Abstract

A novel in-fiber modal interferometer based on a long period grating (LPG) inscribed in a two-mode all-solid photonic bandgap fiber (AS-PBGF) is presented. After inserting a small piece of the AS-PBGF into two sections of standard single-mode fiber (SMF) via being spliced slight core offset, LPG is inscribed in the AS-PBGF. The LPG is especially designed to realize the coupling between two core modes of LP01 and LP11 in the AS-PBGF. Two core modes LP01 and LP11 of the AS-PBGF are excited firstly at the input spliced point and actualized energy exchange when they pass through the LPG. Then the two beams will interfere at the output spliced point to form a high-contrast in-fiber modal interferometer. The proposed interferometer has some advantages such as configuration compact, high interference contrast and the wavelength spacing well controlled by changing the position of the LPG without changing the total length of AS-PBGF.

© 2011 OSA

1. Introduction

The development of fiber modal interferometers has been a recent and active research topic nowadays. Based on the high sensitivity and high resolution due to narrow width of interference fringes, they have been widely applied in WDM communications [1], wavelength filters and sensors for measurement of many physical parameters including strain, temperature, refractive index and curvature [29].

Several types of in-fiber interferometers have been reported such as interferometers made of a pair of identical LPGs [1, 10] or a fiber LPG with a reflector [11], and the intermodal interferometers based on SMF–special fiber–SMF structures [29]. The interferometers based on fiber LPG pair have a series of interference fringes in each stop band of a conventional LPG's spectrum. The interferometer’s two optical paths are the transmission core mode and one of the cladding modes. A drawback of fiber LPG pair interferometer is that it is difficult to fabricate two absolutely identical LPGs along the fiber. The intermodal interferometers are based on the modal interference effect in special fibers, especially photonic crystal fibers (PCFs). By core-offsetting splice joints of a compact SMF–special fiber–SMF structure, the excited cladding modes [3, 4] or higher order core mode [9] can re-couple with the fundamental mode propagating in the special fiber at the output splice joint. Some methods to excite cladding modes or higher order core modes like collapsing air holes in a piece of PCF [8, 12] or using a tapered fiber [7] were also proposed. The intermodal interferometers have the advantages of simple and compact structure, small size. However, large insert loss of 2-5 dB has been induced in those interferometers because of the large core off-setting splicing, the air hole collapsing or tapering the fiber [7, 8]. Moreover, the free spectrum range (FSM) in those interferometers is dependent on the used special fiber length and thus most of them have to using a very short fiber length like millimeters in order to get a wide FSM filter or sensor, which is not easy in experimental operation.

In this paper, a novel LPG assistant in-fiber modal interferometer is proposed and demonstrated. The interferometer consists of a specially designed LPG inscribed in a two-mode all-solid photonic bandgap fiber (AS-PBGF), whose both ends are fusing spliced to SMF with slight core offset. An interference contrast of 9.1 dB is achieved at the resonant wavelength of the LPG. Compared to the intermodal interferometers reported in [3, 8], our interferometer have lower insert loss and can achieve high extinction ratio without large lateral offset at the fusion spliced points.

2. Interferometer structure and operation principle

As shown in Fig. 1 , the proposed modal interferometer consists of a strong resonance LPG inscribed in a two-mode fiber, whose both ends are fusion spliced with SMF with slight core offset. L1/L2 is the distance between the middle of the grating and the incident spliced point/output spliced point. The LPG is designed to realize the coupling between two core modes of LP01 and LP11 in the two-mode fiber. At the incidence spliced point, a small fraction of propagating power from the SMF goes to LP11 core mode and most goes to the fundamental mode in the two-mode fiber. LP11 core mode propagates a distance of L1 before it couples to the fundamental mode (LP01 core mode) by the LPG and continues to propagate a distance of L2 as the fundamental mode. Meanwhile the fundamental mode of the two-mode fiber propagates L1 distance from the incidence spliced point to the LPG, then couples to the LP11 core mode by the LPG and continues to propagate a distance of L2 as LP11 mode reaching the output end. Because only the fundamental mode can propagate in SMF losslessly, some power of LP11 core mode couples to the fundamental mode in the SMF and another portion is lost when LP11 core mode passes through the output point, where interference obtains. The LP01-LP11 and LP11-LP01 paths are the two arms of this interferometer.

 

Fig. 1 Schematic configuration of the proposed interferometer.

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The interference depends on the optical path difference (OPD) between the two arms. Since the LP11 core mode has a lower effective index than the LP01 core mode, when the beams pass through the two-core fiber, index difference induces an optical path difference:

OPD=(neff11×L1+neff01×L2)(neff01×L1+neff11×L2)=Δn×ΔL.
Where neff01 and neff11 are the effective indices of the LP01 and LP11 core modes, respectively. Δn=neff01neff11, ΔL=L2L1.

If we approximate the wavelengths of two adjacent intensity minima near the resonance wavelength of the LP in the interference spectrum to the resonance wavelength λ and ignore the effect of dispersion, based on the Eq. (1), we deduce that the interference wavelength spacing is:

ΔS=λ2Δn×ΔL.

We can see the OPD and the wavelength spacing ΔS depends on ΔL rather than the total fiber length (L1 + L2). If we fix a wavelength λ, the effective index difference can be calculated by phase matching condition, and ΔS is in inverse proportion to ΔL, so we can control the wavelength spacing by changing the position of LPG rather than the total length of the two-mode fiber. When the two beams interference, the extreme value of obtained intensities can be mathematically described by:

Imax=I1+I2+2I1I2
Imin=I1+I22I1I2

The contrast of interference fringes can be expressed as:

V=ImaxIminImax+Imin

We suppose that the input intensity of LP01 in SMF is I, the energy coupling efficiencies of the input and output spliced points are α1 and α2for LP11, β1 and β2for LP01, respectively, α1+β11,α2+β21, and that of the grating is γ(90%γ1) . Therefore, after passing through the output spliced point, the intensities of LP11 and LP01 are γα2β1I andγα1β2I , respectively. According to Eq. (3)-(5), Imax=γ(α1β2+α2β1+2α1α2β1β2)I, Imin=γ(α1β2+α2β12α1α2β1β2)I and V=2α1α2β1β2α1β2+α2β1 are obtained. Obviously, V is independent of γ and V = 1 as long as α1β2=α2β1 or α1=α2, β1=β2. However, if we don’t introduce the LPG in this interferometer, at the output spliced point the intensities of LP11 and LP01 are α1α2I andβ1β2I, respectively. We getImax=(α1α2+β1β2+2α1α2β1β2)I, Imin=(α1α2+β1β22α1α2β1β2)IandV=2α1α2β1β2α1α2+β1β2. Thus V = 1 as long as the condition α1α2=β1β2is satisfied. That means sufficient core offset at the fusion spliced points is needed to excite enough great power of LP11 in order to achieve a large V, for exampleα1=α2=β1=β2=50%. The large lateral core offset will not only weaken the strength of the spliced point but also introduce large insert loss in the interferometer.

If we assume that α1=5%,α2=10%, and β1=85%,β2=80%,calculated value of the V is 0.933 and 0.17 for the interferometers with and without the LPG. It is obvious that the use of the LPG immensely heightens contrast of the interference spectrum.

3. Experimental results

The two-mode fiber used in this work is an all solid photonic bandgap fiber (AS-PBGF), whose cross section is shown in the inset of Fig. 2 , fabricated by Yangtze Optical Fiber and Cable Corporation. In the fiber a high index rod surrounded by a low index ring lattice of five layers is embedded in pure silica background, the core is formed by omitting a high index rod and a low index ring. The diameter of the fiber is about 125 µm, and the pitch between adjacent rods Λ is 9.24 µm. The outer radii of the high index rod and the low index ring are 0.181Λ and 0.3786Λ, respectively. Compared with the pure silica background, the average refractive index differences of the high index rods and the low index rings are approximately 0.028 and −0.008.

 

Fig. 2 The calculated bandgaps and modes of the AS-PBGF, the black curves represent the edges of bandgaps, red and green curves indicate core modes confined with the core. The inset is the structure of PCF.

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By means of plane wave expansion method and a commercial finite element method, the bandgaps, the effective refractive indices of fundamental core mode and LP11core mode are calculated, which are shown in Fig. 2. It can be seen that the AS-PBGF only supports two core modes in its photonic bandgaps.

Figure 1 shows the schematic configuration of the experimental setup. The AS-PBGF is spliced with SMFs at both ends. Light from a supercontinuum source (650nm ~1750nm) is launched into the input SMF and the transmission spectra are measured with an ANDO AQ6317B optical spectrum analyzer (OSA).

The higher-order core modes can be excited by lateral core-offset splicing between AS-PBGF and SMF. Unlike some early reports [4, 6, 9], we don’t need to excite great power of LP11 mode to improve interference depth. In this structure, a small quantity of LP11 mode excited at the input spliced point is sufficient to obtain intense interference after mode coupled by the LPG. Before LPG inscription, obvious interference patterns can be observed as shown as the black curve shown in Fig. 3(a) , with a fringe contrast of ~1 dB, which indicates LP11 core mode is not excited much. The formation of those shallow, intensive interference fringes outside the LPG resonant wavelength is similar with that in Ref [9].

 

Fig. 3 (a)The measured transmission spectrum of the interferometer. The insets are modal distribution for the grating with pitch 620um measured at (i)1550.00 nm, (ii)1582.20 nm, (iii)1597.27nm,and (iv)1609.15nm . (b)Comparison of the measured interference spectra with different length of AS-PBGF. Black and red curves are the measured spectrum of the interferometer for ΔL 1=8.3 cm and ΔL 2=7.0 cm, respectively.

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In experiment, we inscribe an LPG with a period of 610 μm in the AS-PBGF through a point by point side illumination process using a CO2 inscription platform which is similar to that in Ref [13]. The red curve shown in Fig. 3 is the measured spectrum of the interferometer. We can observe a resonant wavelength near 1609nm of LPG,and distinct interference peaks at ii:1582.20 nm, iii:1597.27nm, iv:1609.15 nm, v:1621.48 nm and vi:1633.75nm. The minimum 3 dB bandwidth of those peaks is about 2.97 nm. It is notable that far away from resonant wavelength of the LPG, the interference ripples are similar to that before the LPG inscription. The maximum extinction ratio reaches 9.1 dB while the extinction ratio is only ~1dB before the LPG inscription. Therefore, as forecast in the theoretic analysis, the interference contrast is greatly enhanced by introducing the LPG in the interferometer.

We use infrared CCD to observe near field images of peak ii-iv shown in the inset of Fig. 3(a). Evidently, the ii-iv peaks all come from the coupling between fundamental core mode and LP11 core mode, which also gives evidence of high coupling efficiency of the LPG.

Moreover, we also did a series of AS-PBGF cutback experiments to validate the interference effect. Figure 3(b) shows two typical transmission spectra with different ΔL. We assume that the mode coupling is finished at the middle point of the LPG. We measure L 1 and L 2 based on this assumption, and obtain two arm length differences, ΔL 1 = 8.3 cm (L 1 = 10.4 cm, L 2 = 2.1 cm) and ΔL 2 = 7.0 cm (L 1 = 9.1 cm, L 2 = 2.1 cm). In an LPG, the phase match condition is Δn = λ/Λ, where λ represents resonant wavelength of the LPG and Λ represents the period of grating. According to the calculated phase-matching curve in Fig. 4(a) the resonant wavelength of the LPG is 1605 nm if Λ = 610 μm, and the corresponding index difference around resonant wavelength, Δn = 0.0026311. According to Eq. (2), when ΔL is 8.3 cm and 7.0 cm, the calculated values of ΔS is 11.8 nm and 14.0 nm, respectively. Contrastively, the experimentally measured values are about 12.2 nm and 13.2 nm, respectively. Thus the theoretical results agree well with the experimental data. The slight deviation between the calculating results and experimental results is due to several reasons such as the assumption that modes coupling is finished at the middle point of the LPG, the estimated resonant center wavelength of the LPG is not very accurate and the Δn is a approximate value.

 

Fig. 4 Comparison of the spectra of interferometers made up of LPGs with different grating pitch. (a) phase-matching curve of AS-PBGF, spectra of interferometer for the LPGs with a pitch of (b) 610 μm and (c) 620 μm.

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We note that as ΔL changes from 8.3 cm to 7.0 cm, the wavelength spacing increases from 12.2 nm to 13.2 nm. So we can control wavelength spacing by adjusting the length difference of L 1 and L 2.We can get a wide FSM as long as choosing an appropriate ΔL value even if the total length of the interferometer is large.

We also fabricated an interferometer including an LPG with a grating pitch of 620 μm. With the period increasing, the resonant wavelength and the interference peaks move to the shorter wavelength. According to the dispersion curve of the two core modes, we calculate the phase-matching curve of LPG as shown in Fig. 4 and the resonance wavelength λ of the LPG deceases with the grating pitch Λ increases. So we can control the wavelength of the interference peaks by fabricating the LPGs with different periods.

Compared with the inferferometer as shown in Ref [3, 8], our interferometer have some advantages of higher interference contrast without obvious core off-setting splicing or taping and more flexible design to get different interference spacing without changing total length. In addition, our interferometer can also be applied in the measurements of strain, temperature and curvature like the interferometers proposed in the previous reports [29]. Furthermore, the wavelength spacing ΔS and the LPG resonant wavelength λ are both affected by Δn, so the proposed interferometer has a promising future for dual parameter sensing measurement.

4. Conclusion

In summary, a novel modal interferometer based on a specially designed LPG inscribed in a two-mode all-solid PCF is proposed and demonstrated. The resonance peak of the LPG arises from coupling between the fundamental core mode and the LP11 core mode. OPD between the two modes before and after the LPG causes interference fringes. We can change the distance between splicing points and the LPG to control the interference wavelength spacing. The theoretical results agree well with the experimental results. The interferometer has advantages of high interference contrast and structure compact. It may be applied in sensing and wavelength filter system.

Acknowledgments

This work was supported by the National Key Basic Research and Development Program of China under grant No. 2010CB327605, the National Natural Science Foundation of China under grants No. 50802044, 60736039, and 11004100, Program for New Century Excellent Talents in University (NCET-09-0483) and National Undergraduate Innovative Test Program (091005554).

References and links

1. B. H. Lee and J. Nishii, “Dependence of fringe spacing on the grating separation in a long-period fiber grating pair,” Appl. Opt. 38(16), 3450–3459 (1999). [CrossRef]   [PubMed]  

2. S. H. Aref, R. Amezcua-Correa, J. P. Carvalho, O. Frazão, P. Caldas, J. L. Santos, F. M. Araújo, H. Latifi, F. Farahi, L. A. Ferreira, and J. C. Knight, “Modal interferometer based on hollow-core photonic crystal fiber for strain and temperature measurement,” Opt. Express 17(21), 18669–18675 (2009). [CrossRef]   [PubMed]  

3. J. H. Bo Dong and Z. Xu “Temperature insensitive curvature measurement with a core-offset polarization maintaining photonic crystal fiber based interferometer ,” Opt. Fiber Technol. 17(3), 233–235 (2011). [CrossRef]  

4. H. Y. Choi, M. J. Kim, and B. H. Lee, “All-fiber Mach-Zehnder type interferometers formed in photonic crystal fiber,” Opt. Express 15(9), 5711–5720 (2007). [CrossRef]   [PubMed]  

5. M. Deng, C.-P. Tang, T. Zhu, and Y.-J. Rao, “Highly sensitive bend sensor based on Mach–Zehnder interferometer using photonic crystal fiber,” Opt. Commun. 284(12), 2849–2853 (2011). [CrossRef]  

6. B. Dong, J. Z. Hao, C. Y. Liaw, B. Lin, and S. C. Tjin, “Simultaneous strain and temperature measurement using a compact photonic crystal fiber inter-modal interferometer and a fiber Bragg grating,” Appl. Opt. 49(32), 6232–6235 (2010). [CrossRef]   [PubMed]  

7. Z. B. Tian and S. S. H. Yam, “In-Line Single-Mode Optical Fiber Interferometric Refractive Index Sensors,” J. Lightwave Technol. 27(13), 2296–2306 (2009). [CrossRef]  

8. W. Chen, S. Lou, L. Wang, S. Feng, H. zou, W. Lu, and S. Jian, “In-fiber modal interferometer based on dual-concentric-core photonic crystal fiber and its strain, temperature and refractive index characteristics,” Opt. Commun. 284(12), 2829–2834 (2011). [CrossRef]  

9. Y. F. Geng, X. J. Li, X. L. Tan, Y. L. Deng, and Y. Q. Yu, “Sensitivity-enhanced high-temperature sensing using all-solid photonic bandgap fiber modal interference,” Appl. Opt. 50(4), 468–472 (2011). [CrossRef]   [PubMed]  

10. B. H. Lee and J. J. Nishii, “Bending sensitivity of in-series long-period fiber gratings,” Opt. Lett. 23(20), 1624–1626 (1998). [CrossRef]   [PubMed]  

11. B. H. Lee and J. Nishii, “Self-interference of long-period fibre grating and its application as temperature sensor,” Electron. Lett. 34(21), 2059–2060 (1998). [CrossRef]  

12. R. Jha, J. Villatoro, and G. Badenes, “Ultrastable in reflection photonic crystal fiber modal interferometer for accurate refractive index sensing,” Appl. Phys. Lett. 93(19), 191106 (2008). [CrossRef]  

13. J. Xu, Y. G. Liu, Z. Wang, and B. Tai, “Simultaneous force and temperature measurement using long-period grating written on the joint of a microstructured optical fiber and a single mode fiber,” Appl. Opt. 49(3), 492–496 (2010). [CrossRef]   [PubMed]  

References

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  1. B. H. Lee and J. Nishii, “Dependence of fringe spacing on the grating separation in a long-period fiber grating pair,” Appl. Opt. 38(16), 3450–3459 (1999).
    [CrossRef] [PubMed]
  2. S. H. Aref, R. Amezcua-Correa, J. P. Carvalho, O. Frazão, P. Caldas, J. L. Santos, F. M. Araújo, H. Latifi, F. Farahi, L. A. Ferreira, and J. C. Knight, “Modal interferometer based on hollow-core photonic crystal fiber for strain and temperature measurement,” Opt. Express 17(21), 18669–18675 (2009).
    [CrossRef] [PubMed]
  3. J. H. Bo Dong and Z. Xu “Temperature insensitive curvature measurement with a core-offset polarization maintaining photonic crystal fiber based interferometer ,” Opt. Fiber Technol. 17(3), 233–235 (2011).
    [CrossRef]
  4. H. Y. Choi, M. J. Kim, and B. H. Lee, “All-fiber Mach-Zehnder type interferometers formed in photonic crystal fiber,” Opt. Express 15(9), 5711–5720 (2007).
    [CrossRef] [PubMed]
  5. M. Deng, C.-P. Tang, T. Zhu, and Y.-J. Rao, “Highly sensitive bend sensor based on Mach–Zehnder interferometer using photonic crystal fiber,” Opt. Commun. 284(12), 2849–2853 (2011).
    [CrossRef]
  6. B. Dong, J. Z. Hao, C. Y. Liaw, B. Lin, and S. C. Tjin, “Simultaneous strain and temperature measurement using a compact photonic crystal fiber inter-modal interferometer and a fiber Bragg grating,” Appl. Opt. 49(32), 6232–6235 (2010).
    [CrossRef] [PubMed]
  7. Z. B. Tian and S. S. H. Yam, “In-Line Single-Mode Optical Fiber Interferometric Refractive Index Sensors,” J. Lightwave Technol. 27(13), 2296–2306 (2009).
    [CrossRef]
  8. W. Chen, S. Lou, L. Wang, S. Feng, H. zou, W. Lu, and S. Jian, “In-fiber modal interferometer based on dual-concentric-core photonic crystal fiber and its strain, temperature and refractive index characteristics,” Opt. Commun. 284(12), 2829–2834 (2011).
    [CrossRef]
  9. Y. F. Geng, X. J. Li, X. L. Tan, Y. L. Deng, and Y. Q. Yu, “Sensitivity-enhanced high-temperature sensing using all-solid photonic bandgap fiber modal interference,” Appl. Opt. 50(4), 468–472 (2011).
    [CrossRef] [PubMed]
  10. B. H. Lee and J. J. Nishii, “Bending sensitivity of in-series long-period fiber gratings,” Opt. Lett. 23(20), 1624–1626 (1998).
    [CrossRef] [PubMed]
  11. B. H. Lee and J. Nishii, “Self-interference of long-period fibre grating and its application as temperature sensor,” Electron. Lett. 34(21), 2059–2060 (1998).
    [CrossRef]
  12. R. Jha, J. Villatoro, and G. Badenes, “Ultrastable in reflection photonic crystal fiber modal interferometer for accurate refractive index sensing,” Appl. Phys. Lett. 93(19), 191106 (2008).
    [CrossRef]
  13. J. Xu, Y. G. Liu, Z. Wang, and B. Tai, “Simultaneous force and temperature measurement using long-period grating written on the joint of a microstructured optical fiber and a single mode fiber,” Appl. Opt. 49(3), 492–496 (2010).
    [CrossRef] [PubMed]

2011 (4)

J. H. Bo Dong and Z. Xu “Temperature insensitive curvature measurement with a core-offset polarization maintaining photonic crystal fiber based interferometer ,” Opt. Fiber Technol. 17(3), 233–235 (2011).
[CrossRef]

W. Chen, S. Lou, L. Wang, S. Feng, H. zou, W. Lu, and S. Jian, “In-fiber modal interferometer based on dual-concentric-core photonic crystal fiber and its strain, temperature and refractive index characteristics,” Opt. Commun. 284(12), 2829–2834 (2011).
[CrossRef]

Y. F. Geng, X. J. Li, X. L. Tan, Y. L. Deng, and Y. Q. Yu, “Sensitivity-enhanced high-temperature sensing using all-solid photonic bandgap fiber modal interference,” Appl. Opt. 50(4), 468–472 (2011).
[CrossRef] [PubMed]

M. Deng, C.-P. Tang, T. Zhu, and Y.-J. Rao, “Highly sensitive bend sensor based on Mach–Zehnder interferometer using photonic crystal fiber,” Opt. Commun. 284(12), 2849–2853 (2011).
[CrossRef]

2010 (2)

2009 (2)

2008 (1)

R. Jha, J. Villatoro, and G. Badenes, “Ultrastable in reflection photonic crystal fiber modal interferometer for accurate refractive index sensing,” Appl. Phys. Lett. 93(19), 191106 (2008).
[CrossRef]

2007 (1)

1999 (1)

1998 (2)

B. H. Lee and J. J. Nishii, “Bending sensitivity of in-series long-period fiber gratings,” Opt. Lett. 23(20), 1624–1626 (1998).
[CrossRef] [PubMed]

B. H. Lee and J. Nishii, “Self-interference of long-period fibre grating and its application as temperature sensor,” Electron. Lett. 34(21), 2059–2060 (1998).
[CrossRef]

Amezcua-Correa, R.

Araújo, F. M.

Aref, S. H.

Badenes, G.

R. Jha, J. Villatoro, and G. Badenes, “Ultrastable in reflection photonic crystal fiber modal interferometer for accurate refractive index sensing,” Appl. Phys. Lett. 93(19), 191106 (2008).
[CrossRef]

Bo Dong, J. H.

J. H. Bo Dong and Z. Xu “Temperature insensitive curvature measurement with a core-offset polarization maintaining photonic crystal fiber based interferometer ,” Opt. Fiber Technol. 17(3), 233–235 (2011).
[CrossRef]

Caldas, P.

Carvalho, J. P.

Chen, W.

W. Chen, S. Lou, L. Wang, S. Feng, H. zou, W. Lu, and S. Jian, “In-fiber modal interferometer based on dual-concentric-core photonic crystal fiber and its strain, temperature and refractive index characteristics,” Opt. Commun. 284(12), 2829–2834 (2011).
[CrossRef]

Choi, H. Y.

Deng, M.

M. Deng, C.-P. Tang, T. Zhu, and Y.-J. Rao, “Highly sensitive bend sensor based on Mach–Zehnder interferometer using photonic crystal fiber,” Opt. Commun. 284(12), 2849–2853 (2011).
[CrossRef]

Deng, Y. L.

Dong, B.

Farahi, F.

Feng, S.

W. Chen, S. Lou, L. Wang, S. Feng, H. zou, W. Lu, and S. Jian, “In-fiber modal interferometer based on dual-concentric-core photonic crystal fiber and its strain, temperature and refractive index characteristics,” Opt. Commun. 284(12), 2829–2834 (2011).
[CrossRef]

Ferreira, L. A.

Frazão, O.

Geng, Y. F.

Hao, J. Z.

Jha, R.

R. Jha, J. Villatoro, and G. Badenes, “Ultrastable in reflection photonic crystal fiber modal interferometer for accurate refractive index sensing,” Appl. Phys. Lett. 93(19), 191106 (2008).
[CrossRef]

Jian, S.

W. Chen, S. Lou, L. Wang, S. Feng, H. zou, W. Lu, and S. Jian, “In-fiber modal interferometer based on dual-concentric-core photonic crystal fiber and its strain, temperature and refractive index characteristics,” Opt. Commun. 284(12), 2829–2834 (2011).
[CrossRef]

Kim, M. J.

Knight, J. C.

Latifi, H.

Lee, B. H.

Li, X. J.

Liaw, C. Y.

Lin, B.

Liu, Y. G.

Lou, S.

W. Chen, S. Lou, L. Wang, S. Feng, H. zou, W. Lu, and S. Jian, “In-fiber modal interferometer based on dual-concentric-core photonic crystal fiber and its strain, temperature and refractive index characteristics,” Opt. Commun. 284(12), 2829–2834 (2011).
[CrossRef]

Lu, W.

W. Chen, S. Lou, L. Wang, S. Feng, H. zou, W. Lu, and S. Jian, “In-fiber modal interferometer based on dual-concentric-core photonic crystal fiber and its strain, temperature and refractive index characteristics,” Opt. Commun. 284(12), 2829–2834 (2011).
[CrossRef]

Nishii, J.

B. H. Lee and J. Nishii, “Dependence of fringe spacing on the grating separation in a long-period fiber grating pair,” Appl. Opt. 38(16), 3450–3459 (1999).
[CrossRef] [PubMed]

B. H. Lee and J. Nishii, “Self-interference of long-period fibre grating and its application as temperature sensor,” Electron. Lett. 34(21), 2059–2060 (1998).
[CrossRef]

Nishii, J. J.

Rao, Y.-J.

M. Deng, C.-P. Tang, T. Zhu, and Y.-J. Rao, “Highly sensitive bend sensor based on Mach–Zehnder interferometer using photonic crystal fiber,” Opt. Commun. 284(12), 2849–2853 (2011).
[CrossRef]

Santos, J. L.

Tai, B.

Tan, X. L.

Tang, C.-P.

M. Deng, C.-P. Tang, T. Zhu, and Y.-J. Rao, “Highly sensitive bend sensor based on Mach–Zehnder interferometer using photonic crystal fiber,” Opt. Commun. 284(12), 2849–2853 (2011).
[CrossRef]

Tian, Z. B.

Tjin, S. C.

Villatoro, J.

R. Jha, J. Villatoro, and G. Badenes, “Ultrastable in reflection photonic crystal fiber modal interferometer for accurate refractive index sensing,” Appl. Phys. Lett. 93(19), 191106 (2008).
[CrossRef]

Wang, L.

W. Chen, S. Lou, L. Wang, S. Feng, H. zou, W. Lu, and S. Jian, “In-fiber modal interferometer based on dual-concentric-core photonic crystal fiber and its strain, temperature and refractive index characteristics,” Opt. Commun. 284(12), 2829–2834 (2011).
[CrossRef]

Wang, Z.

Xu, J.

Xu, Z.

J. H. Bo Dong and Z. Xu “Temperature insensitive curvature measurement with a core-offset polarization maintaining photonic crystal fiber based interferometer ,” Opt. Fiber Technol. 17(3), 233–235 (2011).
[CrossRef]

Yam, S. S. H.

Yu, Y. Q.

Zhu, T.

M. Deng, C.-P. Tang, T. Zhu, and Y.-J. Rao, “Highly sensitive bend sensor based on Mach–Zehnder interferometer using photonic crystal fiber,” Opt. Commun. 284(12), 2849–2853 (2011).
[CrossRef]

zou, H.

W. Chen, S. Lou, L. Wang, S. Feng, H. zou, W. Lu, and S. Jian, “In-fiber modal interferometer based on dual-concentric-core photonic crystal fiber and its strain, temperature and refractive index characteristics,” Opt. Commun. 284(12), 2829–2834 (2011).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

R. Jha, J. Villatoro, and G. Badenes, “Ultrastable in reflection photonic crystal fiber modal interferometer for accurate refractive index sensing,” Appl. Phys. Lett. 93(19), 191106 (2008).
[CrossRef]

Electron. Lett. (1)

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Opt. Lett. (1)

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Figures (4)

Fig. 1
Fig. 1

Schematic configuration of the proposed interferometer.

Fig. 2
Fig. 2

The calculated bandgaps and modes of the AS-PBGF, the black curves represent the edges of bandgaps, red and green curves indicate core modes confined with the core. The inset is the structure of PCF.

Fig. 3
Fig. 3

(a)The measured transmission spectrum of the interferometer. The insets are modal distribution for the grating with pitch 620um measured at (i)1550.00 nm, (ii)1582.20 nm, (iii)1597.27nm,and (iv)1609.15nm . (b)Comparison of the measured interference spectra with different length of AS-PBGF. Black and red curves are the measured spectrum of the interferometer for ΔL 1=8.3 cm and ΔL 2=7.0 cm, respectively.

Fig. 4
Fig. 4

Comparison of the spectra of interferometers made up of LPGs with different grating pitch. (a) phase-matching curve of AS-PBGF, spectra of interferometer for the LPGs with a pitch of (b) 610 μm and (c) 620 μm.

Equations (5)

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O P D = ( n eff 11 × L 1 + n eff 01 × L 2 ) ( n eff 01 × L 1 + n eff 11 × L 2 ) = Δ n × Δ L .
Δ S = λ 2 Δ n × Δ L .
I max = I 1 + I 2 + 2 I 1 I 2
I min = I 1 + I 2 2 I 1 I 2
V = I max I min I max + I min

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