High-Order Interference Effect Introduced by Polarization Mode Coupling in Polarization—Maintaining Fiber and Its Identification
<p>A distributed PMC measurement schematic for PMF. (C: coupler, PD: photodiode, ISO: Isolator, M: motor, MZI: Mach-Zehnder interferometer, DSF: dispersion-shifted fiber, DAQ: data acquisition) The PMF under test with multiple perturbation points (Points <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">X</mi> <mn>1</mn> </msub> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">X</mi> <mn>2</mn> </msub> </mrow> </semantics> </math>, …, <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">X</mi> <mi mathvariant="normal">J</mi> </msub> </mrow> </semantics> </math>) is spliced to Polarizers 1 and 2 at Points <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">X</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">X</mi> <mn>2</mn> </msub> </mrow> </semantics> </math>, respectively.</p> "> Figure 2
<p>The graphics of any two adjacent units of PMF. Segment <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="normal">X</mi> <mrow> <mi>j</mi> <mo>−</mo> <mi>p</mi> </mrow> </msub> <mo>,</mo> <msub> <mi mathvariant="normal">X</mi> <mrow> <mi>j</mi> <mo>+</mo> <mi>q</mi> </mrow> </msub> <mo stretchy="false">]</mo> </mrow> </semantics> </math> are denoted by <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mi>i</mi> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </msub> <mo>∪</mo> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mi>i</mi> <mo>,</mo> <mo>+</mo> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </semantics> </math> , where the subscript <math display="inline"> <semantics> <mi>i</mi> </semantics> </math> represents the <math display="inline"> <semantics> <mi>i</mi> </semantics> </math>th adjacent unit combination of PMF, the subscripts (0) and (+) represent the corresponding OPD = 0 and OPD ≠ 0, respectively, <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">X</mi> <mrow> <mi>j</mi> <mo>−</mo> <mi>p</mi> </mrow> </msub> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">X</mi> <mi>j</mi> </msub> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">X</mi> <mrow> <mi>j</mi> <mo>+</mo> <mi>q</mi> </mrow> </msub> <mtext> </mtext> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>≥</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics> </math> are the perturbation points of PMF, respectively, <math display="inline"> <semantics> <mrow> <msub> <mi>ρ</mi> <mi>j</mi> </msub> </mrow> </semantics> </math> is the coupling coefficient of the corresponding Point <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">X</mi> <mi>j</mi> </msub> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi>P</mi> <mi mathvariant="normal">F</mi> </msub> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <msub> <mi>P</mi> <mi mathvariant="normal">S</mi> </msub> </mrow> </semantics> </math> are the light intensities out of the fast-axis and slow-axis of PMF, respectively.</p> "> Figure 3
<p>Depending on the two end unit types (<math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mi>i</mi> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </semantics> </math> or <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mi>i</mi> <mo>,</mo> <mo>+</mo> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </semantics> </math>), the scanning OPDs of the entire PMF under test are categorized into four kinds, which are notated by (A) {<math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mi>out</mi> <mo>,</mo> <mo>+</mo> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </semantics> </math>}, (B) {<math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mi>i</mi> <mi>n</mi> <mo>,</mo> <mo>+</mo> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mi>out</mi> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </semantics> </math>}, (C) {<math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mi>out</mi> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </semantics> </math>} and (D) {<math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mi>i</mi> <mi>n</mi> <mo>,</mo> <mo>+</mo> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </semantics> </math>, <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mi>out</mi> <mo>,</mo> <mo>+</mo> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </semantics> </math>}, respectively. The consecutive units between the two black boxes in each kind conform with sequence of <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mi>i</mi> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </msub> <mo>∪</mo> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mi>i</mi> <mo>,</mo> <mo>+</mo> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </semantics> </math>. Besides, <math display="inline"> <semantics> <mrow> <msub> <mi>ρ</mi> <mtext>in</mtext> </msub> </mrow> </semantics> </math> and <math display="inline"> <semantics> <mrow> <msub> <mi>ρ</mi> <mtext>out</mtext> </msub> </mrow> </semantics> </math> represent the coupling coefficients of the points before the first unit <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </semantics> </math> and after the last unit <math display="inline"> <semantics> <mrow> <msub> <mi mathvariant="normal">B</mi> <mrow> <mo stretchy="false">(</mo> <mi>last</mi> <mo>,</mo> <mo>+</mo> <mo stretchy="false">)</mo> </mrow> </msub> </mrow> </semantics> </math>, respectively.</p> "> Figure 4
<p>Experimental results of a PMF with the angle combination of 45°–0°. Interferograms A, B, and D can be directly identified by Equation (5). The notation NF represents the noise floor of the interference signal, which indicates the sensitivity of measurement system.</p> "> Figure 5
<p>Experiment results of a PMF with additional three angle combinations of (<b>a</b>) 0°–0°; (<b>b</b>) 0°–45° and (<b>c</b>) 45°–45°. They demonstrate the enhancement or suppression of the interferograms marked with box in <a href="#sensors-16-00419-f004" class="html-fig">Figure 4</a>, which can be used to identify the HOI.</p> "> Figure 6
<p>The intensity variation trend of different orders’ HOIs with varying angle <math display="inline"> <semantics> <mrow> <msub> <mi>θ</mi> <mn>2</mn> </msub> </mrow> </semantics> </math>. The input polarizer 1 angle <math display="inline"> <semantics> <mrow> <msub> <mi>θ</mi> <mn>1</mn> </msub> </mrow> </semantics> </math> is set to 0° (<b>a</b>) and 45° (<b>b</b>), respectively. The experimental results are marked by different dot notations, and the theoretical curves are expressed by the solid lines. The maximum values of each curve represent the meaning of coupling intensities at the corresponding scanning OPD.</p> ">
Abstract
:1. Introduction
2. Model and Analysis
2.1. WLI System with a Large Dynamic Range
2.2. Optical Path Tracking (OPT) Method
2.2.1. Stable Unit and Recursion Formula
2.2.2. Classifications and General Formulas
3. Experimental Results
3.1. Theoretical Estimation
3.2. Identification of HOI and Results
4. Discussions
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Interferogram | Position Meaning | Interferogram Meaning | Position (mm) | Normalized Intensity/Error (dB) | Order N | |||
---|---|---|---|---|---|---|---|---|
0°–0° | 0°–45° | 45°–0° | 45°–45° | |||||
0 | 1 | 0 | 0 | 0 | 0 | 0 | ||
M | 13.33 | <−70 | <−50 | <−50 | −7.8/1.8 | 0th | ||
A | 1.22 | <−70 | <−70 | −15.6/0.7 | <−50 | 1st | ||
D | 4.09 | <−70 | <−70 | −15.7/0.7 | <−50 | |||
I | 9.27 | <−50 | −16.5/1.5 | <−70 | <−50 | |||
L | 12.12 | <−50 | −16.3/1.4 | <−70 | <−50 | |||
C | 2.87 | −29.7/0.2 | <−60 | <−60 | <−70 | 2nd | ||
E | 5.21 | <−70 | <−70 | <−70 | −36.7/0.7 | |||
H | 8.08 | <−70 | <−70 | <−70 | −30.6/0.7 | |||
J | 10.47 | <−70 | <−70 | <−70 | −31.0/1.1 | |||
K | 10.95 | <−70 | <−70 | <−70 | −36.9/1.1 | |||
B | 1.70 | <−70 | <−70 | −45.1/0.3 | <−70 | 3rd | ||
F | 6.38 | <−70 | −45.7/0.8 | <−60 | <−70 | |||
G | 7.60 | <−70 | <−70 | <−70 | −67.7/1.9 | 4th |
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Li, C.; Yang, J.; Yu, Z.; Yuan, Y.; Zhang, J.; Wu, B.; Peng, F.; Yuan, L. High-Order Interference Effect Introduced by Polarization Mode Coupling in Polarization—Maintaining Fiber and Its Identification. Sensors 2016, 16, 419. https://doi.org/10.3390/s16030419
Li C, Yang J, Yu Z, Yuan Y, Zhang J, Wu B, Peng F, Yuan L. High-Order Interference Effect Introduced by Polarization Mode Coupling in Polarization—Maintaining Fiber and Its Identification. Sensors. 2016; 16(3):419. https://doi.org/10.3390/s16030419
Chicago/Turabian StyleLi, Chuang, Jun Yang, Zhangjun Yu, Yonggui Yuan, Jianzhong Zhang, Bing Wu, Feng Peng, and Libo Yuan. 2016. "High-Order Interference Effect Introduced by Polarization Mode Coupling in Polarization—Maintaining Fiber and Its Identification" Sensors 16, no. 3: 419. https://doi.org/10.3390/s16030419