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Abstract
We propose a two-mode optical fiber (TMF) with a low sensitivity of differential modal group delay (DMD) to change of the core radius and the refractive index of the core in the index profile which are major factors for DMD deviation. This was done to achieve high reproducibility of fiber fabrication. The proposed TMF has a graded index (GI) core and a depressed inner cladding, and we optimize structural parameters. We fabricated different kinds of TMFs to confirm the low DMD sensitivity of our proposed fiber. The fabricated TMF showed that the DMD sensitivity to changes in core radius of the TMF was approximately 8 ps/km/μm which is 98% smaller than that of a GI-TMF without a depressed inner cladding.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Mode-division-multiplexed (MDM) transmissions using few-mode fibers (FMFs) have recently received considerable attention, because of their potential to multiply the capacity of single-mode transmissions. In MDM transmissions using FMFs, a multiple-input-multiple-output (MIMO) is usually applied to recover signals that have degraded because of mode coupling along the transmission line [1]. In contrast, the computations for recovering the signals become more complex with an increase of differential modal group delay (DMD) in FMF [2]. Therefore, FMFs with low DMD are of great benefit to MDM transmission systems utilizing MIMO. Furthermore, low DMD in a wide wavelength range is more attractive for MDM and wavelength division multiplexed (WDM) combined transmission applications. To achieve such requirements, low DMD FMFs [3–7] and DMD compensation transmission lines [7–9] have recently been reported. However, DMD is known to be fundamentally sensitive to the index profile variations that occur during manufacturing processes [4]. If a FMF design with DMD insensitivity to small variations in the index profile can be clarified, more productivity for FMF can be expected due to its design.
In this paper, we propose a two-mode optical fiber (TMF) with a low DMD sensitivity to change of the core radius and the refractive index of the core in the index profile which are major factors for DMD deviation. This will allow for high reproducibility of fiber fabrication. The proposed TMF profile has a graded index (GI) core, a depressed inner cladding, and an outer cladding. We optimize the structural parameters of the index profile and experimentally confirm low DMD across the C + L band. We also confirm low DMD sensitivity to the change of the core radius for the prepared TMF that is fabricated according to our design.
2. Fiber design
Figure 1 shows the proposed TMF refractive index profile, which consists of a graded index (GI) core, a depressed inner cladding around the core, and an outer cladding (P-GI-TMF). The index profile is given by
where n1 and n2 are the indices of the core and an outer cladding, respectively, Δ+ is the relative-index difference between the core and the outer cladding, which is defined as (n12-n22)/(2n12), r is the distance from the center of the core, a is the core radius, and α is the index profile parameter. The depressed inner cladding is defined by W and nd, which are the width and index of the depressed inner cladding, respectively. The relative-index difference Δ− between the depressed inner and the outer claddings is defined as (nd2-n22)/(2nd2). The index profile can be determined in terms of a, Δ +, Rd, which is defined as Δ-/Δ+, Ra, which is defined as a/(a + W), and α. The normalized frequency T for the arbitrary index profile is defined as follows [10, 11]where, k ( = 2π/λ) is a wave number and λ is a wavelength, and A is a constant value that depends on the index profile parameter α.DMD is defined as
where vg01 and vg11 are the group velocities of LP01 and LP11 modes, respectively. As a reference, a GI core fiber without a depressed inner cladding profile (GI-TMFR) has a large DMD sensitivity to change of a and α as shown in our previous work [6]. If the α for GI-TMFR is deviated from a target value, we can adjust the DMD by changing the design value of the other core parameters to achieve the target value of DMD though the DMD sensitivity to change of α is large as shown in ref [6]. Moreover, the DMD sensitivity due to a or relative-index difference Δ+ changes for GI-TMFR is much larger than that for P-GI-TMF as we shall see later. Therefore, in the case of GI-TMFR fabrication, we have to adjust the core radius and Δ+ accurately to keep the target value of DMD. Therefore, it is essential to design a TMF with low DMD sensitivity to change of all parameters for mass production. In our previous work of ref [7], we reported that when Ra is greater than or equal to 0.4 and less than or equal to 0.6, small DMD slope SDT over T values can be obtained. However, SDT and DMD values were not optimized to enhance reproducibility of fiber fabrication in the previous work where DMD slope SDλ over wavelength was optimized for WDM-MIMO application. Here, we clarify the optimum design of FMF with a low DMD and low DMD sensitivity to the structural parameter changes in the index profile. Figure 2 shows the calculated DMDs at 1550 nm for different α and Δ+ values as a function of T. We set Δ+ = 0.40%, 0.425%, and 0.45%, Ra = 0.5, and Rd = 0.38. Because Δ+ and wavelength are kept constant as shown in Fig. 2, the change of T means the core radius change. In addition, because the normalized effective cutoff frequency of the third mode of LP21 or LP02 was obtained to be approximately T = 4.5, the two mode propagation region was T ≤ 4.5. From Fig. 2, it appears that DMD depends on α. However, SDT remains approximately constant. Moreover, DMD property as a function of T was almost independent of Δ+ in the range of 0.40% to 0.45% as well as ref [6]. Therefore, the flattened sensitivity SDT indicates low DMD sensitivity to the change of both of a and Δ + . Figure 3 shows the calculated DMD value as a function of T in the range of Rd values from 0.36 to 0.43. We set Δ+ = 0.425%, α = 1.71 and Ra = 0.5. It is confirmed from Fig. 3 that both DMD and SDT depend on Rd for our proposed index profile.
Fig. 2 DMD properties for different α and Δ+ with Δ+ = 0.40%, 0.425%, and 0.45%, Ra = 0.5 and Rd = 0.38.
Figure 4 shows the sensitivity of SDT to changes in parameters Ra, α, and Rd for P-GI-TMF and GI-TMFR. The parameter deviations in Ra, α, and Rd for P-GI-TMF are normalized by 0.5, 1.71, and 0.38, respectively and for GI-TMFR, α is normalized by 2.3. SDT was obtained by linear fitting to the DMD in the normalized frequency region T, ranging from 4.2 to 4.5. It can be seen from Fig. 4 that in the case of P-GI-TMF, SDT varies as a function of Rd and α. However, SDT does not depend on Ra. Moreover, the absolute value of SDT of GI-TMFR is around 1 order larger than that of P-GI-TMF. Therefore, even when α, Rd, and Ra of P-GI-TMF is deviated from a design value, P-GI-TMF can be obtained low DMD sensitivity to small change of a and Δ+. Here, we assumed that Ra, Rd, α, a and Δ+ for the target of P-GI-TMF were 0.5, 0.38, 1.71, 11.6 μm and 0.425%, respectively. Figure 5 shows the relationship between normalized variation of each parameter and DMD at 1550 nm for the P-GI-TMF and GI-TMFR. Solid and dashed lines show the calculated results of the P-GI-TMF and GI-TMFR, respectively. From Fig. 5(a), the DMD deviations to the changes of Rd and Ra for the P-GI-TMF are negligible small. Moreover, it is seen from Figs. 5(b) and (c) that the DMD deviations to the changes of a and Δ+ for P-GI-TMF become much smaller than those for GI-TMFR. However, P-GI-TMF has still large DMD deviation to the change of α as well as GI-TMFR as shown in Fig. 5(d). Figure 6 shows the calculated DMD value and DMD slope SDa over a, plotted as a function of a for the P-GI-TMF. It is expected that DMD values below 10 ps/km and DMD sensitivity SDa to change of core radius below 10 ps/km/μm for the P-GI-TMF could be obtained.
Fig. 5 Relationship between normalized parameter deviation and DMD at 1550 nm. (a) Rd, Ra, for the P-GI-TMF, (b) a, (c) Δ+ and (d) α for the P-GI-TMF and GI-TMFR
3. Properties of fabricated fibers
3.1 Refractive index profile
We fabricated TMF1 with a length of 23.5 km, according to our fiber design. Table 1 summarizes the approximate values of the structural parameters for the fabricated TMF, obtained from the measured index profile. The fabricated TMF had α and Rd values close to designed values. However, Ra, T, and a were a little smaller than the designed values, respectively. The effects of the difference between the design and fabrication values on the DMD will be discussed in the section of 3.3 DMD properties.
Table 1. Structural Parameters of the Fabricated TMF1 Compared to Our Design Values
3.2 Optical properties
In order to investigate the DMD sensitivity to a change of structural fiber parameters, two kinds of TMFs, TMF2 and TMF3, with different cladding diameters were fabricated using the same preform and under the same drawing conditions of TMF1. This means that each fabricated TMF has a different core radius. Table 2 summarizes the optical properties of the fabricated TMFs. The italic values in Table 2 are calculated ones using measured index profiles and finite element methods [12]. We can confirm from the cable cutoff wavelengths that the LP01 and LP11 modes are propagated in the C + L band for all fibers. Effective area of each TMF is one-and-a-half times as large as that of a standard single mode fiber [13]. Figure 7 shows the measured OTDR traces of TMF1 for the LP01 and LP11 modes at the wavelength of 1550 nm using a mode-multiplexer [14]. The transmission losses of LP01 and LP11 modes were less than 0.20 dB/km, respectively.
Table 2. Optical Properties of the Fabricated TMFs
3.3 DMD properties
The DMD properties were measured using a swept frequency method and modal interferometer technique [15]. Figure 8 shows the measured impulse response of TMF1 at the length of 23.5 km and at the wavelength of 1550 nm, with and without offset connections to a launched fiber using the swept frequency method. Two peaks were observed with the offset connection, while one peak was disappeared without the offset. Therefore, the disappeared peak was identified from the LP11 mode pulse, and the DMD at 1550 nm was estimated to be −52 ps/km from the signal.
Fig. 8 Measured impulse response of TMF1 at 1550 nm with or without offset connection to a launched fiber.
Figure 9 shows the interference spectrum of TMF1 with the length of 100 m cut out from one end. The beat period λB in the interference spectrum is represented by the following equation [16,17]:
where λ is the central wavelength of two amplitude peaks, L is the fiber length, and c is the speed of light in a vacuum.Figure 10 shows the measured DMD as a function of wavelength for TMF1, TMF2 and TMF3. The solid lines are obtained from the interference spectrum and the broken blue line is obtained by the swept frequency method. The absolute value of DMD for all fibers was below 60 ps/km across the C + L band. The dependence of DMD on wavelength was observed for all fibers. In addition, the DMD slope of SDλ over wavelength slightly shifted with changes in core radius. However, the DMD at 1.55 μm of each the P-GI-TMFs was approximately the same. As references for evaluating DMD insensitively, we measured the DMDs of four our fabricated GI-TMFR [9] samples. These are shown in Fig. 11 with the result for TMF1. All GI-TMFR samples were fabricated using the same preform and under the same drawing conditions, except for the cladding diameters. The core radius and fiber cutoff wavelength of the third mode for the GI-TMFR were 11.6 μm/1.50 μm, 11.3 μm/1.46 μm, 11.1 μm/1.43 μm and 11.0 μm/1.42 μm. It was found from Fig. 11 that the DMD of GI-TMFR dramatically changed due to a small change in the core radius. Moreover, a large SDλ was observed for GI-TMFR compared with P-GI-TMF. This could have occurred because the SDT of GI-TMFR was much larger than that of P-GI-TMF, as shown in Fig. 4. Thus, P-GI-TMF could be suitable for combined MDM and WDM transmission applications, because P-GI-TMF has low DMD across wide wavelength range. Figure 12 shows the measured DMD at the wavelength of 1.55 μm as a function of core radius for the fabricated P-GI-TMF and GI-TMFR. From Fig. 12, thesensitivities of SDa to changes in core radius for P-GI-TMF and GI-TMFR were estimated to be approximately 8 ps/km/μm and 662 ps/km/μm, respectively. This means that P-GI-TMF can reduce SDa by more than 98% compared with GI-TMFR. It has been reported that the core radius tolerance of the design value for a fiber fabrication could be approximately ± 4% [4]. Therefore, P-GI-TMF could keep the DMD variation caused by only core radius changes in the fiber fabrication, within ± 5 ps/km. Incidentally, the Ra, T, and a values of the fabricated TMF were a little smaller than the designed values, as mentioned in the section of 3.1 Refractive index profile. The fabrication error of Ra has negligible influence on SDa, as shown in Fig. 4.
However, it seems from Fig. 6 that the fabrication error in a could cause a slight increase in SDa. Conversely, if a P-GI-TMF with optimum parameters is fabricated, it is expected that an SDa value lower than 8 ps/km/μm could be achieved. However, when we fabricate the P-GI-TMF, we have to consider combination of the DMD sensitivities to changes of the core radius and index parameter α. P-GI-TMF has still large DMD deviation to the change of α as mentioned in the section 2. Here, we can roughly estimate the DMD at 1550 nm to be ~1 order magnitude larger than the theoretical value by using Figs. 5(b) and (d) when taking account of the variations of α and a to be ± 1% and ± 4%. On the other hand, for GI-TMFR we can estimate the DMD to be over 200 ps/km. However, the DMD sensitivity to change of index parameter α is the further study issue.
4. Conclusions
We proposed a TMF with low DMD sensitivity to changes in the structural fiber parameters in an index profile. This was done to achieve high reproducibility of fiber fabrication. We clarified the optimum structural parameters of P-GI-TMF to obtain low DMD sensitivity to small changes of parameters, a, Δ+, Rd, and Ra in the index profile. The TMF fabricated according to our fiber design at the length of 23.5 km showed a low DMD of below 60 ps/km across the C + L band. Moreover, it was confirmed experimentally that DMD sensitivity to core radius changes in the TMF was approximately 8 ps/km/μm, which is 98% smaller than that of a GI-TMFR. Therefore, our proposed TMF could be suitable for combined MDM and WDM transmission applications, and is expected to be more reproducible than previous TMFs.
References and links
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