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Abstract
A signal picked-up technique to improve the demodulation stability and accuracy of sapphire fiber external Fabry-Perot interferometer is proposed and demonstrated. Through fusion splicing four pieces of multimode fiber in sequence with different core diameters, the in-step change of the core diameter is found to introduce a sufficient fliting effect on the transmitted higher-order guided modes in the sapphire fiber and further reduce their influence on the fundamental mode interference demodulation. Experimental results show that the proposed multi-stage coupling technique can suppress by five-fold the additional phase imposed on the fundamental mode demodulation when compared with the conventional single-stage coupling approach in which single-mode fiber is spliced with only one piece of multimode fiber. The standard deviation of the demodulated optical phase and cavity length can also be reduced by more than two times. The proposed technique provides a simple yet sufficient solution for the long-standing difficulty of multimode sapphire fiber Fabry-Perot interferometer demodulation.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Sapphire-fiber Fabry-Perot (FP) sensors have been widely used in varieties of high-temperature sensing scenarios including temperature, pressure, strain and vibration measurements [1–6]. Limited by the sapphire fiber manufacturing process, existing sapphire-core air-cladding fibers exhibit multimode guidance at telecommunication wavelength. In multimode fibers (MMFs), the modal excitation and thus energy distribution among the modes are easily affected by environmental perturbations. As a result, in MMF based FP interferometers, the excited higher-order modes (HOMs) can severely reduce the visibility as well as the signal-to-noise ratio of collected interference signal from the fundamental mode. In addition, the irregular interference between HOMs will affect the temporal phase distribution of the modal interference fringe of the fundamental mode and further introduce jumps in the demodulated phase, bringing in great difficulties to achieve high-accuracy and stable white-light signal demodulation.
Sufficient HOM suppression is therefore the key to improve the demodulation accuracy in sapphire fiber interferometers. Existing techniques for suppressing HOMs in sapphire fibers mainly include bending mode selection, fiber tapering and sapphire core doping. The bending mode selection approach aims to filter out the HOMs through bending the sapphire fiber so as to introduce high losses for HOMs and thus to realize fundamental mode propagation [7–8]. For commercial available sapphire fibers (i.e. core diameter of 150 µm), the required bending radius for sufficient HOM suppression is ∼70 mm [9]. Such a bending radius, however, may also introduce loss on the fundamental mode. Tapered fiber with suitable waist diameter can phase match with and to excite the fundamental mode of the sapphire fiber with a high efficiency [10–11]. While the tapered fiber itself is mechanically fragile and it is challenge to maintain a stable and constant coupling with the sapphire fiber. Single-mode output of a sapphire fiber can also be achieved by doping ions into the sapphire core to reduce the core-cladding contrast [12–13]. However, due to the influence of the doped ions, the operation temperature of the doped sapphire fiber is significantly decreased, limiting its application on high temperature sensing. Haas et al. [14] proposed to fuse a section of single-mode fiber (SMF) at both ends of MMFs to filter out HOMs at the fiber interface due to the different core diameters. This approach however has not yet been optimized producing a close to 10 dB loss on the fundamental mode.
In this paper, a multi-stage coupling technique is for the first time proposed to suppress the HOMs in the multimode sapphire fiber and to pick up the signal of a sapphire fiber external Fabry-Perot interferometer (EFPI) with high accuracy. In this scheme, the incident SMF is fusion spliced with MMFs with core diameters of 23 µm, 50 µm and 62.5 µm in sequence, and finally with the sapphire fiber. The HOMs of the reflected light from the sapphire fiber FP cavity were sufficiently filtered out by the mode field mismatch at the fusion interface between MMFs. The additional phase imposed on the fundamental mode demodulation can be greatly suppressed by the multi-stage coupling technique, offering a superior demodulation accuracy and stability comparing with standard single-stage coupling approach.
2. Theory
When light is coupled from SMF to MMF, several radiation and guided core modes will be excited due to the mode field mismatch, with the mode excitation efficiencies depending on modal overlap integral [15–17]. The electric field distribution of the guided core modes in MMF can be expressed as:
The coupling efficiency from SMF to mode LP0ν in MMF can be obtained by calculating the overlap integral [18]:
3. Device design
The structure of the proposed multi-stage coupling scheme from SMF to sapphire fiber EPFI is shown in Fig. 1(a). The SMF was spliced in sequence to silica MMFs (commercial available) with core diameters of 23 µm, 50 µm and 62.5 µm, which was finally fusion spliced with a sapphire fiber with 75 µm diameter. The cladding diameter of the used silica MMF is 125 µm, being matched with that of the SMF. The mechanical strength of the spliced fiber was tested by hanging a mass block of 100 g at the end of the vertically positioned fiber after splicing. The overall fiber transmission remained the same after the test. The length of MMFs used in the experiment with 23 µm, 50 µm and 62.5 µm core diameter is 10 cm, 10 cm and 15 cm respectively. The length of the sapphire fiber is 15 cm. The EFPI cavity (i.e. the temperature sensor) was formed by the free end of the sapphire fiber with another piece of sapphire fiber or a sapphire chip. Figure 1(b) shows the structure of the conventional single-stage coupling scheme, in which SMF is directly fused with a MMF with 62.5 µm core diameter. The use of bridge MMFs with intermediate core diameter can guide the fundamental mode to transit from SMF to the sapphire fiber, greatly suppressing the excitation of the HOMs. At the same time multi-stage coupling can also reduce the loss induced by the mismatch between SMF and MMF and to boost the collection efficiency of reflected light. Note that the length of MMFs does not affect the suppression performance of HOMs since the excitation coefficient of all waveguide modes are determined by the modal mismatch at the interface between the fibers. Figure 1(c) plots the recorded output interference spectrum from the sapphire fiber EFPI under different lengths of the 23/125 µm, 50/125 µm and 62.5/125 µm MMF (indicated by the three numbers in sequence). It can be seen that the spectrum and thus the interference condition barely change with the fiber length. Figure 1(d) shows the optical image of the fusion splicing point between fibers. The left panel shows the splicing points between SMF and MMF and among MMFs with different core diameters for the multi-stage coupling scheme. The middle panel shows the splicing point between MMF (core diameter 62.5 µm) with the sapphire fiber. The right panel shows the image of the integrated sapphire fiber EFPI sensor. Table 1 lists the splicing loss between the related fibers in the experiment. The overall splicing loss of multi-stage coupling scheme is 0.33 dB, which is comparable with the single-stage coupling scheme (0.34 dB). Note that in the application of the sapphire optical fiber sensor, normally only the sensor head thus the sapphire fiber itself is placed in the high-temperature area. The coupling and leading silica SMF and MMF fibers are well located in the low-temperature region (<400 °C).
Fig. 1. Scheme for picking-up the sapphire fiber EFPI interference signal using (a) multi-stage and (b) single-stage coupling. (c) Collected interference spectra of the multi-stage coupling scheme with different lengths of MMF. (d) Optical image of the fusion splicing point between SMF and MMF and among MMFs (top panel), between MMF and sapphire fiber (middle panel). The bottom panel shows the image of the integrated fiber EFPI sensor.
Table 1. Measured splicing loss between fibers in multi-stage and single-stage coupling scheme (unit dB).
The calculated coupling efficiency (using Eq. (3)) from SMF (9.3 µm core diameter, 125 µm cladding diameter) to the LP0ν (ν = 1 to 10) modes of the sapphire fibers with core diameter of 75 µm, 100 µm, and 150 µm is shown in Fig. 2(a). The fiber splicing was achieved with aligned fiber axis using a commercial available core-alignment fusion splicer. The alignment accuracy is some hundreds of nanometer determined by the optical imaging resolution. Given the relatively large mode area of the 23/125 µm, the estimated coupling efficiencies from SMF to the μ≠0 series of modes are well below 1% for such small offset value [20] and therefore can be neglected. It can be seen that with the increasing of the sapphire fiber core diameter, the mode with the maximum coupling efficiency shifts to higher orders, indicating that a smaller mode mismatch with the incident SMF is more favorable for the excitation of fundamental mode. This effect can also be seen in Fig. 2(b), which shows the coupling efficiency from different types of fibers to a 75-µm-core sapphire fiber. For direct coupling from SMF to sapphire fiber (green), LP02 mode has the highest coupling efficiency (31.2%), while when MMFs with core diameters of 23 µm, 50 µm, and 62.5 µm are used, the fundamental mode can be most effectively excited in the sapphire fiber with an efficiency up to 92.5%.
Fig. 2. (a) Calculated coupling efficiency between SMF and sapphire fibers with different core diameter. (b) Coupling efficiency from different types of fiber to sapphire fibers with 75 µm diameter. (c) Coupling efficiency for each step of single-stage and multi-stage coupling. The insets in (b) and (c) are zoom-in pictures around the fundamental mode.
In order to directly compare the results of single-stage and multi-stage coupling technique, Fig. 2(c) displays the coupling efficiency in steps. For single-stage coupling, SMF is firstly coupled to MMF with 62.5 µm diameter (pink), and then couples to the sapphire fiber (orange). The overall coupling efficiency to the LP01 mode of the sapphire fiber is 23.5%. While for multi-stage coupling, SMF firstly couples to 23/125 µm MMF (red), then to 50/125 µm MMF (green) and 62.5/125 µm MMF (blue), and finally to the sapphire fiber (orange). The overall coupling efficiency to the fundamental mode of sapphire fiber is 56.1%, which is more than two times comparing with that of single-stage coupling.
4. Experimental results
The experimental setup is sketched in Fig. 3. A broadband laser covering λ1 = 1521 nm to λ2 = 1567 nm wavelength range was injected into the single-stage coupled, multi-stage coupled EFPI, and SMF-EFPI through 2×2 couplers. In SMF-EFPI, both the connection fiber and the EFPI were made by fused-silica SMFs and was used as a reference cavity (not shown in Fig. 3). The interference signal of the two sapphire fiber EFPIs was collected by an optical spectrum analyzer. The EFPIs were fixed on an one-dimensional translation platform so as to tune the cavity length.
The stability of the EFPI cavities was firstly compared. Figure 4(a) shows the collected interference signal from single-stage coupled EFPI (top), multi-stage coupled (middle) and SMF-EFPI (bottom) at two different time moments t1 and t2 (Δt = t2 - t1 ∼ 120 s). The cavity length was set as 1000 µm. In this experiment, the multimode EFPIs were formed by the end face of 62.5/125 µm MMF and SMF. The single-stage and multi-stage coupled fiber EFPI were fixed on the same optical table, then a mass block of 646 g was placed on top of the 62.5/125 µm MMFs of the two EFPIs to introduce external perturbation and the spectra with and without the mass block were collected. Δt = 120 s was chosen to guarantee that the collected spectrum was stable over time after the perturbation. For single-stage EFPI, significant deviation between the measured spectrum at t1 and t2 and irregular envelopes can be observed due to the change in excitation conditions of the HOMs. In contrast, interference signal of the multi-stage coupled EFPI is only slightly changed from t1 to t2. As a reference, the interference data collected from SMF-EPFI is also shown, which is almost identical at t1 and t2. The visible intensity envelop of the spectrum represents as the profile of ASE light source. Figure 4(b) compares the Fourier transform of the interference spectra for the three situations shown in Fig. 4(a) at t = t1. It can be seen that the spectrum obtained from multi-stage coupling approach is almost the same as that of SMF-EFPI, while the spectrum picked-up by single-stage coupling has a relatively lower amplitude at the resonant frequency, indicating a more irregular periodicity in the spectrum.
Fig. 4. (a) Collected interference spectra and time moment t1 and t2 for single-stage coupled (top), multi-stage coupled (middle), and SMF-EFPI (bottom). (b) The corresponding frequency spectra at t1 for the three cases.
The effect of HOMs on the demodulation can be quantified by an additional phase superimposed on the demodulated signal for fundamental mode. The additional phase is defined as the change of demodulated phase for the fundamental mode interference signal induced by the contribution from HOMs in MMF. Figure 5 compares the amount of additional phase in single-stage and multi-stage coupled EFPIs versus cavity length. In the experiment, a 3 Hz external vibration was imposed on the 62.5/125 µm MMF through a vibration platform with the direction of motion orthogonal to the fiber axis, and the maximum and minimum demodulated phase were recorded by the fast Fourier transform algorithm. The cavity length was increased from 150 µm to 1200 µm with a step of 50 µm, and the corresponding phase change was recorded. It can be seen that the value of additional phase for single-stage coupled EFPI fluctuates about 0.5π, with a standard deviation of 0.2π. While for multi-stage coupled EFPI, the additional phase value varies about 0.1π, with a standard deviation of 0.1π. The smaller value of additional phase as well as standard deviation indicate that multi-stage coupling EFPI can demodulate cavity with a higher precision and is more robust to environmental perturbation compared with the single-stage coupling one.
Fig. 5. Additional phase value picked-up by the single-stage and multi-stage coupling approach versus cavity length.
When the sapphire fiber EFPI was inserted into the system, Fig. 6(a) shows the collected interference spectrum picked-up by single-stage (black) and multi-stage (red) coupling scheme, and Fig. 6(b) plots the corresponding frequency spectrum. For single-stage coupling scheme, it can be seen that clear interference fringes only appear in the wavelength range of 1538 nm to 1567 nm. The amplitude of the interference signal is also varying over wavelength. In addition, visible multiple peaks are also present in some part of fringes (e.g. around 1525 nm, 1563 nm wavelength) induced by the intermodal interference effect. The collected spectrum by multi-stage coupling approach has been obviously improved. Interference fringes exist in the entire wavelength spectrum along with about 5 times stronger visibility. The demodulated cavity length of the sapphire fiber EFPI (not the same cavity, see Fig. 3) picked-up by the single-stage (a) and multi-stage coupling (b) is shown in Fig. 7. The measurement time was 100 s. The cavity length resolved from single-stage coupling technique is 542.0 ± 0.4 µm, while for multi-stage coupling the result is 549.3 ± 0.15 µm, showing a more than two times improvement in the standard deviation.
Fig. 6. (a) Interference spectrum picked-up by single-stage (black) and multi-stage (red) coupling sapphire fiber EFPI. (b) The corresponding frequency spectrum.
Fig. 7. Demodulate cavity length over 100 s time duration for the case of single-stage and multi-stage coupling EFPI.
5. Conclusion
We demonstrate that by fusion splicing multiple bridge MMFs with core diameter increasing in smaller steps can significantly reduce the amount the HOMs excited in the sapphire fiber, further improving the accuracy and stability of the cavity length demodulation for sapphire fiber EFPI interferometer. The concept of multi-stage coupling scheme is simple to realize and may be further optimized by inserting more MMFs with suitable core diameters, or using tapered MMFs. The proposed technique is applicable for any multimode FP cavities, and is also useful for many other MMF-based applications to optimize the excitation condition, such as optical imaging [21], shape sensing [22], and nonlinear optics [23].
Funding
National Natural Science Foundation of China (U20B2057, 61775020).
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (NSFC) (U20B2057, 61775020).
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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