- Email: [email protected]
Pressure and temperature sensor based on a dual core photonic quasi-crystal fiber
Accepted Manuscript Title: Pressure and Temperature Sensor Based on a Dual Core Photonic Quasi-Crystal Fiber Author: S. Revathi Srinivasa Rao Inabathini Jatin Pal PII: DOI: Reference:
S0030-4026(15)00694-4 http://dx.doi.org/doi:10.1016/j.ijleo.2015.07.141 IJLEO 55857
To appear in: Received date: Accepted date:
17-6-2014 18-7-2015
Please cite this article as: S. Revathi, S.R. Inabathini, J. Pal, Pressure and Temperature Sensor Based on a Dual Core Photonic Quasi-Crystal Fiber, Optik - International Journal for Light and Electron Optics (2015), http://dx.doi.org/10.1016/j.ijleo.2015.07.141 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Pressure and Temperature Sensor Based on a Dual Core Photonic Quasi-Crystal Fiber Corresponding Author:
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S.REVATHI, [email protected] Asst.Prof(S.G) School of Electronics Engineering VIT University Vellore, 632014. Tamil Nadu. Co-Authors:
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JATIN PAL School of Electronics Engineering VIT University Vellore
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Dr. SRINIVASA RAO INABATHINI , [email protected] Associate Prof School of Electronics Engineering VIT University Vellore
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Abstract—A new type of microstructured fiber known as dual core photonic quasi-crystal fiber is proposed for pressure and temperature sensor based on the mode coupling of the two fiber cores. The proposed fiber is highly birefringent and hence efficiently useful for sensing application. Temperature sensitivity of about 20pm/℃ is observed over the range of 0 to 1000 ℃ and a pressure
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sensitivity of -10.5nm/MPa is observed under a pressure of range 0 to 1000MPa.
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Keywords— Birefringence, Dual core, Finite element method (FEM), Mode Coupling, Perfectly matched layer (PML), Photonic quasi-crystal fiber (PQF), Pressure sensor, Temperature sensor.
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I. INTRODUCTION Optical sensors are analysed using physical parameters such as temperature, curvature, displacement, torsion, pressure, refractive index, electric field, and vibration. The measurement, monitoring, and control of these parameters are of great interest for many applications. Fiber sensors are used for this purpose, since they provide continuous measurement and analysis of key structural and environmental parameters under operating conditions [1, 2]. The microstructured fiber also known as photonic crystal fiber (PCF)[3] has attracted considerable attention because of their properties like high birefringence, high nonlinearity, high negative and flattened dispersion, etc. Unlike conventional optical fiber, PCF is a novel optical fiber which guides light in a single material with an ordered array of air holes running along its length. PCF guide light by two mechanisms i.e., index guiding mechanism [5] and photonic band gap mechanism [4-5]. An optical fiber with a quasi-periodic array of air holes in cladding known as photonic quasi-crystal fiber (PQF) [6].
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The proposed PQF comprises of both square and triangular lattice symmetry in cladding. Classical theory allows only 2, 3, 4 and 6 folds rotational symmetries but quasi-crystal introduced other order folds like pentagonal (5-folds), octagonal (8-folds), decagonal (10-folds) and dodecagonal (12-folds) according to their rotational symmetries. Compared to conventional optical fiber, PCF offers eminent features such as single-mode transmission, flexible dispersion [7-9] and high nonlinearity. In the future for optical networks, the PCF coupler is the most important component which is mainly based on PCF devices. Realization of multi-core specifically, dual-core PCFs [10-13] has enabled a new efficient way of designing PCF couplers, wavelength multiplexers and de-multiplexers, polarization splitters, narrow band pass filters, and sensors [13-25]. Dual-core PCF couplers have many advantages over the conventional optical couplers. They are more flexible to design, easy to make, and have shorter coupling length. Dual core PCF are used in sensing applications. PCFs are widely used in optical communications, supercontinuum sources, fiber lasers etc. Because of the remarkable flexibility in the structural design of the PCF compared with the conventional single mode fiber, fiber sensors based on PCFs have many advantages such as high sensitivity to gas sensing, refractive index sensing, biochemical sensing, and pressure sensing and temperature insensitivity to strain sensing. A pressure or a temperature sensor based on dual core PCF works on the principle of thermo elastic and thermo-optic effect. In this paper, we have proposed a dual core PQF with two fiber cores separated by an air hole in the crosssection of the fiber for pressure and temperature sensing. The working principle of pressure and temperature sensing is based on photoelastic effect/thermo-optic effect and mode coupling between the two fiber cores which is sensitive to pressure and temperature applied on the DC-PQF. The DC-PCF based
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pressure/temperature sensor has potential advantages of compact, good stability, low cost and capability for mass production. Fig. 1 Cross-sectional view of dual core PQF for, Λ=2µm, d=1.4 µm (a) with PML (b) with square and triangular lattice
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II. DUAL CORE PHOTONIC QUASI CRYSTAL FIBER The structure of proposed dual core PQF is shown in fig.1 where, Λ is the air hole pitch and ‘d’ is the diameter of the air holes. The PQF structure is enclosed by PML layer [12] shown in fig.1 (a). PML layer is drawn to absorb the scattered light in x and y direction. We have proposed a dual core PQF structure with pitch ,Λ of 2µm and air holes diameter , ‘d’ of 1.4 µm. The two cores are encircled by 12 air holes in the slab and separated by inner holes as shown in fig.1 (b) with square and triangular lattice symmetry. The proposed structure is 12-fold quasi photonic fiber. The material used is silica of refractive index 1.45 and the light is guided by the index guiding mechanism. The proposed dual core PQF can be fabricated by the stack and draw technique. Fig.2 shows the two dimensional plot of the confined light into the two cores at 1.55µm. Fig. 2 Two-Dimensional plot of the simulated structure Fig.3. (a) X-polarized (even mode), (b) X-polarized (odd mode)
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Two fiber cores inside the DC-PQF form two waveguides, which are independent due to small spacing between two cores accompanying with mode coupling. By using the FEM we tend to calculate the two basic modes i.e., the even mode and the odd mode of the DC-PQF. Fig.3 shows the electric field amplitude and the electric field vector of (a) the x-polarized even mode and (b) the x-polarized odd mode of the DC-PQF. III. OPTICAL PROPERTIES
(1)
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x B R e n eff R e n effy
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Birefringence- Birefringence is responsible for the phenomenon of double refraction, when a ray of light incident upon a birefringent material, it is split by polarization into two rays taking slightly different paths. The mode birefringence B can be given as
Where n exf f and n eyf f are the effective indices in the x- polarized and y-polarized directions, respectively. Fig. 4 Birefringence varying with wavelength for different d/Λ ratio.
Coupling length-According to the theory of mode coupling, the coupling of a dual-core fiber can be described by the use of the even and odd super modes [21], which are formed by modes of the individual cores and have symmetric and anti-symmetric field distributions, respectively. In dual-core PCFs the coupling length is defined as Li i , i x, y ( m) i i e o 2( ne noi ) (2) Where ei and oi are the propagation constants of i-polarized even and odd super modes i i and n e and n o are the effective refractive indices of i-polarized even and odd supermodes respectively. The effective index for x-polarized even mode at 1550nm is 1.407962 and 1.407612 for x-polarized odd mode. Coupling length calculated for x-polarized is 2.21mm.
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Fig.5 Coupling length of x and y-polarized light varying with diameter of air holes
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Coupling length of the fiber is dependent on the structural parameters of the fiber. Coupling length for both x and y polarized light is calculated. We have noticed that for small air holes the fiber achieves stronger mode coupling i.e., shorter coupling length but birefringence is low for smaller air holes in the structure and also the confinement loss is larger. If the birefringence is small then the coupling length for x and ypolarized light is almost same and hence it would become difficult to split the light. But we can see from fig.4 that for 1.4µm air hole diameter and 2µm air hole pitch (d/Λ=0.7), we achieve a high birefringence of 1.432x10-3 and the confinement loss is found to be 9x10-6 dB/km. High birefringence is due to asymmetry in structure.
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In fig.5 we can see ,coupling length for x-polarized light is smaller than the y-polarized light. Thus the proposed DC-PQF with air hole diameter of 1.4µm and 2µm air pitch can be used for practical applications. From the mode coupling of two fiber cores in the DC-PQF a transmission spectrum is observed. For a DCPQF with a length ( l ), assume that the power injected at input side in two fiber core A and core B is 1 and 0, respectively. According to the conventional coupled-mode theory [26], the output power on the output side of the fiber core-A and the fiber core-B of the DC-PQF is given by
an
P1 l , cos 2 ul cos 2 sin 2 ul
P2 l , sin sin ul 2
2
(3) (4)
(5)
The maximum power transferred at coupling length i.e., l CL / 2 s
(6)
Where,
u
2
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u | ne no | /
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d
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The maximum power transferred from core A to core B is P2 |max sin 2
k2
tan k /
(7) (8) (9)
For a straight DC-PQF, = 0, because the core A and core B are symmetrical in DC-PQF, thus we rewrite eq. 3, 4, 5 as
P1 l , cos2 ul P2 l , sin ul 2
P2 |max 1 Fig.6 Variation of
(10) (11) (12)
n for x-polarized light with wavelength
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Fig.6 shows the effective index difference between x-polarized even and odd mode, n ,is linearly varying with wavelength. Using n value, we plot the transmission of x-polarized light with wavelength. Fig.7 shows the transmission curve for x-polarized light for different length of fiber with 7cm and 12cm for temperature and pressure sensors respectively. Fig.7 Transmission curve for x-polarized light with different fiber length
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IV. TEMPERATURE/PRESSURE SENSOR BASED ON DC-PQF
n y n 0 C 1
x
C 2 (
y
C 2 (
y
z)
x
z)
(13)
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n x n 0 C 1
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When a fiber is subjected to air or hydrostatic pressure, the stress induced by the pressure changes the refractive index due to photoelastic effect. The refractive index of pure silica subjected to pressure is given by
(14)
an
Where, x , y and z are stress components and C 1 6 . 5 1 0 1 3 m 2 / N and C 2 4 .2 1 0 1 2 m 2 / N are the stress optic coefficients of fused silica [21]. Stress components of the silica can be obtained based on the FEM analysis of the optical fiber under the hydrostatic pressure. Young’s modulus of E S iO 7 3 .1 Gpa and 2
Poisson’s ratio of S iO 0 .1 7 for silica are used in our calculations. The applied air/hydrostatic pressure on DC-PQF results in the change of neo and hence there is a continuous change in the transmission spectrum. Thus a shift is noticed in the transmission spectrum of the DC-PQF based pressure sensor. As the pressure applied on the fiber, we see a deformation in its structure which is shown in fig.8.
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Fig 8 Displacement in the structure after applying pressure
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dn 1 0 5 (1 / O C ) dt
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. When temperature is applied on the fiber, the refractive index gets changed due to the well-known thermooptic effect. The thermo-optic coefficient of silica is (15)
and we have the refractive index of silica under temperature is n 1.45 T 10 5
(16) which indicates the effective index of the DC-PCF depends on the temperature. Hence as temperature changes neo also changes and results in shift of the transmission spectrum of DC-PQF based temperature sensor. The transmission spectra of DC-PQF based temperature sensor is shown in Fig.9. When a 7-cm DC-PQF is observed under the temperature of 0, 200, 400, 600, 800 and 1000 C, a shift in its transmission spectrum is noticed. The spectra is shifted to the longer wavelength because of the reduced value of neo for high temperature. As we increases the temperature of surrounding where the fiber is kept for observation, the transmission curve shifts towards the right side and gives the transmission spectra for overall operation. Fig.9 Transmission spectra for x-polarized light under different temperature
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Fig.10, shows the shift of peak wavelength when temperature is increased from 0 to 1000 C . The transmission curve is shifted to higher wavelength when temperature increases and this gives a linear graph as shown in figure 10. For every 200 C , there is a shift of 4nm noticed in transmission curve. Hence the sensitivity for temperature sensor is calculated as 20pm/ C for 7cm fiber. Fig.10 Peak wavelength shift under different temperature Fig.11 Birefringence varying with temperature at 1550nm
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As the temperature is increased , the fiber’s geometry and its properties are changed. Therefore we can notice some changes in birefringence when temperature is applied on the fiber. The change in birefringence with temperature at 1550nm is shown in fig.11. The changes are noticeable at 1550nm or higher wavelengths. We can see that birefringence is increasing linearly with increase in temperature from fig.11.
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Fig.12 shows the transmission spectrum of fiber with 12cm length under different applied pressure. When we increase the pressure we observe from the figure, the transmission curve for x-polarized light is shifting in left side or we can say the peak is shifting at lower wavelengths. Pressure applied is increased from 0 to 1000KPa. Fig.12 shows the transmission spectra for x-polarized light in PQF under different pressure.
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Fig.12 Transmission spectra under different pressure Fig.13 Peak wavelength shift under different pressure
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Fig.13 shows the shift of peak of transmission curve under different pressures. As we increases the pressure in both direction of PQF, the transmission curve shifts to lower wavelengths or decreases linearly as shown in above figure. With every increase in pressure of 200KPa, the peak of transmission curve is shifted to lower wavelength of 2.1nm. The sensitivity calculated is of -10.5nm/MPa.
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Fig.14 Birefringence varying with temperature at 1550nm
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Fig.14 shows the changes in birefringence with increase in applied pressure at 1550nm. As we can see from above shown figure that when applied pressure increases from 0 to 1000 KPa, the birefringence decreases linearly at 1550nm. V. CONCLUSION
In this paper, we have designed a DC-PQF as a pressure sensor which has a little temperature cross sensitivity. The sensitivity calculated for DC-PQF pressure sensor is -10.5nm/MPa which is quite large than given in ref.[21]. And temperature sensitivity is 20pm/ O C which is also small than given in ref.[21]. Though the fiber length of our sensor is larger than in [21] but the sensitivity is high. The proposed sensor can be used in tsunami sensing, because of little temperature sensitivity and high pressure sensitivity. Therefore we can use this fiber at the bottom of ocean as a practical application. REFERENCES
[1]
H. N. Li, D. S. Li, and G. B. Song, Recent applications of fiber optic sensors to health monitoring in civil engineering. Engineering Structures, vol. 26, no. 11, pp. 1647–1657, 2004.
[2]
C. Sonnenfeld, S. Sulejmani, T. Geernaert et al., Microstructured optical fiber sensors embedded in a laminate composite for smart material applications, Sensors, vol. 11, no. 3, pp. 2566–2579, 2011.
[3]
Knight and Russell, Photonic crystal fibers: New way to guide light, Science 296, 276-277 (2002).
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Limin Xiao, Wei Jin, M.S. Demokan, Photonic crystal fibers confining light by both index-guiding and bandgap-guiding: hybrid PCFs, Optical society of America, Vol. 15, No. 24, 26 November 2007, Optics express 15637
[5]
Knight, Broeng, Birks, T A., and Russell, P. St., Photonic band gap guidance in optical fibers, Science 282, 1476-1478 (1998).
[6]
Ritapa Bhattacharjee, K. Senthilnathan, S. Sivabalan, P. Ramesh Babu Exploring a photonic quasi-crystal fiber for enhancing the efficiency of second harmonic generation: Modelling and analysis, Optical Materials (2013)
[7]
Soan Kim and Chul-SikKee, Dispersion properties of dual-core photonic quasi crystal fiber”, Optical Society of America, Vol. 17, No. 18 , 31 August 2009, Optics express 15885
[8]
RajniIdiwal,RekhaMehra, Manish Tiwari, Photonic Crystal Fiber as Low Loss Dispersion Flattened Fiber and Ultra-Low Confinement Loss, International Journal of Emerging Technology and Advanced Engineering (ISSN 2250-2459, Volume 1, Issue 2, December 2011)
[9]
Albert Ferrando, Enrique Silvestre, and Pedro Andres, Designing the properties of dispersion-flattened photonic crystal fibers, Optical Society of America, Vol. 9, No. 13, 17 December 2001, Optics express 687
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[4]
[10] José R. Salgueiro and Yuri S. Kivshar, Nonlinear dual-core photonic crystal fiber coupler, Optical Society of America, Vol. 30, No. 14, July 15, 2005, Optics express
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[11] Bo Fu, Shu-Guang Li, Yan-Yan Yao, Lei Zhang, Mei-Yan Zhang, Design of two kinds of dual-core high birefringence and high coupling degree photonic crystal fibers, Optics Communications 283 (2010) 4064–4068 [12] Feifei Shi, Yun Wu, Meicheng Li, Yu Zhao, and Liancheng Zhao, Highly birefringent two mode photonic crystal fiber with non-zero flattened dispersion, Vol.3, No.6, December, 2011 IEEE
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[13] Zhengyong Liu, Ming-Leung Vincent Tse, Chuang Wu, Daru Chen, Chao Lu, and Hwa-Yaw Tam, Intermodal coupling of supermodes in a twincore photonic crystal fiber and its application as a pressure sensor, Optical Society of America, Vol. 20, No. 19, 10 September 2012 Optics express 21749
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[14] R.T.Jadhav, Fiber optic based pressure sensor using comsol multiphysics software, International Archive of Applied Sciences and Technology Volume 3, March 2012, pp40 – 45 [15] Daru Chen, Gufeng Hu, and Lingxia Chen, Dual-Core Photonic Crystal Fiber for Hydrostatic Pressure Sensing, IEEE Photonics Technology letters, Vol 23, no.24, December 15, 2011
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[16] F. C. Fávero, S. M. M. Quintero, C. Martelli et al., Hydrostatic pressure sensing with high birefringence photonic crystal fibers, Sensors, vol. 10, no. 11, pp. 9698–9711, 2010.
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[17] Y. S. Shinde and H. K. Gahir, Dynamic pressure sensing study using photonic crystal fiber application of tsunami sensing, IEEE Photonics Technology Letters, vol 20, no.4, pp.279-281, 2008.
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[18] H. Y. Fu, C. Wu, M. L. V. Tse et al., High pressure sensor based on photonic crystal fiber for downhole application, Applied Optics, vol. 49, no. 14, pp. 2639–2643, 2010. [19] T. Nasilowski, T. Martynkien, G. Statkiewicz et al., Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry, Applied Physics B, vol. 81, no. 2-3, pp. 325–331,2005. [20] T. Martynkien, M. Szpulak, G. Statkiewicz et al., Measurements of sensitivity to hydrostatic pressure and temperature in highly birefringent photonic crystal fibers, Optical and Quantum Electronics, vol. 39, no. 4–6, pp. 481–489, 2007. [21] DaruChen,a,b, GufengHUa,b, Lingxia Chena Pressure/temperature based on dual core photonic crystal fiber, (2011)SPIE-OSA-IEEE CCC code: 0277-786X/11/$18 . doi: 10.1117/12.904029 [22] Y. Geng, X. Li, X. Tan, Y. Deng, and Y. Yu, Sensitivity-enhanced high-temperature sensing using all-solid photonic bandgap fiber modal interference, Applied Optics, vol. 50, no. 4, pp. 468–472, 2011 [23] W. Qian, C. L. Zhao, S. He et al., High-sensitivity temperature sensor based on an alcohol-filled photonic crystal fiber loop mirror, Optics Letters, vol. 36, no. 9, pp. 1548–1550, 2011. [24] B. Larrion, M. Hernandez, F. J. Arregui, J. Goicoechea, J. Bravo, and I. R. Matias, Photonic crystal fiber temperature sensor based on quantum dot nanocoatings, Journal of Sensors, vol. 2009, Article ID 932471, 6 pages, 2009. [25] A. Bozolan, R. M. Gerosa, C. J. S. de Matos, and M. A. Romero, Temperature sensing using colloidal-core photonic crystal fiber, IEEE Sensors Journal, vol. 12, no. 1, pp. 195–200, 2012. [26] Huang, W. P., Coupled-mode theory for optical waveguide, an overview, J. Optical Society of America ll, 963983,(1994).
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(b)
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(a)
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Fig. 1 Cross-sectional view of dual core PQF for, Λ=2µm, d=1.4 µm (a) with PML (b) with square and triangular lattice
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Fig. 2 Two-Dimensional plot of the simulated structure
Fig.3. (a) X-polarized (even mode), (b) X-polarized (odd mode)
Page 8 of 12
-3
4
Birefringence for d(varied) and p(constant)
x 10
d/=0.4 3.5
d/=0.5
3
d/=0.6 d/=0.7 d/=0.8
e c n e g ni rf er i B
d/=0.9
2.5 2 1.5
ip t
1 0.5 0 0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
cr
Wavelength(µm)
4
4.5
Coupling length for d(varied) and p(constant)
x 10
=CLx =CLy
4
an
3.5
) m µ( ht g n el g nil p u o C
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Fig. 4 Birefringence varying with wavelength for different d/Λ ratio.
3 2.5
M
2 1.5 1
0 0.8
0.9
d
0.5
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Diameter of air holes(µm)
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Fig.5 Coupling length of x and y-polarized light varying with diameter of air holes -4
3.7
x 10
n versus wavelength
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3.65 3.6
3.55
n
3.5
3.45 3.4
3.35
3.3 1530
1535
1540
1545
1550
1555
1560
1565
1570
Wavelength(nm)
Fig.6 Variation of
n for x-polarized light with wavelength
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1
0.6 0.4 0.2 0 1530
1535
1540
1545
1550
1555
1560
1565
1570
Wavelength(nm)
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n oi ss i ms na r T
=12 cm
=7 cm
0.8
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Fig.7 Transmission curve for x-polarized light with different fiber length
0C
1000C
te
1 0.9 0.8
0.6 0.5 0.4 0.3 0.2 0.1 0 1520
Ac ce p
0.7
n oi ss i ms na r T
d
Fig 8 Displacement in the structure after applying pressure
1530
1540
1550
1560
1570
1580
Wavelength(nm)
Fig.9 Transmission spectra for x-polarized light under different temperature
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Peak wavelength of the temperature around 1550nm 1555
1550
1545
ip t
1540
1535
1530
0
100
200
300
400
500
600
700
800
900
cr
) m n( k a e p ht g n el e v a W
1000
Temperature(C)
-3
1.446
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Fig.10 Peak wavelength shift under different temperature Birefringence v/s temperature 1550nm
x 10
an
1.444
1.442
M
1.44
1.438
d
1.436
1.432
0
100
200
300
400
500
600
te
1.434
700
Temperature(C)
800
900
1000
Fig.11 Birefringence varying with temperature at 1550nm
Ac ce p
e c n e g ni rf er i B
0KPa
1000KPa
1
0.9 0.8 0.7
n oi ss i ms na r T
0.6 0.5 0.4 0.3 0.2 0.1
0 1530
1535
1540
1545
1550
1555
1560
1565
1570
Wavelength(nm) Fig.12 Transmission spectra under different pressure
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Peak wavelength of the pressure around 1550nm 1558
1556
1554
1552
1550
1548
1546
0
100
200
300
400
500
600
700
800
900
1000
Pressure(KPa)
-3
x 10
Change in Birefringence v/s pressure at 1550nm
us
1.44
cr
Fig.13 Peak wavelength shift under different pressure
1.435
an
1.43
1.425
1.42
M
1.415
1.41
100
200
300
400
500
600
Pressure(KPa)
700
800
900
1000
d
0
Fig.14 Birefringence varying with temperature at 1550nm
te
1.405
Ac ce p
ec n eg ni rf er i B
ip t
) m n( k a e p ht g n el e v a W
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S0030-4026(15)00694-4 http://dx.doi.org/doi:10.1016/j.ijleo.2015.07.141 IJLEO 55857
To appear in: Received date: Accepted date:
17-6-2014 18-7-2015
Please cite this article as: S. Revathi, S.R. Inabathini, J. Pal, Pressure and Temperature Sensor Based on a Dual Core Photonic Quasi-Crystal Fiber, Optik - International Journal for Light and Electron Optics (2015), http://dx.doi.org/10.1016/j.ijleo.2015.07.141 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Pressure and Temperature Sensor Based on a Dual Core Photonic Quasi-Crystal Fiber Corresponding Author:
us
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S.REVATHI, [email protected] Asst.Prof(S.G) School of Electronics Engineering VIT University Vellore, 632014. Tamil Nadu. Co-Authors:
M d
te
Ac ce p
JATIN PAL School of Electronics Engineering VIT University Vellore
an
Dr. SRINIVASA RAO INABATHINI , [email protected] Associate Prof School of Electronics Engineering VIT University Vellore
Page 1 of 12
Abstract—A new type of microstructured fiber known as dual core photonic quasi-crystal fiber is proposed for pressure and temperature sensor based on the mode coupling of the two fiber cores. The proposed fiber is highly birefringent and hence efficiently useful for sensing application. Temperature sensitivity of about 20pm/℃ is observed over the range of 0 to 1000 ℃ and a pressure
ip t
sensitivity of -10.5nm/MPa is observed under a pressure of range 0 to 1000MPa.
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Keywords— Birefringence, Dual core, Finite element method (FEM), Mode Coupling, Perfectly matched layer (PML), Photonic quasi-crystal fiber (PQF), Pressure sensor, Temperature sensor.
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I. INTRODUCTION Optical sensors are analysed using physical parameters such as temperature, curvature, displacement, torsion, pressure, refractive index, electric field, and vibration. The measurement, monitoring, and control of these parameters are of great interest for many applications. Fiber sensors are used for this purpose, since they provide continuous measurement and analysis of key structural and environmental parameters under operating conditions [1, 2]. The microstructured fiber also known as photonic crystal fiber (PCF)[3] has attracted considerable attention because of their properties like high birefringence, high nonlinearity, high negative and flattened dispersion, etc. Unlike conventional optical fiber, PCF is a novel optical fiber which guides light in a single material with an ordered array of air holes running along its length. PCF guide light by two mechanisms i.e., index guiding mechanism [5] and photonic band gap mechanism [4-5]. An optical fiber with a quasi-periodic array of air holes in cladding known as photonic quasi-crystal fiber (PQF) [6].
Ac ce p
te
d
The proposed PQF comprises of both square and triangular lattice symmetry in cladding. Classical theory allows only 2, 3, 4 and 6 folds rotational symmetries but quasi-crystal introduced other order folds like pentagonal (5-folds), octagonal (8-folds), decagonal (10-folds) and dodecagonal (12-folds) according to their rotational symmetries. Compared to conventional optical fiber, PCF offers eminent features such as single-mode transmission, flexible dispersion [7-9] and high nonlinearity. In the future for optical networks, the PCF coupler is the most important component which is mainly based on PCF devices. Realization of multi-core specifically, dual-core PCFs [10-13] has enabled a new efficient way of designing PCF couplers, wavelength multiplexers and de-multiplexers, polarization splitters, narrow band pass filters, and sensors [13-25]. Dual-core PCF couplers have many advantages over the conventional optical couplers. They are more flexible to design, easy to make, and have shorter coupling length. Dual core PCF are used in sensing applications. PCFs are widely used in optical communications, supercontinuum sources, fiber lasers etc. Because of the remarkable flexibility in the structural design of the PCF compared with the conventional single mode fiber, fiber sensors based on PCFs have many advantages such as high sensitivity to gas sensing, refractive index sensing, biochemical sensing, and pressure sensing and temperature insensitivity to strain sensing. A pressure or a temperature sensor based on dual core PCF works on the principle of thermo elastic and thermo-optic effect. In this paper, we have proposed a dual core PQF with two fiber cores separated by an air hole in the crosssection of the fiber for pressure and temperature sensing. The working principle of pressure and temperature sensing is based on photoelastic effect/thermo-optic effect and mode coupling between the two fiber cores which is sensitive to pressure and temperature applied on the DC-PQF. The DC-PCF based
Page 2 of 12
pressure/temperature sensor has potential advantages of compact, good stability, low cost and capability for mass production. Fig. 1 Cross-sectional view of dual core PQF for, Λ=2µm, d=1.4 µm (a) with PML (b) with square and triangular lattice
us
cr
ip t
II. DUAL CORE PHOTONIC QUASI CRYSTAL FIBER The structure of proposed dual core PQF is shown in fig.1 where, Λ is the air hole pitch and ‘d’ is the diameter of the air holes. The PQF structure is enclosed by PML layer [12] shown in fig.1 (a). PML layer is drawn to absorb the scattered light in x and y direction. We have proposed a dual core PQF structure with pitch ,Λ of 2µm and air holes diameter , ‘d’ of 1.4 µm. The two cores are encircled by 12 air holes in the slab and separated by inner holes as shown in fig.1 (b) with square and triangular lattice symmetry. The proposed structure is 12-fold quasi photonic fiber. The material used is silica of refractive index 1.45 and the light is guided by the index guiding mechanism. The proposed dual core PQF can be fabricated by the stack and draw technique. Fig.2 shows the two dimensional plot of the confined light into the two cores at 1.55µm. Fig. 2 Two-Dimensional plot of the simulated structure Fig.3. (a) X-polarized (even mode), (b) X-polarized (odd mode)
M
an
Two fiber cores inside the DC-PQF form two waveguides, which are independent due to small spacing between two cores accompanying with mode coupling. By using the FEM we tend to calculate the two basic modes i.e., the even mode and the odd mode of the DC-PQF. Fig.3 shows the electric field amplitude and the electric field vector of (a) the x-polarized even mode and (b) the x-polarized odd mode of the DC-PQF. III. OPTICAL PROPERTIES
(1)
Ac ce p
x B R e n eff R e n effy
te
d
Birefringence- Birefringence is responsible for the phenomenon of double refraction, when a ray of light incident upon a birefringent material, it is split by polarization into two rays taking slightly different paths. The mode birefringence B can be given as
Where n exf f and n eyf f are the effective indices in the x- polarized and y-polarized directions, respectively. Fig. 4 Birefringence varying with wavelength for different d/Λ ratio.
Coupling length-According to the theory of mode coupling, the coupling of a dual-core fiber can be described by the use of the even and odd super modes [21], which are formed by modes of the individual cores and have symmetric and anti-symmetric field distributions, respectively. In dual-core PCFs the coupling length is defined as Li i , i x, y ( m) i i e o 2( ne noi ) (2) Where ei and oi are the propagation constants of i-polarized even and odd super modes i i and n e and n o are the effective refractive indices of i-polarized even and odd supermodes respectively. The effective index for x-polarized even mode at 1550nm is 1.407962 and 1.407612 for x-polarized odd mode. Coupling length calculated for x-polarized is 2.21mm.
Page 3 of 12
Fig.5 Coupling length of x and y-polarized light varying with diameter of air holes
ip t
Coupling length of the fiber is dependent on the structural parameters of the fiber. Coupling length for both x and y polarized light is calculated. We have noticed that for small air holes the fiber achieves stronger mode coupling i.e., shorter coupling length but birefringence is low for smaller air holes in the structure and also the confinement loss is larger. If the birefringence is small then the coupling length for x and ypolarized light is almost same and hence it would become difficult to split the light. But we can see from fig.4 that for 1.4µm air hole diameter and 2µm air hole pitch (d/Λ=0.7), we achieve a high birefringence of 1.432x10-3 and the confinement loss is found to be 9x10-6 dB/km. High birefringence is due to asymmetry in structure.
us
cr
In fig.5 we can see ,coupling length for x-polarized light is smaller than the y-polarized light. Thus the proposed DC-PQF with air hole diameter of 1.4µm and 2µm air pitch can be used for practical applications. From the mode coupling of two fiber cores in the DC-PQF a transmission spectrum is observed. For a DCPQF with a length ( l ), assume that the power injected at input side in two fiber core A and core B is 1 and 0, respectively. According to the conventional coupled-mode theory [26], the output power on the output side of the fiber core-A and the fiber core-B of the DC-PQF is given by
an
P1 l , cos 2 ul cos 2 sin 2 ul
P2 l , sin sin ul 2
2
(3) (4)
(5)
The maximum power transferred at coupling length i.e., l CL / 2 s
(6)
Where,
u
2
Ac ce p
u | ne no | /
te
d
M
The maximum power transferred from core A to core B is P2 |max sin 2
k2
tan k /
(7) (8) (9)
For a straight DC-PQF, = 0, because the core A and core B are symmetrical in DC-PQF, thus we rewrite eq. 3, 4, 5 as
P1 l , cos2 ul P2 l , sin ul 2
P2 |max 1 Fig.6 Variation of
(10) (11) (12)
n for x-polarized light with wavelength
Page 4 of 12
Fig.6 shows the effective index difference between x-polarized even and odd mode, n ,is linearly varying with wavelength. Using n value, we plot the transmission of x-polarized light with wavelength. Fig.7 shows the transmission curve for x-polarized light for different length of fiber with 7cm and 12cm for temperature and pressure sensors respectively. Fig.7 Transmission curve for x-polarized light with different fiber length
ip t
IV. TEMPERATURE/PRESSURE SENSOR BASED ON DC-PQF
n y n 0 C 1
x
C 2 (
y
C 2 (
y
z)
x
z)
(13)
us
n x n 0 C 1
cr
When a fiber is subjected to air or hydrostatic pressure, the stress induced by the pressure changes the refractive index due to photoelastic effect. The refractive index of pure silica subjected to pressure is given by
(14)
an
Where, x , y and z are stress components and C 1 6 . 5 1 0 1 3 m 2 / N and C 2 4 .2 1 0 1 2 m 2 / N are the stress optic coefficients of fused silica [21]. Stress components of the silica can be obtained based on the FEM analysis of the optical fiber under the hydrostatic pressure. Young’s modulus of E S iO 7 3 .1 Gpa and 2
Poisson’s ratio of S iO 0 .1 7 for silica are used in our calculations. The applied air/hydrostatic pressure on DC-PQF results in the change of neo and hence there is a continuous change in the transmission spectrum. Thus a shift is noticed in the transmission spectrum of the DC-PQF based pressure sensor. As the pressure applied on the fiber, we see a deformation in its structure which is shown in fig.8.
M
2
d
Fig 8 Displacement in the structure after applying pressure
Ac ce p
dn 1 0 5 (1 / O C ) dt
te
. When temperature is applied on the fiber, the refractive index gets changed due to the well-known thermooptic effect. The thermo-optic coefficient of silica is (15)
and we have the refractive index of silica under temperature is n 1.45 T 10 5
(16) which indicates the effective index of the DC-PCF depends on the temperature. Hence as temperature changes neo also changes and results in shift of the transmission spectrum of DC-PQF based temperature sensor. The transmission spectra of DC-PQF based temperature sensor is shown in Fig.9. When a 7-cm DC-PQF is observed under the temperature of 0, 200, 400, 600, 800 and 1000 C, a shift in its transmission spectrum is noticed. The spectra is shifted to the longer wavelength because of the reduced value of neo for high temperature. As we increases the temperature of surrounding where the fiber is kept for observation, the transmission curve shifts towards the right side and gives the transmission spectra for overall operation. Fig.9 Transmission spectra for x-polarized light under different temperature
Page 5 of 12
Fig.10, shows the shift of peak wavelength when temperature is increased from 0 to 1000 C . The transmission curve is shifted to higher wavelength when temperature increases and this gives a linear graph as shown in figure 10. For every 200 C , there is a shift of 4nm noticed in transmission curve. Hence the sensitivity for temperature sensor is calculated as 20pm/ C for 7cm fiber. Fig.10 Peak wavelength shift under different temperature Fig.11 Birefringence varying with temperature at 1550nm
cr
ip t
As the temperature is increased , the fiber’s geometry and its properties are changed. Therefore we can notice some changes in birefringence when temperature is applied on the fiber. The change in birefringence with temperature at 1550nm is shown in fig.11. The changes are noticeable at 1550nm or higher wavelengths. We can see that birefringence is increasing linearly with increase in temperature from fig.11.
us
Fig.12 shows the transmission spectrum of fiber with 12cm length under different applied pressure. When we increase the pressure we observe from the figure, the transmission curve for x-polarized light is shifting in left side or we can say the peak is shifting at lower wavelengths. Pressure applied is increased from 0 to 1000KPa. Fig.12 shows the transmission spectra for x-polarized light in PQF under different pressure.
an
Fig.12 Transmission spectra under different pressure Fig.13 Peak wavelength shift under different pressure
M
Fig.13 shows the shift of peak of transmission curve under different pressures. As we increases the pressure in both direction of PQF, the transmission curve shifts to lower wavelengths or decreases linearly as shown in above figure. With every increase in pressure of 200KPa, the peak of transmission curve is shifted to lower wavelength of 2.1nm. The sensitivity calculated is of -10.5nm/MPa.
d
Fig.14 Birefringence varying with temperature at 1550nm
Ac ce p
te
Fig.14 shows the changes in birefringence with increase in applied pressure at 1550nm. As we can see from above shown figure that when applied pressure increases from 0 to 1000 KPa, the birefringence decreases linearly at 1550nm. V. CONCLUSION
In this paper, we have designed a DC-PQF as a pressure sensor which has a little temperature cross sensitivity. The sensitivity calculated for DC-PQF pressure sensor is -10.5nm/MPa which is quite large than given in ref.[21]. And temperature sensitivity is 20pm/ O C which is also small than given in ref.[21]. Though the fiber length of our sensor is larger than in [21] but the sensitivity is high. The proposed sensor can be used in tsunami sensing, because of little temperature sensitivity and high pressure sensitivity. Therefore we can use this fiber at the bottom of ocean as a practical application. REFERENCES
[1]
H. N. Li, D. S. Li, and G. B. Song, Recent applications of fiber optic sensors to health monitoring in civil engineering. Engineering Structures, vol. 26, no. 11, pp. 1647–1657, 2004.
[2]
C. Sonnenfeld, S. Sulejmani, T. Geernaert et al., Microstructured optical fiber sensors embedded in a laminate composite for smart material applications, Sensors, vol. 11, no. 3, pp. 2566–2579, 2011.
[3]
Knight and Russell, Photonic crystal fibers: New way to guide light, Science 296, 276-277 (2002).
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Limin Xiao, Wei Jin, M.S. Demokan, Photonic crystal fibers confining light by both index-guiding and bandgap-guiding: hybrid PCFs, Optical society of America, Vol. 15, No. 24, 26 November 2007, Optics express 15637
[5]
Knight, Broeng, Birks, T A., and Russell, P. St., Photonic band gap guidance in optical fibers, Science 282, 1476-1478 (1998).
[6]
Ritapa Bhattacharjee, K. Senthilnathan, S. Sivabalan, P. Ramesh Babu Exploring a photonic quasi-crystal fiber for enhancing the efficiency of second harmonic generation: Modelling and analysis, Optical Materials (2013)
[7]
Soan Kim and Chul-SikKee, Dispersion properties of dual-core photonic quasi crystal fiber”, Optical Society of America, Vol. 17, No. 18 , 31 August 2009, Optics express 15885
[8]
RajniIdiwal,RekhaMehra, Manish Tiwari, Photonic Crystal Fiber as Low Loss Dispersion Flattened Fiber and Ultra-Low Confinement Loss, International Journal of Emerging Technology and Advanced Engineering (ISSN 2250-2459, Volume 1, Issue 2, December 2011)
[9]
Albert Ferrando, Enrique Silvestre, and Pedro Andres, Designing the properties of dispersion-flattened photonic crystal fibers, Optical Society of America, Vol. 9, No. 13, 17 December 2001, Optics express 687
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[10] José R. Salgueiro and Yuri S. Kivshar, Nonlinear dual-core photonic crystal fiber coupler, Optical Society of America, Vol. 30, No. 14, July 15, 2005, Optics express
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[11] Bo Fu, Shu-Guang Li, Yan-Yan Yao, Lei Zhang, Mei-Yan Zhang, Design of two kinds of dual-core high birefringence and high coupling degree photonic crystal fibers, Optics Communications 283 (2010) 4064–4068 [12] Feifei Shi, Yun Wu, Meicheng Li, Yu Zhao, and Liancheng Zhao, Highly birefringent two mode photonic crystal fiber with non-zero flattened dispersion, Vol.3, No.6, December, 2011 IEEE
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[13] Zhengyong Liu, Ming-Leung Vincent Tse, Chuang Wu, Daru Chen, Chao Lu, and Hwa-Yaw Tam, Intermodal coupling of supermodes in a twincore photonic crystal fiber and its application as a pressure sensor, Optical Society of America, Vol. 20, No. 19, 10 September 2012 Optics express 21749
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[14] R.T.Jadhav, Fiber optic based pressure sensor using comsol multiphysics software, International Archive of Applied Sciences and Technology Volume 3, March 2012, pp40 – 45 [15] Daru Chen, Gufeng Hu, and Lingxia Chen, Dual-Core Photonic Crystal Fiber for Hydrostatic Pressure Sensing, IEEE Photonics Technology letters, Vol 23, no.24, December 15, 2011
d
[16] F. C. Fávero, S. M. M. Quintero, C. Martelli et al., Hydrostatic pressure sensing with high birefringence photonic crystal fibers, Sensors, vol. 10, no. 11, pp. 9698–9711, 2010.
te
[17] Y. S. Shinde and H. K. Gahir, Dynamic pressure sensing study using photonic crystal fiber application of tsunami sensing, IEEE Photonics Technology Letters, vol 20, no.4, pp.279-281, 2008.
Ac ce p
[18] H. Y. Fu, C. Wu, M. L. V. Tse et al., High pressure sensor based on photonic crystal fiber for downhole application, Applied Optics, vol. 49, no. 14, pp. 2639–2643, 2010. [19] T. Nasilowski, T. Martynkien, G. Statkiewicz et al., Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry, Applied Physics B, vol. 81, no. 2-3, pp. 325–331,2005. [20] T. Martynkien, M. Szpulak, G. Statkiewicz et al., Measurements of sensitivity to hydrostatic pressure and temperature in highly birefringent photonic crystal fibers, Optical and Quantum Electronics, vol. 39, no. 4–6, pp. 481–489, 2007. [21] DaruChen,a,b, GufengHUa,b, Lingxia Chena Pressure/temperature based on dual core photonic crystal fiber, (2011)SPIE-OSA-IEEE CCC code: 0277-786X/11/$18 . doi: 10.1117/12.904029 [22] Y. Geng, X. Li, X. Tan, Y. Deng, and Y. Yu, Sensitivity-enhanced high-temperature sensing using all-solid photonic bandgap fiber modal interference, Applied Optics, vol. 50, no. 4, pp. 468–472, 2011 [23] W. Qian, C. L. Zhao, S. He et al., High-sensitivity temperature sensor based on an alcohol-filled photonic crystal fiber loop mirror, Optics Letters, vol. 36, no. 9, pp. 1548–1550, 2011. [24] B. Larrion, M. Hernandez, F. J. Arregui, J. Goicoechea, J. Bravo, and I. R. Matias, Photonic crystal fiber temperature sensor based on quantum dot nanocoatings, Journal of Sensors, vol. 2009, Article ID 932471, 6 pages, 2009. [25] A. Bozolan, R. M. Gerosa, C. J. S. de Matos, and M. A. Romero, Temperature sensing using colloidal-core photonic crystal fiber, IEEE Sensors Journal, vol. 12, no. 1, pp. 195–200, 2012. [26] Huang, W. P., Coupled-mode theory for optical waveguide, an overview, J. Optical Society of America ll, 963983,(1994).
Page 7 of 12
ip t cr
(b)
us
(a)
te
d
M
an
Fig. 1 Cross-sectional view of dual core PQF for, Λ=2µm, d=1.4 µm (a) with PML (b) with square and triangular lattice
Ac ce p
Fig. 2 Two-Dimensional plot of the simulated structure
Fig.3. (a) X-polarized (even mode), (b) X-polarized (odd mode)
Page 8 of 12
-3
4
Birefringence for d(varied) and p(constant)
x 10
d/=0.4 3.5
d/=0.5
3
d/=0.6 d/=0.7 d/=0.8
e c n e g ni rf er i B
d/=0.9
2.5 2 1.5
ip t
1 0.5 0 0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
cr
Wavelength(µm)
4
4.5
Coupling length for d(varied) and p(constant)
x 10
=CLx =CLy
4
an
3.5
) m µ( ht g n el g nil p u o C
us
Fig. 4 Birefringence varying with wavelength for different d/Λ ratio.
3 2.5
M
2 1.5 1
0 0.8
0.9
d
0.5
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Diameter of air holes(µm)
te
Fig.5 Coupling length of x and y-polarized light varying with diameter of air holes -4
3.7
x 10
n versus wavelength
Ac ce p
3.65 3.6
3.55
n
3.5
3.45 3.4
3.35
3.3 1530
1535
1540
1545
1550
1555
1560
1565
1570
Wavelength(nm)
Fig.6 Variation of
n for x-polarized light with wavelength
Page 9 of 12
1
0.6 0.4 0.2 0 1530
1535
1540
1545
1550
1555
1560
1565
1570
Wavelength(nm)
ip t
n oi ss i ms na r T
=12 cm
=7 cm
0.8
M
an
us
cr
Fig.7 Transmission curve for x-polarized light with different fiber length
0C
1000C
te
1 0.9 0.8
0.6 0.5 0.4 0.3 0.2 0.1 0 1520
Ac ce p
0.7
n oi ss i ms na r T
d
Fig 8 Displacement in the structure after applying pressure
1530
1540
1550
1560
1570
1580
Wavelength(nm)
Fig.9 Transmission spectra for x-polarized light under different temperature
Page 10 of 12
Peak wavelength of the temperature around 1550nm 1555
1550
1545
ip t
1540
1535
1530
0
100
200
300
400
500
600
700
800
900
cr
) m n( k a e p ht g n el e v a W
1000
Temperature(C)
-3
1.446
us
Fig.10 Peak wavelength shift under different temperature Birefringence v/s temperature 1550nm
x 10
an
1.444
1.442
M
1.44
1.438
d
1.436
1.432
0
100
200
300
400
500
600
te
1.434
700
Temperature(C)
800
900
1000
Fig.11 Birefringence varying with temperature at 1550nm
Ac ce p
e c n e g ni rf er i B
0KPa
1000KPa
1
0.9 0.8 0.7
n oi ss i ms na r T
0.6 0.5 0.4 0.3 0.2 0.1
0 1530
1535
1540
1545
1550
1555
1560
1565
1570
Wavelength(nm) Fig.12 Transmission spectra under different pressure
Page 11 of 12
Peak wavelength of the pressure around 1550nm 1558
1556
1554
1552
1550
1548
1546
0
100
200
300
400
500
600
700
800
900
1000
Pressure(KPa)
-3
x 10
Change in Birefringence v/s pressure at 1550nm
us
1.44
cr
Fig.13 Peak wavelength shift under different pressure
1.435
an
1.43
1.425
1.42
M
1.415
1.41
100
200
300
400
500
600
Pressure(KPa)
700
800
900
1000
d
0
Fig.14 Birefringence varying with temperature at 1550nm
te
1.405
Ac ce p
ec n eg ni rf er i B
ip t
) m n( k a e p ht g n el e v a W
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