1. Introduction

Over the past decade optical fiber-based sensors have found numerous applications to environmental sensing [1,2]. We demonstrate that long-period gratings written in the core of a photosensitive optical fiber can be used for temperature, strain and index of refraction sensing. The basic functionality of such devices is discussed and the dependence on the host fiber parameters, the grating periodicity and the order of the cladding mode is outlined. It is also shown that long-period gratings can be implemented using a simple intensity demodulation scheme. Finally, the multiple bands of a single grating are use for simultaneous measurement of temperature and axial strain.

2. Long-period gratings

Gratings are fabricated by exposing the core of a photosensitive optical fiber to a spatially varying ultra-violet beam [3]. Typically the impinging UV beam is periodic in space and results in a regular pattern of index of refraction modulation in the fiber core. The periodicity and amplitude of this refractive index variation determines the coupling of light between the guided mode(s) and the non-guided modes through the phase-matching condition [4,5].

For standard telecommunication optical fiber, grating periodicity of the order of 0.5 μm causes the fundamental guided more to couple light to the reverse propagating guided mode over a narrow range of wavelength [4]. This coupling of light shows up as a loss in transmitted intensity through the Bragg grating. The phase-matched wavelength is reflected back and can be retrieved using an input coupler or an optical circulator. Such gratings are typically several millimeters long and any external perturbation that varies the effective index or the periodicity in the localized region causes the coupling wavelength to shift. For example, for a 100 °C change in ambient temperature, a fiber Bragg grating at 1550 nm undergoes a shift of 1 to 1.3 nm to longer wavelengths [6]. A similar shift corresponds to about 1% axial strain on the grating [6]. To demodulate this wavelength shift optical spectrum analyzers are commonly utilized. For higher sensitivities complex unbalanced interferometer's have been demonstrated in the past [7]. Although Bragg gratings present an attractive sensing platform, these are limited by either sensitivity to strain or temperature, or by expensive demodulation schemes. Additionally, index of refraction sensors using Bragg gratings require the user to etch the cladding to gain access to the evanescent filed of the guided mode [8]. Since the Bragg grating-based sensor is sensitive to both strain and temperature, separating these parameters requires multiple co-located gratings [9], adding to the system cost.

A long-period grating is formed by using a ultra-violet beam that has a spatial intensity variation with periods ranging from tens to several hundred micrometers [10]. For these gratings, the energy typically couples from the fundamental guided mode to discrete, forward-propagating cladding modes. The cladding modes are quickly attenuated and this results in series of loss bands in the transmission spectrum of the grating. Each of these attenuation bands corresponds to coupling to a distinct cladding mode that has an effective index that is a strong function of the host fiber parameters. For an unglazed long-period grating with periodicity Λ, the wavelength λ^(m) at which the mode coupling occurs is given by:

where n_eff and n_cl,m are the effective indices of the guided mode and the LP_0m cladding mode, respectively [10]. For a given fiber, the grating period determines the cladding modes to which light can be coupled. Also the so-called characteristic curves that depict the variation of the coupling wavelength as function of the grating period for different cladding modes can be obtained once the guided and cladding modes’ effective indices are known [10]. The variation in the grating period and the modal effective indices due to strain and temperature causes the coupling wavelength to shift [11]. This spectral shift is distinct for each loss band and is a function of the order m of the corresponding cladding mode. This implies that the multiple bands of a long-period grating can be used to effectively separate strain and temperature effects acting simultaneously on the grating [12]. Moreover, long-period gratings can be employed as refractive index sensors since the evanescent field of the cladding modes extends beyond the cladding of the host fiber [11]. Additionally, the wide resonance bands of a long-period grating lend themselves to simple demodulation techniques by converting wavelength shift to an intensity variation.

3. Single-parameter sensing

3.1 Temperature

The sensitivity of a long-period grating to temperature T can be examined by expanding Eq. (1) to yield:

where L is the length of the grating, δn_eff=n_eff-n_cl is the differential effective index, and the ordinal m has been dropped for the sake of simplicity.

 

Fig. 1. Shift in a band of a long-period grating with temperature. The spectra correspond to temperatures of 22.7 °C, 49.1 °C, 74.0 °C, 100.9 °C, 127.3 °C and 149.7 °C from left to right [14]. The resonant wavelength shifts from 1607.8 nm at 22.7 °C to 1619.6 nm at 149.7 °C.

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The two terms on the right hand side of Eq. (2) separated by the + sign represent the contributions to the grating thermal sensitivity due to the change in the differential effective index and the grating periodicity, and will henceforth be referred to as the material and waveguide effects, respectively [13]. The material contribution arises from the change in the indices of refraction of the core and the cladding due to temperature and is a function of the composition of the fiber. The waveguide contribution has its basis in the thermal sensitivity of the grating periodicity and can be negative or positive depending strongly on the slope dλ/dΛ of the characteristic curve corresponding to the appropriate cladding mode [14]. The wavelength shift due to the material effect can similarly have either polarity and its magnitude is a function of the relative change between the effective indices of the guided and cladding modes. For standard long-period gratings with periodicity of hundreds of micrometers, the material effect typically dominates the waveguide contribution to the temperature-induced shift. The strong dependence of the material effect on the order of the cladding modes results in the distinct wavelength shifts of the individual loss bands of a long-period grating. Moreover, since the period of the grating dictates the order of the coupled cladding mode, the temperature response for a given fiber can vary considerably with periodicity.

To study the effect of temperature, a long-period grating with Λ=280 μm was fabricated in Corning SMF-28 fiber using a continuous-wave UV laser [14]. Fig. 1 illustrates the thermally-induced shift in the loss band from 1607.8 nm at 22.7 °C to 1619.6 nm at 149.7 °C. A linear fit to the wavelength shift data yields a slope of 0.093 nm/°C and that is almost an order of magnitude higher than that observed in a fiber Bragg grating. In Fig. 1 the intensity variation with temperature at a particular wavelength is very significant. This will be used to implement a simple demodulation scheme for long-period gratings in Section 4.

 

Fig. 2. Shift in the peak loss wavelengths (with respect to that at 31.2 °C) with temperature for various resonance bands of a long-period grating [14]. The location of the bands A, B, C and D are 1608.6 nm, 1332.9 nm, 1219.7 nm and 1159.6 nm, respectively at 31.2 °C. The experimental data (symbols) are and approximated by linear curve fits. The dashed line (E) is the shift for a Bragg grating at 1550 nm with a temperature coefficient 1.3 nm/100 °C.

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Fig. 2 shows the wavelength shifts in the four resonance bands of the long-period grating described above. The distinct spectral displacement of the four bands is clearly visible. Also shown is the temperature sensitivity of a standard Bragg grating. The non-linearity in the wavelength shift for the long-period grating bands can be attributed primarily to the temperature dependence of the thermo-optic coefficients of the core and the cladding. For this particular grating the sensitivity to temperature increases with the order of the cladding mode due to the different material contributions for distinct cladding modes. The thermal sensitivity is a strong function of the grating period, the order and the coupling wavelength of the cladding mode and the host fiber parameters [14]. It has been shown recently that the wavelength shift can be further enhanced by using appropriate coating around the grating [15]. It has also been demonstrated that the temperature sensitivity can be suppressed by tailoring the fiber profile [13] or by coupling to specific cladding modes in standard fibers [16].

3.2 Axial strain

As with temperature, the sensitivity of a long-period grating to axial strain ε can be studied by expanding Eq. (1) and re-arranging to yield:

where the two terms on the right-hand side can again be divided into material (first term) and waveguide (second term) contributions. In this case the two contributions can have either polarity depending on the grating period and the order of the cladding mode. The waveguide effect can be significant and is a function of the local slope dλ/dΛ for a particular cladding mode [14]. Moreover, the two contributions can be equal in magnitude but opposite in polarity, resulting in a strain-insensitive grating that can be employed as a pure temperature sensor [17].

 

Fig. 3. Shift in the peak loss wavelengths with strain for various resonance bands of a long-period grating [14]. The dashed line (E) is the shift for a Bragg grating with coefficient 11.55 nm/%ε.

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Fig. 3 depicts the axial strain-induced shift in the resonance bands of the long-period grating written in SMF-28 fiber (with Λ=280 μm). The dependence on the order of the cladding mode is clearly evident from the fact that the resonance bands corresponding to curves A and D have linear fits of 19.42 nm/%ε and -0.32 nm/%ε, respectively. Figs. 2 and 3 also reveal the cross-sensitivity of long-period gratings to strain and temperature. The strong dependence of this cross-sensitivity on the order of the cladding mode will be employed for simultaneous strain and temperature sensing in Section 5.

3.3 Index of refraction

The influence of variation in the index of refraction n₃ around the cladding of a long-period grating can be explained by arranging Eq. (1) to produce:

For each cladding mode, the term dn_cl/dn₃ is distinct and hence a long-period grating is expected to have a strong dependence on the order of the coupled cladding mode. The shift with refractive index changes, for a given fiber and cladding mode, may be positive or negative depending on the local slope of the characteristic curve dλ/dΛ [14].

 

Fig. 4. Experimental shift in the four resonance bands of a long-period grating as a function of the index of the ambient medium [14]. The bands at 1496.6 nm (A), 1329.3 nm (B), 1243.8 nm (C) and 1192.1 nm (D) were used for the experiment. The shifts are measured with respect to the locations at n₃=1.0. The indices of the oils are calculated at the corresponding resonant wavelengths of the bands.

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Fig. 4 shows the wavelength shifts in the resonance bands (with respect to n₃=1.0) for a long-period grating written in Corning SMF-28 fiber with Λ=320 μm [13]. For this particular grating, the shift is negative for all bands and increases with the order of the cladding mode. At approximately n₃=1.444 the distinct loss bands disappear since the cladding modes get converted to radiation mode losses. Wavelength shifts as large as -66.9 nm were measured for one of the resonance bands. The sensitivity to index of refraction changes can be enhanced or reduced by manipulating the fiber parameters and choosing the appropriate grating period for coupling to specific cladding modes [14].

4. Demodulation

The demodulation of long-period gratings is typically implemented by detecting the wavelength shift using an optical spectrum analyzer. The spectrum analyzers are expensive and are additionally limited by resolution. The wavelength shift of the broad resonance bands can be converted into an intensity variation by using a laser source centered on either side of the grating center wavelength. A simple photodetector can then be used to determine the applied perturbation for a calibrated sensor [11]. Alternatively, a broadband source can be used as the input and an optical filter can be employed at the output end with the photodetector. The demodulation technique is potentially low cost, offers improved sensitivity and can be used for applications where the parameter to be measured is varying rapidly. Typically the shift in the wavelength of a resonance band under an applied perturbation is accompanied by a variation in the amplitude of the loss. This can easily be accounted for during the calibration of the sensor assuming the change in the amplitude is repeatable. For applications to index of refraction sensing the variation in amplitude can be significant around the value n₃=1.444 for conventional fibers and might limit the system performance.

 

Fig. 5. Change in transmission through a grating for increasing (circles) and decreasing (squares) temperature [14]. The resonance band for the grating under test is centered at 1294 nm (50 °C) while the laser diode is located at 1312 nm. The transmission is normalized to 0 dB at 50 °C. Inset shows the grating spectra in steps of 50 °C.

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Fig. 5 shows the effectiveness of this demodulation scheme [14]. The resonance band of a long-period grating was subjected to temperature variation. The inset in Fig. 5 illustrates the shift in the band due to temperature. A laser diode at 1312 nm was used at the light source while the transmission through the grating was monitored using a photodetector. Once calibrated, the transmitted intensity can be used for determining the local temperature at the grating.

5. Simultaneous strain and temperature sensing

As discussed in Section 3, the wavelength shift for a particular band of a long-period grating due to axial strain or temperature is a strong function of the host fiber parameters and the order of the corresponding cladding mode. The differential shift in two or more resonance bands of a long-period grating can be utilized for multi-parameter sensing [12]. As a simple analysis, let us consider two bands of a grating centered at λ₁ and λ₂. Let A and B be the temperature and axial strain coefficients of wavelength shift for the first band and let C and D be the corresponding coefficients of the second band. The shifts in the wavelengths of the two bands due to concurrent temperature change ΔT and strain change Δε, assuming a linear system, are given by:

Assuming A, B, C and D are known, the two simultaneous equations can be solved for ΔT and Δε. The non-linearity in the four coefficients requires that they be expanded in higher order terms [14]. Additionally, the cross-sensitivity between strain and temperature causes the linear and higher order coefficients of B and D to be functions of temperature [14]. If the non-linearity and cross-sensitivity can be appropriately characterized, the grating can be used for simultaneous strain and temperature measurements.

 

Fig. 6. Comparison between measured (symbols) and actual (lines) values of (a) temperature (b) strain using a long-period grating [14]. The average rate of temperature change was -1.08 °C/min.

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To test this concept an experiment was performed, the details of which can be found elsewhere [12]. Fig. 6 shows the simultaneous variation in the applied temperature and axial strain on the long-period grating as a function of time. The corresponding calculated values of the perturbations are also plotted. The maximum errors in strain and temperature were found to be 42 με and 0.6 °C, respectively. This system may be extended to include index of refraction measurements also. Moreover, the simple intensity demodulation technique proposed in Section 4 can be used with multiple laser sources and optical filters to improve sensitivity and speed.

6. Conclusions

Long-period gratings have been demonstrated as highly sensitive temperature, axial strain and index of refraction sensors. The response of these sensors is a strong function of the grating period, the fiber parameters and the order of the cladding mode. The wavelength shift in the broad resonance loss bands due to an external perturbation can be used to implement simple demodulation techniques. Additionally, the multiple bands of a single long-period grating can be utilized for simultaneous strain and temperature sensing. Long period gratings possess a high degree of versatility that can be used to configure various optical fiber-based sensing systems. Over the next few years these sensors are expected to find widespread use in commercial and military applications.