Embedded whispering-gallery mode microsphere resonator in a tapered hollow annular core fiber

Jiawei Wang; Xiaobei Zhang; Ming Yan; Lei Yang; Fengyu Hou; Wen Sun; Xiaotong Zhang; Libo Yuan; Hai Xiao; Tingyun Wang

doi:doi:10.1364/PRJ.6.001124

Photonics Research, 2018, 6 (12): 12001124, Published Online: Dec. 3, 2018

Embedded whispering-gallery mode microsphere resonator in a tapered hollow annular core fiber Download： 630次

论文大纲

Jiawei Wang ¹Xiaobei Zhang ^1,*Ming Yan ¹Lei Yang ¹Fengyu Hou ¹Wen Sun ¹Xiaotong Zhang ²Libo Yuan ³Hai Xiao ⁴Tingyun Wang ¹

Author Affiliations

¹ Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Joint International Research Laboratory of Specialty Fiber Optics and Advanced Communication, Shanghai Institute for Advanced Communication and Data Science, Shanghai University, Shanghai 200444, China

² The Key Laboratory of In-Fiber Integrated Optics, Ministry of Education, College of Science, Harbin Engineering University, Harbin 150001, China

³ School of Electronic Engineering and Automation, Guilin University of Electronic Technology, Guilin 541000, China

⁴ Department of Electrical and Computer Engineering, Clemson University, Clemson, South Carolina 29634, USA

Abstract

We propose and demonstrate a tapered hollow annular core fiber (HACF) coupler for excitation of whispering-gallery modes (WGMs) of an embedded microsphere resonator. The coupler is simply fabricated by fusion splicing of a segment of HACF with the single-mode fiber (SMF), and then improved by tapering the splicing joint to reduce the cone-apex angle. Therefore, the coupling efficiency from the SMF to the HACF is enhanced to excite various WGMs via evanescent field coupling. Normal positive, negative symmetrical Lorentzian and asymmetric Fano line shapes can be obtained by varying the resonator size and location. Another interesting phenomenon is observed that a higher Q-factor mode in a lower Q-factor mode has a contrast as high as 58. Temperature sensing with good stability is also demonstrated. This embedded WGM microsphere resonator in the tapered HACF is expected to promote environmental adaptability in practical applications due to its simplicity and robustness.

1. INTRODUCTION

Optical whispering-gallery mode (WGM) resonators confine the electromagnetic wave by continuous total internal reflection at the resonator edge ^[1,2], and usually have symmetrical Lorentzian ^[3,4], asymmetric Fano ^{[5–8" target="_self" style="display: inline;">–8]}, and electromagnetically induced transparency (EIT) line shapes ^{[911" target="_self" style="display: inline;">–11]}. Due to extremely high values of the $Q$ -factor and small mode volumes of WGMs, they also have broad application prospects for filters ^[12], sensors ^{[4,1315" target="_self" style="display: inline;">–15]}, low-threshold lasers ^{[1618" target="_self" style="display: inline;">–18]}, cavity optomechanics ^[19,20], and nonlinearities ^[21,22]. It is particularly important to couple the light from the outside into resonators to excite WGMs. Common WGM excitation schemes are generally based on phase-matching of the evanescent fields, for example, using prisms ^[23], fiber tapers ^[11], D-shaped fiber ^[6,24], angle polished fiber ^[25], optical waveguides ^[10], free-space coupling ^[26], and chaos-assisted broadband momentum transformation ^[27]. The above coupling method is, however, less robust, and the resonance wavelength can shift or even disappear due to external air flow, dust, or slight movements and vibrations of the coupler. So some methods have been proposed to improve the robustness, such as using glue encapsulation ^[28].

Recently, some novel coupling methods have been proposed, such as attaching microspheres on the end of micro-structured optical fibers, of which the coupler is robust and gets a $Q$ -factor of 500 ^[29]. Furthermore, the microsphere is embedded into micro-structured optical fibers, and the $Q$ -factor increases to $2.2 \times 10^{3}$ ^[30]. In order to enhance the robustness and $Q$ -factor, the microsphere is encapsulated inside a photonic crystal fiber (PCF) ^[31] or a silica capillary ^{[3234" target="_self" style="display: inline;">–34]} with a small inner diameter, both of which are fabricated by chemical etching, with a $Q$ -factor of about $1.58 \times 10^{4}$ and $2.57 \times 10^{4}$ , respectively. However, the chemical etching causes the coupling position and the reflective surface to be coarse. The core in the PCF and the fiber pigtailed thin wall are fragile. Moreover, the etching process is complicated. The key point is to couple the light into the resonator, while the hollow annular core fiber (HACF) ^[35] fortunately has an inner high-index core to confine the light with an opening to embed a resonator for exciting WGMs.

In this paper, an embedded WGM microsphere resonator in a tapered HACF is proposed for excitation of WGMs to avoid the etching process in the previous configurations and maintain a high robustness. First, we theoretically and experimentally study the effect of the taper length on the coupling efficiency between the single-mode fiber (SMF) and HACF. Second, the effects of the size and embedded position of the microsphere resonator on the reflection spectra are also investigated in both theory and experiment. As the high-index annular core restricts light energy to several micrometers to excite the evanescent wave, it is possible to realize the robustness of the device and the easiness of the effective coupling between the microsphere and the HACF.

Figure 1(a) shows the schematic structure of the microsphere resonator embedded in the tapered HACF. The device is composed of a section of SMF (Corning, SMF-28), a section of HACF, and a barium titanate glass microsphere with a refractive index (RI) $n_{eff}$ of 1.93. The scattering loss is the dominant reason for the final $Q$ -factor, as the intrinsic radiative loss and absorption loss are much smaller. The HACF has a low RI ${SiO}_{2}$ cladding with its diameter $D_{1}$ of 125 μm, a high RI doped ${SiO}_{2}$ annular core with its diameter $D_{2}$ of 66 μm, and an air hole with its diameter $D_{3}$ of 54 μm as shown in Fig. 1(b). The simulated cross-section mode (fundamental mode) profile of the HACF can be seen in the inset. The RIs of the HACF annular core $n_{core}$ and cladding $n_{clad}$ are measured as 1.462 and 1.457 as shown in Fig. 1(c). It is worth noting that the RI of the air core is denoted as 1.448 because the RI profile is measured with the matching liquid. The input beam enters into the HACF annular core from the SMF, through the taper region, and couples into the microsphere through the evanescent wave via the inner annular core, and the other light is reflected at the HACF end face and couples into the microsphere again. Expected WGMs can be excited as a result of the anterior resonance principle.

(a) Schematic of the tapered HACF coupled microsphere resonator. (b) Cross-sectional view with the inset as the simulated mode field distribution and (c) RI profile of HACF.

Fig. 1. (a) Schematic of the tapered HACF coupled microsphere resonator. (b) Cross-sectional view with the inset as the simulated mode field distribution and (c) RI profile of HACF.

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2. FABRICATION AND SIMULATION OF THE COUPLER

The fabrication process of the device is illustrated in Fig. 2. First, a segment of HACF is fusion spliced with a segment of SMF by a commercial fusion splicer (FITEL-S178) as shown in Fig. 2(a), with the distance $l_{0}$ between end faces as about 10 μm and the propulsion distance of fiber $d_{0}$ as 15 μm. The splicing parameters include an arc power of 100, a prefuse time of 100 ms, and an arc time of 500 ms. Arc 1 is slightly modified from the SMF splice mode to perform a splice with a sharp cone-apex angle $θ$ in the transition area as shown in Fig. 2(b). The cone shape arises from the incomplete collapse of the annular core of HACF near the electrodes. However, the cone-apex angle $θ_{1}$ is measured to be up to 34°, though the welding parameters are optimized, which results in a low coupling between the SMF and the HACF. Moreover, the light will directly transmit into the air hole due to the large angle. It is found that Fabry–Perot-type reflection can be observed when the microsphere resonator is embedded into this structure. An intuitive method to solve this problem is to taper the coupling region between the SMF and HACF. During the tapering experiment, the arc 2 intensity is weak, so the arc power is adopted as 5, the prefuse time as 50 ms, and the arc time as 200 ms to prevent excessive collapse, and the single tapering distance $d_{1}$ is adopted as 100 μm. Due to the elasticity of silica material, the actual tapered length is in fact less than 100 μm. The HACF is then cut to a desirable length as about 500 μm, and fixed on a precision fiber alignment stage (M-562, Newport). We operate a fiber taper on another stage to attach the microsphere with the diameter from 45 to 54 μm through van der Waals force, and embed it into the air hole of HACF, under a CCD as shown in Fig. 2(e). The fabricated device can be seen in Fig. 2(f).

(a) Schematic of splicing HACF with SMF. (b) Schematic of tapering the area, with the cone-apex angle as θ and the single tapering distance as d1. (c) Micrograph of SMF-HACF transition area without tapering, with the multi-mode transition area highlighted in the blue dotted box. Micrographs of (d) SMF-HACF transition area with tapering, (e) microsphere resonator manipulated by a section of tapered fiber, and (f) microsphere resonator embedded into the coupler.

Fig. 2. (a) Schematic of splicing HACF with SMF. (b) Schematic of tapering the area, with the cone-apex angle as $θ$ and the single tapering distance as $d_{1}$ . (c) Micrograph of SMF-HACF transition area without tapering, with the multi-mode transition area highlighted in the blue dotted box. Micrographs of (d) SMF-HACF transition area with tapering, (e) microsphere resonator manipulated by a section of tapered fiber, and (f) microsphere resonator embedded into the coupler.

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To verify the enhancement of the coupling efficiency, we simulate the coupling efficiency as a function of the cone-apex angle $θ$ , using the commercial software (Rsoft, BeamProp module) as shown in Fig. 3. Simulation parameters including the RI and sizes are the same as in Fig. 1. The energy distribution at 1550 nm can be seen in the inset of Fig. 3(a). An interesting phenomenon is that the total reflection condition at the interface between cladding and annular core is destroyed when the angle exceeds 9°, which can be estimated by the formula of the total reflection condition $θ_{c} = 2 \arccos (n_{clad} / n_{core})$ . Therefore, two fusion splicing arcs are necessary for decreasing the cone-apex angle to meet the condition of high-efficiency coupling of incident light. As the angle is large, a portion of the light energy is transmitted to the air core at the fusion point and forms a Fabry–Perot cavity with three mirrors after embedding the microsphere into the HACF. When the angle is small and less than about 9°, there are several peaks because the periodic reflection of light in the annual core constitutes a damping oscillation function related to the propagation length, as shown in Fig. 3(a).

(a) Simulation of the coupling efficiency as a function of cone-apex angle θ, with the inset as the energy distribution in the device. (b) Taper times versus the cone-apex angle θ by experimental and theoretical fitting results.

Fig. 3. (a) Simulation of the coupling efficiency as a function of cone-apex angle $θ$ , with the inset as the energy distribution in the device. (b) Taper times versus the cone-apex angle $θ$ by experimental and theoretical fitting results.

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In addition, the collapse deforms into a high RI cylindrical core with a diameter of about 42.1 μm; it can be seen in the blue dotted box in Fig. 2(c). It is calculated and excellently validated by the volume conservation formula [ $π D_{4}^{2} / π D_{1}^{2} = (π D_{2}^{2} - π D_{3}^{2}) / (π D_{1}^{2} - π D_{3}^{2})$ ], with $D_{4}$ as the cylindrical core diameter. As the diameter of the collapsing core is much larger than that of an SMF core, the two modes will not match well, which makes the coupling of reflection light difficult ^[36]. Figure 3(b) shows the relationship between the tapering length and the cone-apex angle based on the experiment and fitting with $θ = 2 \arctan [a / (b + L)]$ , where $b$ and $a$ are the width and half height of the cone area without tapering, and $L$ is the tapering length. We find that after several times of tapering operation, the cone-apex angle decreases gradually to 7°, and if we try another tapering, it will completely collapse. In Fig. 2(d), the device is shown after more than 10 times tapering and obtains a high-efficiency coupling with the $θ_{2}$ at about 7°, which satisfies the high coupling condition as shown in Fig. 3(a). Meanwhile, it will also increases the efficiency of reflection light coupling by decreasing the diameter of the collapsing core from 42.1 μm to around 20.0 μm.

3. THEORETICAL MODEL AND ANALYSIS

The normalized reflection with the transfer matrix method (TMM) is used to analyze the proposed device, similar to the previous work ^[37]. When there is no microsphere resonator in the coupler, the reflection spectrum is a relatively flat straight line caused by the end face. However, a WGM-associated phenomenon will appear after embedding the microsphere resonator. As shown in Fig. 4(a), the cross section of the coupling between the resonator and HACF generally has different coupling gaps in a whole circumference for the case of a resonator size smaller than the air hole. To solve this problem, we divide the cross section as $m$ parts in a quadrant, with the corresponding angle of the coupling region between the microsphere and the HACF as $φ_{i} (i = 1, \dots, m)$ . The normalized reflection $P_{R}$ can be obtained as follows: where $r$ is the amplitude reflectivity at the HACF end face satisfying $r = (n_{core} - n_{air}) / (n_{core} + n_{air})$ , with $n_{air}$ as the RI of air. $t_{i 1}$ and $t_{i 2}$ are the equivalent amplitude transmission coefficients for part $i$ , under the condition of lossless coupling. When the gap between the microsphere and the inner wall is too large to be coupled, the equivalent amplitude transmission coefficient is equal to 1. $τ$ is the resonator round-trip transmission coefficient. $p$ is the halfway phase factor satisfying $p = \exp (i 2 π^{2} n_{eff} R / λ)$ . $R$ and $λ$ are the radius of the microsphere and the wavelength in vacuum, respectively. $δ$ and $L_{1}$ are the phase difference and distance from the resonator–HACF coupling point to the end face of the HACF, respectively, with $δ = 2 π n_{core} L_{1} / λ$ .

(a) Cross section of the model. (b),(c) Model of the microsphere (b) without and (c) with being locked by the HACF. (d) Evolution of reflection spectra with t11 from 0.8 to 0.995 for the case of (b). (e) Reflection spectrum for the case of (c).

Fig. 4. (a) Cross section of the model. (b),(c) Model of the microsphere (b) without and (c) with being locked by the HACF. (d) Evolution of reflection spectra with $t_{11}$ from 0.8 to 0.995 for the case of (b). (e) Reflection spectrum for the case of (c).

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Two typical cases are considered as shown in Figs. 4(b) and 4(c). The microsphere is not locked by HACF when the diameter of the microsphere is smaller than the inner diameter $D_{3}$ as shown in Fig. 4(b). Since the upper part of the microsphere is far enough from the HACF inner wall that it cannot be coupled, $t_{i 2}$ is equal to 1. In the simulation, the quadrant is divided into three parts, with $φ_{1}$ , $φ_{2}$ , and $φ_{3}$ adopted as 1°, 10°, and 79°, respectively. We investigate the theoretical characteristics as a function of $t_{11}$ from 0.8 to $t_{21}$ , with $t_{21}$ and $t_{31}$ adopted as 0.995 and 1, respectively. Other parameters used in the simulation are chosen as $L_{1} = 100 μm$ , $R = 22.40 μm$ , and $τ = 0.995$ . Evolutions of reflection spectra are obtained as shown in Fig. 4(d), which reveals a higher $Q$ mode in a relatively lower $Q$ mode, arising from the two different coupling parts with different coupling coefficients. Due to the relation between $t$ and the corresponding $Q$ -factor satisfying $Q \sim \sqrt{τ t} / (1 - τ t)$ , the higher the coupling efficiency, the higher the $Q$ value. Another case corresponds to the situation of the microsphere fully locked by HACF, for example, in the cone region of the coupler as shown in Fig. 4(c). Therefore, the microsphere is in close contact with the inner wall. We assume $φ_{1} = 90 °$ , $φ_{2} = φ_{3} = 0 °$ , $t_{11} = 0.995$ , $τ = 0.95$ , $L_{1} = 456 μm$ , and $R = 21.15 μm$ . Various types of resonance shapes can be obtained as shown in Fig. 4(e), including symmetrical Lorentzian and asymmetric Fano line shapes. Besides, positive and negative Lorentzian line shapes are also found with peaks and dips corresponding to resonance wavelengths ^[8].

4. EXPERIMENTAL RESULTS

In the experiment, we embed the microsphere into the tapered HACF and observe the reflection spectra through the optical sensing analyzer (si125, Micron Optics, Inc.) in real time. Figure 5(a) shows the experimental and simulated reflection spectra with the microsphere with a diameter of $\sim 42.3 μm$ , which is slightly smaller than the HACF inner diameter $D_{3}$ . A Lorentzian line shape with a free spectral range (FSR) of 9.00 nm and $Q$ -factor of about 13,000 is obtained. There are also resonance peaks due to high-order modes. By the formula of FSR and the diameter of the microsphere $[FSR = λ^{2} / (2 π n_{e ff} R)]$ , it is found that the size of the microsphere matches the experimental results well.

(a) Experiment results and simulation results of the device with a 42.30 μm diameter microsphere in the position very close to the end face. Experiment results of the device with a 42.60 μm diameter microsphere in the position very close to the end face, shown as symmetric Lorentzian line shapes with Q-factors about (b) 1300 and 76,000, and (c) 1700 and 35,000. (d) Experiment results of the device with microsphere locked by HACF inner wall with insets corresponding to detailed views of the negative symmetrical Lorentzian, asymmetrical Fano, and positive symmetrical Lorentzian line shapes.

Fig. 5. (a) Experiment results and simulation results of the device with a 42.30 μm diameter microsphere in the position very close to the end face. Experiment results of the device with a 42.60 μm diameter microsphere in the position very close to the end face, shown as symmetric Lorentzian line shapes with $Q$ -factors about (b) 1300 and 76,000, and (c) 1700 and 35,000. (d) Experiment results of the device with microsphere locked by HACF inner wall with insets corresponding to detailed views of the negative symmetrical Lorentzian, asymmetrical Fano, and positive symmetrical Lorentzian line shapes.

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Furthermore, another larger microsphere with a diameter of $\sim 42.6 μm$ is inserted with the reflection spectra shown in Figs. 5(b) and 5(c). As the microsphere is bigger, the coupling region increases, and hence the equivalent amplitude transmission coefficient $t$ decreases. As shown in Fig. 5(b), the reflection spectrum is formed by a higher $Q$ -factor mode in a lower $Q$ -factor mode with a contrast as high as 58. The center of both resonance wavelengths has a deviation of 0.25 nm, due to the irregularity of the microsphere shape or distance from the resonator–HACF coupling point to the end face of the HACF. Two modes with different radial numbers and hence different $Q$ -factors can also be possible reasons. Because the $Q$ -factor between the two resonances is quite different, two small peaks are generated on the two sides of the high $Q$ -factor resonance peak. The reflection spectrum is also formed by a higher $Q$ -factor mode in a lower $Q$ -factor mode with nearly the same resonance wavelength, as shown in Fig. 5(c). And the intensity of the higher $Q$ -factor mode is quite large, which is different from the interference peak as EIT ^[10]. These results have been well theoretically predicted as shown in Fig. 4(d). If the microsphere continues to be embedded into the depth by the fiber taper until being locked by the HACF inner wall, a symmetrical Lorentzian line shape and asymmetric Fano line shape can be observed as shown in Fig. 5(d). This is in good agreement with the simulation as shown in Fig. 4(e). Insets show the detailed negative and positive symmetrical Lorentzian line shapes around 1517.90 nm and 1549.85 nm, with full width at half-maximum of 0.255 nm and 0.135 nm, respectively, while the asymmetric Fano line shape around 1529.30 nm has a slope about 36.0 dB/nm.

The fabricated device is then placed into the temperature cabinet (ESL-04KA) for characterizing its temperature sensing properties. As the temperature increases from $- 50 ° C$ to 80°C with a step of 10°C, the resonant dip around 1532.5 nm shows a red shift with a sensitivity of 10.8 pm/°C, as shown in Fig. 6. The temperature sensitivities of each resonant dip or peak are nearly the same. The reason for the red shift of the resonance wavelengths is the change of the optical path caused by the thermo-optical effect and the thermal-expansion effect of the microsphere. Even if the device experiences several temperature changes and vibrations in the experiment, it still has good stability and robustness, due to the unique HACF coupling structure.

Fig. 6. Temperature response of the device, with inset as the reflection spectra under different temperatures.

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5. CONCLUSION

In summary, we demonstrate an embedded WGM microsphere resonator in a tapered HACF, through the circularly peripheral contact between the microsphere and the supporting annular core. By tapering the splicing joint to sharpen the cone-apex angle for increasing the coupling, periodical symmetrical Lorentzian and asymmetric Fano line shape resonances are observed and well validated by a transfer matrix model. A higher $Q$ -factor mode in a lower $Q$ -factor mode that has contrast as high as 58 is also obtained. Temperature sensing with good stability and robustness is also demonstrated. Besides the advantage of the reflection mode ^[38], the merits of this fiber-based device also include good integration and being alignment-free and etching-free, making it simple in processing and robust in structure, which shows broad potential for WGM-related applications such as sensors, optical filters, and lasers.

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[38] F. Shu, X. Jiang, G. Zhao, L. Yang. A scatterer-assisted whispering-gallery-mode microprobe. Nanophotonics, 2018, 7: 1455-1460.

1. INTRODUCTION

2. FABRICATION AND SIMULATION OF THE COUPLER

3. THEORETICAL MODEL AND ANALYSIS

4. EXPERIMENTAL RESULTS

5. CONCLUSION

Jiawei Wang, Xiaobei Zhang, Ming Yan, Lei Yang, Fengyu Hou, Wen Sun, Xiaotong Zhang, Libo Yuan, Hai Xiao, Tingyun Wang. Embedded whispering-gallery mode microsphere resonator in a tapered hollow annular core fiber[J]. Photonics Research, 2018, 6(12): 12001124.

Embedded whispering-gallery mode microsphere resonator in a tapered hollow annular core fiber Download： 630次

1. INTRODUCTION

Fig. 1. (a) Schematic of the tapered HACF coupled microsphere resonator. (b) Cross-sectional view with the inset as the simulated mode field distribution and (c) RI profile of HACF.

2. FABRICATION AND SIMULATION OF THE COUPLER

Fig. 3. (a) Simulation of the coupling efficiency as a function of cone-apex angle $θ$ , with the inset as the energy distribution in the device. (b) Taper times versus the cone-apex angle $θ$ by experimental and theoretical fitting results.

3. THEORETICAL MODEL AND ANALYSIS

Fig. 4. (a) Cross section of the model. (b),(c) Model of the microsphere (b) without and (c) with being locked by the HACF. (d) Evolution of reflection spectra with $t_{11}$ from 0.8 to 0.995 for the case of (b). (e) Reflection spectrum for the case of (c).

4. EXPERIMENTAL RESULTS

Fig. 6. Temperature response of the device, with inset as the reflection spectra under different temperatures.

5. CONCLUSION

Article Outline

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Embedded whispering-gallery mode microsphere resonator in a tapered hollow annular core fiber Download： 630次

1. INTRODUCTION

Fig. 1. (a) Schematic of the tapered HACF coupled microsphere resonator. (b) Cross-sectional view with the inset as the simulated mode field distribution and (c) RI profile of HACF.

2. FABRICATION AND SIMULATION OF THE COUPLER

Fig. 3. (a) Simulation of the coupling efficiency as a function of cone-apex angle θ, with the inset as the energy distribution in the device. (b) Taper times versus the cone-apex angle θ by experimental and theoretical fitting results.

3. THEORETICAL MODEL AND ANALYSIS

Fig. 4. (a) Cross section of the model. (b),(c) Model of the microsphere (b) without and (c) with being locked by the HACF. (d) Evolution of reflection spectra with t11 from 0.8 to 0.995 for the case of (b). (e) Reflection spectrum for the case of (c).

4. EXPERIMENTAL RESULTS

Fig. 6. Temperature response of the device, with inset as the reflection spectra under different temperatures.

5. CONCLUSION

Article Outline

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Fig. 3. (a) Simulation of the coupling efficiency as a function of cone-apex angle $θ$ , with the inset as the energy distribution in the device. (b) Taper times versus the cone-apex angle $θ$ by experimental and theoretical fitting results.

Fig. 4. (a) Cross section of the model. (b),(c) Model of the microsphere (b) without and (c) with being locked by the HACF. (d) Evolution of reflection spectra with $t_{11}$ from 0.8 to 0.995 for the case of (b). (e) Reflection spectrum for the case of (c).