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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 11 — May. 21, 2012
  • pp: 12111–12118
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Photonic crystal self-collimation sensor

Yufei Wang, Hailing Wang, Qikun Xue, and Wanhua Zheng  »View Author Affiliations


Optics Express, Vol. 20, Issue 11, pp. 12111-12118 (2012)
http://dx.doi.org/10.1364/OE.20.012111


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Abstract

A novel refractive index sensor based on the two dimensional photonic crystal folded Michelson interferometer employing the self-collimation effect is proposed and its performances are theoretically investigated. Two sensing areas are included in the sensor. Simulation results indicate the branch area is suitable for the small index variety range and fine detection, whereas the reflector area prone to the large index change range and coarse detection. Because of no defect waveguides and no crosstalk of signal, the sensor is desirable to perform monolithic integrated, low-cost, label-free real-time parallel sensing. In addition, a flexible design of self-collimation sensors array is demonstrated.

© 2012 OSA

1. Introduction

Optical sensors based on total reflection, such as Mach-Zehnder interferometer sensors of optical fibre type [1

1. A. D. Kersey, T. A. Berkoff, and W. W. Morey, “High-resolution fibre-grating based strain sensor with interferometric wavelength-shift detection,” Electron. Lett. 28(3), 236–238 (1992). [CrossRef]

, 2

2. S. J. Spammer, P. L. Swart, and A. Booysen, “Interferometric distributed optical-fiber sensor,” Appl. Opt. 35(22), 4522–4525 (1996). [CrossRef] [PubMed]

] or light waveguide type [3

3. B. Drapp, J. Piehler, A. Brecht, G. Gauglitz, B. J. Luff, J. S. Wilkinson, and J. Ingenhoff, “Integrated optical Mach-Zehnder interferometers as simazine immunoprobes,” Sens. Actuators B Chem. 39(1-3), 277–282 (1997). [CrossRef]

, 4

4. R. G. Heideman and P. V. Lambeck, “Remote opto-chemical sensing with extreme sensitivity: design, fabrication and performance of a pigtailed integrated optical phase-modulated Mach-Zehnder interferometer system,” Sens. Actuators B Chem. 61(1-3), 100–127 (1999). [CrossRef]

], always cannot meet practical demands: small, high sensitivity, cheap and low power consumption. Photonic crystal (PhC) sensors, as a new type of sensors at present, are approximately three orders of magnitude less than commercial integrated-optic sensors. They have different types, such as the point-defect type [5

5. M. Lončar, A. Scherer, and Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82(26), 4648–4650 (2003). [CrossRef]

, 6

6. S. Chakravarty, J. Topol’ančik, P. Bhattacharya, S. Chakrabarti, Y. Kang, and M. E. Meyerhoff, “Ion detection with photonic crystal microcavities,” Opt. Lett. 30(19), 2578–2580 (2005). [CrossRef] [PubMed]

], the line-defect type [7

7. J. Topol’ančik, P. Bhattacharya, J. Sabarinathan, and P.-C. Yu, “Fluid detection with photonic crystal-based multichannel waveguides,” Appl. Phys. Lett. 82(8), 1143–1145 (2003). [CrossRef]

, 8

8. S. Xiao and N. A. Mortensen, “Proposal of highly sensitive optofluidic sensors based on dispersive photonic crystal waveguides,” J. Opt. A, Pure Appl. Opt. 9(9), S463–S467 (2007). [CrossRef]

], guided resonance type [9

9. M. El Beheiry, V. Liu, S. Fan, and O. Levi, “Sensitivity enhancement in photonic crystal slab biosensors,” Opt. Express 18(22), 22702–22714 (2010). [CrossRef] [PubMed]

] and PhC laser type [10

10. S. H. Kim, J. H. Choi, S. K. Lee, S. H. Kim, S. M. Yang, Y. H. Lee, C. Seassal, P. Regrency, and P. Viktorovitch, “Optofluidic integration of a photonic crystal nanolaser,” Opt. Express 16(9), 6515–6527 (2008). [CrossRef] [PubMed]

, 11

11. S. Kita, S. Hachuda, S. Otsuka, T. Endo, Y. Imai, Y. Nishijima, H. Misawa, and T. Baba, “Super-sensitivity in label-free protein sensing using a nanoslot nanolaser,” Opt. Express 19(18), 17683–17690 (2011). [CrossRef] [PubMed]

].

In order to realize multiple sensing sites, PhC sensor arrays have been developed. Mandal et al. [12

12. S. Mandal and D. Erickson, “Nanoscale optofluidic sensor arrays,” Opt. Express 16(3), 1623–1631 (2008). [CrossRef] [PubMed]

] demonstrated a nanoscale opto-fluidic sensors array based on a silicon waveguide with an adjacent one-dimensional (1D) photonic crystal micro-cavity. Yang et al. [13

13. D. Yang, H. Tian, and Y. Ji, “Nanoscale photonic crystal sensor arrays on monolithic substrates using side-coupled resonant cavity arrays,” Opt. Express 19(21), 20023–20034 (2011). [CrossRef] [PubMed]

] theoretically investigated the performance of sensors array based on lattice-shifted resonant cavities side-coupled to a single PhC waveguide. However, the former realized sensors array on many separate silicon strips, rather than a monolithic silicon slab. While to the latter, the sensing signal of every cavity may interact each other due to some coupling (i.e. crosstalk) in multi-cavity parallel sensing, and if the variety of one signal caused by the index change is so large that beyond the engenfrequency peak of adjacent cavity, the sensing signal recognition will become difficult. So the crosstalk which is always causing the signal distortion restricts the distribution of the sensors on the monolithic platform.

2. Simulation model

As shown in Fig. 1(a)
Fig. 1 (a) Schematic structure of the FMSI. (b) Equal frequency contours of f = 0.255 c/a (big square) and f = 0.275 c/a (small square) as nsensor = 1.0 (solid lines) and 1.5 (dashed lines), respectively. (c) Band structures as r1 = 0.26 a and r2 = 0.392 a, respectively. The shaded area is the band gap as r2 = 0.392 a, which covers the self-collimation frequency range. The inset shows the perfect PhC formed by the square lattice air cylinders etched in silicon. (d) Transmittivity and reflectivity of the splitter.
, the proposed FMSI is composed of one splitter and four reflector mirrors M1, M2, M3 and M4. The perfect 2D PhC as the design platform consists of square lattice air cylinders etched in silicon with the refractive index 3.5. The radius of the air cylinders r1 = 0.26 a, where a is the lattice constant. TE (the magnetic field is parallel to the axis of air cylinders) equal frequency contours (EFCs) of the second band in the wave-vector space show the PhC has square-shaped EFCs in the frequency range between 0.255 c/a and 0.275 c/a (c is the speed of light in free space), which are shown as the big and small solid line squares in Fig. 1(b), respectively. At these frequencies and in the direction perpendicular to the four flat dispersion surfaces of the EFCs, a narrow light beam can propagate within the PhC without diffraction, which is so-called self-collimation effect. It is interesting that if air cylinders are injected some nanofluid with nsensor = 1.5, the two contours retract without destroying the square shape, which are shown as the big and small dashed line squares in Fig. 1(b). This is because with the increase of nsensor, the effective refractive index increases and the whole band structure moves down. However, the light still keeps the characteristics of self-collimated transmittance as before.

The mirrors are formed by another type of PhCs with the radius 0.392 a, which results in the bandgap between 0.2526 c/a and 0.2762 c/a (see Fig. 1(c)), hence the reflectivity 100% is obtained for the self-collimation beams. By enlarging the radius of a row of PhC air cylinders in the ΓΜ direction to 0.434 a, the splitter has the transmittivity between 26.44% and 54.61%, and the reflectivity between 72.74% and 41.46%, which are shown in Fig. 1(d). A 5 a wide light is incident from the input port. After the splitter, it is divided into two beams which transmit along two different branchs, i.e. Banch 1 and Branch 2 (see Fig. 1(a)). When they reach M4, they are reflected respectively, then splitted again and finally interfere in the output port. In Fig. 1(a), the thick red arrow lines indicate the propagation paths of the self-collimated beams in the FMSI. The air cylinders in M4 and parts of branch 2, which are shown as RSA and BSA in Fig. 1(a) respectively, are open to be filled with the nanofluid whose refractive index nsensor is increased from 1.0 to 1.5.

3. Simulation results and analysis

The simulation area is 50 × 50 a2. Perfectly matched layer (PML) absorbing boundary conditions are applied surrounding the computation domain. Firstly, only RSA is used. The calculation results validated by the 2D FDTD demonstrate five transmission peaks in the self-collimation frequency range with transmittivities over 80% are obtained when nsensor in the air cylinders of RSA is 1.0, which is shown in Fig. 2(a)
Fig. 2 (a) Transmission spectra of the FMSI as nsensor in RSA is changed from 1.0 to 1.5. The inset displays the third transmission peak as nsensor is varied between 1.0 and 1.15. (b) Band gap of M4 in the nsensor range. (c) Transmission spectrum of FMSI without M4. (d), (e) Steady-state magnetic field distributions of the light with frequency 0.2643 c/a as nsensor is 1.0 and 1.5, respectively. (f) FOM* of the sensor functioning in RSA.
. With the increase of nsensor, the intensity of each transmission peak is decreased. Such decrease is small in case of nsensor between 1.0 and 1.15, which is shown in the inset of Fig. 2(a). But when nsensor is kept increasing to 1.5, the transmission is below 5% for the peaks in the central frequency range due to the gradual disappearance of M4 band gap, which results in the decreased reflectivity for the self-collimation beam. Figure 2(b) clearly reveals the increase of nsensor leads to the band gap of M4 narrowing and moving towards lower frequencies. When nsensor is increased over 1.33, the band gap moves out of the self-collimation frequency range. In that case, M4 has a low reflectivity only originating from the heterostructure formed by M4 and the perfect PhC. The splitter causes the nearly equal intensity destructive interference of the self-collimation beams. Consequently, the transmission corresponding to the nsensor region decreases drastically. While at those frequencies far from the center, the transmission increases a little because there is a large difference of intensity between the two beams thus the incompletely destructive interference happens. From the transmission spectrum corresponding to nsensor = 1.5, we can see some peaks occur. The transmission spectrum is analogy to the spectrum got from the FMSI without M4 (i.e. Sagnec self-collimation interferometer), which is shown in Fig. 2(c). The number of peaks is about 2 times of that when nsensor is below 1.4 (see Fig. 2(a)), since the light path length is increased to two times in the interferometer. For nsensor below 1.33, although the light depth of penetration in M4 is changed with nsensor, the light path length difference between beams in two branches is not influenced. Therefore, the peak frequencies are almost unchanged. Figures 2(d) and 2(e) show the steady-state magnetic field distributions of the light with frequency 0.2643 c/a when nsensor = 1.0 and 1.5, respectively. It is clear that when nsensor = 1.5, the self-collimation beams transmit through M4 completely, forming the intensive standing wave oscillation in the FMSI without the output intensity. The detected transmission is only 2.97%, agreeing well with the theoretical presumption. While for nsensor = 1.0, the constructive interference makes the input light totally output, and the detected transmission is as high as 98.68%. Other transmissions are 94.82%, 83.10%, 50.84% and 11.16% for nsensor = 1.1, 1.2, 1.3 and 1.4, respectively. Figure 2(f) displays the figure of merit (FOM*) according to
FOM*=max|dI(λ)/dnI(λ)|
(1)
where dI(λ)/I(λ) is the relative intensity change at a fixed wavelength induced by a refractive index change dn [24

24. J. Becker, A. Trügler, A. Jakab, U. Hohenester, and C. Sönnichsen, “The optimal aspect ratio of gold nanorods for plasmonic bio-sensing,” Plasmonics 5(2), 161–167 (2010). [CrossRef]

]. The maximum 14.7 corresponds to the frequency 0.2718 c/a, which means that a self-collimation beam with such frequency is most sensitive to the change of refractive index in RSA sensing.

Secondly, only BSA is utilized. When nsensor in the air cylinders of BSA is increased from 1.00 to 1.15, the effective refractive index is increased, leading to the decrease of peak frequency. All the obtained spectra corresponding to various nsensor have the sinusoidal shapes, and the transmission peaks shift to lower frequencies with nearly the same peak spacing, which are shown in Fig. 3(a)
Fig. 3 (a) Transmission spectra as nsensor in BSA is increased from 1.00 to 1.15. The red arrow head indicates the red shift of one transmission peak. (b) Sensitivity obtained by the linear fit of the shifting peak wavelength. k is the slope. (c), (d) Steady-state magnetic field distributions of the light with frequency 0.2643 c/a as nsensor is 1.15 and 1.09, respectively.
. One shifting peak corresponding to j is marked with the red arrow head. Here, j is an integer, representing the jth peak. It can be seen that the total shift of the peak is almost a peak spacing. We deduce the relation of the light path length difference with the same order jth interference peak as following:
2[neff1(L2Lsensor)+nsensoreff1Lsensor+2neffM1Lpneff1L1]=jλ1
(2)
2[neff2(L2Lsensor)+nsensoreff2Lsensor+2neffM2Lpneff2L1]=jλ2
(3)
where neff,neffM,nsensoreff are the effective refractive indexes of the PhC, mirror (M2 or M3) and BSA, respectively. L1,L2,Lsensor are the lengths of the branch 1, 2 and BSA, respectively. Lp is the light depth of penetration in mirror and λ is the shifting peak wavelength. We assume in the frequency shift range of the peak, the effective refractive index varieties of PhCs can be neglected, i.e. neff1neff2,neffM1neffM2. In other words, the change of effective refractive index originates not from the variety of frequency but from nsensor. We subtract Eq. (2) with Eq. (3) and get
2ΔnsensoreffLsensor=jΔλ
(4)
From the corresponding peak wavelengths at nsensor = 1.00 and 1.15, and the relation of nsensor-eff with r/a, by solving Eq. (4) we obtain j = 52.93, i.e. j ≈53. Bringing j and other parameters into Eq. (2), we confirm the numerical values by the two sides are equal. The above theoretical analysis is necessary for the confirmation of sensitivity of the sensor.

Figures 3(c) and 3(d) display the steady-state magnetic field distributions of the light with frequency 0.2643 c/a when nsensor = 1.15 and 1.09, respectively. It is clear that as nsensor = 1.15, the light almost comes out from the output port entirely, and the detected transmission is 94.60%. While for nsensor = 1.03, the light mainly oscillates in the FMSI. All the peak transmissions cannot reach the unit due to the inserting loss introduced by the splitter and mirrors.

When RSA is used, the transmission of the light with frequency 0.2643 c/a in the range of nsensor between 1.00 and 1.15 is decreased slowly, from 98.68% to 86.94% (see Fig. 4
Fig. 4 Transmissions of the light with frequency 0.2643 c/a as nsensor is changed from 1.00 to 1.15 in the air cylinders of BSA (black dotted line) and RSA (red dotted line), respectively.
). But if we use BSA, the transmission is varied largely, from 98.68% to 5.78%, and back to 94.60%. In this range, the RSA-based sensor has much lower sensitivity than that of the BSA-based sensor. However, if the range of nsensor is expanded, i.e. from 1.0 to 1.5, the transmission peaks of the BSA-based sensor will red shift over a peak spacing. Thus the sensing range is limited. While for the RSA-based sensor, the transmission will keep monotone decreasing with the increase of nsensor. Considering if something wrong with the intensity reading, the RSA-based sensor is not easy to recognize, we only apply it in the detection of large index change range. The BSA-based sensor is prone to the small range and fine index detection. Accordingly, both large and small index range detection of nanofluid can be realized in such a single FMSI sensor. Maybe we can firstly do the RSA-based sensing and know the approximate index variety region, then confirm the index of nanofuid precisely by the BSA-based sensing.

4. Design of sensors array

Here, we give our design of the monolithic integrated parallel self-collimation sensors array, which sufficiently utilizes no crosstalk of self-collimation beam in perfect PhC. As shown in Fig. 5
Fig. 5 Schematic structure of the monolithic integrated parallel self-collimation sensors array. S1:1 represents energy reflection/transmission ratio of the splitter is 1:1 at the self-collimation central frequency, while S1:2 represents the ratio is 1:2. M is the reflector mirror. Except the integrated splitters and reflector mirrors, the perfect PhC is distributed in the blank place of the chip.
, the light is input by the external optical fiber at the input port, then splitted into three beams which fulfil the sensing tasks in three separate FMSI sensors, respectively. Some mirrors are shared by flexibly arranging the sensors to reduce the fabrication process. Finally, three sensing signals output from port 1, 2 and 3, respectively, and are coupled into the fibers and received by the external power meters or spectrometers. Though the sensing signals intercross with the input light in the PhC, there is no crosstalk to cause distortion. The more practical self-collimation sensors array will be based on PhC slabs, or Silicon-On-Insulator. The simulation and experimental results will be shown in our future work. For the operating wavelength around 1550 nm, the size of single sensor is approximately 20 × 20 μm2. Although here only 3 sensors are integrated on the monolithic platform, but according to the supercollimation beams with the transmittance distance as far as centimeter scale [31

31. P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006). [CrossRef] [PubMed]

], the ideal integrated number in parallel sensing can reach 250 without considering the inserting loss of single element.

5. Summary

We have proposed a novel refractive index sensor based on the 2D PhC FMSI and investigated its performance by the FDTD simulation. Two sensing areas, i.e. RSA and BSA, play different roles for the sensor. It can realize not only the large index change range and coarse detection, but also the small index variety range and fine detection. Fully utilizing the advantage of no crosstalk, we applied the sensor to a parallel sensors array. Although some parameters have not been optimized, it does not affect our analysis of device sensing characteristics. Because of no defect waveguides, no crosstalk and small size, the sensor and sensors array are desirable to perform monolithic integrated, low-cost, label-free real-time sensing.

Acknowledgments

The authors thank Prof. Xiyao Chen and Prof. Zexuan Qiang for valuable discussions. This work is supported by the Chinese National Key Basic Research Special Fund/CNKBRSF (Grant Nos. 2012CB933501 and 2011CB922002), the National Natural Science Foundation of China (Grant Nos. 61025025, 61137003 and 60838003) and the Technology of Fujian Education Office of China (Grant No. JA09226).

References and links

1.

A. D. Kersey, T. A. Berkoff, and W. W. Morey, “High-resolution fibre-grating based strain sensor with interferometric wavelength-shift detection,” Electron. Lett. 28(3), 236–238 (1992). [CrossRef]

2.

S. J. Spammer, P. L. Swart, and A. Booysen, “Interferometric distributed optical-fiber sensor,” Appl. Opt. 35(22), 4522–4525 (1996). [CrossRef] [PubMed]

3.

B. Drapp, J. Piehler, A. Brecht, G. Gauglitz, B. J. Luff, J. S. Wilkinson, and J. Ingenhoff, “Integrated optical Mach-Zehnder interferometers as simazine immunoprobes,” Sens. Actuators B Chem. 39(1-3), 277–282 (1997). [CrossRef]

4.

R. G. Heideman and P. V. Lambeck, “Remote opto-chemical sensing with extreme sensitivity: design, fabrication and performance of a pigtailed integrated optical phase-modulated Mach-Zehnder interferometer system,” Sens. Actuators B Chem. 61(1-3), 100–127 (1999). [CrossRef]

5.

M. Lončar, A. Scherer, and Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82(26), 4648–4650 (2003). [CrossRef]

6.

S. Chakravarty, J. Topol’ančik, P. Bhattacharya, S. Chakrabarti, Y. Kang, and M. E. Meyerhoff, “Ion detection with photonic crystal microcavities,” Opt. Lett. 30(19), 2578–2580 (2005). [CrossRef] [PubMed]

7.

J. Topol’ančik, P. Bhattacharya, J. Sabarinathan, and P.-C. Yu, “Fluid detection with photonic crystal-based multichannel waveguides,” Appl. Phys. Lett. 82(8), 1143–1145 (2003). [CrossRef]

8.

S. Xiao and N. A. Mortensen, “Proposal of highly sensitive optofluidic sensors based on dispersive photonic crystal waveguides,” J. Opt. A, Pure Appl. Opt. 9(9), S463–S467 (2007). [CrossRef]

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M. El Beheiry, V. Liu, S. Fan, and O. Levi, “Sensitivity enhancement in photonic crystal slab biosensors,” Opt. Express 18(22), 22702–22714 (2010). [CrossRef] [PubMed]

10.

S. H. Kim, J. H. Choi, S. K. Lee, S. H. Kim, S. M. Yang, Y. H. Lee, C. Seassal, P. Regrency, and P. Viktorovitch, “Optofluidic integration of a photonic crystal nanolaser,” Opt. Express 16(9), 6515–6527 (2008). [CrossRef] [PubMed]

11.

S. Kita, S. Hachuda, S. Otsuka, T. Endo, Y. Imai, Y. Nishijima, H. Misawa, and T. Baba, “Super-sensitivity in label-free protein sensing using a nanoslot nanolaser,” Opt. Express 19(18), 17683–17690 (2011). [CrossRef] [PubMed]

12.

S. Mandal and D. Erickson, “Nanoscale optofluidic sensor arrays,” Opt. Express 16(3), 1623–1631 (2008). [CrossRef] [PubMed]

13.

D. Yang, H. Tian, and Y. Ji, “Nanoscale photonic crystal sensor arrays on monolithic substrates using side-coupled resonant cavity arrays,” Opt. Express 19(21), 20023–20034 (2011). [CrossRef] [PubMed]

14.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999). [CrossRef]

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D. W. Prather, S. Shi, J. Murakowski, G. J. Schneider, A. Sharkawy, C. Chen, B. Miao, and R. Martin, “Self-collimation in photonic crystal structures: a new paradigm for applications and device development,” J. Phys. D Appl. Phys. 40(9), 2635–2651 (2007). [CrossRef]

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X. Yu and S. Fan, “Bends and splitters for self-collimated beams in photonic crystal,” Appl. Phys. Lett. 83(16), 3251–3253 (2003). [CrossRef]

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24.

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25.

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28.

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30.

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31.

P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacić, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nat. Mater. 5(2), 93–96 (2006). [CrossRef] [PubMed]

OCIS Codes
(120.1680) Instrumentation, measurement, and metrology : Collimation
(130.6010) Integrated optics : Sensors
(250.5300) Optoelectronics : Photonic integrated circuits
(350.4238) Other areas of optics : Nanophotonics and photonic crystals

ToC Category:
Sensors

History
Original Manuscript: April 3, 2012
Revised Manuscript: April 27, 2012
Manuscript Accepted: April 28, 2012
Published: May 14, 2012

Citation
Yufei Wang, Hailing Wang, Qikun Xue, and Wanhua Zheng, "Photonic crystal self-collimation sensor," Opt. Express 20, 12111-12118 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-11-12111


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References

  1. A. D. Kersey, T. A. Berkoff, and W. W. Morey, “High-resolution fibre-grating based strain sensor with interferometric wavelength-shift detection,” Electron. Lett.28(3), 236–238 (1992). [CrossRef]
  2. S. J. Spammer, P. L. Swart, and A. Booysen, “Interferometric distributed optical-fiber sensor,” Appl. Opt.35(22), 4522–4525 (1996). [CrossRef] [PubMed]
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