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所提出的基于拉锥光纤耦合PMMA微球腔的温度传感器结构示意图如图1所示。根据目前能够达到的工艺参数和材料参数,首先利用有限时域差分法对该结构进行仿真分析。该结构由拉锥光纤耦合器和聚合物微球腔构成,拉锥光纤耦合器绿色部分是光纤的包层,黄色部分是光纤的纤芯。拉锥光纤耦合器导出消逝场,而后该消逝场进入聚合物微球腔激发回音壁模式。在仿真中,拉锥光纤的束腰直径和折射率分别设置为1.8 μm和1.4682,PMMA微球腔的直径和材料折射率分别设置为85 μm和1.4809。为了与微球腔的实际使用状态保持一致,将拉锥光纤与PMMA之间的间距设置为零,即两者保持接触状态。
采用上述参数,在外界环境为空气的情况下仿真得到的谐振光谱如图2(a)所示。从图2(a)中可以看出,对于直径为85 μm的PMMA微球腔而言,其自由光谱范围(FSR)约为6.00 nm。与根据理论公式FSR=λ2/2πnr (其中,λ为光谱的中心波长,r为微球半径,n为微球腔中回音壁模式的有效折射率)计算得到的FSR (6.07 nm)吻合。图2(b)为谐振波长1551.47 nm处的回音壁模式光场分布,可以看出,采用束腰直径为1.8 μm的拉锥光纤可有效激发PMMA微球腔中的回音壁模式。
图 2 (a) 采用有限时域差分法仿真得到的谐振光谱;(b) 在谐振波长1551.47 nm处的回音壁模式光场分布
Figure 2. (a) Resonant spectrum of the microsphere cavity obtained by the finite-difference time-domain method; (b) Whispering gallery mode field distribution at the resonant wavelength 1551.47 nm
在利用回音壁模式光学微腔进行温度传感时,拉锥光纤的消逝场将根据相位匹配条件耦合到PMMA微球腔中激发回音壁模式。微球腔的谐振波长与其半径和有效折射率之间的关系可以近似表示为:
$$ 2\pi {n_{{\rm{eff}}}}r = m{\lambda _r} $$ (1) 式中:m为回音壁模式的角模式数;λr为微球腔的谐振波长。
当微球腔所处的环境温度发生变化时,微球腔自身的热光效应和热膨胀效应将导致回音壁模式的有效折射率和微腔尺寸发生改变,从而导致微球腔的谐振波长发生漂移。微球腔的谐振波长漂移量(dλ)与温度变化量(dT)之间的关系可表示为:
$$ \frac{{{\rm{d}}\lambda }}{{{\rm{d}}T}} = {\lambda _{{r}}}\left( {\frac{1}{{{n_{{\text{eff}}}}}} \cdot \frac{{{\rm{d}}{n_{{\text{eff}}}}}}{{{\rm{d}}T}}{\text{ + }}\frac{1}{r} \cdot \frac{{{\rm{d}}r}}{{{\rm{d}}T}}} \right) $$ (2) 式中:dλ/dT为微球腔的温度灵敏度;λr为微球腔的谐振波长;neff为回音壁模式的有效折射率;dneff/dT=−1.2×10−4/℃为PMMA微球腔的热光系数;dr/dT= 7×10−5/℃为PMMA微球腔的热膨胀系数。从公式(2)可以看出,材料的热光系数和热膨胀系数越大,微腔性质随温度的变化量越大,器件的温度灵敏度越高。实验中使用的PMMA材料具有正的热膨胀系数和负的热光系数。根据公式(2),当温度升高时,PMMA微球腔热光效应导致谐振波长发生蓝移,而热膨胀效应导致谐振波长发生红移。由于PMMA微球腔的热膨胀系数比小于其热光系数,其谐振波长随外界环境温度升高发生蓝移。
Highly sensitive temperature sensor based on polymer spherical microcavity (invited)
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摘要: 提出了一种基于聚合物微球腔的温度传感器,该温度传感器利用微球腔谐振波长漂移量测量外界环境温度变化量,兼具结构紧凑和高度灵敏的特点。首先利用有限时域差分法对拉锥光纤耦合聚甲基丙烯酸甲酯(PMMA)微球的谐振结构进行了仿真分析,验证了拉锥光纤激发聚合物微球腔中回音壁模式的可行性。实验结果表明,束腰直径为1.8 µm的拉锥光纤与直径为数十微米的聚合物微球之间通过消逝场耦合的方式能够激发品质因子为104量级的回音壁模式。利用点式封装和全包裹封装相结合的方式将拉锥光纤和聚合物微球封装一体,一方面可保持两者之间稳定的耦合状态,另一方面保护拉锥光纤和微球腔免受外界污染。由于聚合物微球腔的负热光系数大于其热膨胀系数,其谐振光谱随外界温度降低发生红移。当外界环境温度在20~30 ℃范围内变化时,聚合物微球腔温度灵敏度为68 pm/℃。与传统光纤温度传感器相比,该传感器的高品质因子使其具有更低的探测极限,在受限空间内的原位温度精密测量中具有潜在的应用前景。Abstract: A temperature sensor based on polymer microsphere cavity is proposed, which measures the change of external temperature through the resonant wavelength shift and demonstrates the characteristics of high compactness and sensitivity. The finite-difference time-domain method is firstly employed to simulate the structure of tapered fiber coupled polymethyl methacrylate (PMMA) microspheres to verify its feasibility of whispering gallery mode excitation. Experimental results show that whispering gallery mode with a quality-factor on the order of 104 can be excited by evanescently coupling a polymer microsphere with a diameter of tens of micrometers through a tapered fiber with a diameter of 1.8 μm. Packaging the device by combining spot and complete coating can keep a stable coupling state between the tapered fiber and the microsphere and protect them from external contaminant. Red shift happens in the resonant spectrum of the microsphere cavity as the external temperature decreases since its negative thermo-optic coefficient is larger than the thermal expansion coefficient. When the external temperature varies in the range of 20-30 ℃, the polymer microsphere demonstrates a sensitivity of 68 pm/℃. In comparison with the conventional optical fiber sensors, lower detection limit can be achieved by the proposed temperature sensor with a higher quality-factor, which can be potentially used in the in-situ temperature precise measurement in a limited space.
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Key words:
- temperature sensor /
- microcavity /
- whispering gallery mode /
- polymer
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图 3 拉锥光纤耦合的PMMA微球腔封装过程示意图:(a) 将低折射率胶垫片固定在TEC上;(b) 将拉锥光纤固定在垫片上;(c) 将PMMA微球腔转移至拉锥光纤束腰处并用低折射率胶点涂固化;(d) 用低折射率胶将整个器件全包裹并固化
Figure 3. Schematic diagram of the tapered fiber coupled PMMA microsphere cavity packaging process: (a) Placing a low-index rubber gasket on the TEC; (b) Fixing the tapered optical fiber on the gasket; (c) Transferring a PMMA microsphere cavity to the waist of the tapered fiber and then packaging them together by spot curing; (d) Coating and curing the whole device with the low refractive index adhesive
图 5 (a) 1535~1565 nm范围内直径为85 μm的PMMA微球腔的谐振光谱;(b) PMMA微球腔在不同温度下的谐振光谱;(c) 图(b)中1559.7 nm附近谐振光谱细节;(d) PMMA微球腔谐振波长随温度漂移结果
Figure 5. (a) Resonant spectrum of the PMMA microsphere with a diameter of 85 μm in the range from 1535 nm to 1565 nm; (b) Resonant spectra of the PMMA microsphere under different temperatures; (c) The details of the spectra around 1559.7 nm in (b); (d) Wavelength shift of the PMMA microsphere with respect to temperature
图 6 (a) 1535~1565 nm范围内直径为102 μm的PMMA微球腔的谐振光谱;(b) PMMA微球腔在不同温度下的谐振光谱;(c) 图(b)中1560.5 nm附近谐振光谱细节;(d) PMMA微球腔谐振波长随温度漂移结果
Figure 6. (a) Resonant spectrum of the PMMA microsphere with a diameter of 102 μm in the range from 1535 nm to 1565 nm; (b) Resonant spectra of the PMMA microsphere under different temperatures; (c) The details of the spectra around 1560.5 nm in (b); (d) Wavelength shift of the PMMA microsphere with respect to temperature
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