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Abstract
We demonstrate optical spectrum detection of a synthetic silica microsphere (SSM) resonator with whispering gallery modes fabricated by chemical methods using an optical nanofiber to touch the SSM. Critical coupling, under coupling and over coupling are obtained by controlling the nanofiber radius. The SSM radius deviation, 0.51 nm, can be obtained through multiple measurements when the nanofiber touches the SSM equatorial planes randomly. The scheme opens a new avenue for accurate sample characterization and sample tracking for microparticle detection.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Synthetically fabricated silica microspheres have attracted much attention due to their broad applications in many scientific fields such as chemistry [1–3], medicine [4–6], biochemistry [7,8], standardization [9]and optics [10–12]. In recent years, the method of producing microspheres by chemical synthesis has been widely studied by researchers because of its simple mass production and stable physical and chemical properties [13–17].
Synthetic silica microspheres (SSMs) are nontoxic, odorless, nonpolluting white powdery nonmetallic nanomaterials that have outstanding optical properties. For applications in chemistry and chemistry biology, appropriate particle morphology, including size and shape, enhances the bioavailability of the administered drug for optimal efficacy [18–26]. For standardization applications, SSMs can be used as standard materials to accurately measure the size of tiny particles and to calibrate electron microscopes, optical microscopes, light scattering instruments, photo correlation instruments [9]. The size and shape of particles are considered parameters that need to be measured very precisely by the Technical Committee on the Standardization of Nanomaterials (ISO TC229) [27]. For optics applications, SSMs have been used as key components of optical sensors due to their optical properties [28–30]. The size of the SSM has an effect due to cavity-enhanced Raman [31]. The sizes of SSMs determine the super-resolution window when the SSMs are used for the far-field imaging as microscale spherical lenses [32,33]. Besides, due to their uniform particle size distribution, SSMs can be used for the self-assembly of photonic crystal materials [34]. The SSM size affects the focal length greatly when SSMs are used as objective lenses to focus processing laser, which can achieve near-field direct writing and subwavelength nanopatterning [35]. For these applications mentioned above, the SSMs or other types microspheres with controlled and appropriate size distribution have a very important impact [36]; thus, the high-precision characterization of the radius of the microspheres is very important for their applications.
To describe the size of SSMs, scanning electron microscopy (SEM) or transmission electron microscopy (TEM) are used to measure SSM radii with nanometer resolution [27,37]. However, the conductive coating required by SEM measurements destroys the SSM surface. In addition, SEM or TEM measurements are time-consuming and require specific facilities. To avoid these problems, optical methods are powerful tools to measure SSM radii, because SSMs have spherical profile and can support optical whispering gallery modes (WGMs) [38,39]. However, in [38], the microspheres are fabricated by $C{O_2}$ laser melting the fused optical fiber, and the microsphere radii range from fifty to a few hundred micrometers. Due to the developed production method, it is not easy to achieve large-scale production [40]. The microsphere radii can be obtained through the free spectral range of the WGMs [41]. Due to the optical modes of microspheres, high-low threshold lasers [42], narrow-band optical filters [43], high-sensitivity acceleration, pressure [44], and biological sensors are realized [45,46].
In this paper, we demonstrate a scheme to measure the radius deviation of an SSM through the optical spectrum of the SSM’s WGMs by using a nanofiber to touch and couple the SSM. Based on the mode coupling theory, the coupling strength between nanofibers and microspheres is determined by the nanofiber radius. First, we numerical simulate and experimentally couple nanofibers with various radii to the SSM. Then, the coupling strength between the nanofiber and the SSM as a function of the nanofiber radius is demonstrated. The critical coupling is achieved by contacting the SSM with the nanofiber with an appropriate radius. Finally, the radius of the SSM is calibrated according to free spectral range by a quartz tungsten halogen light source, and the resonant frequencies of various equators of the SSM are measured for many times. The deviation of the SSM radius is obtained. Compared to many traditional methods for measuring submicron microsphere size, such as scanning electron microscope (SEM), transmission electron microscopy (TEM), scanning mobility particle sizing (SMPS), and atomic force microscopy (AFM) [27,37], it is a common and significant method to use the free spectral range or Mie scattering for radius measurement of transparent microspheres [39]. However, the method of free spectra range can only obtain the average radius of all equators of the SSM, instead of the SSM radius deviation of the SSM. The method based on the nanofiber-SSM structure provides higher accuracy along with the nondestructive and accurate radius characterization of individual particles. Such a system would be directly applicable for microparticle detection. Nanofiber-SSM structures can also be used to couple quantum emitters for quantum optics and chemistry biology [47–49].
2. Models and simulations
Optical fibers with sub-wavelength diameters, called nanofibers, are a powerful tool to efficiently excite WGMs of SSM resonators [50,51]. Nanofibers exhibit a significant evanescent field on the surface. When a nanofiber touches a microsphere, the nanofiber evanescent field can be efficiently coupled into and out of the microsphere; thus, the optical spectrum of an SSM can be detected. The coupling strength of a nanofiber and an SSM is related to the radius of the nanofiber. (See Supplement 1 Appendix A for detail.)
According to mode-coupling theory [52], the coupling strength between nanofibers and microspheres is given by overlapping integrals
The field decay rate $\kappa $ of the nanofiber and SSM systems includes the intrinsic field decay rate ${\kappa _0}$ and the coupling strength ${\kappa _{ext}}$, which is $\kappa = {\kappa _0} + {\kappa _{ext}}$.${\kappa _{ext}}$ can be obtained from formula (1). The lowest transmittance of the nanofiber and SSM systems can be obtained from the coupling strength:
According to center frequency of the resonance peak f, the microsphere radius [53]
According to Eq. (3), and the measured microsphere radius and resonance wavelength in Supplement 1 Appendix C, the number of angular modes $l$ can be deduced.
The deviation of the resonance frequency is converted into the radius deviation of the SSM resonator. Equatorial radius deviation $\delta R$ is the difference between the radius of the SSM and the average radius of each measurement, which can be calculated by the expression
The relative radius deviation of the SSM resonator is statistically obtained according to the expression
The three-dimensional finite difference time domain (FDTD) method (Lumerical Solutions, Inc.) is applied to numerically simulate the transmission spectra of an SSM touched by a nanofiber. An illustration of the model is shown schematically in Fig. 1. The nanofiber is a silica-glass cylinder $({n_f} = \textrm{ }1.45)$ with a radius of a. The SSM is directly attached to the surface of the nanofiber The SSM radius ${R_0}$ is 3.25 µm, which is a common value in our experiments. The distance ${S_0}$ between SSM and nanofiber is 0.
Fig. 1. Schematic of the coupling between an SSM and a nanofiber. The SSM and nanofiber radius are ${R_0}$ and a, respectively. ${n_s}$, ${n_f}$ and ${n_0}$ are the indices of sphere, nanofiber and air. The TE mode electric field is parallel to the equatorial surface, and the TM mode is perpendicular to the equatorial surface.
The SSM resonator includes two cases with an electric field either parallel to the equator surface (TE mode) or perpendicular to the equator surface (TM mode). The interaction strength depends on the overlap between the evanescent field of a nanofiber and an SSM. The intensity of the evanescent field of nanofibers depends on the nanofiber radius. Thus, the coupling state critically depends on the radius of the nanofiber. We can change the nanofiber radius to change the coupling states from under-coupling $({\kappa _{ext}} < {\kappa _0})$ to critical coupling $({\kappa _{ext}} = {\kappa _0})$ and the over-coupled regime $({\kappa _{ext}} > {\kappa _0})$. The simulation results are shown in Fig. 2. Fig. 2 (a) shows the normalized transmission spectra of the SSM with a TM-polarized electric field with various nanofiber radii from 250 to 550 nm. The wavelength range is 820-870 nm. The nanofiber radius is less than the wavelength. Due to the scattering effect of the microspheres on the evanescent field when the nanofiber radius is small than 200 nm, the nanofiber transmittance decreases significantly, and most of the light is scattered. As the nanofiber radius becomes larger, the field of the nanofiber can be coupled into the SSM. Resonant dips with near zero transmittance can be observed. The coupling between the nanofiber and SSM can be changed with increasing nanofiber radius. Fig. 2 (b) shows the minimum transmittance (black solid squares) and resonant wavelength (red solid circles) as a function of the nanofiber radius. The coupling states vary from over-coupling when the nanofiber radius is less than 300 nm to critical coupling when the nanofiber radius is approximately 300 nm, and then to under-coupling when the nanofiber radius is more than 300 nm. Due to the small nanofiber radius, the overlap of other excited higher-order modes with the fundamental mode causes a slight shift in the lowest transmittance (red solid circles) of the resonant peak of the SSM, resulting in a change in the resonant wavelength. In addition, the coupling states and the resonance frequencies depend on the overlap of the evanescent field of the nanofiber and the SSM. The structure of the nanofiber with the SSM touched provides more complicated situation of the overlap. Thus, the optical path of the SSM’s WGM is affected due to the complicated overlap. This causes the shift of resonance wavelength. The normalized transmission spectra of the SSM with of a TE-polarized electric field are plotted in Supplement 1 Appendix B.
Fig. 2. (a) Normalized transmission spectra of the SSM with of a TM-polarized electric field with various nanofiber radii from the under-coupling state (blue dot curve), critical coupling state (red solid curve) and over-coupling state (green dash dot curve). The black dashed line represents the boundaries of zero transmittance. (b) Minimum transmittance (black solid squares) and resonant wavelength (red solid circles) as a function of the nanofiber radius.
3. Experiments
The experimental setup is shown schematically in Fig. 3 (a). The SSM is made of silica by chemical synthesis and the surface of the SSM is nonsmooth (6-7-0650, Baseline Chromtech Research Centre). Fig. 3(b) shows a typical SEM image of an SSM. The radius of the SSM is calibrated according to the free spectral range. For calibrated details, see Supplement 1 Appendix C. The nanofiber had ultralow loss and sub-wavelength radius waist was done by pulling a standard step-index silica fiber (Fiber Core SM 800) by heating and stretching. The nanofiber radius varies along its axis. The fabricated nanofiber has a total length of approximately 54 mm and consists of three parts: 1) a common single-mode fiber with a radius of 62.5 µm; 2) Two tapered transition regions with total length of approximately 46 mm; 3) Waist with a uniform radius of approximately 3 mm in length and a minimum radius of approximately 283 nm. The tapered transition region serves as the contact point with the SSM for coupling strength adjustment. Fig. 3(c) shows a typical SEM image of a nanofiber. The nanofiber is moved to touch the SSM. A widely tunable laser (TLB-6716-P, New Focus) is used as a probe source with a power of 12 µW to measure the transmission spectrum of the SSM with a spectral range of 830- 853 nm. When tuning the wavelength of the probe light, the laser power drifts substantially. To solve this problem, we use a fiber beam splitter to simultaneously measure the output of the SSM resonator and the power of the laser. It can eliminate the deformation of the SSM optical spectrum caused by the power drift of the probe laser. With the aid of the polarization controller, the polarization of the fields inside the SSM resonator can be aligned to ensure the system operates in the TE or TM modes. In the experiment, we only use a single nanofiber to contact the SSM. We adjust the axial position of the nanofiber in contact with the SSM to change the radius of the nanofiber. Because the nanofiber radius varies along the axis of the tapered transition range. For fabrication details and profile of nanofibers, see reference [55]. The nanofiber is glued to a U-shaped aluminum holder and the fiber with the SSM is positioned on a 3D positioner with a spatial resolution of 500 nm (M-461-XYZ-M, Newport). The axial position of the nanofiber was calibrated with the helical micrometer of the translation stage. For every measurement of different nanofiber radius, we record the relative displacement to the last measurement. After the last measurement, the nanofiber with the SSM sticked is placed on a silicon substrate and all of those are move to a SEM. We give a mark at the position of the SSM on the silicon substrate as a reference because the SSM attached to the nanofiber is very easy to lose during the transfer. And then the SEM is used to measure the radii along the nanofiber. The nanofiber radius varies along its axis slowly and the nanofiber radii increase or decrease by 0.08 nm when the nanofiber radius changes by 500 nm which is the spatial resolution of the 3D positioner. Thus, the nanofiber radii are easy to control by moving it. Finally, we use the relative displacement with the last measurement to calibrate the nanofiber radii for every measurement.
Fig. 3. (a) Schematic diagram of the experimental setup. A widely tunable laser is used as the probe source with a range of 830- 853 nm. The polarization is controlled by the polarization controller. The transmission spectrum is obtained by an optical detector. The oscilloscope is used to monitor and record the optical spectra of the microspheres. (b) Typical SEM image of an SSM. (c) Typical SEM image of a nanofiber.
The procedure of attaching the SSM to the nanofiber consists of three steps: 1) we dilute the SSM solution to a suitable concentration with alcohol $4 \times {10^5}\textrm{/ml}$. 2) we transfer the SSM to the donor fiber. The donor fiber is fabricated from a standard optical fiber. The optic polymer layer of a normal fiber is stripped off using fiber stripping pliers to make a bare fiber as a donor fiber with a radius of 62.5 µm. The surface of the donor fiber is repeatedly wiped with a methanol solution to clean it, and then we placed it on a self-contained holder. The diluted SSM solution is dropped onto the donor fiber utilizing a pipette (Eppendorf Research plus, Eppendorf). 3) we use the nanofiber as the acceptor to stick the bottom of the SSM and move the nanofiber to make the SSM be away from the donor fiber. The SSM is sticked on the nanofiber finally. The donor and acceptor fiber are crossed, (see Fig. 3 (a) inset). The transfer of the SSM from the donor fibers to the nanofibers is achieved by finding the positions of the individual SSMs with the help of microscopy. In order to avoid the influence of the donor fiber on the SSM spectra, after transferring the SSM to the nanofiber, the nanofiber and SSM system will eventually be more than 2 mm apart from the donor fiber. We adopt the method of directly contacting the SSM with nanofibers of various radii, which can make as many contacts with various equators of the SSM as possible, and its contact position is more random. Compared with the traditional method of adjusting the distance between the nanofiber and the SSM to get critical coupling, our method avoids the fluctuation of the distance between the nanofiber and the SSM. The fluctuation will have a very sensitive effect on the critical coupling, which will cause great errors to the experimental results. The method is more robust. Besides, it does not require precise adjustment of the distance, and also reduces the experimental difficulties. During the experiment, we did not encounter the situation that the optical fiber is broken or the Q value of the SSM decreases after the nanofiber contacts the SSM for many times. Thus, this method is more practical.
As shown by the previous simulations, two polarization modes can resonate with the SSM resonator. The polarization of the probe light is always adjusted to the TM mode of the SSM resonator using the optical fiber polarization controller setting in the coupling beam path. TE mode cannot be measured because the resonance frequency exceeds the scanning range of the tunable laser. The nanofiber has a tapered shape with the radius gradually decreasing from the standard fiber with a radius of 62.5 µm and increasing to the normal radius again along its axis. By controlling the touched position along the nanofiber axis to control the nanofiber radius, we obtain the SSM optical spectrum under coupling (blue solid triangles), critical coupling (red solid dots) and over coupling (black solid squares), as shown in Fig. 4 (a). The asymmetric peaks are mainly due to the input laser with strong power resonated with the small-size SSM, which makes the SSM thermally-induced self-locking [56]. The resonant wavelength is $840.6 \pm 0.1\textrm{ }nm$, and the transmittance can reach zero for the critical coupling. It is worth noting that as the radius of the nanofiber decreases, the coupling efficiency between the nanofiber and the SSM increases, and the scattering of the SSM to the nanofiber also increases. In the resonance range, the laser cut-off wavelength of the nanofiber is greater than the resonance wavelength, the scattering loss is insensitive to the wavelength [57,58], so the experimental results can still characterize the coupling strength with the minimum transmittance. Fig. 4 (b) shows the minimum transmission of the SSM resonator as a function of the fiber radius with the polarization controller tuned to maximize the transmittance of one of the resonant modes. The coupling strength of the coupled nanofibers and microspheres can be adjusted by adjusting the contact points between the SSM resonator and the nanofibers of different radii. The nanofibers of various radii coupled to the SSM may cause differences in the optical path length of the WGM of the SSM, resulting in a fluctuation in the measured resonance wavelength. The resonance frequency at the minimum transmittance will also change slightly under different coupling states when nanofiber radius is increased. These small changes of resonance frequency can be found in both theoretical and experimental results, as shown in Fig. 2(b) and Fig. 4(a). The radiation loss due to the coupling between the nanofiber and the SSM is related to the radius of the nanofiber and the wavelength of the laser. For the critical coupling, the transmittance of the nanofiber is affected slightly by the scattering of the SSM, which can be found in Fig. 3(a). Thus, the scattering effect of the SSM on the nanofiber is small. The nanofiber has small effects on the resonance frequency of the SSM and the resonance frequency measured are almost around the realistic resonant frequency. Besides, the shift of the resonance frequency due to the nanofiber have no influence on the measurement of the radius deviation of the SSM. The nanofiber radius of various coupling states is measured by an SEM, where the nanofiber radius of the critical coupling state is $351 \pm 4\textrm{ nm}$. The coupling states range from over coupling when the nanofiber radius is less than $351 \pm 4\textrm{ nm}$ nm to critical coupling when the nanofiber radius is approximately $351 \pm 4\textrm{ nm}$, and then to under coupling when the nanofiber radius is more than $351 \pm 4\textrm{ nm}$. The standard deviation of the nanofiber radius is obtained from its SEM images.
Fig. 4. (a) Typically measured coupling states of SSM and nanofibers with various radii: under coupling (blue solid triangles), critical coupling (red solid dots) and over coupling (black solid squares). (b) Minimum transmittance (red circles) of the SSM resonator as a function of nanofiber radius. The green dashed line indicates the boundaries of zero transmittance.
Experimentally, we have the nanofiber touch the SSM resonator for many times to measure optical modes in different equatorial planes of this SSM resonator. Then, the deviation of the SSM radius can be obtained according to the fluctuation of the resonance frequency. From the under coupling to the over coupling can be realized when the nanofiber radius is in a large range. Conversely, it is easier to control the critical coupling with the lowest transmittance of zero nearly. For every time, we ensure that the critical couplings are achieved by contacting the SSM with the nanofiber with an appropriate radius. This way can prevent the influence of the mode shift. Compare to the traditional method by adjusting the distance between nanofibers and microspheres, our method is more robust. Besides, it does not require precise adjustment of the distance, and also reduces the experimental difficulties. To determine the deviation of the resonance frequency of the SSM resonator, we record the optical spectra for 23 times using the nanofiber to touch the SSM resonator with different equatorial planes. Experimental devices are placed in an ultra-clean room with constant temperature and humidity to avoid the influence of dust and water vapor. During the measurement, the nanofiber touches the SSM for all cases with various equators of the SSMs to eliminate the errors due to different coupling states, the transmittance of the nanofibers was monitored, and the transmittance is always constant when the nanofiber and the SSM were not touched. Therefore, it can be considered that the nanofibers and the SSM were not affected by external impurities and water vapor. The resonant frequencies and radii are shown in Fig. 5. The purple circles are the experimental results, while the green dashed line indicates the average for different equatorial planes. The SSM radius is approximately $R = 3.22 \pm 0.05\mathrm{\ \mu m}$ according to the free spectral range. The number of resonance modes can be calculated with the average center frequency of the resonance peak $f \approx \textrm{356}\textrm{.61 THz}$. The more accurate SSM radius is obtained from the value $l = 30$ determined by the above method according to Expression(3). The resonant frequency and the radius of equators are also shown in Fig. 5. The radius deviation of the SSM resonator $\Delta R = 0.51\textrm{ nm}$. We can also obtain $U = 1.59 \times {10^{ - 4}}$.
Fig. 5. The resonant frequency and the radius of equators of the SSM resonator. The purple circles are the experimental results, while the green dashed line indicates the average for different equatorial planes.
The SSM radius is small enough, thus the Q factor is mainly determined by the tunneling loss of the SSM resonator. According to [59], and the calculated Q factor of SSM in Supplement 1 Appendix D. The Q factor is determined by several factors: 1) intrinsic radiative (curvature) losses ${Q_{rad}} = 3260$ for the SSM of radius, 3.25 µm, which is simulated by COMSOL. 2) The scattering loss caused by the rough surface. As shown in Fig. 3 (b), its surface is so rough that it can cause large scattering loss. The RMS size $\sigma = 60\textrm{ nm}$ and the correlation length of surface inhomogeneities $B = 60\textrm{ nm}$ are estimated from SEM image (Fig. 3(b)). According to ${Q_{s.s}} = 2R{\lambda ^2}/2{\pi ^2}{\sigma ^2}B$ [60], where R and $\lambda$ are the SSM radius and the resonance wavelength, respectively, ${Q_{s.s}} = 1075$. $Q = 1/(1/{Q_{rad}} + 1/{Q_{s.s}}) = 808$ can be obtained. 3) The SSMs are synthesized in liquid solution and stored in alcohol solution. During the experiment, the stains generated during the synthesis process may remain on the surface of the SSM after the liquid is volatilized, which cause the scattering loss. Ultimately, considering the loss due to the nanofiber contacting the SSM, absorption loss caused by material impurity and residual stains, the measured Q factor is around 380, which is reasonable. By cleaning the SSM sample, choosing the appropriate nanofiber radius, and adjusting the polarization of the optical modes, an SSM resonator with a high Q factor can be achieved. In the experiment, the Q factor of the SSM resonator is given by the expression
according to the optical spectrum of the SSM resonator measured at the critical coupling. Here $\nu$ is the resonant frequency of the SSM resonator and $\Delta \nu$ is the linewidth. The average Q factor of the SSM resonator is $Q = 380 \pm 40$. For optical experiments using SSM as an optical resonator, it is very important to obtain SSM resonators with a high Q. This method can be used to choose the SSM nondestructively.The method is feasible for the larger microspheres with the closer modes spectrally because the losses in the SSM will be smaller and the Q factor will be bigger when the SSM radius increases. When the radius of the SSM is less than 15 µm, the value of Q factor decreases sharply due to the presence of tunneling loss with decreasing radius [59]. When the SSM is too small, for example below 2.5 µm, the tunneling loss is too big and the SSM cannot form WGMs, this method will be invalid. Thus, the criterion for judging whether it is applicable is whether stable and distinguishable resonance modes are formed. For larger microspheres this method must be feasible. Larger microspheres lead to higher Q factor, while higher Q factor will result in higher measurement accuracy. Besides, because the bigger SSM provides closer modes, it is more convenient to use a tunable laser or a white light to measure the free spectral range directly. The main limitations of this method will happen for smaller SSMs. SSMs with too small radius will lead to larger tunneling loss, so the Q factor will decrease heavily and the measurement accuracy will be reduced seriously. This method is not suitable for SSMs with very small radii below 2.5 µm.
4. Conclusions
To summarize, we proposed and demonstrated a method to measure the optical resonance spectrum of an SSM by coupling the SSM with a nanofiber. We obtain the critical coupling by contacting the SSM with the nanofiber in appropriate radius. The radius of the SSM is calibrated according to the free spectral range by a LED light source. The SSM resonator Q factor is approximately $380 \pm 40$. The relative radius deviation of the SSM is obtained with high precision of $U = 1.59 \times {10^{ - 4}}$. The radius deviation in different equatorial planes of the SSM resonator is 0.51 nm. Compared to the other traditional methods, the SSM-nanofiber structure is more robust against the experimental imperfections, such as the clean sample substrate and high magnification microscope. This method can measure SSM radii to an accuracy of the order of nanometer. The accuracy of this method is comparable to SEMs. At the same time, our measurement method is nondestructive, and the repeated use of samples also has a good advantage.
Funding
National Key Research and Development Program of China (2017YFA0304502, 2021YFA1402002); National Natural Science Foundation of China (11974223, 11974225, 12104277, U21A20433, U21A6006); Fund for Shanxi Key Subjects Construction (the Fund for Shanxi “1331 Project” Key Subjects).
Acknowledgments
The authors would like to thank Yuanbin Jin and Chen Qin for valuable discussions.
Disclosures
There are no conflicts of interest related to this article.
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.
Supplemental document
See Supplement 1 for supporting content.
References
1. A. J. Sandee, J. N. H. Reek, P. C. J. Kamer, and P. W. N. M. van Leeuwen, “A silica-supported, switchable, and recyclable hydroformylation - Hydrogenation catalyst,” J. Am. Chem. Soc. 123(35), 8468–8476 (2001). [CrossRef]
2. M. K. Richmond, S. L. Scott, and H. Alper, “Preparation of new catalysts by the immobilization of palladium(II) species onto silica: An investigation of their catalytic activity for the cyclization of aminoalkynes,” J. Am. Chem. Soc. 123(43), 10521–10525 (2001). [CrossRef]
3. K. Li and H. D. H. Stöver, “Synthesis of monodisperse poly(divinylbenzene) microspheres,” J. Polym. Sci., Part A: Polym. Chem. 31(13), 3257–3263 (1993). [CrossRef]
4. S. Radin, P. Ducheyne, T. Kamplain, and B. H. Tan, “Silica sol-gel for the controlled release of antibiotics. I. Synthesis, characterization, and in vitro release,” J. Biomed. Mater. Res. 57(2), 313–320 (2001). [CrossRef]
5. M. Vallet-Regi, A. Rámila, R. P. del Real, and J. Pérez-Pariente, “A new property of MCM-41: Drug delivery system,” Chem. Mater. 13(2), 308–311 (2001). [CrossRef]
6. C. Y. Lai, B. G. Trewyn, D. M. Jeftinija, K. Jeftinija, S. Xu, S. Jeftinija, and V. S. Y. Lin, “A mesoporous silica nanosphere-based carrier system with chemically removable CdS nanoparticle caps for stimuli-responsive controlled release of neurotransmitters and drug molecules,” J. Am. Chem. Soc. 125(15), 4451–4459 (2003). [CrossRef]
7. S. Tabassum, S. Zahid, F. Zarif, M. A. Gilani, F. Manzoor, F. Rehman, A. Jamal, A. A. Chaudhry, S. A. Siddiqi, and I. U. Rehman, “Efficient drug delivery system for bone repair by tuning the surface of hydroxyapatite particles,” RSC Adv. 6(107), 104969 (2016). [CrossRef]
8. A. François, N. Riesen, H. Ji, S. Afshar V, and T. M. Monro, “Polymer based whispering gallery mode laser for biosensing applications,” Appl. Phys. Lett. 106(3), 031104 (2015). [CrossRef]
9. S. L. Chen, G. Yuan, and C. T. Hu, “Preparation and size determination of monodisperse silica microspheres for particle size certified reference materials,” Powder Technol. 207(1-3), 232–237 (2011). [CrossRef]
10. H. Yamada, T. Nakamura, Y. Yamada, and K. Yano, “Colloidal-crystal laser using monodispersed mesoporous silica spheres,” Adv. Mater. 21(41), 4134–4138 (2009). [CrossRef]
11. Y. Yamada, H. Yamada, T. Nakamura, and K. Yano, “Manipulation of the spontaneous emission in mesoporous synthetic opals impregnated with fluorescent guests,” Langmuir 25(23), 13599–13605 (2009). [CrossRef]
12. X. Jiao, W. Gao, and S. Shen, “Optical properties of silica microspheres with different functional groups,” J. Opt. Soc. Am. A 36(5), 782 (2019). [CrossRef]
13. Y. Liu, C. Xu, Z. Zhu, D. You, R. Wang, F. Qin, X. Wang, Q. Cui, and Z. Shi, “Controllable Fabrication of ZnO Microspheres for Whispering Gallery Mode Microcavity,” Cryst. Growth Des. 18(9), 5279–5286 (2018). [CrossRef]
14. S. Schiller and R. L. Byer, “High-resolution spectroscopy of whispering gallery modes in large dielectric spheres,” Opt. Lett. 16(15), 1138 (1991). [CrossRef]
15. J. Wang, X. Zhang, M. Yan, L. Yang, F. Hou, W. Sun, X. Zhang, L. Yuan, H. Xiao, and T. Wang, “Embedded whispering-gallery mode microsphere resonator in a tapered hollow annular core fiber,” Photonics Res. 6(12), 1124 (2018). [CrossRef]
16. B. Tang, H. Dong, L. Sun, W. Zheng, Q. Wang, F. Sun, X. Jiang, A. Pan, and L. Zhang, “Single-Mode Lasers Based on Cesium Lead Halide Perovskite Submicron Spheres,” ACS Nano 11(11), 10681–10688 (2017). [CrossRef]
17. K. Kosma, G. Zito, K. Schuster, and S. Pissadakis, “Microsphere resonator integrated inside a microstructured optical fiber,” Opt. Lett. 38(8), 1301 (2013). [CrossRef]
18. N. Ferroudj, J. Nzimoto, A. Davidson, D. Talbot, E. Briot, V. Dupuis, A. Bée, M. S. Medjram, and S. Abramson, “Maghemite nanoparticles and maghemite/silica nanocomposite microspheres as magnetic Fenton catalysts for the removal of water pollutants,” Appl. Catal., B 136-137, 9–18 (2013). [CrossRef]
19. M. Fr, V. Rebbin, M. Jakubowski, and P. Steffen, “Synthesis and characterisation of spherical periodic mesoporous organosilicas (sph-PMOs) with variable pore diameters,” 72, 99–104 (2004).
20. K. H. Park, I. K. Sung, and D. P. Kim, “A facile route to prepare high surface area mesoporous SiC from SiO 2 sphere templates,” J. Mater. Chem. 14(23), 3436–3439 (2004). [CrossRef]
21. F. Chen, R. Shi, Y. Xue, L. Chen, and Q. H. Wan, “Templated synthesis of monodisperse mesoporous maghemite/silica microspheres for magnetic separation of genomic DNA,” J. Magn. Magn. Mater. 322(16), 2439–2445 (2010). [CrossRef]
22. Y. Deng, C. Deng, D. Qi, C. Liu, J. Liu, X. Zhang, and D. Zhao, “Synthesis of core/shell colloidal magnetic zeolite microspheres for the immobilization of trypsin,” Adv. Mater. 21(13), 1377–1382 (2009). [CrossRef]
23. C. C. Huang, W. Huang, and C. S. Yeh, “Shell-by-shell synthesis of multi-shelled mesoporous silica nanospheres for optical imaging and drug delivery,” Biomaterials 32(2), 556–564 (2011). [CrossRef]
24. L. Barner, “Synthesis of microspheres as versatile functional scaffolds for materials science applications,” Adv. Mater. 21(24), 2547–2553 (2009). [CrossRef]
25. B. Chaurasiya and Y. Y. Zhao, “Dry powder for pulmonary delivery: A comprehensive review,” Pharmaceutics 13(1), 31 (2020). [CrossRef]
26. Y. Wang, J. He, J. Chen, L. Ren, B. Jiang, and J. Zhao, “Synthesis of monodisperse, hierarchically mesoporous, silica microspheres embedded with magnetic nanoparticles,” ACS Appl. Mater. Interfaces 4(5), 2735–2742 (2012). [CrossRef]
27. A. Delvallée, N. Feltin, S. Ducourtieux, M. Trabelsi, and J. F. Hochepied, “Direct comparison of AFM and SEM measurements on the same set of nanoparticles,” Meas. Sci. Technol. 26(8), 085601 (2015). [CrossRef]
28. M. S. Ferreira, J. L. Santos, and O. Frazão, “Silica microspheres array strain sensor,” Opt. Lett. 39(20), 5937 (2014). [CrossRef]
29. M. S. Ferreira, J. Bierlich, J. Kobelke, K. Schuster, J. L. Santos, and O. Frazão, “Towards the control of highly sensitive Fabry-Pérot strain sensor based on hollow-core ring photonic crystal fiber,” Opt. Express 20(20), 21946 (2012). [CrossRef]
30. Y. Yang, S. Saurabh, J. M. Ward, and S. Nic Chormaic, “High-Q, ultrathin-walled microbubble resonator for aerostatic pressure sensing,” Opt. Express 24(1), 294 (2016). [CrossRef]
31. R. S. Liu, W. L. Jin, X. C. Yu, Y. C. Liu, and Y. F. Xiao, “Enhanced Raman scattering of single nanoparticles in a high- Q whispering-gallery microresonator,” Phys. Rev. A 91(4), 043836 (2015). [CrossRef]
32. Z. Wang, W. Guo, L. Li, B. Luk’Yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2(1), 218 (2011). [CrossRef]
33. M. Guo, Y.-H. Ye, J. Hou, and B. Du, “Experimental far-field imaging properties of high refractive index microsphere lens,” Photonics Res. 3(6), 339 (2015). [CrossRef]
34. A. Birner, R. Wehrspohn, B. A. Birner, R. B. Wehrspohn, U. M. Gösele, and K. Busch, “Silicon-Based Photonic Crystals,” Advanced Materials 4095, 377–388 (2001). [CrossRef]
35. E. McLeod and C. B. Arnold, “Subwavelength direct-write nanopatterning using optically trapped microspheres,” Nat. Nanotechnol. 3(7), 413–417 (2008). [CrossRef]
36. X. Jiao, R. Hao, Q. Pan, X. Zhao, and X. Bai, “Size effect of optical silica microsphere pressure sensors,” Optics Communications 419(January), 67–70 (2018).
37. C. Motzkus, T. Macé, F. Gaie-Levrel, S. Ducourtieux, A. Delvallee, K. Dirscherl, V. D. Hodoroaba, I. Popov, O. Popov, I. Kuselman, K. Takahata, K. Ehara, P. Ausset, M. Maillé, N. Michielsen, S. Bondiguel, F. Gensdarmes, L. Morawska, G. R. Johnson, E. M. Faghihi, C. S. Kim, Y. H. Kim, M. C. Chu, J. A. Guardado, A. Salas, G. Capannelli, C. Costa, T. Bostrom, A. K. Jämting, M. A. Lawn, L. Adlem, and S. Vaslin-Reimann, Size Characterization of Airborne SiO2 Nanoparticles with On-Line and off-Line Measurement Techniques: An Interlaboratory Comparison Study (2013), 15(10).
38. K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003). [CrossRef]
39. T. C. Preston and J. P. Reid, “Accurate and efficient determination of the radius, refractive index, and dispersion of weakly absorbing spherical particle using whispering gallery modes,” J. Opt. Soc. Am. B 30(8), 2113 (2013). [CrossRef]
40. M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, “Fiber-coupled microsphere laser,” Opt. Lett. 25(19), 1430 (2000). [CrossRef]
41. M. Michihata, T. Hayashi, A. Adachi, and Y. Takaya, “Measurement of probe-stylus sphere diameter for micro-CMM based on spectral fingerprint of whispering gallery modes,” CIRP Ann. 63(1), 469–472 (2014). [CrossRef]
42. W. von Klitzing, E. Jahier, R. Long, F. Lissillour, V. Lefèvre-Seguin, J. Hare, J. M. Raimond, and S. Haroche, “Very low threshold green lasing in microspheres by up-conversion of IR photons,” J. Opt. B: Quantum Semiclassical Opt. 2(2), 204–206 (2000). [CrossRef]
43. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997). [CrossRef]
44. M. Manzo, T. Ioppolo, U. K. Ayaz, V. Lapenna, and M. V. Ötügen, “A photonic wall pressure sensor for fluid mechanics applications,” Rev. Sci. Instrum. 83(10), 105003 (2012). [CrossRef]
45. F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: Label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008). [CrossRef]
46. A. Francois and M. Himmelhaus, “Optical biosensor based on whispering gallery mode excitations in clusters of microparticles,” Appl. Phys. Lett. 92(14), 141107–2015 (2008). [CrossRef]
47. R. Yalla, F. le Kien, M. Morinaga, and K. Hakuta, “Efficient channeling of fluorescence photons from single quantum dots into guided modes of optical nanofiber,” Phys. Rev. Lett. 109(6), 063602 (2012). [CrossRef]
48. S. M. Skoff, D. Papencordt, H. Schauffert, B. C. Bayer, and A. Rauschenbeutel, “Optical-nanofiber-based interface for single molecules,” Phys. Rev. A 97(4), 043839 (2018). [CrossRef]
49. E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104(20), 203603 (2010). [CrossRef]
50. J. E. Hoffman, S. Ravets, J. A. Grover, P. Solano, P. R. Kordell, J. D. Wong-Campos, L. A. Orozco, and S. L. Rolston, “Ultrahigh transmission optical nanofibers,” AIP Adv. 4(6), 067124 (2014). [CrossRef]
51. F. Lei, G. Tkachenko, X. Jiang, J. M. Ward, L. Yang, and S. N. Chormaic, “Enhanced Directional Coupling of Light with a Whispering Gallery Microcavity,” ACS Photonics 7(2), 361–365 (2020). [CrossRef]
52. H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, “Coupled-mode theory of optical waveguides,” J. Lightwave Technol. 5, 16–23 (1987). [CrossRef]
53. V. v Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. v Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Communications 158, 305–312 (1998). [CrossRef]
54. I. H. Malitson, “Interspecimen Comparison of the Refractive Index of Fused Silica*,†,” J. Opt. Soc. Am. 55(10), 1205 (1965). [CrossRef]
55. P. Zhang, F. Cheng, X. Wang, L. Song, C.-L. Zou, G. Li, and T. Zhang, “Nondestructive measurement of nanofiber diameters using microfiber tip,” Opt. Express 26(24), 31500 (2018). [CrossRef]
56. P. Dubé, L.-S. Ma, J. Ye, P. Jungner, and J. L. Hall, “Thermally induced self-locking of an optical cavity by overtone absorption in acetylene gas,” J. Opt. Soc. Am. B 13(9), 2041 (1996). [CrossRef]
57. Y. Chen, Z. Ma, Q. Yang, and L.-M. Tong, “Compact optical short-pass filters based on microfibers,” Opt. Lett. 33(21), 2565 (2008). [CrossRef]
58. P. F. Zhang, L. J. Song, C. L. Zou, X. Wang, C. X. Wang, G. Li, and T. C. Zhang, “Tunable Optical Bandpass Filter via a Microtip-Touched Tapered Optical Fiber,” Chinese Phys. Lett. 37(10), 104201 (2020). [CrossRef]
59. B. E. Little, J.-P. P. Laine, and H. A. Haus, “Analytic theory of coupling from tapered fibers and half-blocks into microsphere resonators,” J. Lightwave Technol. 17(4), 704–715 (1999). [CrossRef]
60. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21(7), 453 (1996). [CrossRef]
