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Abstract
High order modes in a six-mode fiber are separately observed and characterized using an Optical Frequency Domain Reflectometry (OFDR) method. Due to the difference in group refractive index between fundamental mode and the high order modes, Fresnel reflection peaks for each mode can be separated in beat frequency domain with their corresponding time delay. In the experiment, the fundamental mode and high order modes are excited in turn and observed at a 6.6 m six-mode fiber end, which agree with their beat frequency difference in theoretical simulation. The demonstration provides a flexible and feasible method for mode identification and characterization of all kinds of fibers.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High-capacity and stable light wave guiding is a primary concern in mass data transmission or low-consumption mode division multiplexing [1]. High order modes are proved to be an efficient way to increase the channels using multimode fibers, while its mode purity and walk-off effects affect its performances in signal transmission [2,3]. To balance the transmission capacity and dispersion control, few-mode fiber is recognized as an ideal combination and trade-off between single mode fiber and multimode fiber for its appropriate mode number and controllable inter-mode dispersion. Also, the graded-index distribution and down-doping trench were used to optimize its mode confinement [4]. However, the characterization of the few-mode fiber still remains challenging for its practical performances, including the dispersion, effective mode area, loss, and differential mode delay (DMD) [5–8].
As a conventional approach for mode observation or identification, time of flight method requires an ultra-short optical pulse and a high speed photo-detector for DMD measurement [9]. The spatially and spectrally (S2) resolved imaging provides a technique capable of imaging multiple, coherent, higher-order modes in an optical fiber [10]. Yet the modes are recognized with a poor signal noise ratio (SNR) and a complex free-space alignment [11]. Since Optical Frequency Domain Reflectometry (OFDR) is proposed in optical band based on Frequency Modulated Continuous Wave (FMCW) [12], it could be taken as a mode analysis method for the DMD measurement in optical fibers [13]. However, to achieve a precise optical path difference between the fundamental mode and high order modes, its reference fiber length is strictly fixed. Moreover, the dynamic range of the fiber length is restricted as well in such a mode analysis method based on intermodal interferences. Thus, a flexible all-fiber system for high order mode excitation and observation is in urgent need for mode identification and characterization.
In this paper, we proposed and demonstrated a coherent OFDR method for observation and characterization of high order modes in six-mode fiber. The numerical analysis shows the difference in group refractive index between fundamental mode and the high order modes, leading to the differential mode delay and beat-frequency difference at the fiber end. In experiment, the fundamental mode and high order modes are excited and observed at a 6.6 m six-mode fiber end in turn, with a high signal-noise ratio (SNR) through the dual-polarization OFDR. Each Fresnel peak appear in beat frequency domain in turn with its order, where its location agrees well with its expectation from the numerical simulation. Subject to dimensional deformation and doping diffusion in actual manufacturing, the averaged deviation in beat frequency difference is about 5.82 Hz (11.3%). Our demonstration promises a flexible and feasible method for mode observation and identification, which is applicable to all kinds of optical fibers including the microstructured optical fibers.
2. Principle
Multiplexing in few-mode fiber can be achieved with high order mode channels via enlarging the core size or increasing its index gradient. Figure 1 illustrates the cross sectional structure and the mode distribution of the six-mode fiber used in this paper, which possesses a core diameter (d) of 19.2 µm with a relative index gradient of 0.006. Typical linear polarized (LP) modes are analyzed at 1550 nm in six-mode fiber using the finite element method (FEM), including the fundamental mode LP01 and the high order mode LP11, LP21, LP02, LP31, LP12. Each linear polarized mode group degenerates to orthogonal vector modes with similar propagation constants.
The wavelength dependent index dispersion of the six-mode fiber is demonstrated as the line-scatter present from 1515 nm to 1575 nm in Fig. 2. The dispersion curves all show a negative correlation to wavelength increment, where the effective refractive index difference between the fundamental mode and high order modes exceeds 7.01 × 10−4.
Thus, the group refractive index ng can be further calculated with the negative derivative of linear fitting of the effective refractive index in Eq. (1) [14],
where neff refers to the effective refractive index of the linear polarized mode with azimuthal order m and radial order n. The group refractive index difference between the fundamental mode and high order modes exceeds 6.74 × 10−4.Due to the close but not identical slopes of the dispersion curves, the different group refractive index results in different group velocity νg and group time delay τg as shown in Eq. (2) [15].
Because c denotes the constant velocity of light in the vacuum, the time delay τg is proportional to its group refractive index ng. For the Fresnel reflection from the same point, the time delay divides as different modes with different group velocity and frequency components. Therefore, the multiple beat-frequency f induced can be recognized as an indicator for mode identification and characterization.
In an ideal coherent OFDR system, the beat frequency linearly depends on the scanning rate γ, group refractive index ng and the length of fiber under test L as shown in Eq. (3) [16].
For an actual OFDR system, however, the optical path difference and group time delay are caused by the round-trip in few-mode fiber and in single mode fiber “pig-tail” as well. Thus, the positioning of the beat frequency is expected as an overall group time delay in single-mode fiber tail and in few-mode fiber, given by:
In numerical analysis, the total fiber length is set to 7.2 m, including 0.6 m single mode fiber “pig-tail” and 6.6 m six-mode fiber under test, where the beat-frequency is determined by the group refractive index with its order. In Fig. 3, the calculation shows the beat-frequency of LP01, LP11, LP21, LP02, LP31, and LP12 mode around 90 kHz, where the high order modes are separated from the fundamental mode. Theoretical analysis indicates that the positions of the peaks are in good agreement with its corresponding mode orders. Accordingly, the high-resolution OFDR technique promises a non-destructive method for mode identification and characterization.
3. Experimental results
Figure 4 shows the experimental setup of our coherent OFDR [17]. The light from tunable laser source (TLS) propagates through an 8:2 polarization coupler, where 80% optical power goes to a heterodyne coherent detection (HCD) module. Meanwhile, the other 20% enters a reference Michelson interferometer consisting of a 1:1 coupler and two Faraday Rotation Mirrors (FRMs). The 5 m delay fiber provides a resampling Sine signal as an optical clock for scanning nonlinearity calibration. The 80% splits once again through another 8:2 PC and goes to the fiber under test (FUT) from port 1 to port 2 via a circulator. Both the Fresnel reflection from port 3 and the local light from the 2 m delay fiber, split into the S/P polarizations by a hybrid (SMF-in and PMF-out) and a conventional (PMF-in and PMF-out) polarization beam splitter (H-PBS and C-PBS), respectively. The 2 m delay fiber is used to make up the optical path difference between the reference arm and test arm. So, the fiber end of port 2 is set as the origin of the round-trip optical path, as well as the zero in beat frequency. The probe light enters the fiber under test, including the single mode fiber “pig-tail” and few-mode fiber. Finally, the Fresnel reflection turns back at the end face and goes to HCD module with DMDs in few-mode fiber. The polarized beams interfere at the couplers C1 and C2 according to their corresponding polarization, which are harvested by two balanced photo detectors (BPDs) and then collected by a 4-channel digital data acquisition (DAQ) for post processing.
Fig. 4. Schematic setup of the all-fiber coherent OFDR system for mode observation and identification.
As the single mode fiber tail is aligned with a few-mode fiber on the fusion splicer, the high order modes are excited at the core offset for mode mismatch. Although it brings an insertion loss and strong reflection in frequency domain, the mode identification will not be affected due to its lower frequency away from those Fresnel peaks. Also, the 8° fiber interfaces are designed to restrain the reflections between the single mode fiber and few-mode fiber, ensuring the intensity insignificant. Because of the different group velocity of high order modes, their Fresnel reflections return to the origin with different time delay and interfere with the local light at different frequencies. Therefore, the high order modes with multiple frequencies are separated in frequency domain using the Fourier transformation. Moreover, the central frequencies of the Fresnel peaks are strictly proportional to the group time delay according to Eq. (3).
The Agilent 8164B TLS is employed with a tuning rate at 1.25 THz/s (10 nm/s) from 1540 nm to 1560 nm. A 6.6 m six-mode fiber is connected to the 0.6 m test tail of port 2, where the high order modes are excited with a slight core offset. Thus, the mode excitation from LP01 to LP12 can be controlled by mode mismatch and observed by a coherent OFDR in real time.
Figure 5 shows the excitation and growth of the LP01, LP11, LP21, LP02, LP31, and LP12 mode around 90 kHz with a high SNR, where high order modes gradually appear in turn on the right side of the fundamental mode as their orders. In case that the six-mode fiber is strictly aligned with the SMF tail in Fig. 5(a), the power mainly concentrates in LP01. With the core offset increment in Figs. 5(b) to (f), however, the energy in fundamental core mode gradually couples into high order modes with a significant contrast. The six guided modes in this six-mode fiber are simultaneously observed and identified till the core offset reaches 7 µm.
Fig. 5. Excitation and observation of high-order modes in beat-frequency domain for a six-mode fiber with offset of (a) 0 µm (b) 1 µm (c) 2 µm (d) 3 µm (e) 5 µm (f) 7 µm.
Considering the accuracy in length measurement, the Fresnel peak of LP01 mode is located at 90.54 kHz in experiment, which is close to that of 90.50 kHz in theoretical analysis. However, due to the differences between the actual fiber and numerical model caused by dimensional deformation and doping diffusion in the manufacturing, the position deviation of the Fresnel peaks in beat frequency is estimated at 5.82 Hz in average. As the blue slash and red hollow histogram shown in Fig. 6, the beat-frequency differences among the fundamental mode and high order modes are in fair agreement with those in numerical simulation. The proposed OFDR technique indicates the high order modes as separate Fresnel peaks in turn, promising a flexible and versatile method for mode observation and identification via the group time delay. We believe it helps in mode identification and characterization, not just for few-mode fiber but for all kinds of fibers.
4. Conclusion
An all-fiber coherent OFDR is proposed and demonstrated for mode observation and identification in six-mode fiber. The theoretical analysis indicates that the different group refractive index causes group time delay and beat-frequency difference among the high order modes. In experiment, the beat-frequency peaks are observed at the 6.6 m six-mode fiber end, corresponding to the six guided modes in few-mode fiber. Considering the deviations between the numerical model and the actual fiber, the beat-frequency differences are in fair agreement with the theoretical analysis. Our demonstration promises a flexible and versatile method for mode observation and characterization, not just for few-mode fibers but for all kinds of fibers as well.
Funding
National Natural Science Foundation of China (Grant No. 62105092); Natural Science Foundation of Hebei Province (A2020202013, F2021202054); Foundation of Key Laboratory of Opto-Electronics Information Technology of Ministry of Education, Tianjin University (2021KFKT013).
Acknowledgments
The authors thank Yangtze Optical Fiber and Cable Co. Ltd. (Wuhan, China) for providing the few-mode fiber.
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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