1.Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026, China 2.Science and Technology on Optical Radiation Laboratory, Beijing 100039, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos.61775209, 41871229, 61275011)
Received Date:21 August 2019
Accepted Date:11 October 2019
Available Online:13 December 2019
Published Online:05 January 2020
Abstract:Optical microcavity has an important and promising application in high sensitivity sensing, but thermal drift hinders its practical use. In this study, we propose a triple-layer-coated microsphere resonator, which has a high sensitivity in refractive index sensing with low thermal drift. The refractive indexes of the three layers from the inside to the outside are high, low, and high, respectively. The two high refractive index layers can support their own whispering-gallery modes, called the inner mode (IM) and the outer mode (OM). We study the performance of IM and OM with waveguide coupling in refractive index sensing and temperature sensing. The results show that when the thickness of the middle layer is 550 nm, the refractive index sensitivity of IM and OM will be 0.0168 nm/RIU, 102.56 nm/RIU, and the temperature sensitivity will be –19.57 pm/K and –28.98 pm/K, respectively. The sensing is carried out by monitoring the difference in resonant wavelength between IM and OM and the sensing characteristics are optimized by adjusting the thickness of the middle layer. Further, when ${t_B}$ = 400 nm, the refractive index sensitivity can arrive at 75.219 nm/RIU, the detection limit can reach 2.2 × 10–4 RIU, and the thermal drift is reduced to 3.17 pm/K, thereby eliminating the effect of thermal drift to a great degree. This study provides the guidance for designing and improving the microsphere refractive index sensors. Keywords:optical microcavity/ coated layer structure/ whispering-gallery modes/ refractive index sensing
其中${z_{A1}} = {n_A}k\left( {R - {t_A}} \right)$, ${z_{B2}} = {n_B}k\left( {R - {t_A}} \right)$. 系数${M_l}$, ${N_l}$, ${C_{l1}}$, ${D_{l1}}$, ${C_{l2}}$, ${D_{l2}}$, ${C_{l3}}$, ${D_{l3}}$由边界条件$r = R$, $r = R - {t_A}$, $r = R - {t_A} - {t_B}$, r = R – tA – tB – tC确定. 具体地, SiO2球腔本体尺寸${R_{\rm{S}}}$ = 9.05 μm, 两高折射率膜层厚度${t_A} = {t_C}$ = 200 nm, 图2是不同中间膜层厚度${t_B}$对应谐振模式的电场分布, 以及模式的径向电场分布曲线. 由电场分布可以看出, 内外两个高折射率膜层支持各自的WGM, 称之为内层模式(inner mode, IM)、外层模式(outer mode, OM). 图 2 不同中间膜层厚度时内外模式的电场径向分布曲线及电场分布云图 Figure2. Electric field distributions of the inner and outer modes and the distributions along the radial direction with a various ${t_B}$.
其中${n_{{\rm{glucose}}}}$和${n_{{{\rm{H}}_{\rm{2}}}{\rm{O}}}}$分别是葡萄糖溶液以及纯水的折射率, 取${n_{{{\rm{H}}_{\rm{2}}}{\rm{O}}}} = 1.33$[17], ${c_{{\rm{glucose}}}}$为葡萄糖溶液的浓度, 单位为g/ml. 内外模式的谐振波长与外界环境折射率变化的关系如图4所示. 谐振波长随外界环境折射率的增大而增大, 即发生了红移. 这是因为环境的折射率增加, 使得耦合体系的有效折射率${n_{{\rm{eff}}}}$增大, 由谐振相位匹配条件有$2{\text{π}}R{n_{{\rm{eff}}}} = {\lambda _{\rm{R}}}m$, m为角向模式数, 因此${n_{{\rm{eff}}}}$ 增大, 谐振波长${\lambda _{\rm{R}}}$也随之增大. 外界环境折射率变化范围为1.33— 1.335, 在该范围内, 经过线性拟合, OM的折射率灵敏度${S_{{\rm{o}}, n}} = $ 102.56 nm/RIU, IM的折射率灵敏度${S_{{\rm{i, }}n}} = $ 0.0168 nm/RIU, 灵敏度相差六千多倍. 图 4 外层模式(a)与内层模式(c)透射谱随外界环境折射率的变化趋势; 外层模式(b)与内层模式(d)谐振波长偏移量${\rm{\text{δ}}}{\lambda _{\rm{R}}}$与外界环境折射率变化量${\rm{\text{δ} }}n$的关系 Figure4. Transmission spectra for the outer mode (a) and the inner mode (c) with the change of the external environment RI; The relationship between the shift of the resonance wavelength ${\rm{\text{δ} }}{\lambda _{\rm{R}}}$ and the change of the external environment RI $\text{δ} n$for the outer mode (b) and the inner mode (d).
三层膜结构微球腔相对于镀一层膜的微腔而言, 优势在于多了一个可调节的维度, 即中间膜层厚度${t_B}$. 不同中间层厚度时, 内外层模式折射率灵敏度如图6(a)所示. ${t_B}$减小时, OM有更多的能量穿过中间层, 在内层发生微弱的谐振, 渗透到外界环境的能量也随之减少, 折射率灵敏度下降; 同样地, IM有更多的能量渗透到外界环境, 折射率灵敏度也随之增加. 这一结论与本征模式仿真的结果相符合. 图 6 不同中间层厚度${t_B}$时内外模式的折射率灵敏度(a)和温度灵敏度(b) Figure6. The refractive index sensitivity (a) and temperature sensitivity (b) for the inner mode and the outer mode with a various ${t_B}$.