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奇偶探测超分辨率折射率测量的理论研究

王强 王倩倩 王振 郝利丽

王强, 王倩倩, 王振, 郝利丽. 奇偶探测超分辨率折射率测量的理论研究[J]. 中国光学(中英文). doi: 10.37188/CO.2022-0119
引用本文: 王强, 王倩倩, 王振, 郝利丽. 奇偶探测超分辨率折射率测量的理论研究[J]. 中国光学(中英文). doi: 10.37188/CO.2022-0119
WANG Qiang, WANG Qian-qian, WANG Zhen, HAO Li-li. Theoretical investigation on super-resolving refractive index measurement with parity detection[J]. Chinese Optics. doi: 10.37188/CO.2022-0119
Citation: WANG Qiang, WANG Qian-qian, WANG Zhen, HAO Li-li. Theoretical investigation on super-resolving refractive index measurement with parity detection[J]. Chinese Optics. doi: 10.37188/CO.2022-0119

奇偶探测超分辨率折射率测量的理论研究

doi: 10.37188/CO.2022-0119
基金项目: 东北石油大学引导性创新基金(No. 2021YDL-16);黑龙江省教育规划重点课题(No. GJB1320038,No. GJB1422173);东北石油大学教育教学改革项目(No. JGXM_NEPU_202114)
详细信息
    作者简介:

    王 强(1980—),男,黑龙江拜泉人,博士,副教授,硕士生导师,2006年、2016年分别于哈尔滨工业大学获得硕士、博士学位,主要从事量子干涉度量及传感,量子激光雷达等方面的研究。E-mail:wangqiang8035@163.com

    郝利丽(1981—),女,黑龙江绥化人,博士,副教授,硕士生导师,2007年、2015年分别于哈尔滨工业大学获得硕士、博士学位,主要从事量子光学,空间光孤子及光控器件等方面的研究。E-mail:haolili0820@126.com

  • 中图分类号: O436.1;TN249

Theoretical investigation on super-resolving refractive index measurement with parity detection

Funds: Supported by Guiding Innovation Fund of Northeast Petroleum University (No. 2021YDL-16), Heilongjiang Province education planning key project (No. GJB1320038 and No. GJB1422173). The education teaching reform project of Northeast Petroleum University (No. JGXM_NEPU_202114)
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  • 摘要:

    传统波动光学法测量样品折射率所采用的探测方法主要是强度探测和波长探测。波长的最佳检测器件普遍采用干涉型光谱仪,干涉型光谱仪是通过光功率计测量信号强度、分析条纹数目变化及所对应的光程差进而计算出信号光波长,因此,其本质仍是以强度探测为基础的。然而,强度探测干涉信号的分辨率受经典衍射极限限制,分辨率很难进一步提升。为了解决这一瓶颈问题,本文提出利用奇偶探测突破经典分辨率极限限制,实现超分辨率折射率测量。根据量子探测与估计理论,推导了奇偶探测和强度探测折射率测量信号及其灵敏度表达式,并进行了数值对比分析。同时,研究了损耗对系统输出信号分辨率和灵敏度的影响。数值结果表明奇偶探测分辨率是强度探测的${\text{2{\text{π}} }} \sqrt {\text{N}}$倍,实现了超分辨率折射率测量,最佳灵敏度达到了折射率测量散弹噪声极限${\lambda \mathord{\left/ {\vphantom {\lambda {\left( {2{\text{π}} l\sqrt N } \right)}}} \right. } {\left( {2{\text{π}} l\sqrt N } \right)}}$,损耗降低了信号的分辨率和灵敏度,除极大损耗和极低光子数外,奇偶探测信号分辨率始终优于强度探测。最后,从探测手段本身出发分析了奇偶探测超分辨率折射率测量的物理本质。

     

  • 图 1  奇偶探测超分辨率折射率测量原理图

    Figure 1.  Scheme of super-resolution refractive index measurement with parity detection

    图 2  (a) 强度探测折射率测量灵敏度曲线及(b)信号最佳灵敏度随光子数和透过率的变化关系。

    Figure 2.  (a) Sensitivity curve of refractive index measurement with intensity detection and (b) its best sensitivity against with the photon number and transmittance.

    图 3  奇偶探测信号和归一化强度探测信号,输入信号的平均光子数$N = 100$,红色点线和黑色实线分别代表奇偶探测 (parity detection,PD)信号和归一化强度探测 (Intensity detection,ID) 信号。

    Figure 3.  Signals of parity and normalized intensity detections are plotted as a function of refractive index n for the average photon number of $N = 100$. The red dashed and black solid lines represent parity detection (PD) and intensity detection (ID) respectively.

    图 4  奇偶探测和强度探测的FWHMs随着平均光子数(a)和透过率(b)的变化规律。

    Figure 4.  FWHMs of parity and intensity detections against with the average photon number(a) and transmittance(b).

    图 5  奇偶探测(红色点线)和强度探测(蓝色实线)信号灵敏度曲线,黑色虚线为两条曲线的公切线。

    Figure 5.  Sensitivity curves of parity detection (red dotted line) and intensity detection (blue solid line), and the black dashed line represents their common tangent.

    图 6  奇偶探测和强度探测信号最佳灵敏度随着透过率 (a) 和光子数 (b) 的变化曲线,红色点虚线表示奇偶探测,蓝色实线代表强度探测。

    Figure 6.  Best sensitivity of parity and intensity detections against with the transmittance (a) and average photon number (b). The red dot-dashed line indicates parity detection and the blue solid line represents intensity strategy.

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  • 收稿日期:  2022-06-10
  • 录用日期:  2022-09-09
  • 网络出版日期:  2022-09-28

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