Investigation of intermodal interference of LP01 and LP11 modes in the liquid-core optical fiber for temperature measurements

Optik 122 (2011) 707–710

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Investigation of intermodal interference of LP01 and LP11 modes in the liquid-core optical fiber for temperature measurements Ivan Martincek a,∗ , Dusan Pudis a , Daniel Kacik a , Kay Schuster b a b

Dept. of Physics, University of Zˇ ilina, Univerzitná 1, SK-01026 Zˇ ilina, Slovakia Institute of Photonic Technology Jena, D-07745 Jena, Germany

a r t i c l e

i n f o

Article history: Received 10 December 2009 Accepted 24 May 2010

Keywords: Liquid-core optical fiber Intermodal interference

a b s t r a c t The intermodal interference of the LP01 and LP11 modes and determination of the equalization wavelength in the liquid-core optical fiber is presented. Theoretically was described the weakly guiding optical fiber with the constant core radius, where equalization wavelength is a function of the refractive indices of core and cladding. The dependence of equalization wavelength on refractive indices is employed for measurement of temperature. Temperature sensitivity using intermodal interference of modes LP01 and LP11 was documented in the liquid-core optical fiber consisted of fused silica as cladding and medicinal oil as a core. In the investigated temperature range the intermodal interference allows the temperature measurement with resolution of about 0.02 ◦ C. © 2010 Elsevier GmbH. All rights reserved.

1. Introduction The various detection methods of physical quantities employ optical fibers, where typically dependence of intensity, wavelength or phase of a propagating electromagnetic radiation on measured physical quantity is monitored. Different devices have been proposed for the measurement of a large number of physical parameters including temperature, acoustic, electric and magnetic fields, pressure, strain rotation, displacement, etc. [1]. Subset of group of optical fiber sensors is represented by sensors, which use intermodal interference of propagating modes of electromagnetic radiation. Most attractive from this group are sensors using intermodal interference of fundamental mode LP01 and first higher order mode LP11 , which propagate in optical fibers with elliptical core. Various sensors of pressure, temperature and distributed strain based on interference of presented modes were published [2,3]. Another group of optical fiber sensors based on intermodal interference typically use interference of modes LP01 and LP02 propagating in cylindrical optical fiber. From this group sensors of acoustics waves, fiber elongation, longitudinal strain, temperature and hydrostatic pressure have been published [4–6]. In this paper an exploitation of the equalization wavelength e of intermodal interference between LP01 and LP11 modes in a liquid-core optical fiber (LCOF) for temperature measurement is

∗ Corresponding author. Tel.: +421 41 5132343; fax: +421 41 5131516. E-mail addresses: [email protected] (I. Martincek), [email protected] (D. Pudis), [email protected] (D. Kacik), [email protected] (K. Schuster). 0030-4026/$ – see front matter © 2010 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2010.05.012

theoretically and experimentally described. The LCOF consists of a fused silica cladding and a core with medicinal oil. In such LCOF the equalization wavelength is sensitive to temperature due to the different thermal coefficient of refractive index core and cladding. It can be used for sensing applications, where the equalization wavelength is measured for defined modes. 2. Approach The time-averaged instantaneous power Pco of the electromagnetic fields along the fiber inside the core of an optical fiber is Pco = P1 + P2 , where P1 =

1 ∗ aj aj 2 j

and P2 =

(1)



ej × h∗j .ˆz dS

(2)

Sco



1  ∗ aj ak exp(i(ˇj − ˇk )z) 2 j

k= / j

ej × h∗k .ˆz dS,

(3)

Sco

where aj is the amplitude of jth mode, ej , hj are the functions describing jth mode field distributions, z is the coordinate along which the modes propagate and ˇj are the phase constants of modes. P1 is the sum of the time-averaged power of all of the modes and does not depend on the phase constants of modes or the fiber length (while the absorption and radiative losses of light is not taken into account). P2 is the interference term depends on the amplitudes of

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the modes, the length z of the fiber and the difference of the phase constants of particular interfering modes ˇj − ˇk . If we suppose the contribution of only LP01 and LP11 modes and the weakly guiding optical waveguide with cylindrical symmetry and step index profile of core and cladding the interference part of Eq. (3) can be expressed as a dependence on wavelength 



P2 () = nco ()

2

 .

ε0 a01 ()a11 () cos[(ˇ01 () − ˇ11 ())z] 0



J0 (U01 ()R)J1 (U11 ()R)R dR R

cos ϕ dϕ,

(4)

ϕ

where nco is the core refractive index, a01 , a11 are the amplitude of LP01 and LP11 modes, ˇ01 and ˇ11 are the phase constants of LP01 and LP11 modes, J0 , J1 are the Bessel functions of the first kind zero and first-order, R = r/, where  is the core radius of optical fiber and r is the radial coordinate, U01 , U11 are the normalized propagation constants in the transverse direction in the core of LP01 and LP11 modes given by Uj2 = 2 (k2 n2co − ˇj2 ), where k = 2/ and  is the wavelength in vacuum. Phase constant of jth modes ˇj can be expressed as [7]



ˇj = k

n2co −

Uj2 (V ) V2

(n2co − n2cl ),

(5)

where ncl is the cladding refractive index and V is normalized frequency defined by equation



V = k

n2co − n2cl .

(6)

If we suppose the weak dependence of nco , ncl , a01 , a11 , J0 (U01 R) and J1 (U11 R) on wavelength in Eq. (4), then the interference signal P2 is satisfied by harmonic function P2 () ≈ cos[(ˇ01 () − ˇ11 ())z].

(7)

Eq. (7) documents that spectral dependence of interference signal of two modes mainly depends on the length of fiber z and the difference of phase constants ˇ01 , ˇ11 of interfering modes. This difference of phase constants ˇ01 , ˇ11 shows extreme in wavelength dependence, which corresponds to the equalization wavelength. However, according Eqs. (5) and (6) the difference of phase constants of two modes depends on the core radius  and the refractive indices nco , ncl . This fact indicate, that for the step index optical fiber with constant length z and constant core radius  the value of the equalization wavelength e is only the function of refractive indices nco and ncl [8]. Refractive index of optical fiber nco and ncl , which cladding consists of fused silica and core of medicinal oil can be described by dispersion equations. Dispersion of cladding refractive index ncl () for fused silica at temperature T = 20 ◦ C can be described by the Sellmeier equation [9] n2cl (, 20 ◦ C) = 1 + +

0.69616632 2

2

− 0.0684043

0.89747942 2 − 9.8961612

+

Fig. 1. Calculated spectral dependence of ˇ01 − ˇ11 at temperature 24, 26 and 28 ◦ C. Maximum corresponds to the equalization wavelength e .

to fused silica. While the thermal coefficient of refractive index for fused silica at temperature T = 20 ◦ C and at wavelength 589 nm is 1 × 10−5 K−1 [10], whereas the thermal coefficient of the refractive index for medicinal oil at temperature T = 20 ◦ C and at wavelength 589 nm is −3.9 × 10−4 K−1 . This considerable difference of thermal coefficients of refractive indices causes the strong dependence of equalization wavelength on temperature. Due to the fact that the refractive index of medicinal oil is slightly higher than for fused silica in all investigated spectral range the weakly guiding approximation can be used for description of waveguide properties of such optical fiber. A dependence of ˇ01 − ˇ11 on wavelength was calculated for step index weakly guiding optical fiber, which core with radius  = 2.75 ␮m consists of medicinal oil and cladding of fused silica. The calculated spectral dependence for temperatures 24, 26, 28 ◦ C is shown in Fig. 1, where maximum corresponds to the equalization wavelength e . In Fig. 2 are shown numerically calculated spectral dependencies of interference of modes LP01 − LP11 given by (7) for considered optical fiber of length z = 6.82 cm and phase constant difference ˇ01 − ˇ11 from Fig. 1. It is evident from Fig. 2, that the equalization wavelength e can be well identified from spectral dependence of interference for considered modes. Generally, the material and geometrical parameters of optical fibers are changing with temperature. For optical fiber where the core is represented by oil (or another liquid) and cladding by fused

0.40794262 2

− 0.11624142

,

(8)

where  is the light wavelength in micrometers. The core refractive index nco () for medicinal oil (medicinal oil 15, Slovak Institute of Metrology) can be described by the dispersion equation at temperature T = 20 ◦ C nco (, 20 ◦ C) = 1.4551 +

400280 3.1 × 1011 + , 2  4

(9)

where  is the light wavelength in nanometers. Medicinal oil has been chosen as an appropriate core medium because of higher thermal coefficient of refractive index comparing

Fig. 2. Calculated spectral dependencies of optical power for interference of modes LP01 − LP11 at phase difference of ˇ01 − ˇ11 taken from Fig. 1.

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Fig. 3. Experimental configuration for local spectral analysis of LCOF – liquid-core optical fiber, HL – halogen lamp, L – lens, EF – excitation optical fiber, DF – detection optical fiber, 3D – nanopositioning stage, OSA – optical spectral analyzer, PC – personal computer.

Fig. 4. Experimental arrangement for detection of intermodal interference of the modes LP01 and LP11 in the LCOF.

silica, the change of geometrical parameters of optical fiber with temperature can be neglected, because the coefficient of thermal expansion for fused silica is 5.5 × 10−7 K−1 [10]. Then only changes of refractive index with temperature are taken into account for analyze of optical properties of such optical fiber. 3. Experimental Intermodal interference of modes LP01 and LP11 in temperature dependence was investigated in capillary optical fiber with cladding from fused silica with core filled with medicinal oil of radius  = 2.75 ␮m and of length z = 6.82 cm. Experimental setup for investigation of intermodal interference in LCOF is shown in Fig. 3. The light from the halogen lamp is focused to the excitation optical fiber with the core diameter 10 ␮m and fixed on positioning stage with possibility of the 3D axis motion. Such arrangement allows adjust optimal excitation of the LP01 and LP11 modes in the LCOF. Optical field of the LCOF is detected via detection optical fiber with core diameter 10 ␮m. Signal from detection fiber is analyzed in OceanOptics USB2000 spectrometer operating in the wavelength range 350–1000 nm and spectral resolution 1.5 nm. The core of the detection fiber was off-centered by distance d from the LCOF axis (Fig. 4) in order to detect the intermodal interference of modes LP01 and LP11 . The LCOF was thermally stabilized and temperature was measured with accuracy of 0.1 ◦ C.

Fig. 5. Interference signal in spectral range taken at different off-centering values of detection fiber.

Fig. 6. Shift of the equalization wavelength shown on measured spectra for temperatures 28.2, 27.5, 26.2 ◦ C.

In Fig. 5 is shown measured optical signal of intermodal interference for LCOF at temperature T = 27.7 ◦ C and offset of detection optical fiber from LCOF axis of d = ±4.5 ␮m. The clear antiphase of measured signal in this figure documents the interference of modes LP01 and LP11 . From this spectral dependence can be clearly identified the equalization wavelength e . Change of the equalization wavelength e of the investigated LCOF in dependence on temperature is documented in Fig. 6. Figure shows the measured signal of intermodal interference for three different temperatures of optical fiber. The temperature increase causes a blue shift of equalization wavelength e . Values of the equalization wavelength e were determined from spectral dependencies of intermodal interference for measured temperatures (Fig. 6). In temperature range from T = 24.2 ◦ C to T = 29.0 ◦ C the equalization wavelength e changed from 826 to 588 nm. Then in the investigated temperature range was observed the equalization wavelength shift of 238 nm at temperature change of 4.8 ◦ C. For the defined radius and refractive indices of LCOF the temperature dependence of the equalization wavelength e was calculated. The equalization wavelength e was determined as a maximum of the function ˇ01 () − ˇ11 () at different temperatures. Calculated dependence of e (T) is then shown in Fig. 7 (solid line). Fig. 6 documents well agreement between measured and calculated e in investigated temperature range.

Fig. 7. The calculated dependence of equalization wavelength e on temperature (solid line) and measured values (square).

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fused silica as cladding and medicinal oil as core. In the investigated temperature range from 24.2 to 29.0 ◦ C for this LCOF the e value was changed of 238 nm, what ensures the temperature resolution of about 0.02 ◦ C. The determination of the equalization wavelength e using intermodal interference for weakly guiding optical fiber could find application area in design of optical fiber sensors for measurement of different physical quantities if refractive indices are a function of these quantities. Acknowledgements

Fig. 8. The calculated thermal sensitivity of the equalization wavelength e on temperature.

For sensitivity characterization of temperature measurement using e was calculated thermal sensitivity of the equalization wavelength de /dT from function e (T) (Fig. 8). Calculated dependence documents sensitivity in the range from −56 nm K−1 at 24 ◦ C to −34 nm K−1 at 29 ◦ C. From these values results, that in the case of determination of the equalization wavelength e with accuracy 1 nm this technique allows measuring of temperature with precision of about 0.02 ◦ C. 4. Conclusion We demonstrate the intermodal interference of the LP01 and LP11 modes and determination of the equalization wavelength e in LCOF. Theoretically was described the weakly guiding optical fiber with the constant core radius, where e is a function of the refractive indices of core and cladding. This dependence of e on refractive indices is employed for measurement of temperature. Then by choice of materials with appropriate thermal coefficient of refractive indices for core and cladding in LCOF the dependence of e on temperature can be observed. We documented such properties in LCOF consisted of

This work was financially supported by Slovak Academy of Sciences No. VEGA-1/0868/08 and 1/0683/10 and by the European Action COST 299 “FIDES – Optical fibres for new challenges facing the information society”. The authors wish to thank for the support to the R&D operational program Centre of excellence of power electronics systems and materials for their components. The project is funded by European Community, ERDF – European regional development fund. References [1] S. Yin, P.B. Ruffin, F.T.S. Yu, Fiber Optic Sensors, 2nd ed., CRC Press, Taylor & Francis Group, 2008. [2] D. Kumar, S. Sengupta, S.K. Ghorai, Distributed strain measurement using modal interference in a birefringent optical fiber, Meas. Sci. Technol. 19 (2008) 065201. [3] W.J. Bock, T.A. Eftimov, Polarimetric and intermodal interference sensitivity to hydrostatic-pressure, temperature and strain of highly birefringent optical fibers, Opt. Lett. 18 (1993) 1979–1981. [4] M.R. Layton, J.A. Bucaro, Optical fiber acoustic sensor utilizing mode–mode interference, Appl. Opt. 18 (1979) 666–670. [5] M. Spajer, Linear phase detection for bimodal fiber sensor, Opt. Lett. 13 (1988) 239–241. [6] T.A. Eftimov, W.J. Bock, Sensing with a LP01 − LP02 intermodal interferometer, J. Lightwave Technol. 11 (1993) 2150–2156. [7] I. Turek, I. Martincek, R. Stransky, Interference of modes in optical fibers, Opt. Eng. 39 (2000) 1304–1309. [8] I. Martincek, D. Kacik, I. Turek, P. Peterka, The determination of the refractive index profile in ␣-profile optical fibres by intermodal interference investigation, Optik 115 (2004) 86–88. [9] I.H. Malitson, Interspecimen comparison of the refractive index of fused silica, J. Opt. Soc. Am. 55 (1965) 1205–1209. [10] M.J. Weber, Handbook of Optical Materials, CRC Press, New York, 2003.