Whispering gallery modes in a single silica microparticle attached to an optical microfiber and their application for highly sensitive displacement sensing

Ningyu Liu; Lei Shi; Song Zhu; Xinbiao Xu; Shixing Yuan; Xinliang Zhang

doi:10.1364/OE.26.000195

1. Introduction

Displacement sensors have been widely employed for measuring length, vibration, temperature, speed, etc. However, traditional displacement sensors based on electronic and magnetic effects are of big volume, high cost, and very sensitive to electromagnetic interference [1]. Optical fiber displacement sensors (OFDSs) are compact, lightweight and immune to electromagnetic interference, and thus they can be applied in many areas. Usually, OFDSs can be divided into two types: interferometry-based and intensity-based sensors [2]. For interferometry-based sensors, OFDSs based on microfiber couplers were proposed by Chen et al. to measure the force with a sensitivity of 0.1 nm/μm and a measurement range of only ~4 μm [3]. Sun et al. demonstrated an OFDS based on a Fabry-Perot interferometer with the maximum detection distance of 180 cm and a detection resolution of up to hundreds of micrometers [4]. A multimode interference effect-based OFDS with a measurement range of 200 μm was also proposed by Mehta et al., but the fabrication process is complex [5]. By contrast, intensity-based OFDSs are simple to construct. The optical fiber bundle displacement sensor is the most popular intensity-based OFDS, and several theoretical studies on this OFDS have been carried out to quantitatively calculate its sensing performance [6–8].

On the other side, whispering gallery modes (WGMs) have been observed in various optical microcavities [9–13]. Displacement sensors based on coupled optical microcavities [14–16] were also reported. Micrometer-diameter silica microparticles, which are fabricated by chemical vapor deposition (CVD), can also be regarded as WGM microcavities. How to effectively excite WGMs in a single dielectric microparticles based on a compact and stable coupling scheme is an attracting issue. Kosma et al. and Wang et al. placed polystyrene and Ba-Ti oxide microparticles into microstructured optical fibers [17] and chemical etched photonic crystal fibers [18], respectively, and excited WGMs in the microparticles were observed. The diameter of the silica microparticles is much smaller than that of the conventional silica microsphere cavity, which is fabricated by melting the tip of an optical fiber taper [19,20]. Though quality (Q) factors of the microparticles-based microcavities are limited due to their small-size induced radiation losses and surface non-regularity [21,22], they are still good candidates for sensing applications. Furthermore, the direct contact coupling between the microparticles and the microfiber avoids the use of a high-precision 3-D displacement stage, and thus this system is compact and relatively stable. In this work, a single silica microparticles was attached to an optical microfiber and efficient excitation of WGMs in the microparticles was realized. Standard single-mode fiber (SMF) with a certain length was processed to form a displacement controller (DC), the bending radius of the SMF was changed by the DC to affect the polarization state of the signal light. The extinction ratios (ERs) of the WGMs in the microparticles were determined by the polarization state of the signal light. By measuring the change of the ER as a function of the moving distance, we obtained a high displacement sensitivity of 33 dB/mm with a detection range of over 400 μm.

2. Device fabrication and principle

The diameter of the silica microparticles is around 10.6_{μm with a refractive index (RI) of 1.45, and the non-uniformity of the diameter results from fabrication error of CVD (Sphere Scientific Corporation, Wuhan, China). The coupling optical microfiber is fabricated by the flame-heated drawing method from the SMF [23,24]. By adjusting the control parameters of the drawing platform, an optical microfiber with a diameter of around 1 μm, which possesses the strong evanescent field, can be obtained [25–27]. Since silica microparticles exist as the form of powders, a fiber taper is used to transfer the microparticles onto the coupling microfiber. Through dipping the fiber taper into the microparticles powders, the microparticles will cling to the fiber taper tightly due to the Van der Waal’s force, as shown in Fig. 1(a). After that, we make the fiber taper in contact with the microfiber, and the microparticles can be attached onto the microfiber. Another fiber taper is used to wipe out the superfluous microparticles to make sure there exists only a single microparticles on the microfiber. As shown in Fig. 1(b), we can find that the microfiber is attached with a single microparticles due to the Van der Waal’s force. The coupling scheme is compact and relatively stable compared with conventional optical micro cavity coupling system [28]. Because of the strong evanescent field of the microfiber, WGMs in the microparticles can be easily excited when the signal light is transmitted through the microfiber. Since the coupling gap between the microfiber and the microparticles is fixed, high ER can only be realized by adjusting the polarization state of the signal light through the polarization controller (PC). The experimental setup is shown in Fig. 2(a). The signal light, which is derived from a superluminescent light emitting diode (SLED) with a spectrum range from 1220 nm to 1400 nm, is controlled by a PC. Then it is fed into the microfiber to excite WGMs in the silica microparticles. The transmission spectrum is measured by an optical spectrum analyzer (OSA). The DC is formed by fixing the SMF onto two 3-D displacement stages, as shown in Fig. 2(a). Figure 2(b) shows the bending process of the SMF with the movement of two stages, and the bending radius becomes smaller as the distance between two stages decreases.}

Fig. 1 (a) Silica microparticless transferred by a fiber taper. (b) A single silica microparticles attached to an optical microfiber.

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Fig. 2 (a) Experimental setup for displacement sensing. (b) Sensing component.

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Light field with any polarization state propagating in an optical fiber can be divided into x polarization state and y polarization state. The electric field component of the light field in the fiber can be expressed as:

E = [\begin{matrix} E_{x} \\ E_{y} \end{matrix}] = [\begin{matrix} E_{0} \cos θ \exp j (ω t - β_{x} z) \\ E_{0} \sin θ \exp j (ω t - β_{y} z) \end{matrix}] = E_{x} [\begin{matrix} 1 \\ \tan θ \exp j (Δ β z) \end{matrix}]

where E₀ is the amplitude of the electric field component, θ is the direction angle of the x-axis, ω is the angular frequency, β is the propagation constant and Δβ is the propagation constant difference. As seen from Eq. (1), it is obviously that the polarization state of the signal light is mainly determined by Δβ. As for the DC, the bending radius of the fiber fixed on two manual positioners changes with the distance between them. The bending radius becomes smaller when the distance is reduced. Because of the birefringence effect [29,30], Δβ changes with the bending radius of the fiber, and it can be represented as [31,32]:

Δ β = \frac{1}{2} k_{0} n^{3} (p_{11} - p_{12}) (1 + v_{p}) {(\frac{r}{R})}^{2} + \frac{1}{2} n^{2} (p_{11} - p_{12}) \frac{(1 + v_{p}) (2 - 3 v_{p})}{(1 - v_{p})} \frac{r}{R} S_{x x}

where k₀ is the wave vector, n is the refractive index of the fiber core, p₁₁ = 0.12 and p₁₂ = 0.27 are the elasto-optical coefficients of the fiber, v_p = 0.17 is the Poisson’s ratio of the fiber, r and R are the cladding radius and the bending radius of the fiber, respectively, and S_xx is the plus axial tensile strain. The first half of Eq. (2) represents the birefringence effect caused by the fiber bending while the second half describes the birefringence effect caused by the axial tension. In the experiments, UV glue was used to fasten the contact position between the fiber and the positioner, so the birefringence effect caused by the axial tension can be regarded as constant. According to the coupled mode equations [33], two orthogonal eigenmodes are coupled with each other when propagating in the fiber, expressed by Eq. (3) and (4):

\frac{d P_{x}}{d z} = - α z + h [P_{x} (z) - P_{y} (z)]

\frac{d P_{y}}{d z} = - α z - h [P_{x} (z) - P_{y} (z)]

where P_x and P_y are the powers of two orthogonal modes, α is the loss coefficient of the fiber and h represents the mode coupling coefficient. Assuming P_x (0) = P₀, P_y (0) = 0, we obtained the solutions of Eq. (3) and (4):

P_{x} (z) = P_{0} e^{- h z} \cos h (h z) e^{- α z}

P_{y} (z) = P_{0} e^{- h z} \sin h (h z) e^{- α z}

For a normal mode input with polarization x, the output of the optical fiber possesses two normal modes with polarization x and y. The power ratio between two normal modes is expressed as:

η = \frac{P_{y}}{P_{x}} = \tan h (h z)

According to Eq. (2) and (7), the mode coupling coefficient h is determined by the propagation constant difference Δβ, we can conclude that the polarization state of the signal light can be controlled by the distance between two positioners.

The mode field distributions with TE and TM polarizations were numerically calculated using the finite element method (COMSOL Multiphysics). The silica microparticles was treated as a rotationally axisymmetric dielectric cavity, and the 2-D axisymmetric simulation was carried out. Figures 3(a) and 3(b) illustrate the electric field distributions in the silica microparticles with a radius of 5.3 μm. According to the simulation results, we find that the effective RIs of two polarization modes increase with the increasing of the microparticles radius, as shown in Fig. 3(c). The effective RI difference between two orthogonal polarization modes indicates that there exists natural birefringence effect for the fundamental WGM. Figure 3(d) demonstrates a fact that the effective RI difference decreases with the increase of the microparticles radius, that is, there exists the larger effective RI difference in the smaller microparticles. In the experiments, the microparticles with a radius of around 5.3 μm is used to observe the WGMs. Moreover, the conventional silica microsphere cavity with a large diameter of tens or hundreds of micrometers is generally fabricated by melting an optical fiber, and a complex coupling system is required to control the coupling condition between the microsphere and the microfiber. Here, the coupling system is simplified by making the micrometer-diameter silica microparticles attached to the microfiber, which enables the device to be compact and relatively stable.

Fig. 3 (a) TE mode and (b) TM mode electric field distribution in the silica microparticles. The red arrow shows the electric field direction. (c) Effective RI of two orthogonal polarization modes and (d) corresponding effective RI difference as a function of the microparticles radius.

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Because of the strong evanescent field of the microfiber, light propagating in the microfiber can be easily coupled into the microparticles. The resonance wavelengths of WGMs in the microparticles with TE and TM polarizations are expressed as $λ_{T E} = 2 π R \cdot n_{e f f}^{T E} / m$ and $λ_{T M} = 2 π R \cdot n_{e f f}^{T M} / m$ , respectively, where λ is the vacuum resonance wavelength, R is the radius of the microparticles, and n_eff is the effective RI. The resonance wavelengths of two orthogonal polarization modes are separate due to the different effective RIs, and the resonance wavelength difference is described as $Δ λ = λ_{T M} \cdot Δ n_{e f f} / n_{e f f}^{T M}$ , where Δλ and Δn_eff represent λ_TE−λ_TM and $n_{e f f}^{T E} - n_{e f f}^{T M}$ , respectively. Therefore, only one polarization mode can meet the resonant condition when the polarization state of the signal light is adjusted into TE or TM polarization. The PC is used to make sure that the signal light with either TE or TM polarization is coupled into the microparticles to achieve high coupling efficiency. The polarization state of the signal light changes with the distance between two positioners, as discussed in Eq. (2) and (7). The polarization state will convert between TE polarization and TM polarization because of the orthogonal relation between them. When the polarization state of the signal light changes, the resonance wavelengths shift due to the separate resonance wavelengths for two polarization states. The resonance dips of TE (or TM) mode will gradually disappear with the change of the polarization state. Since a single polarization can be split into two components (TE and TM polarizations) after propagation through the device [34], we calculate the transmission spectra with different power ratios between two polarization states of the signal light by using the coupled mode theory [35]. As revealed in Fig. 4, the ER of the resonance dip is determined by the polarization state of the signal light, and η = P_TE/P_TM represents the power ratio between the TE polarization and the TM polarization of the signal light. Since the diameter of the microparticles is very small, Δλ is large enough to be distinguished between two polarization states. Therefore, the ER change of the resonance dip can verify the change of the polarization state of the signal light. Due to the relation between the polarization state and the moving distance of the DC, this simple and compact fiber-optic device can be used to detect the micro-displacement.

Fig. 4 (a)-(d) Transmission spectra of the silica microparticles attached to the microfiber with different power ratios between the TE mode and the TM mode of the signal light.

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3. Experimental results and discussion

Figure 5 shows the WGM spectra with a displacement range of 0.38 mm when the radiuses of the silica microparticles and the microfiber are around 5.37 µm and 0.66 µm, respectively. The periodic resonance dips in the transmission spectrum indicate the WGMs in the microparticles, and the free spectrum range (FSR) of 40.78 nm agrees well with FSR = λ²/2πn_effR. There are two groups of resonance dips in the transmission spectrum. The ERs of one group of dips decrease with the displacement while those of the other group of dips increase with the displacement. The difference between the resonance dips indicates a fact that there exist two orthogonal polarization modes in the microparticles. As revealed in Fig. 5, WGM notches with different azimuthal or radial orders are excited [36,37] and they show different responses to the polarization effect [38], TM1 33 mode makes the best performance both in the sensitivity and the dynamic range. By adjusting the PC, we obtain the maximum ER of 14.04 dB for TM polarization and the minimum ER of 0.88 dB for TE polarization. The wavelength difference Δλ of the two dips is 21.21 nm, which agrees well with $Δ λ = λ_{T M} \cdot Δ n_{e f f} / n_{e f f}^{T M}$ . Though Q factors of ~300 are low, Δλ is still large enough to observe the change of the polarization state. Figures 6(a) and 6(b) show the ER change of TM1 33 mode in the rising and falling processes, respectively. The ER of TM1 33 mode decreases from 14.04 dB to 2.29 dB when the displacement increases from 0 mm to0.38 mm. The increase of the displacement in the opposite direction from 0 mm to 0.31 mm is also measured in order to prove the reversibility of the sensor, and the ER change of TM1 33 mode from 3.39 dB to 13.39 dB is observed. Figures 6(c) and 6(d) show the linear fitting of the relation between the displacement and the ER in the two processes. The sensitivities of 31.4 dB/mm and 33.5 dB/mm are achieved in the rising and falling processes, respectively. Accordingly, the measurement resolution can reach to ~10 μm using the OSA with a power accuracy of 0.3 dB. The sensitivity could be enhanced through optimizing the number of the SMF coils and the length of the SMF fixed on two positioners. The experimental results are consistent in the two processes, and this verifies that the sensor is capable of the reversible operation.

Fig. 5 WGM spectra of the silica microparticles with a radius of around 5.37 μm, corresponding to a distance range from 0 mm to 0.38 mm.

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Fig. 6 (a) Enlarged resonance dip of the WGM in the silica microparticles with a radius of around 5.37 μm in the rising process and (b) the falling process. ER change in (c) the rising process and (d) the falling process. (e-h) The same measurement process as in (a-d) using the silica microparticles with a radius of around 5.16 μm.

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We also carry out an experiment to verify the repeatability of this displacement sensor, in which the silica microparticles with a radius of around 5.16 μm and the microfiber with a radius of around 0.48 µm are used. As shown in Fig. 6 (e), the maximum ER of the resonance dip is 11.7 dB at the displacement of 0.43 mm, and the ER decreases to 2.03 dB at the displacement starting point. Figure 6(f) shows the result that the DC moves in the opposite direction (i.e., the falling process). The ER of the resonance dip increases from 2.31 dB to 11.51 dB when the displacement increases in the opposite direction from 0 mm to 0.44 mm. Figures 6(g) and 6(h) show the linear fitting of the relation between the displacement and the ER in the two processes. Furthermore, the sensitivities in two processes are 17.7 dB/mm and 18.7 dB/mm, and they still maintain good consistency. The experimental results prove that this displacement sensor is repeatable with different microparticles and microfibers. Due to the good reversibility and repeatability, the device can be utilized in tiny displacement sensing with a measurement range of over 400 μm. The measurement range could be improved by optimizing the radius of the microfiber to achieve higher coupling efficiency and thus larger ER of the fundamental mode of TM or TE polarization.

4. Conclusion

In this work, we have demonstrated an in-line fiber-optic displacement sensor based on WGMs in a single silica microparticles attached to an optical microfiber. This sensor has a high displacement sensitivity of 33 dB/mm and a high measurement resolution of ~10 μm with good reversibility and repeatability. This device is compact, in-line, low-cost and easy to be fabricated. It has a great potential for applications in micro-distance measurement, vibration detection and structure monitoring of constructions.

Funding

National Natural Science Foundation of China (NSFC) (11774110, 61307075); National Key Research and Development Program of China (2016YFB0402503).

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Whispering gallery modes in a single silica microparticle attached to an optical microfiber and their application for highly sensitive displacement sensing

Abstract

1. Introduction

2. Device fabrication and principle

3. Experimental results and discussion

4. Conclusion

Funding

References and links

Cited By

Figures (6)

Equations (7)

Optics Express