meanwhile, the Q factor is always maintained above 105. Importantly, under the action of pressure, the sandwich structure as the core layer of NOA65 resonator is formed, which has the ability to tune the equivalent thermal expansion coefficient (ETEC). The range of temperature response is dynamically adjusted from 0.12 nm/°C to −0.056 nm/°C. It is a promising candidate for the temperature insensitivity resonators on a chip.
2. Experiments
Figure 1(a) schematically illustrates the fabrication of high-Q UV-curable adhesive resonators. The syringe with 1 µL precision gives the sample accurately through the contact angle (CA) measuring instrument, so as to control the single droplet volume of UV-curable adhesive. The droplets rest on a quartz slide coated with a commercial superoleophobic material (Fig. 1(b)), and then cured by exposing under a UV lamp. The whole process can be completed in tens of minutes. By controlling the volume of a single droplet, combined with parameters such as gravity, surface tension, and contact angle, the size characteristics of the resonator will be adjusted. In the experiment, the volume of UV-curable adhesive is about 5 µL, and the maximum CA is 134°, as shown in Fig. 1(c).
Fig. 1. (a) Schematic fabrication setup of the NOA65 resonators employing superoleophobic. (b) Micrograph for the superoleophobic coating on the quartz slide. (c) Image of the contact angle of 134° for NOA65 droplet.
3. Experimental results and discussion
3.1 Temperature dependence of contact angle
In the preparation process of the UV-curable adhesive resonator, the influence of temperature should be mainly considered. The reason is that with the temperature increasing, the increased kinetic energy leads to weaken the interaction force between the molecules, and also reduce the density difference between liquid/gas two phases. Therefore, an increase in temperature is often accompanied by a decrease in surface tension, which reduces the contact angle. It even causes the polymer droplets to collapse, failing to form spheroidal resonators.
The morphological characteristics of NOA65 and PDMS droplets at different temperatures are observed by heating with a hot plate, with the latter as a contrast experiment. When the temperature rises from 20°C to 90°C, the contact angle of PDMS droplet decreases obviously, and then the change tends to be gentle. In contrast, the case of NOA65 droplet is more interesting. During the temperature rise to 200°C, as shown in Fig. 2, the change of contact angle is not significant, and the approximate linear slope is only about 0.12 nm/°C. The whole process is carried out in an environment close to the dark room, the purpose is to eliminate the influence of ultraviolet radiation from the lighting equipment. The possible reason is the exothermic nonhazardous polymerization during the temperature rise of NOA65 [29], and the film formed on the surface alleviates the further collapse of droplets. Obviously, the low dependence on temperature is conducive to the preparation of NOA65 resonators with high stability.
Fig. 2. Effect of temperature on polymer droplets during the preparation process. Left: the images at diffident temperature of NOA65 and PDMS droplets, respectively. Right: the contact angles of the two types of droplets as functions of temperature.
3.2 Remolding resonator by pressure
Because of the refractive index mismatch between silica (n = 1.45) fiber and NOA65 (n = 1.509) resonator [30], the tapered fiber is attached to the surface of the resonator for better phase matching. The coupling region in the experiment is selected to deviate from the center of the taper region, while is parallel to the equator. At a pressure of 0 N, the radius of the fiber at the coupling position is 2.8 µm, with the effective refractive index nfiber of 1.4362. As increasing in pressure, the radius of the fiber at the coupling position needs to be readjust due to the increasing size of the resonator. When the pressure is 26 N, the radius of the fiber at the coupling position is about 3.3 µm, and nfiber increases to 1.4399.
In order to analyse the phase matching condition, the effective refractive index of the higher-order modes of WGM are calculated. According to the experimental transmission spectrum, the azimuthal mode l = 6693 with the wavelength of 1550.542 nm in Fig. 3(a), and then we calculate the relationship between the radial mode n and the effective refractive index nWGM. Assuming azimuthal mode l and the angular mode m are equal (l = m = 6693), when the radial mode n increases to 99, the higher-order mode nWGM = nfiber = 1.4362. On the other hand, the reduction of the angular m also decreases the effective refractive index nWGM [31,32], which can be obtained by the formula nWGM≈βm/k = m/ (R·k) [33]. It can be inferred that there are a variety of permutations (n, 6693, m), which meet the phase matching condition. Figures 3(a) and (b) respectively show the calculation results based on the external pressure are 0 N and 26 N.
Fig. 3. (a) and (b) are the calculated results of effective refractive index matching between the higher-order modes of WGM and the coupling tapered fiber at pressures of 0 N and 26 N, respectively. (c) The approximately linear changes of FSR with the increase of pressure. Inset: the surface roughness near the equatorial plane of the resonator at the pressure of 0 N and 26 N by atomic force microscope.
The advantage of the on-chip polymer resonator with millimeter-sized is flexible remodeling. NOA65 has become a candidate material, compared to the commonly used NOA61 and NOA81, which has the smaller Modulus of Elasticity (20000 psi), and the larger Elongation at Failure (80%) [29]. Figure 3(c) shows that the free spectral range (FSR) changes from 0.227 nm to 0.181 nm within the pressure range from 0 N to 26 N, which indicates that the rate of change in resonator diameter is more than a quarter. It is worth noting that as the pressure increasing, the curvature near the equatorial plane of the resonator increases significantly, which provides the feasibility for improving the spectral purity of the resonator, even for single-mode operation. In addition, the surface of the resonator induced by surface tension has very smooth boundaries. The atomic force microscope is used to analyze the surface roughness near the equatorial plane of the resonator before (0 N) and after (26 N) the additional pressure. Within the range of elastic deformation, the surface roughness is maintained in the range of 0.48∼0.78 nm. It provides operability for subsequent adjustment of ETEC by pressure.
3.3 Optical characteristic under different pressure
The measurement system for analyzing the cured NOA65 resonator presents in Fig. 4(a). In the 1550 nm band, a tunable laser with a linewidth of 10 kHz is used to characterize the Q factor. The light is connected to one end of a single tapered fiber, which is used to evanescently excite the modes of the resonator. The other end is connected with the beam splitter to transmit the signal into the power meter and the oscilloscope connected to the low-noise photo-detector respectively. The tapered fiber is attached to the surface of the resonator also suppresses mechanical vibrations. Moreover, to reduce the heat accumulation in the resonator, the laser power entering the cavity is lower than 10 µW. The inset of Fig. 4(a) indicates that in terms of morphology, the diameter of the resonator is almost around 2.3 mm. Correspondingly, the FSR of transmission spectra is kept at the level of 0.227 nm (Fig. 4(b)). Therefore, it is considered that the proposed method is conducive to fabricate the NOA65 resonator with repeatability.
Fig. 4. (a) Schematic measurement setup for evanescently coupling NOA65 resonators with a tapered fiber under additional pressure. Inset: the imaging of resonators. (b) Transmission spectra of six resonators and corresponding FSR. (c) The measurement of Q factor under different additional pressure.
The Q factor is at the order of 105, which is mainly limited by the absorption loss of the material, and also affected by the coupling situation. For the intrinsic Qi factor, the radiation loss Qr can be ignored for the millimeter-scale resonator. Since the surface roughness is in range of 0.48∼0.78 nm, the surface scattering loss Qss is at the order of 109 [34]. We assume the absorption coefficient of NOA 65 refers to that of NOA61. When the absorption coefficient αNOA65 is 0.42 dB/cm [35], the calculated Qabs = (2πn)/(αλ) = 6.6 × 105, so it is inferred that material absorption Qabs is one of the main reasons for limiting intrinsic Qi factor. In the experiment, the measured Q factor is maintained at the order of 105 under different coupling distance. This indicates that the influence of coupling distance on Q factor of the higher order modes is not obvious. We infer that this is due to the large radius of the coupling fiber as well as the excitation of higher order modes, which theoretically leads to low mode overlap, thus leading to the maintenance of external Qe at a certain level [31].
3.4 Adjustment of ETEC and temperature sensitivity
Based on the pressure-controllable on-chip polymer resonator, the resonant mode shift corresponding to temperature is measured under different pressure. Figure 5(a) shows the change of the resonant mode at different temperatures without additional pressure. According to the Eq. (1), the redshift or blueshift can be analyzed.
The coefficients of thermal-optic and thermal expansion for NOA65 are α=−1.83 × 10−4 /°C [36] and βeff = 2.0 × 10−4 /°C [37], respectively. ΔT denotes the temperature change of the resonator. According to Eq. (1), when βeff takes the initial value, the result in parentheses is obviously positive, indicating that the resonant mode is redshift with the temperature increasing. The theoretical slope Δλ/ΔT is 0.122 nm/°C, and the corresponding experimental result is 0.12 nm/°C. The slight difference is that the coating is not very strong (micron-sized particles are observed at the bottom of the resonator). In addition, the the Q factor increases slightly with the increasing in temperature, but the overall trend of change is not obvious, and remains at the order of 105. With the increase of additional pressure, a sandwich structure as the core layer of NOA65 resonator is gradually formed. The ETEC approaches the quartz slides (10−6∼10−7 /°C), that is, the ETEC gradually decreases. From the Eq. (1), Δλ/ΔT changes from a positive value to a negative value, and the corresponding shifting of resonant mode is converted from redshift to blueshift, as shown in Fig. 5(b).
Fig. 5. (a) The redshift of resonant mode with the increase of temperature under the additional pressure of 0 N. (b) The temperature response of the resonant mode varies pressure. Inset: the imaging of the coupling fiber with the radius of 2.8 µm at 0 N pressure.
Finite element method is used to quantitatively analyze the influence of pressure on ETEC. The Young's modulus of the flexible material is adjusted to 4 MPa in the simulation, the deformation caused by external pressure is almost consistent with the experimental results. The larger deformation caused by pressure leads to a larger contact area with the sandwich structure, making the thermal expansion coefficient of the resonator closer to that of glass, and the modulation of the ETEC is more obvious. When the absolute value of the ETEC is less than the thermal-optical coefficient, the slope of the temperature response changes from positive to negative, corresponding to 0.12 nm/°C to −0.056 nm/°C in the experiment. The slope of the linear fitting is substituted into Eq. (1) to obtain the βeff and plotted in Fig. 6(b). The βeff shows an approximate exponential decrease with the increasing of pressure, which reduces more than 50% at 26 N. Under the pressure of 10 N(Fig. 5(b)), the resonator exhibits low temperature response of 0.006 nm/°C. This is already better than the temperature stability of silicon microresonator, indicating this method has the potential to realize polymer resonators with temperature insensitivity. Meanwhile, Fig. 6(c) shows the internal pressure near the equatorial plane of the resonator during the deformation process. According to the theory of elastic-optical effect, it can be inferred that the refractive index change caused by the pressure is 10−4∼10−5.
Fig. 6. (a) Simulation results of flexible resonators under different pressures. (b) ETEC coefficients obtained from experiment and simulation at different Young's modulus. (c) The internal pressure near the equatorial plane of the resonator during the deformation process.
4. Conclusion
In summary, we demonstrate a fabricating method of polymer resonators with large-scale volume on a chip coated by superoleophobic. UV-curable adhesive NOA65 as an alternative material for resonators exhibits good temperature stability during the manufacturing process. Due to the advantage of on-chip and millimeter-sized, more than one quarter of the diameter variation is achieved at additional pressure, meanwhile, the Q factor is always maintained above 105. More importantly, the ETEC of the NOA65 resonator is reduced by increasing additional pressure, which provides the feasibility for the realization of polymer resonators with temperature insensitivity. Although the relatively low Q factor is a challenge for the application of high-precision optical sensing, the proposed method provides a platform for the preparation of a variety of polymer resonators. In the future, the Q value can be improved by replacing materials with high transmittance or material modification. Therefore, we believe that the proposed fabrication method will produce resonators with higher Q factor to meet the application in high-precision optical sensing, such as optical gyroscope.
Funding
Joint Funds of the National Natural Science Foundation of China (U21A20141); National Natural Science Foundation of China (51922009, 52005457, 62004179); Key Laboratory of Shanxi Province (201905D121001); Shanxi "1331 Project" Key Subjects Construction, the Innovative Research Group Project of National Natural Science Foundation of China (51821003); Shanxi Key Laboratory of Advanced Semiconductor Optoelectronic Devices and Integrated Systems (2022SZKF01).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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