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Abstract
A micro-fiber Mach–Zehnder interferometer (MZI), with a thousands-µm-long ring-core fiber (RCF), is demonstrated, and its performance investigation is also implemented. In this paper, the proposed MZI is manufactured by ends-splicing the short RCF segment with single-mode fiber (SMF-28), respectively. The scheme of the MZI is a typically core-mismatch structure, which has the advantages of miniaturization and simplification. Due to the core mismatch between RCF and SMF, the light from the SMF can be well separated into ring core (RC) and silica center (SC) of the RCF at the first splicing point. After transmitting through the RC and SC, the two separated light beams encounter each other and interfere at the second splicing point. Different from conventional micro-fiber MZIs using SMFs or few-mode fibers, the RCF has a higher numerical aperture, which can generate a larger optical path-length difference with a short length fiber, accumulates a higher extinction ratio and suppresses the crosstalk between the core and cladding modes. Therefore, our proposed MZI is more stable and the best extinction ratios can reach up to 18.2 dB. Meanwhile, owing to the core structure of RCF (where SC is surrounded by high-index ring core), the power propagating through low-index area of RCF is mostly confined into SC (termed the silica-center modes). These characteristics would lead to the lower sensitivity to external disturbances.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Micro-fiber Mach–Zehnder interferometers (MZIs) have been extensively studied due to their miniaturization, simplification, high stability, and anti-electromagnetic interference. The MZIs are widely used in various fields, including physical, chemical and biological sensing, optical modulation, and signal processing [1–8].
Varieties of structures are utilized to manufacture the micro-fiber MZIs [9–14], such as abrupt tapers [9], core-mismatch structure [10], and long-period fiber gratings (LPG) [11]. However, all schemes have their own limitations. For example, the fabrication of LPGs requires precise control, complicated operations, and high cost. It is sensitive to external disturbances, and the interference spectral range is limited by the LPGs’ bandwidth.
Compared to LPGs, abrupt tapers [9] and core-mismatch structures [10], mainly based on core-cladding interference, are easy to be fabricated. When designing micro-fiber MZIs, some parameters must be considered, such as extinction ratios (ER) and the free spectral range (FSR). In order to achieve a high ER, the two interfering lights are required to be stable, and the value of the light intensities should be almost equal. These attributes are related to the effective index difference ($\Delta {n_{eff}}$) between core and cladding of the fiber and mode-coupling patterns. In addition, for different application scenarios, a suitable FSR can be obtained by adjusting the optical path-length difference (OPLD). The OPLD is proportional to the effective index difference ($\Delta {n_{eff}}$) between core and cladding modes and the length of interferometers. To generate a larger OPLD within a few-thousands-µm-long or shorter length fiber, a larger effective index difference is needed. The effective index difference in the fiber interferometer mainly depends on the numerical aperture (NA) of the fiber. A higher NA corresponds to a larger index difference between core and cladding. However, existing structures of micro-fiber MZI are mostly based on single-mode fibers (SMF) or few-mode fibers (FMF) [15]. These fibers usually have small index differences between core and cladding to smaller OPLD and ER [16]. What’s more, the interference spectra of the abovementioned MZI are uneven and complicated, due to the unstable cladding modes and the higher crosstalk between cladding modes. Moreover, cladding modes can be perturbed simultaneously by various external surrounding disturbances (e.g., temperature, vibration, and external reflective index), which also lead to strong crosstalk. Meanwhile, for these structures, many unwanted cladding modes are excited, which will induce more energy loss and result in spatial-mode beating. These factors may not be good for generating proper spectral range, because the OPLD highly depends on mode orders [17].
Recently, ring-core fiber (RCF), a special fiber with a high-index ring core (RC), is designed for orbital angular momentum (OAM) transmission [18,19]. In this paper, a micro-fiber MZI fabricated using RCF is proposed and demonstrated based on core-cladding interference and core-mismatch structure. Compare to SMFs or FMFs, the RCF has a higher NA, which not only can generate a larger OPLD in the same length fiber, but also can suppress the crosstalk between core and cladding modes during propagation. Meanwhile, the cladding modes in RCF are mostly limited to the silica center (SC), which has the same reflective index (RI) of cladding. This characteristic can lower the number of unwanted cladding modes and reduce the impact of external disturbances on cladding modes. The MZI, based on RCF, can improve stability and provide smooth spectra. Additionally, the length of the MZI can be precisely controlled and fabricated easily.
2. Principle of micro-fiber Mach–Zehnder interferometer based on RCF
The schematic of measured index profile and cross-sectional view of RCF are shown in Figs. 1(a) and 1(b), respectively. It should note that the insert in Fig. 1(b) is the cross-sectional view of RCF photographed with an electron microscope. The RCF has a high-index ring core, a pure silica center and outer cladding. In the proposed structure, a thousands-µm-long RCF is ends-spliced with a single-mode fiber (SMF-28), respectively, as shown in Fig. 2. L, D, ${d_1}$, and ${d_2}$ indicate the length of RCF, the cladding diameter of RCF, the outer diameter, and the inner diameter of RC, respectively. The values of D, ${d_1}$, and ${d_2}$ are 122.82, 15.76, and 9.59 µm, respectively, and the SC diameter of RCF is 9.59 µm. The core and cladding diameters of SMF-28 are 8.20 and 125.00 µm, respectively.
Fig. 1. (a) The schematic of measured reflective index profile and (b) cross-sectional views of RCF. $D$: cladding diameter of RCF; ${d_1}$: outer diameter of RC; and ${d_2}$: inner diameter of RC.
Fig. 2. Schematic of the proposed MZI with RCF. $L$: length of RCF; $D$: cladding diameter of RCF; ${d_1}$: outer diameter of RC; and ${d_2}$: inner diameter of RC.
Figure 3(a) displays the simulated propagation field distribution along the MZI with a 5,000-µm-long RCF. The simulated mode field distribution in the RCF region at L = 2000, 2500, 3000, 3500 µm are shown in Figs. 3(b)–3(e), respectively. The obtained distributed field shown in Figs. 3(a)–3(e) are all based on the beam propagation method (BPM) at the wavelength of 1,550 nm. For the proposed scheme, as depicted by Figs. 2 and 3, the incident light is firstly launched into the SMF. When light reaches the first splicing point, owing to the core mismatch between the SMF and RCF, a fractional amount of the core mode from SMF is converted into the RC of the RCF as ring-core modes (RCMs). Meanwhile, the residual power of the core mode from SMF is mostly confined to the silica center (SC) of the RCF. Little energy is leaked to the outer silica cladding, which is from the scattering light at the splicing point due to the rough touched surface between SMF and RCF. Since the most energy in silica parts is confined in SC, the modes are called silica-center modes (SCMs). During the optical field propagating through the RCF, the RCMs and SCMs interact each other and occur interference, thus the intensities distribution in SC appears periodic along the RCF, and the period length is around 2000 µm. At the second splicing point, the interfered light in RCF coupled into the SMF.
Fig. 3. (a) Propagation field distribution along the MZI with 5,000-µm-long RCF and (b)-(e) simulated mode field distribution in the RCF region at L = 2000, 2500, 3000, 3500 µm under input wavelengths of 1,550 nm, respectively.
Suppose that the intensity of RCMs and SCMs are ${I_{RC}}$ and ${I_{SC}}$, respectively, the output intensity ${I_O}$ after interference can be expressed as
Fig. 4. Transmission spectra of MZIs with different RCF lengths along (a) 1,250–1,650 nm and (b) 1,500–1,650 nm.
Table 1. Measured parameters for MZIs with different RCF lengths
Based on Eq. (3) and the measured FSR listed in Table 1, the effective refractive index difference ($\Delta {n_{eff}}$) in the RCF can be estimated as 0.025. According to Eq. (3), the FSR is inversely proportional to the length of the MZI and can be precisely controlled by changing RCF’s length during fabrication. As shown in Fig. 5, good agreement occurs between the measured results and the theoretical predictions.
To further analyze the number and the power distribution of the interference modes, we perform a corresponding fast Fourier transform (FFT) on the spectra of the measured MZIs with RCF lengths of 5,000 and 20,000 µm, as shown in Figs. 6(a) and 6(b). The frequency spectrum has a few peaks corresponding to the transmission spectra. This means several RCMs and SCMs dominate the interference.
3. Experimental results and discussions
To investigate potential applications of MZI with RCF, the response of physical parameter measurements was implemented, including temperature and RI. An MZI with a 5,000-µm RCF was tested. The experimental setup was consistent with that described in Section 2.
Temperature response of MZI wavelength shifts with a 5,000-µm-long RCF was measured by placing the fiber on a heating plate, gradually increasing its temperature from 30 to 90 °C at steps of 10 °C. Figure 7(a) depicts the spectral responses of temperature variations. When the temperature rose, a red shift of the fringe-dip wavelength occurred. A good linear relationship was found, and the temperature sensitivity was 64 pm/°C, as observed in Fig. 7(b).
Fig. 7. (a) Spectral responses of temperature variations and (b) temperature sensitivity of MZI with a 5,000-µm-long RCF.
To explore the device performance on RI sensing, the MZI with a 5,000-µm-long RCF was sequentially immersed into a set of index-matching oils ranging from 1.33 to 1.39 at steps of 0.01 under room temperature (25 °C). Figures 8(a) and 8(b) show the spectral responses and the linear fit of wavelength shifts of RI variations, respectively. With an increasing RI, a clear blue shift of the fringe-dip wavelength can be observed. The RI sensitivity reached 44 nm/RIU (RI units).
Fig. 8. (a) Spectral responses of RI variations and (b) RI sensitivity of MZI with a 5,000-µm-long RCF.
According to experimental results, the temperature and RI sensitivity are around 64 pm/°C and 44 nm/RIU, respectively. Different from the results of some previous works [10,20], the MZI with RCF has lower sensitivity to some external surrounding disturbances. This is because it is more difficult for SCMs to perceive changes in the surroundings, since the SCMs is mostly confined in the SC, and the SC is surrounded by the high-index RC. This structure can reduce the impact of external disturbances and produce more stable interference.
4. Conclusion
In this paper, micro-fiber MZIs with thousands-µm-long RCF were fabricated, and the performance of the MZI with 5,000-µm-long RCF were tested and demonstrated. Owing to the higher NA of the RCF, the proposed MZI reached a higher ER and suppressed the crosstalk between RCMs and SCMs. Meanwhile, the power propagating through low-index area of RCF was mainly concentrated in the SC, which lower the number of unwanted cladding modes and reduce the impact of external disturbances on wavelength shifts. According to the measurement results, the best ER of the MZI with RCF reached 18.2 dB. For the MZI with a 5,000-µm-long RCF, whose ER was around 15 dB, it also had lower sensitivity of wavelength shift to temperature and RI variations of its surroundings. In addition, such a fiber device is simple to manufacture. It also offers precise fiber length control in fabrication and is robust in structure. The designed MZI with thousands-µm-long RCF can be applied to a number of fields, such as optical switching, signal modulation/demodulation, optical sensors, format conversion, etc. In the future works, more modifications of this structure are expected to be developed and will be applied to more disciplines.
Funding
National Natural Science Foundation of China (61875247).
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