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Abstract
We propose orientation-insensitive azimuthally asymmetric mode rotators (OI-AAMR) using chirally-coupled-core fiber. The proposed mode rotator can convert azimuthally asymmetric mode to the orthogonal degenerate mode without the requirement for angle alignment. An LP11 mode rotator with a rotation efficiency and an extinction ratio as high as 97% and 17 dB over C-band respectively, has been successfully demonstrated for any incident lobe orientation for the first time to the best of our knowledge. Owing to its circular center core structure, low insertion loss and crosstalk at the connection with few-mode fibers (FMF) can be expected. The proposed OI-AAMR has good scalability to higher-order modes and a mode rotator for LP21 mode has been demonstrated as an example. The proposed mode rotators are promising for mode rotating applications in mode division multiplexing transmission.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The transmission capacity of conventional single-mode fiber is approaching its theoretical limit due to Shannon nonlinear limit and fiber fuse phenomenon [1–3]. Mode division multiplexing (MDM) is being intensively investigated owing to its large potential for increasing the transmission capacity by adding a new multiplexing dimension [4,5]. Mode (de)multiplexer is one of the key devices to enable MDM transmission and several solutions including free-space optics [6], multi-plane light conversion (MPLC) [7], photonics lantern [8], and mode selective coupler [9–12], have been demonstrated.
All-fiber mode selective coupler (MSC) is a promising candidate of mode (de)multiplexer due to its compact structure, good stability, and low intrinsic loss [9–17]. In order to realize mode conversion between the desired modes, it is necessary to match the phase of the mode of a single-mode fiber with that of the high-order mode of a few-mode fiber (FMF). Several techniques have been proposed to realize all-fiber MSCs such as side polished technique [9] and fused tapering technique [10–12]. However, it is impossible to use a common MSC alone to simultaneously excite or demultiplex two degenerate azimuthally asymmetric linearly-polarized (LP) modes due to the dependence of coupling on the spatial orientation angle [13]. Three-core MSCs fabricated by direct-written technique using femtosecond laser have been used to demultiplex all the power from LP11 mode with random spatial orientation [14,15]. The mode field mismatching at the connecting point with the fiber may lead to increase in both crosstalk and insertion loss. Very recently, monolithic multiplexers with low chip-to-fiber coupling loss about 0.18 dB have been fabricated [16]. MSCs using tapered multicore fiber have also been demonstrated, however, their scalabilities are limited due to the crosstalk of outer cores [17].
Side-polished cascade MSCs have been successfully fabricated and a fiber polarization controller was used as a lobe orientation controller (LOC) to adjust the mode lobe orientation (MLO) between two consecutive MSCs to simultaneously separate the degenerate modes [9]. However, this method requires manual adjustment of LOC and its practical application is limited due to the random variation of MLO. As a result, mode rotators with high rotation efficiency and high stability are necessary for the multiplexing of asymmetric degenerate modes.
Planar lightwave circuit (PLC) based mode rotator was fabricated on an asymmetric silica waveguide [18] and mode rotators based on few-mode polarization maintaining fibers (FM-PMFs) have also been proposed [19,20]. These mode rotators were realized by beating two orthogonal degenerate modes with different propagation constant. Although high rotation efficiency and large bandwidth can be obtained, they require accurate angle alignment to achieve specific mode excitation and the asymmetric fiber core leads to severe mode field mismatch with normal FMFs.
In this paper, we theoretically propose orientation-insensitive azimuthally asymmetric mode rotators (OI-AAMR) using chirally-coupled-core (CCC) fiber. The proposed mode rotator can convert asymmetric mode to the orthogonal degenerate mode without the requirement for angle alignment. An LP11 mode rotator with a rotation efficiency and an extinction ratio as high as 97% and 17 dB over C-band, respectively, has been successfully demonstrated for any incident lobe orientation for the first time to the best of our knowledge. Owing to its circular central core structure, low insertion loss and crosstalk at the connection with FMFs can be expected. It works for the whole C-band with sufficient fabrication tolerance. It can be conveniently fabricated using the technique of chirally-coupled-core fibers which have already been implemented in high-power fiber laser [21–23]. The proposed OI-AAMR has good scalability to higher order modes and a mode rotator for LP21 mode has been demonstrated as an example. The proposed mode rotators are promising for mode rotating applications in MDM transmission.
2. Design principle
As shown in Fig. 1, the OI-AAMR consists of a few-mode central core and a single-mode side core which winds around the central core with a constant helix pitch Λ and offset radius R. There are two major requirements for the design of the proposed mode rotator: obtaining the phase matching condition between the fundamental mode of the side core and the specific high-order mode of the central core, and obtaining the suitable combination between the helix pitch and the coupling coefficient to obtain desired rotation angle. The quasi phase matching condition considering angular momentum has been well discussed in [22,23].
Considering the weak-guidance and slow rotation of the side core, the bound modes of each core are approximately linearly-polarized. In this paper, we define the LP11a mode as the mode at the input port and the other orthogonal LP11 mode is defined as LP11b mode. The LP01 mode refers to the fundamental mode in the side core without special instruction. As shown in Fig. 2, θ0 is the incident angle between the connecting segment of two cores and the line which bisects the two lobes of LP11a mode at the input port. When θ0 = 0, the coupling coefficient C11a-01 between LP11a and LP01 mode reaches its maximum C0, and the coupling coefficient C11b-01 between LP11b and LP01 mode is zero. The analytical expression of C0 for step-index fibers can be referred in [13]. Along the z axis, the angle periodically varies as θ0 + 2πz/Λ which leads to periodic variation in coupling coefficient as following [13]:
Fig. 2 Schematic of relative spatial-orientation of LP11a (central core) and LP01 mode (side core) (a) at the input port and (b) after a propagation distance of z.
Although the LP mode have intrinsic rotation even in a perfectly unperturbed fiber [24], the intrinsic rotation can be ignored in our consideration due to the short length of rotator (several millimeters) compared with large beat length (typically several hundred millimeters). It is reasonable to assume that there is no mode coupling between LP11a and LP11b mode. The impacts of the helical side core can be analyzed using the coupled-mode theory [25]. When the three modes are assumed to be phase-matched with the same propagation constant β, the coupled equations for the forward-modes are given by:
where, A11a(z) and A11b(z) represent the electric field of the LP11a and LP11b mode in the central core, respectively. A01(z) represents the electric field of LP01 mode in the side core. Considering the same propagation constant and weakly-coupled approximation, it is reasonable to assume that C01-11a equals to C11a-01 and C01-11b equals to C11b-01. According to the definition of LP11a and LP11b modes, the initial condition at z = 0 are A11a(0) = 1, A11b(0) = 0, and A01(0) = 0.The power evolution of each mode, which were numerically obtained with C0 = 335, Λ = 16.54 mm and θ0 = 0 and θ0 = π/2, are shown in Fig. 3(a) and 3(b), respectively. The value of β has no influence on the power evolution. Despite of different evolution traces, the relative power of LP11a and LP11b mode turn to be nearly 0 and 1 after propagation of 12.41 mm for both angles, respectively. This result implies that the power of LP11a mode totally transfers into LP11b mode in a propagation distance of 12.41 mm and it is independent on the value of θ0. Moreover, the periodic power evolution of each mode is clearly observed with a period of 3Λ/2 (24.81 mm).
The relationship between coupling coefficient and helix pitch required for the mode rotator is shown in Fig. 4. For a larger helix pitch, a smaller coupling coefficient is required to achieve effective mode rotation. As the dotted line shows, the power of LP11b mode reaches its maximum for the first time when the length of the rotator equals to 3Λ/4. In consideration of the periodic power evolution behavior, the length of the rotator for complete rotation of LP11 mode is (3/4 + 3N/2)Λ, where N is an integer.
3. Performance evaluation
Using the proposed model, we designed an LP11 mode rotator and its main parameters are shown in Table 1. The cladding was assigned to be pure silica with a refractive index of 1.444 at 1550 nm. The central core has the same refractive index of 1.4537 with the FMF in [26]. All of the parameters have been optimized at 1550 nm and the performance of the designed mode rotator was analyzed using a beam propagation method (BPM). In order to achieve a wide range of operation wavelength, the side core was carefully designed to match the neff within a broad bandwidth using the similar method in [27].
Table 1. Parameters of the LP11 mode rotator.
The power evolution of different modes with θ0 = 0 and θ0 = π/2 are shown in Fig. 5. The simulated results using BPM coincide well with the calculated results shown in Fig. 3. Although different evolution traces for different incident lobe orientation are observed, the incident LP11a mode successfully rotates for 90 degrees and evolves into the LP11b mode at the end of the rotator.
Fig. 5 The power evolution of different modes in the LP11 mode rotator at 1550 nm when (a) θ0 = 0 and (b) θ0 = π/2.
The dependences of rotation efficiency and extinction ratio on the incident angle θ0 at different wavelength are shown in Fig. 6. We define P11b/Pin as the rotation efficiency and P11b/P11a as the extinction ratio at the output of the rotator. The OI-AAMR shows the highest rotation efficiency (>99%) and extinction ratio (>29 dB) at 1550 nm for any incident lobe orientation angle as the blue lines show. Moreover, the rotation efficiency and extinction ratio are as high as 97% and 17 dB over the C-band, respectively. Considering the broadband effective index matching in our design, the degradation of rotation efficiency and extinction ratio are mainly caused by the wavelength-dependence of coupling coefficient. Due to the increased wavelength-sensitivity, the operation bandwidth of mode rotators may degrade for LPlm modes with l>>1. Owing to the orientation-insensitive characteristics of our design, the proposed rotator can operate without any requirement for angle alignment.
The tolerance of the major parameters of the mode rotator have also been investigated and the results are shown in Fig. 7. It should be noted that the tolerance for modes with different angles are slightly different and here we show the results of the worst condition with θ0 = 0. The design has large fabrication tolerance in z direction. When Λ is varied within 3.85 mm,the rotation efficiency and extinction ratio are always higher than 90% and 10 dB, respectively. The rotator performance is also insensitive to rotator length as shown in Fig. 7(b). Rotation efficiency and extinction ratio can be maintained larger than 90% and 37 dB, respectively, when the rotator length is varied within 2 mm. The rotation efficiency and extinction are higher than 90% and 10 dB, respectively, when the helix radius is varied between 13.3 μm and 13.8 μm. As a result, it is necessary to precisely control the helix radius in fabrication process.
Fig. 7 The impacts of (a) helix pitch, (b) helix radius, and (c) rotator length on the rotation efficiency and extinction ratio.
The proposed method is also applicable to higher-order modes and a mode rotator for LP21 mode has been designed here as an example. Its parameters are shown in Table 2. Due to the different asymmetric with LP11 mode, the length of the mode rotator is required to be 3Λ/8 instead of 3Λ/4. For LPlm mode (l≠0), the required length of mode rotator is 3Λ/4l. The power evolutions of different modes are shown in Fig. 8. Due to the small effective index difference between LP21 and LP02 mode in the used FMF, part of the energy of LP01 mode in the side core also coupled to the LP02 mode in the central core as the dotted blue line shows.
Table 2. Parameters of the LP21 mode rotator.
Fig. 8 The power evolution of different modes in the LP21 mode rotator at 1550 nm when (a) θ0 = 0 and (b) θ0 = π/4.
Despite of the participation of LP02 mode, the rotator still works well as shown in Fig. 8 and Fig. 9. The rotation efficiency and extinction ratio are always larger than 96% and 30 dB, respectively, for any incident lobe orientation. Although relative large angle-dependence was observed, it can be suppressed by increase the effective index difference between LP21 and LP02 modes. For higher-order modes which have even closer neff with each other, it may be more difficult to design a mode rotator using this approach.
The proposed mode rotator can be fabricated using the similar method of CCC fibers for high power laser application [21–23]. The two-core preform contains one few-mode core on axis and one single-mode core off axis. CCC geometry can be obtained by spinning fiber preform during fiber draw process. The OI-AAMR can be easily obtained by cutting the spun fiber to the desired length owing to the large tolerance in length.
4. Conclusion
In conclusion, we theoretically propose OI-AAMR using CCC fiber. The coupling behavior has been well investigated using both a three-mode coupled model and BPM method. An LP11 mode rotator with a rotation efficiency and an extinction ratio as high as 97% and 17 dB over the C-band, respectively, has been successfully demonstrated for any incident lobe orientation. Owing to its circular center core structure, low insertion loss and crosstalk at the connection with FMFs can be expected. Despite the inherently wavelength-dependence as interference-based devices, it works well over the whole C-band by careful index matching. A mode rotator for LP21 mode has also been demonstrated and this method is also applicable for higher-order modes which have large effective index difference with the closest mode. The proposed mode rotators are promising for mode rotating applications in MDM transmission.
Funding
National Natural Science Foundation of China (NSFC) (61775138, 61620106015).
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