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Abstract
A novel and reliable method enabling to produce an ultra-broad edge-filter (UBEF) is firstly proposed and demonstrated both theoretically and experimentally, which is realized by using a periodically-twisted graded-index few-mode fiber (GI-FMF). By using the proposed method, an UBEF with a dynamic wavelength-range up to ∼380 nm is numerically obtained. Furthermore, an UBEF with a linear dynamic range larger than ∼300 nm in wavelength and ∼12.7 dB in power was successfully demonstrated in experiment, which represent the highest performances among all those achieved from the fiber-based optical edge-filters (OEFs) reported to date. The proposed UBEF can be used as an ultra-broadband power interrogation component to well demodulate the wavelength-dependent signal, meanwhile it can be used as a highly-sensitive power-interrogated sensor as well. As typical application example of the proposed UBEF, a power-interrogated temperature sensor has been successfully demonstrated. The temperature responsivities with respect to the power change and the spectral shift are 0.0179 dB/°C and ∼0.49 nm/°C, respectively. The UBEF-based power-interrogated sensing system has the advantages of fast response, low cost, small size and high reliability.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fiber grating-based sensors capable of monitoring the physical parameters like temperature, torsion, strain, and refractive index, etc., have been comprehensively studied and found various applications in mechanical, biologic, chemical and environmental sensing fields [1–19]. To date, two demodulation methods, i.e., the wavelength interrogation method (WIM) and the power/intensity interrogation method (PIM) have been developed and generally used for the fiber grating-based sensors. For the former one, to precisely detect a tiny wavelength-shift in a wide range, a broadband white-light source (WLS) and an optical spectrum analyzer (OSA) with a high resolution in wavelength or otherwise an extremely narrow line-width tunable laser with both a wide tuning region and a high wavelength-scanning speed are desired. However, all of the devices mentioned above are extremely expensive, bulky, which inevitably make the WIM hardly available to some practical applications where both the high-speed response and in-situs measurement are generally demanded. For the PIM, an additional linearly wavelength-dependent optical filter, i.e., an optical edge-filter (OEF) is generally desired, which enables to turn the wavelength shift linearly into a change in output power of the light. Thus, only an optical power meter is needed for the measurement instead of an OSA, which could considerably simplify the measuring system and provide a more rapid and far more cost-effective measurement than those of the WIM. However, such OEFs are extremely difficult to obtain in optical domain.
In terms of the functionality, the OEFs developed to date can be classified into two categories, i.e., the single-function and the multi-function OEFs, respectively. For the former one, it refers to the conventional OEF but with lack of the sensing function, thus an additional sensing component (such as FBG sensor) is generally required to construct the sensing system. Typical examples of such kind of OEFs like the ones based on the erbium-doped fiber (EDF) [2], Mach–Zehnder filters (MZFs) [3,4], Fabry-Perot filters (FPFs) [5,6], Sagnac loop filter (SLF) [7], wavelength division multiplex coupler [8], fiber grating-based filters [9–11] and spatial optical filter (SPF) [12] etc. have been proposed and demonstrated. However, the maximum dynamic wavelength-range obtained in all the OEFs mentioned above is ∼15 nm, which is not wide enough for some application cases, especially for the distributed sensing case where a large amount of sensors are generally demanded. For the later one, it refers to the OEF having both the power-interrogation and the sensing functions, which can further simplify the sensing system due to elimination of the additional sensing head. In the past decades, the fiber Bragg grating (FBG)-based multi-function OEFs have been firstly reported [13–17], however, all of them are limited to the ones with a very limited wavelength dynamic-range due to the inherently narrow spectral-response the FBG-based components, wide band of such kind of OEFs have rarely been realized in experiment. To increase the dynamic range, the long period fiber grating (LPG)-based multi-function OEFs have also been proposed and demonstrated [18–21]. Of all, the maximum dynamic range in wavelength for the LPGs operated at either a low or a higher radial-order cladding modes are still limited to the ones, ∼10 nm in [18] and 40 nm in [19], respectively. Most recently, based on the phase-modulated LPGs, a multi-function OEF with a bandwidth of 50 nm [20] and a dual-triangular filter with a maximum dynamic range of ∼177 nm [21] have been proposed and numerically demonstrated, respectively, which however, have not been realized in experiment due to the fabrication difficulties.
In this paper, an ultra-broad edge -filter (UBEF) is proposed and experimentally demonstrated for the first time, which is based on a periodically-twisted graded-index few-mode fiber (GI-FMF). As a result, an UBEF with a linear dynamic range larger than ∼300 nm in wavelength and ∼12.7 dB in power was successfully realized, which represent the highest performances among all those achieved from the fiber-based OEFs reported to date. The proposed UBEF can be used as an ultra-broadband power interrogation component enabling to demodulate the wavelength-dependent signal, meanwhile it can be used as a highly-sensitive power-interrogated sensor as well. As typical application example of the proposed UBEF, a power-interrogated temperature sensor has been successfully demonstrated.
2. Principle and the simulation results for the proposed UBEF
Figure 1 shows the schematic diagram of the proposed multi-function OEF, which is composed by two piece of the single-mode fiber (SMF) and the sandwiched a twisted GI-FMF. Here the twisted GI-FMF functions like a special kind of helical LPG (HLPG), which plays a key role enabling to convert the LP01 mode to the LP11 mode in the core region when pitch of the twisted fiber is suitable selected. The LP11 mode generated in the core region of the HLPG will mainly be coupled into the cladding region of the rear SMF due to the large difference in core sizes of these two fibers as shown in Fig. 1. Since the light in the cladding region would undergo strong scattering-loss and thus cannot be allowed to propagate in a long-distance, a loss band in the transmission spectrum of the proposed OEF then can be expected to obtain, and in general the linear response regions lied on both edges of such loss-band can be regarded as the OEFs, respectively.
Next, we will elucidate the principle and the method how to realize an UBEF by using a specially-designed HLPG but written in a GI-FMF. For the LPG/HLPG-based OEF, its linearly-dynamic range in wavelength BEF must be proportional to bandwidth of the resulted rejection-band (dip) ΔλB, which in general can be approximately expressed as [22,23]
On the other hand, the HLPG-based OEF is of multi-function, which can be used as the power-interrogation component and the sensing head as well [18,19]. Particularly, when the HLPG-based OEF is exploited as a temperature sensor, the wavelength sensitivity ${S_{Temp}}$ in terms of temperature changes can be expressed as [23,24]
To numerically validate the above assumption, we performed some calculations, where the maximum refractive-index difference between core and the cladding of the used GI-FMF Δn is assumed to be 0.00794. The core diameter d1 and cladding diameter d2 of the used GI-FMF are assumed to be 23 µm and a 125 µm, respectively. Distribution of the core refractive-index is assumed to be a quadratic one. Moreover, the mode coupling between the LP01 and LP11 and the wavelength range of 1250-2000 nm are considered in this study. By using the finite element method (FEM), the effective-index spectra of the modes LP01 and LP11 were numerically calculated, the results are shown in Fig. 2(a). Based on the data shown in Fig. 2(a) and phase-matching condition obeyed in the HLPG, the relationship between the period and the resonant wavelength (also called the phase-matching curve) for the coupling between LP01 and LP11 modes was further calculated, which is drawn in Fig. 2(b) and labeled by the red color. For comparison purpose, almost the same kind calculations but for other SI-fibers including the SI-FMF and the SI-SMF were also carried out, the results are depicted in Fig. 2(b) as well. Parameters of the SI fibers adopted in the calculation are given as follows: Δn of the SI-FMF and SMF are assumed to be 0.00577 and 0.0044, respectively; d1 of SI-FMF and SMF are assumed to be 18.5 µm and 8.2 µm, respectively. d2 of SI-FMF and SMF are assumed to be 125 µm. From the Fig. 2(b), it can be seen that compared with to the other two curves, i.e., the pitch spectra for SI-FMF and SMF, respectively, the red curve, i.e., the pitch spectrum for GI-FMF, almost remains a horizontal line within the wavelength range of 1250-2000 nm, which means that for HLPG written in a GI-FMF, change of the period with respect to resonant wavelength is much more slowly than those of the SI-FMF and SMF. To make this conclusion more clearly, the slopes of the three curves shown in Fig. 2(b) were also calculated, the results are shown in Fig. 3, where the inset shows the vertically magnified part of the red curve within a range of 0-50. From this figure, one can easily find that, for case of GI-FMF-based HLPG, the slope |dΛ/dλ| remains a relatively small magnitude within the wavelength region of 1250-2000 nm (the magnitudes at wavelength of 1500 nm and 2000 nm are ∼14 and ∼ 45, respectively). Whereas for the cases of the SI-FMF-based and SMF-based HLPGs, within the same wavelength region, the maximum values for the slopes are 881 and 2461, respectively. Particularly, at the central wavelength of 1500 nm, the corresponding slopes |dΛ/dλ| become 380 and 1847, respectively, which are almost the 27 and 132 times larger than that of the GI-FMF-based HLPG. According to the Eq. (1), it is easy for us to come to the conclusion that an OEF with broad dynamic wavelength range can be expected to achieve if the GI-FMF based HLPG instead of the SI-FMF-based and the SMF-based HLPGs is utilized. Meanwhile supposing the GI-FMF-based HLPG is used as a temperature sensor centered at a wavelength of 1500 nm, then from the Eq. (2), it can be directly deduced that the temperature sensitivity obtained could be 27 times larger than that of SI-FMF-based HLPG and 132 times larger than that of SMF-based HLPG, respectively while the coupled two modes and the corresponding thermal-optical effects are assumed to be the same. Nevertheless, the above estimations are approximate results rather than the precise ones, which do reveal that exactly as what we expected from the Eq. (2), an OEF with rather high temperature sensitivity can be obtained by utilizing the GI-FMF-based HLPG.
Fig. 2. (a) The dispersion spectra for LP01 and LP11 modes in GI-FMF. (b) The relationships between the resonant wavelength and the period for the coupling between LP01 and LP11 core modes in GI-FMF, SI-FMF and SMF, respectively.
Based on the results shown in Fig. 2, transmission spectrum of the proposed GI-FMF-based OEF was calculated by using the classical transfer matrix method (TMM). Figure 4 shows the calculated result, where pitch and total length of the HLPG are assumed to be 17.2 mm and 688.5 µm, respectively. As can be seen from the Fig. 4 that an OEF with a dynamic range of ∼ 380 nm (from 1300 nm to 1680 nm) in wavelength and a dynamic range of ∼13 dB (it corresponds to the power of 95%) in transmission loss, and an excellent linearity up to 0.999 has been numerically obtained. The obtained OEF shown in Fig. 4 surely represents the best one among all those OEFs reported to date, which makes us believe that such ultra-broad OEF can be used as a wideband power interrogation device for demodulating signals from either a single sensor head but with ultra-broad measurement range or the distributed sensing system with a large amount of sensor-heads.
Fig. 4. The calculated transmission spectrum of the proposed OEF, where the length and pitch of the twisted GI-FMF are assumed to be 17.2 mm and 688.5 µm, respectively.
3. Fabrication and spectral characteristics of the proposed ultra-broad OEF
By employing the sapphire-tube assisted CO2 laser processing technique [25], the designed GI-FMF-based HLPG (whose spectrum is shown in Fig. 4) was fabricated. The setup configuration is shown in Fig. 5, where the GI-FMF was arranged to freely pass through the sapphire-tube and fixed at center of the rotator and fiber clamp, respectively. As a heat source, the CO2 laser beam was focused onto the surface of sapphire-tube, then the heated sapphire-tube functions like a semi-enclosed stove in which the passed GI-FMF will be immediately be heated to its fused status and twisted in accordance with rotation of the rotator. The helical structure can be formed in GI-FMF by moving the rotator and the motorized stages (S1 and S2 shown in Fig. 5). The twisted pitch was precisely controlled by adjusting the relative speed of the rotator and the stage S1 and S2. The stage S1 moved in same direction as the stage S2, whereas its velocity was arranged to be slightly lower than that of stage S2. Such velocities difference between the two stages can keep the fiber straight all the time during the fiber twisting process. By using a WLS and an OSA, transmission spectrum of the fabricated OEF can be measured. Here, in order to real-time monitor the output spectrum during the HLPG’s fabrication, two ends of the GI-FMF are spliced with SMF and a fiber slip ring is especially arranged on the left side of the rotator which can ensure the fiber part lied on the left side of the rotator no longer twisted with the rotation of the rotator.
Fig. 5. Configuration of sapphire-tube-assisted thermal twisting technique for fabrication of the proposed OEF.
Figure 6 shows the measured transmission spectrum of one typical HLPG fabricated in GI-FMF, where the adopted length and pitch of the grating are exactly the same as the ones used in the simulation above. From Fig. 6, it can be seen that exactly like the simulation results shown in Fig. 4, an OEF with a dynamic range of 300 nm in wavelength, a dynamic range of 12.7 dB (corresponds to the power of 94.6%) in transmission loss, and an excellent linearity ∼ 0.997 has been successfully obtained. Here it must be noted that due to the limited bandwidth of the WLS used in our measurement, the main part of the spectrum ranging from 1350 nm to 1650 nm was precisely measured and presented in Fig. 6 instead of the broader wavelength range used and shown in Fig. 4. Except for that, the experimental result shown in Fig. 6 agree well with the theoretical one shown in Fig. 4, which in return validate that the proposed wide-band OEF can really be obtained by using a HLPG but written in a GI-FMF.
For comparison purpose, the main performances among most of the OEFs reported to date are also summarized in Table. 1, where the abbreviations Exp. and Sim. mean that the corresponding results were obtained either in experiment or in the simulation, respectively. To carefully look the data in Table. 1, it can be found that among all the OEFs reported to date, the proposed GI-FMF-based OEF has an unparalleled ultra-broad linearly-dynamic wavelength range and an almost the largest linearly-dynamic range in transmission-loss, which represent the best performances of the OEF among all those previous ones reported to date. In addition, the obtained HLPG-based OEF is inherently of the polarization-independence [26], i.e., the proposed OEF is completely immune from the polarization disturbance. Such unique property would greatly benefit the real application of the OEF itself, especially when it is utilized in a power-interrogated sensing system. As a typical application example, a power-interrogated temperature sensor enabling to make full use of the wide wavelength-range of the OEF is especially considered below since the fiber-based sensors enabling the high- and wide-range temperature measurement is of the significance [27,28]. By using the proposed OEF, it is believed that a highly-reliable power-interrogated temperature sensing system can be expected to obtain.
Table 1. Performance comparisons for various OEFs
In the following, the thermal performances of the fabricated OEF were investigated before it was practically used as the power-interrogated broad-range temperature sensor. Figure 7 shows the measured transmission spectra under the conditions of three different temperatures, i.e., 24 °C, 170 °C and 290 °C, respectively. From this figure, it can be found that when the temperature increases, the spectrum largely moves to the short-wavelength direction, meanwhile the linearity of the entire spectrum almost remain the same. Particularly, the temperature sensitivity evaluated the central wavelength of 1500 nm is high enough up to ∼0.49 nm/°C, which is almost ten times larger than that of the conventional LPG/HLPG [24,25]. Such high temperature sensitivity once again validates that the theoretical analysis based on the Eq. (1) and Eq. (2) in the last section are reasonably correct.
Fig. 7. The measured transmission spectra of the fabricated OEF under the condition of three different temperatures (i.e., 24 °C, 170 °C and 290 °C).
4. Power-interrogated temperature measurement based on the fabricated ultra-broad OEF
Based on the proposed and the finally fabricated OEF, a power-interrogated temperature measurement system was constructed, the schematic of which is shown in Fig. 8, where in general, a distributed feedback laser diode (DFB-LD) operating at a specific wavelength can be used as the light source. However, for purpose of the proof-of-concept, a tunable laser enabling to work at wavelengths of 1480, 1515, and 1550 nm, respectively was especially used in this experiment. The light emitted from the light source is split into two branches by a fiber coupler, one branch is connected to an attenuator and then the power meter PM1, which is used to monitor the output power of light source. Whereas the other branch is connected to the tested object, i.e., the fabricated OEF and then the power meter PM2, which is used to measure the power of the transmitted light after passing through the OEF. Noted that transmission spectrum of the tested OEF at room temperature is exactly the same as that shown in Fig. 6. Moreover, it was installed in a thermal chamber where the temperature ranges from 20 to 300°C can be adjusted. By precisely measure the power difference (in unit of dBm) between the power meter PM2 and PM1 under different temperatures, changes in temperature can be indirectly known after the demodulation calculation. Based on utilization of the measurement system shown in Fig. 8, the dependence of the power-difference change Δ(P1-P2) on the temperature was investigated. The results are shown in Fig. (9), where Fig. 9(a), 9(b) and 9(c) correspond to the results obtained while the laser is operated at wavelengths the 1480, 1515 and 1550 nm, respectively.
Fig. 8. Schematic diagram of the power-interrogated measurement system. DFB-LD, distributed feedback laser diode; PM, power meter.
Fig. 9. Changes of the power-difference Δ(P1-P2) vs. the temperature, where the utilized light source was operated at wavelengths of (a) 1480 nm, (b) 1515 nm, and (c) 1550 nm, respectively.
As can be seen from Fig. 9 that, for all three cases, the power changes Δ(P1-P2) have an excellent linear relationship with the changes in temperature, the R2 values for linearly fitting the experimental results shown in Figs. 9(a), 9(b) and 9(c) are 0.994, 0.995 and 0.997, respectively. The temperature sensitivities obtained at the three wavelengths (i.e., 1480, 1515 and 1550 nm) are 0.0179 dB/°C, 0.0164 dB/°C and 0.0149 dB/°C, respectively, which all are of the same level. Moreover, since the maximum resolution for both of the power meters used in experiment is 0.01 dBm, the temperature measurement with a resolution 0.56 °C then can be expected to obtain.
5. Conclusion
An UBEF is firstly proposed and experimentally demonstrated, which is based on a twisted GI-FMF. By using the proposed method, an UBEF with a dynamic range in wavelength up to ∼380 nm is numerically obtained. Furthermore, an UBEF with a linear dynamic range larger than ∼300 nm in wavelength and ∼12.7 dB in power was successfully demonstrated in experiment, which represent the highest performances among all those achieved from the fiber-based OEFs reported to date. The proposed UBEF can be used as an ultra-broadband power interrogation component for merely demodulating the wavelength-dependent signal, meanwhile it can be used as a highly-sensitive power-interrogated sensor as well. As typical application example of the proposed UBEF, a power-interrogated temperature sensor has been successfully demonstrated. The temperature responsivities with respect to the power change and the spectral shift, are 0.0179 dB/°C and ∼0.49 nm/°C, respectively, and for the later one which is almost ten times larger than those of the conventional LPGs/HLPGs reported so far. The UBEF-based power-interrogated sensing system has the advantages of fast response, low cost, small size and high reliability.
Funding
Yazaki Memorial Foundation for Science and Technology; Japan Society for the Promotion of Science (JP22H01546); National Natural Science Foundation of China (62003081); Natural Science Foundation of Hebei Province (F2020501003, F2020501040); Colleges and Universities in Hebei Province Science and Technology Research Project (BJ2021101); Fundamental Research Funds for the Central Universities (N2223030).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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