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A novel approach to calibrate a phase-shift formed in a long-period fiber grating (LPG) is firstly proposed and numerically demonstrated, which is based on the use of either intensity- or wavelength-interrogation technique to the main loss-peak of the phase-shift LPG in the spectrum. Moreover, by using a CO2 laser with high-repetition-rate pulses emission, an equivalent phase-shift is successfully created at middle of the LPG. As an application of the proposed calibration scheme, measurement for the temperature and the refractive index of the ambient solution has been proposed and successfully demonstrated by using a phase-shifted LPG.
©2013 Optical Society of America
1. Introduction
In the past decades, long-period fiber gratings (LPFGs) has been comprehensively studied and found widely applications in the fields of optical communications and fiber sensing system [1–6]. Most recently, the phase-shifted LPFG have increasingly attracted a lot of research interests attributed to some of its superior properties, such as the narrow bandwidth for the resulted loss peak, high sensitivity to the environmental parameters which makes it the ideal role being utilized as the all-fiber-type biochemical sensor [7–10], optical switching, and all-optical processing elements (such as the optical differentiator and sub-picosecond pulse shaper) [11]. To date, various methods have been developed to fabricate the phase-shift LPGs. In general the phase shift can be permanently inserted into a fiber grating by using either the UV post-processing [12], or the post-etching technique [7, 8, 13, 14]. For some other cases, a temporary phase shift can be introduced into a grating by using either a local heating or the strain imposed approaches [15–17]. However, among all the above methods, the real magnitude of the phase-shift is hardly to be precisely controlled as what is expected in advance. Moreover, until present the quantitative analyses to calibrate the phase-shift formed in a LPG and the detail relationship between the spectral characteristics of the loss peak (including the loss depth and the peak wavelength at which the loss is maximum) and the amount of the phase-shift have rarely been investigated, which is, however, very important and strongly desirable whenever the phase-shift LPG is practically utilized as either the all-optical signal processing component or as a high-sensitive fiber devices for measuring the environmental parameters, such as the temperature, strain, transverse load, pressure, and the refractive index-change of the surrounding materials [6, 11 18, 19].
In this paper, in order to precisely calibrate the phase-shift formed in a LPG, systematic analyses on the relationship between amount of the phase-shift and wavelength of the resulted loss peak (at which the transmission is minimum), and the relationship between the amount of phase-shift and depth of the loss-dip are numerically investigated at the first time, to the best of our knowledge. A novel scheme for calibration of the resulted phase-shift in LPG is proposed and numerically demonstrated, which is based on the use of either an intensity- or wavelength-interrogation technique to the loss-peak appeared in the transmission spectrum. Moreover, by tapering the LPG with high-repetition-rate CO2 laser pulses, a phase-shift is successfully created at the central part of the LPG. As an application of this kind of phase-shifted LPG, a simultaneous measurement for the temperature and the surrounding refractive index has been proposed and experimentally demonstrated.
2. Quantitative analyses for a phase-shift formed in a long period fiber grating
2.1 Relationship between the transmission spectrum and the amount of the phase-shift
First of all, we perform the spectral analysis for a phase-shifted long-period fiber grating by using the transfer matrix method (TMM) [20, 21]. For convenience, a three-layer with step-index type single-mode fiber is assumed here and the fiber parameters are particularly chosen as follows: refractive indices for the fiber core and cladding are assumed to be 1.4580 and 1.45144, respectively, and the third layer is air; the core and cladding diameter are assumed to be 7.0, and 125 μm, respectively; the length and period of the grating are assumed to be 3.25 cm, and 600 μm, respectively. In addition, the coupling between the fundamental- and the cladding-mode LP11 is only considered here, which is assumed to be resonant at wavelength of 1571.2 nm. The maximum index-modulation of the LPG is assumed to be. Moreover, the phase-shift is assumed to be inserted at the middle of the grating. Different amounts of the phase shifts are adopted here. Figure 1 shows the calculated results for the transmission spectra of the phase-shift LPG, where the phase shift adopted are 0, 0.25π, 0.5π, 0.75π, π, 1.25π, 1.5π,1.75π, and 2π, respectively. In Fig. 1(a), the phase-shift inserted is within the range of (0, π) while in Fig. 1(b) the phase-shift inserted is within the range of (π, 2π). To compare the curve where the phase-shift is absent with the other nine curves shown in Fig. 1, one can easily find that attributed to the inserted phase-shift, the original loss band (i.e., corresponding to the cases where the phase shift is absent or the phase-shift is a integer times of 2π) is split into two loss-dips. When the inserted phase-shift is in the region of (0, π), the new resulted band with a larger loss-dip appears on the right side (longer wavelength side) while the other with less loss-dip appears on the left side of the original LPG’s band. But when the phase-shift is in the region of (π, 2π), the contrary results are obtained, i.e., the resulted band with a larger loss-dip is appeared on the left side while the other one with a relative less loss-dip is lied at the right side, which are shown in Fig. 1(b). Furthermore, from Figs. 1(a) and 1(b), it is easily to see that not only the strength (transmission) but also the peak-wavelength of the resulted loss dips are strongly dependent on the amount of the inserted phase-shift, which obeys the following rules: For a case where the phase-shift is in the region of (0, π) (as shown in Fig. 1(a)), as the amount of the phase-shift increases, the peak wavelength of the larger loss-dip gradually shifts to the longer wavelength direction and becomes the longest one when phase-shift is inserted meanwhile the depth of the resulted dip (band) becomes the minimum. But in a case where the phase-shift is in the region of (π, 2π) (as shown in Fig. 1(b)), as the amount of the phase-shift increases, the peak wavelength of the larger loss-dip gradually shifts to the short direction and becomes the shortest one when phase shift is inserted and meanwhile loss-peak of the resulted band becomes the minimum. To give further detail information, all the data shown in Figs. 1(a) and 1(b) are summarized and plotted again in terms of the phase-shifts as are shown in Figs. 2 and 3, respectively. Figure 2 shows the dependence of the loss peak (for the one with larger loss dip) on the inserted phase-shift, where the red star symbols represent the calculated data and the two black solid lines are the linear fit curves for all the numerical data within the region of (0, π) or (π, 2π)), respectively. Here it must be pointed that there almost exists an ideal linear relationship between amount of the phase-shift and the depth of the resulted loss-dip. The linearity of them is pretty high with R2 value up to ~0.99 (R2 value indicates the degree of the linearity for the fitting data obtained by using the linear regression method), therefore it is natural for us to believe that the amount of the phase shift inserted in the LPG (with a magnitude in the region of either (0, π) or (π, 2π)) can easily be calibrated as long as the depth of the resulted loss-dip can be exactly measured.
Fig. 1 Theoretical results for the transmission spectra of LPG with and without a phase-shift. The phase shift inserted is within the region of (a) (o, π), and (b) (π, 2π).
Fig. 2 Theoretical results for the wavelength of loss peak vs. the amount of the inserted phase-shift.
Fig. 3 Theoretical results for the wavelength of loss peak vs. the amount of the inserted phase-shift.
On the other hand, Fig. 3 shows dependence of the peak-wavelength (only for the one with larger loss-dip) on the inserted phase-shift, where the red-star symbols represent the calculated data and the two black solid lines are the linear fit curves corresponding to the phase shift within the region of (0, π) and (π, 2π), respectively. Form Fig. 3, one can easily find that there also exists an linear relationship between amount of the phase-shift and changes of the peak-wavelength for the resulted loss-dip, the linearity for the peak-wavelength in terms of the phase-shift is high enough with R2 value up to 0.9994 and 0.9988 when the phase-shift is in the region (0, π) and (π, 2π), respectively. The above results can be regarded as the most important finding shown in Fig. 3. In view of the above results, it is certainly for us to believe that any one phase shift induced in the LPG can also be exactly calibrated as long as the peak-wavelength of the resulted loss-dip is exactly measured, which is easily realized by using an optical spectral analyzer (OSA).
2.2 Proposal for the phase-shift formed in a LPG and its application to refractometric sensor
Based on the above results, a new kind of phase-shifted LPG which can directly finds an application to refractometric sensor is proposed. Figure 4 shows scheme of the proposed sensor, where the inserted phase-shift is specially formed by tapering the fiber with a diameter of several micrometers at center of the LPG, which can be realized by using either the electric-arc discharge or the focused CO2 laser technique [22]. Note that due to the extreme narrowness of the fiber, i.e., the whole diameter of the fiber is changed from 125 μm to several μm in the tapering region, the original fiber core (the red color region shown in Fig. 4) become so small (with a diameter of several sub-micrometers) that most of the optical light propagate in the original cladding layer (blue region) rather than the original core layer (red color region), thus for a good approximation, in the tapering region light transmitted in the original core region can be neglected, most of the light is transmitted in the original cladding layer and the ambient medium such as the air or the other measured solution can be regarded as the new cladding layer. Based on the above assumption, the equivalent phase-shift inserted in the middle of the LPG as shown in Fig. 4 can be approximately expressed by
where L is the length of tapering region, is the effective index of the fiber core in whichthe cladding has not been tapered. is the effective index of the core while the cladding is the surrounded solvent with a index of . To be the same as those adopted in the above section, a simple three-layer with step-index fiber model is assumed here and parameters for the fiber, i.e., the radius and refractive index of the core and cladding are typically chosen as: 3.5 μm, 62.5μm, 1.4580, 1.45144, respectively. Moreover, diameter of the tapering fiber at the center of the lengthen region is assumed to be 4 μm and index of the ambient solvent is assumed to be the one which is changed in the range of (1.35, 1.45). The central wavelength of the grating is assumed to be 1571.2 nm. By solving the dispersion equation of the LP01 mode, the effective index of (at the central wavelength) is easily obtained as to be 1.4519, and relationship between and the refractive index of the ambient solvent can be obtained as is shown in Fig. 5. Particularly the length of the sensing region L is assumed to be 0.15 mm and 0.3 mm, respectively. Then by using the Eq. (1), dependence of the phase-shift on the refractive index of the ambient solution can be directly obtained as is shown in Fig. 6. Note that for the case of L = 0.15 mm, the resulted phase-shift lies in the region of (0.4π, 1.0π) when the surrounded index is changed from 1.35 to 1.45 (as is shown in Fig. 6(a)). But for the case of L = 0.3 mm, the resulted phase-shift lies in the region of (1.0π, 2.0π) and the corresponding results are shown in Fig. 6(b). By combining thecurves shown in Fig. 6 with those ones shown in Fig. 2 and Fig. 3, respectively, relationship between the depth and the peak wavelength of the resulted LPG loss-dip with the refractive index of the ambient solvent can easily be obtained, which are shown in Fig. 7 and Fig. 8, respectively, where the Fig. 7 corresponds to the case of L = 0.15 mm and Fig. 8 corresponds to the case of L = 0.3 mm. From the data shown in Fig. 7, it can be seen that both the depth and wavelength of the loss-dip have a one-by-one relationship with the ambient index. Within the index range of (1.35, 1.45), the loss-peak and its peak wavelength will change nonlinearly in accordance with the change of the ambient index. However, when the refractive index measured is limited in the region of (1.34, 1.38) or (1.44, 1.45), there nearly exists a linear relationship between two of these parameters and sensitivities for the loss-change and the wavelength-shift in terms of the ambient index can easily be estimated as (7 dB/RIU, 61 nm/RIU) and (341 dB/RIU, 467 nm/RIU), respectively, which are also plotted and labeled as the lines I and II, respectively in Figs. 7(a) and 7(b). From the lines I and II shown in Fig. 8, the same results as those in Fig. 7 can also be obtained. However, sensitivities for the loss-change and wavelength-shift becomes rather larger than those obtained from Fig. 7(a), which are lain in the range of 33 dB/RIU to 682 dB/RIU, and 45 nm/RIU to 935 nm/RIU, respectively, strongly depended on which amount of the refractive index is measured. Comparing the results shown in Fig. 7 with those shown in Fig. 8, one can also find that a higher sensitivity can be obtained once if the length of the sensing region is increased, but at rhis case, the measuring region for the refractive index will be decreased and the transmitted loss will become larger due to the tapering process of the fiber.Fig. 6 Change of the phase-shifts formed in the LPG vs. the refractive index of the ambient solvent , where the length of sensing area L is (a) 0.15 mm and (b) 0.3 mm.
Fig. 7 Calculated results for the case of L = 0.15 mm. (a) Dependent of the depth of the resulted loss-band on the refractive index of the ambient solvent and (b) dependent of the peak wavelength on the refractive index of the ambient solvent.
Fig. 8 Calculated results for the case of L = 0.3 mm. (a) Dependent of the depth of the resulted loss-band on the refractive index of the ambient solvent and (b) dependent of the peak wavelength on the refractive index of the ambient solvent.
3. Phase-shift formed in a tapered LPG and its application to simultaneous temperature and refractive-index measurements based the phase-shift LPG
3.1 Fabrication of the phase-shift LPG by using CO2 laser
To date, various methods have been developed to fabricate LPFGs. Of which, the grating obtained by using CO2 laser based point-to-point writing technique has attracted considerable interest [23–26]. Hereafter, a simple scheme to write a phase-shift LPFG is proposed, which is based on the directly writing technique realized by using a high-repetition-rate CO2 laser pulses. The experimental setup for the fabrication is shown in Fig. 9, which consists of the CO2 laser controlling system, the beam moving and focusing system (located at a motorized translation stage), the fiber alignment stage, and the measuring system for the transmission spectrum of the LPFG. Here the utilized fiber (FutureGuide®-SR15E) is a single-mode fiber provided by Fujikura Inc, the CO2 laser (SYNRAD-20, emission central wavelength of 10.6 μm) works at a high repetition rate (5 kHz) and its duty-cycle is changeable between %1 to 99%. To fabricate a LPG, the aligned CO2 laser beam is focused on the fiber region by using ZnSe lens with a focus length of 70 cm, the minimum spot size on the fiber is 〜110 μm, which makes the focusing laser mainly absorbed by the fiber in a short period of time, and thus results in a permanent index-change in the fiber core through the effect of the resident-stress relaxation [23]. To measure the transmission spectrum of the LPFG, here an amplified spontaneous emission (ASE) source and an optical spectral analyzer (OSA) are utilized. Period of the LPFG is precisely controlled by periodically turning on/off the laser shutter (THORLAB: SH05) and meanwhile the motorized translation stage (THORLABS: LTS 300/M) is driven forward/backward along the fiber at a constant speed. All the writing procedures are programmable and controlled through a computer with the LabView software. Figure 10(a) shows the transmission spectrum of one typical LPG, where the grating length and grating pitch are 3 cm and 600 μm, respectively. Sooner after the LPG is fabricated, we make use of the same set-up to create a phase shift at middle of the LPG. The grating fixed at the clamps is pulled by moving the two piezo-stages in opposite directions (as is shown in Fig. 9) and meanwhile the central part of the grating is shoot by the focused CO2 laser. Figure 10(b) shows the transmission spectrum of the phase-shift LPG, where the surrounding medium is the air. Figure 11 shows a micrograph for the central part of the phase-shift LPG where the fiber is tapered and diameter of the tapered region is about 10 μm. To compare the results shown in Fig. 10 with the theoretical ones shown in Fig. 2, it is believed that a phase shift is certainly inserted into the fabricated LPG. However, there exists an additional ̴10dB loss in the transmission, which may be due to the extremely narrowing of the fiber in the tapering region, since the single-mode condition cannot be satisfied within this fiber region, especially when the surrounding medium (i.e., the fiber cladding layer) is air.
Fig. 10 Experimental results for the measured transmission spectrum of LPG with and without phase-shift. (a) Without the phase shift and (b) with a phase-shift inserted.
Fig. 11 Micrograph for the central part of the phase shifted LPG, where the fiber is tapered by using CO2 laser.
3.2 Temperature performances for the proposed phase-shift LPG
In the above, all the experimental results are obtained under the room temperature. Now we perform some tests to the temperature performance of the fabricated phase-shifted LPG. The LPG is laid in a temperature-controllable chamber, where the temperature can be discretely changed between 20 °C to 160 °C. Figure 12 shows the measuring results for dependence of the peak wavelength (corresponding to the maximum loss-dip) on temperature. It can be seen that the thermal responsibility (the slope of the fit line) is about 54.12 pm/°C, which is almost the same level with those LPGs obtained by using UV fabrication techniques. Compared with fitted data, accuracy of the measured temperature is estimated to be ± 3.5 °C. But here it must be noted that the temperature accuracy obtained in our experiment is mainly limited by the temperature controller (with a temperature accuracy of ± 2°C in the temperature range of 15-200 °C) utilized in our experiment. Ideally, a temperature resolution of ± 0.2 °C is expected if the measurement error of the peak-wavelength change is assumed to be ± 10 pm. Meanwhile, investigation for depth of the loss-peak in term of the temperatures was also performed. Figure 13 shows the measuring results while the ambient temperature is changed from 20 °C to 160 °C. It is easily for one to find that depth of the loss-dip nearly remains a constant which make us believe that depth of the loss-dip shown in Fig. 2 will merely depend on the amount of the phase-shift, it nearly keeps no changes even if the temperature is changed between 20 °C to 160 °C.
3.3 Proposal scheme for the simultaneous measurement of the temperature and refractive index based on the phase-shifted LPG
Base on the above facts, it is believed that the proposed sensing part shown in Fig. 4 can be utilized for simultaneous measurement of the temperature and the refractive index of the surrounded solution. The basic idea is that we can simultaneously make use of the intensity-interrogated (i.e., measurement for depth of the loss-dip terms of the phase shift as shown in Fig. 2) and wavelength- interrogated scheme (i.e., measurement for the peak wavelength of the loss-dip in terms of the phase-shift as shown in Fig. 3). In concrete, the intensity-interrogated scheme can be used to calculate the phase-shift by using the following equation:
where represents the magnitude of the phase-shift inserted in the LPG, represents the depth of the loss-peak in terms of the phase-shift inserted, is the ratio of and which is equivalent to the slope of the fitted line shown in Fig. 2, but it is a positive value when the phase-shift inserted is in the range of (o, π); and it is negative value when the phase-shift inserted is in the range of (π, 2π). Once the depth of the loss-dip is measured, the corresponding phase-shift is easily obtained by using the Eq. (2), and it can be utilized to calculate the refractive index of the ambient material n through following equationwhere F is a function of the variable , which can be obtained by fitting the data shown in Figs. 6(a) and 6(b), respectively when the length of the tapering region shown in Fig. 11 are 0.15 mm and 0.3 mm, respectively.On the other hand, the wavelength-interrogated scheme is then utilized to measure the peak-wavelength of the new resulted loss-dip (one with larger loss-peak from the two resulted dips). The wavelength change obtained at this time includes two parts which are attributed to the changes of both temperature and the refractive index. Since the spectral shift is very sensitive to both the temperature and refractive index of the ambient solution, and changes linearly with these two parameters; therefore the temperature change can be expressed as follows:
where the parameter of and can be obtained from the slope of the fitted lines shown in Fig. 3 and Fig. 12, respectively, which are equal to 20.20/π (in the unit of nm/radian) and 0.05412 nm/°C. Therefore from Eq. (4), the temperature change of the ambient solution can be precisely calculated once if the peak-wavelength change of the loss-dip is precisely measured by using OSA.To verify the above approach for the measurement of the refractive index, the commonly used saline with different salt concentration of 0, 5%, 10%, 15%, 20%, and 25% (corresponding to the refractive index of 1.333, 1,343, 1,349, 1,359, 1,369, and 1.379) are employed as the ambient solution, which are filled around the tapering region of the fiber as shown in Fig. 4. Meanwhile the room temperature is remained at a constant. Measuring results for the transmission spectra of the phase-shifted LPG are shown in Fig. 14. Figures 15(a) and 15(b) shows the change of the depth and peak wavelength of the loss-dip in terms of the ambient refractive index, respectively, which are directly obtained the data shown in Fig. 14, where the red rectangular symbols represent the experimental data and the black solid curve is a polynomial fitting one. It can be seen that just as what is expected in Figs. 7(a) and 7(b), there really exists a one-by-one relationship between the refractive index, the depth and wavelength of the loss-dip. Changes for the depth and peak wavelength are about 7 dB and 5 nm, respectively, when refractive index is changed from 1.333 to 1.379. By comparing the fitted data in Figs. 7(a) and 7(b), accuracies for the measured refractive index are estimated to be ± 9 × 10−4 and ± 2 × 10−4, respectively, which somehow agrees well with those shown in Figs. 7(a) and 7(b), respectively. However, the linear regions shown in Fig. 13 have shows some differences from the theoretical ones shown in Fig. 7, which may be due to the probable deviations for the parameters adopted in the theoretical model (such as the length of the tapering region, the core and cladding refractive index etc.) and the real ones formed in the phase-shifted LPG.
Fig. 14 Measuring results for the transmission spectra of the phase-shift LPG while concentration of the ambient saline solution refractive are 0%, 5%, 10%, 15%, 20% and 25%, respectively.
Fig. 15 Measurement results. (a) Dependent of the depth of the resulted loss-band on the refractive index of the ambient solution and (b) dependent of the peak wavelength on the refractive index of the ambient solvent.
Finally, it must also be noted that the LPG’s spectrum measured in the above is very sensitive the bending since the LPG on the taper fiber is easy to be curved. In our experiment, the grating is mounted on two clamps and a constant strain is always applied on both side of the grating in order to eliminate the above issue. However, for practical application, the bending effect of the tapered LPG on the change of both the peak-loss and the peak wavelength may become a critical issue to be considered and avoided.
4. Conclusions
A novel approach to calibrate a phase-shift formed in a long-period fiber grating (LPG) is firstly proposed and numerically demonstrated, which is based on the use of either an intensity- or wavelength-interrogation technique to the main loss-peak of the phase-shift LPG. Secondly, a simple scheme for the fabrication of both a phase-shifted long-period fiber grating (LPFG) is proposed and experimentally demonstrated by using a high-repetition-rate CO2 laser pulses. The proposed technique enables to efficiently provide various kinds of robust and cost-efficient LPFGs, which may find potential applications to the high-sensitivity biochemical sensors and all-optical signal processing devices. Thirdly, by using a CO2 laser with high-repetition-rate pulses emission, a phase-shift formed in a LPG is experimentally demonstrated. Finally, as an application of the proposed calibration scheme, a simultaneous measurement for the temperature and the refractive index of the ambient solvent has been proposed and successfully demonstrated.
Acknowledgments
This work was supported in part by the Grant-in-Aid for Scientific Research from JSPS. This work was also partly supported by the Murata Science and Technology Foundation in Japan.
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