Temperature compensated microfiber Bragg gratings

In this paper, temperature compensated microfiber Bragg grating (mFBG) is realized by use of a liquid with a negative thermo-optic coefficient. The effects of grating elongation and the index change of silica glass are compensated by the liquid through evanescent-field interaction. As a result, the reflective wavelength shifts by only 30 pm when the temperature varies from 15 to 60°C. The proposed method is promising due to the compactness and high flexibility of the device.


Introduction
Fiber Bragg grating (FBG) is one of the most important photonic elements in fiber optic communication and sensing systems.Temperature compensation for FBGs have been investigated in the past years, for the requirement of minimizing the temperature/strain cross sensitivity for accurate measurement for FBG sensors, and the implementation of a highly environmentally stable optical filters in fiber communications.Temperature insensitivity has been achieved by bonding or embedding a FBG into a material with negative thermal expansion coefficients [1][2][3] or two materials with different thermal-expansion coefficients [4,5].Complex mechanic structures, e. g., a lever configuration [6], have also been proposed.In these approaches, a thermally induced compressive stress over the grating is created due to the difference in thermal expansion, which effectively compensates the expansion of the grating.Alternatively, liquids and liquid crystals with negative thermo-optic coefficients can be used to alter the temperature sensitivity through the interaction with the mode field.This has been first implemented by using a liquid-core fiber with gratings inscribed in the fiber cladding [7].Recently, microstructured optical fibers with holy cladding have also been used for temperature compensation for FBGs by filling selected liquid into the air holes [8,9].However, the fabrication of the fibers is expensive and the requirement of geometrical precision is high.Furthermore, the connection between single-mode fibers and these specialty fibers could introduce considerable insertion loss.
Microfibers, optical fibers with micron-scaled diameters, have received great interest due to the exceptional advantages including compact sizes, highly flexible structures, and low transmission loss with extreme bends [10,11].The tapered microfibers present natural compatibility to conventional single mode fibers.The minimal insertion loss can be less than 0.1 dB for an adiabatic tapered microfiber.In addition, the interaction between the light and surrounding medium is possible due to the strong evanescent field [12,13].The modal properties, including the propagation constants and transverse mode profiles can be significantly modified by immersing the microfiber into a selected liquid.Consequently, tunable photonic devices and refractive-index (RI) sensors for potential biomedical applications can be implemented.In this paper, temperature compensation of Bragg gratings in microfibers is demonstrated by immersing the grating into a liquid with a negative thermooptic coefficient.The effects of grating elongation and index change of silica can be compensated due to the evanescent-field interaction between the light and the liquid.The Bragg wavelength shifts by only 30 pm when the temperature changes from 15 to 60 °C for the mFBG with the optimal diameter.The corresponding sensitivity is 0.67 pm/°C, which is 1/15 of that of the uncompensated grating.Further theoretical analysis demonstrates that the temperature insensitivity can be realized with different liquids and matched microfiber diameters.The proposed method is promising for sensing and communication applications due to the compact structure and high flexibility.

Principle
The Bragg wavelength B λ of a mFBG immersed into a liquid can be expressed by the well- known phase-matching condition 2 where eff n is the effective index of the fundamental mode and Λ is grating pitch.The temperature sensitivity can be expressed by which represents the influence of temperature on the modal properties of the microfiber.The influence of transverse thermal expansion of the microfiber is ignored in this paper.For the waveguide structure composed by the silica "core" and liquid "cladding", whose material indexes are n si and n liq , respectively, the wavelength-temperature dependence can be extended as

Experimental result
The microfibers are fabricated by tapering standard single-mode fibers by means of the heatand-draw method.The heat source is a 2 mm wide flame generated by the burning of butane.The heat source scans along fiber length back and forth while stretching the fiber with two computer-controlled linear stages.The geometrical parameters, including the microfiber diameter and waist length, are mainly determined by the moving speed and range of the linear stages.The moving speeds of the stages and the heat source have been optimized to minimize the transmission loss.The lengths of the uniform region and transition region of the fiber taper are 3 cm and 3.5 cm, respectively.Bragg gratings are inscribed into the microfibers by use of a 193 nm ArF excimer laser and a phase mask [14].The repetition rate is 200 Hz and the single pulse energy is 3 mJ.The grating pitch is 1089.21nm.The grating length is 3 mm, which is determined by the 193 nm laser beam dimension.The calculated exposure dosage is estimated as 7.2 kJ.The growth of grating is monitored by use of a SLED light source and an optical spectrum analyzer (OSA), with a resolution of 0.05 nm.
The employed liquid for temperature compensation is ethanol with a purity of 99.8%.Its refractive index of the liquid at 20 °C is n liq = 1.36048 and the thermo-optic coefficient is η liq = dn liq /dT = −4 × 10 −4 .Bragg grating is inscribed in a microfiber with a diameter of D = 5.2 µm, which has been optimized in advance to achieve temperature insensitivity.The measured temperature sensitivity of the uncompensated grating is 10 pm/°C.The microfiber is then immersed into the liquid and the reflection spectrum is measured under different temperatures.Figure 1(a) shows the measured reflection spectra at 15 and 60 °C, respectively.The reflection peak blue-shifts by only 30 pm and the spectral profile hardly changes.The weaker reflection band at the short wavelength side is a result of unapodized longitudinal profile of the index modulation.The spectral quality can be improved by enhancing the coupling strength as described in [15] and creating an apodized index modulation.Figure 1(b) shows the measured Bragg wavelength as a function of temperature.The temperature sensitivity is −0.67 pm/°C for the compensated mFBG and it is 1/15 in magnitude of the uncompensated counterparts.For comparison, the measured temperature responses for two mFBGs with different diameters are also shown in Fig. 1(b).The 10.2-µm mFBG presents a temperature sensitivity of 8.73 pm/°C, which is close to the uncompensated grating.In contrast, the 4-µm mFBG presents a sensitivity of −9.68 pm/°C, suggesting that the temperature sensitivity has been over-compensated.

Discussion
The above experimental result suggests that the temperature sensitivity of the immersed mFBG is largely determined by the microfiber diameter for a given liquid.To better understand the result, detailed theoretical analysis is carried out.Figure 2 shows the calculated fundamental-mode profiles for microfibers with diameters of 4.0µm, 5.2µm and 10.2µm, respectively, calculated by use of a mode solver based on finite-element-method (FEM).The 10.2-µm microfiber presents a tight confinement of the fundamental mode.The evanescent field is very weak and the liquid can hardly affect the modal property of the silica microfiber, corresponding to a small amplitude of .As a result, a negative temperature sensitivity can be observed due to the strong interaction between light and the liquid.
Figure 3 shows the calculated and measured temperature sensitivities for the mFBGs immersed in the ethanol as a function of fiber diameter.The sensitivity is then obtained based on the phase-matching condition.The thermal expansion coefficient and thermal optic coefficient of silica are α = 5 × 10 −7 /°C and η si = 6 × 10 −6 /°C, respectively.In the calculation, these coefficients are considered invariant with temperature and the modal dispersion is ignored.The optimal microfiber diameter is D opt = 5.3 µm to obtain temperature insensitivity.The measured result is in good agreement with the calculated curve.When the diameter is down to about 2 µm, the temperature sensitivity can be as high as −100 pm/°C, as a result of much stronger evanescent-field interaction, which indicates that the proposed method can also be used to greatly enhance the temperature sensitivity.However, the reflection peak of mFBG with such small diameter is difficult to observe due to the low transverse overlap between the mode energy and the grating region.

Conclusion
In conclusion, we have presented temperature-compensated mFBGs by immersing them into a liquid with a negative thermo-optic coefficient.The temperature insensitivity can be obtained due to the evanescent-field interaction between light and liquid.In our experiment, the temperature sensitivity has been reduced to its 1/15 for a 5.2-µm microfiber by immersing it into ethanol with a purity of 99.8%.The theoretical analysis suggests that temperature compensation for mFBGs can be achieved by using different liquids, by optimizing the fiber diameter.The proposed method can meet the requirement on stability in dense wavelengthdivision-multiplexing system and dispersion compensation.In addition, the FBGs in microfibers have presented advanced sensing characteristics for mechanic measurands, e. g., hydrostatic pressure [16].The proposed technique can effectively reduce the temperature cross sensitivity, which greatly benefit precise measurement.

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168435 -$15.00USD Received 11 May 2012; revised 3 Jul 2012; accepted 23 Jul 2012; published 25 Jul 2012 (C) 2012 OSA 30 July 2012 / Vol. 20, No. 16 / OPTICS EXPRESS 18282 the thermal-optic coefficients of silica and the employed liquid, respectively.The dependence of the fundamental-mode index on material index eff si expansion coefficient α and η si are all positive.Consequently, it is possible to achieve temperature insensitivity, i. e., d 0 d B T λ = , by using a liquid with a negative thermal-optic coefficient liq η .Note that the contrast between eff si the compensation, which is determined by the transverse index profile of the silica-liquid waveguide.The microfiber diameter needs to be optimized to reach a balance between the contribution of grating elongation/index change of silica and the effect of the liquid.

Fig. 1 .
Fig. 1.(a) Measured reflection spectra of the immersed mFBG with a diameter of 5.2 µm measured at 15°C and 60°C, respectively; (b) Measured wavelength shifts as a function of temperature for the immersed mFBGs with different diameters.The curves are linear fits for individual responses.
(3).In contrast, the 4-µm microfiber presents a considerable portion of mode energy in the form of evanescent field in liquid, which effectively increases the value of eff

Fig. 3 .
Fig. 3. Calculated and measured temperature sensitivity as a function of microfiber diameter for the mFBG immersed in ethanol.According to Eq. (3), the compensation capability of the liquid can be enhanced by two means: (1) using a liquid with larger η liq ; (2) enhancing the evanescent-field interaction, i. e., increasing

Fig. 4 .
Fig. 4. Calculated optimal diameters for temperature insensitivity as a function of the thermaloptic coefficient of liquid for different liquid refractive indexes.