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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 14 — Jul. 4, 2011
  • pp: 12913–12918
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Long period grating assistant photonic crystal fiber modal interferometer

Zhoulu Sun, Yan-ge Liu, Zhi Wang, Boyin Tai, Tingting Han, Bo Liu, Wentao Cui, Huifeng Wei, and Weijun Tong  »View Author Affiliations


Optics Express, Vol. 19, Issue 14, pp. 12913-12918 (2011)
http://dx.doi.org/10.1364/OE.19.012913


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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

2. Interferometer structure and operation principle

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.
(1)
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.
(2)

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
(3)
Imin=I1+I22I1I2
(4)

The contrast of interference fringes can be expressed as:

V=ImaxIminImax+Imin
(5)

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
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.
, 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.

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).

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

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]

]. 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)
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.
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.

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.

4. Conclusion

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]

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(060.2310) Fiber optics and optical communications : Fiber optics
(230.3990) Optical devices : Micro-optical devices

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: April 26, 2011
Revised Manuscript: June 3, 2011
Manuscript Accepted: June 3, 2011
Published: June 20, 2011

Citation
Zhoulu Sun, Yan-ge Liu, Zhi Wang, Boyin Tai, Tingting Han, Bo Liu, Wentao Cui, Huifeng Wei, and Weijun Tong, "Long period grating assistant photonic crystal fiber modal interferometer," Opt. Express 19, 12913-12918 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-14-12913


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References

  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]

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