We propose two mode optical fibers (TMFs) with minimally low differential modal delay (DMD) slope which are suitable for wavelength division multiplexing and multiple input multiple output (MIMO) combined transmission system. We designed and fabricated three different kinds of TMF, nearly zero-DMD (zTMF), positive-DMD (pTMF) and negative-DMD (nTMF) with a graded index core and a depressed inner cladding. We confirmed that the fabricated zTMF has DMD of below 15 ps/km in the C band and the fabricated pTMF and nTMF have the same degree of effective areas. We also confirmed that a DMD compensation line with a length of 100 km composed of pTMF and nTMF can successfully achieve the best properties of low DMD in the C + L band and low mode conversion.
© 2014 Optical Society of America
The traffic of backbone network has been increasing rapidly according to the growth of broadband users in worldwide. It has been reported that the conventional single mode optical fibers (SMFs) used in the current systems will approach the limit of input power, which is directly related to the transmission capacity in the wavelength division multiplexing (WDM) system, because of the optical nonlinear effects and the fiber fuse . Recently, it has been expected that some innovations in both optical fiber and transmission system can overcome the capacity limit. Few-mode fiber [2–13] and multi core fiber [14, 15] have been studied actively to expand the transmission capacity. Moreover, it has been reported that multiple input multiple output (MIMO) is applied in mode division multiplexing (MDM) systems using FMFs [2–7]. MIMO system can recover transmitted signals which are degraded due to mode coupling generating in mode multiplexer/demultiplexer and FMFs. In contract, the computation for recovering the signals becomes more complex with an increase of differential modal delay (DMD) of FMF. Therefore, FMF with low DMD is of great benefit to MDM transmission systems utilizing MIMO. Furthermore, low DMD in wide wavelength range is more attractive for MDM-WDM combined transmission applications. For realizing such requirements, low DMD fibers [7–9] and DMD compensation transmission lines [2–6, 10, 11] have recently proposed.
In this paper, we propose two mode optical fibers (TMFs) with minimally low DMD slope against wavelength (SDMD_λ) which is suitable for WDM-MIMO transmission system. We design and fabricate three different kinds of TMF, nearly zero-DMD (zTMF), positive-DMD(pTMF) and negative-DMD (nTMF) with a graded index core and a depressed inner cladding. We also confirmed that a DMD compensation line with a length of over 100 km composed of fabricated pTMF and nTMF achieve the good properties of low DMD in the wide wavelength range and low mode conversion at the splice points.
2. Design concept for realizing low DMD in wide wavelength range
In order to realize a low DMD transmission line in wide wavelength range, there are two approaches. One is to design a TMF with low DMD in wide wavelength range. It means that a TMF with low DMD and low SDMD_λ is required. In addition, it is preferred to design the TMF with a small sensitivity of DMD due to a small change of fiber parameters. The other way is to construct a DMD compensation line composed of TMF with positive and negative DMD. Figure 1 shows a concept of the DMD compensation line. It is composed of two different kinds of fibers, a positive DMD fiber (Fiber (p)) and a negative DMD fibers (Fiber (n)). Here, DMD (Δτ) is defined asEq. (2).Eq. (3), Δτtotal can be easily controlled to be zero at a given wavelength, independently of the Δτp and Δτn.
For WDM-MIMO combined system, additional condition is also required to compensate DMD in wide wavelength range. Since DMD changes linearly with wavelength [10, 11], the additional DMD compensation condition is expressed as the following simple equations.Fig. 2(a), the DMD compensation condition is given by Eq. (4). However, it is a little bit difficult to satisfy the DMD compensation condition in Eq. (4) because DMD of TMF is sensitive to variation of fiber parameters. On the other hand, if DMD has a zero SDMD_λ as shown in Fig. 2(b), the DMD compensation condition can be expressed as Eq. (5) which can be satisfied regardless of a change in DMD. Therefore, TMFs with minimally low SDMD_λ has a clear advantage to both of a low DMD fiber and a DMD compensation line applied to WDM-MIMO transmission. It is noted that each fiber used for the DMD compensation line has to be designed to have the same effective area because mismatch of effective area could cause additional loss and mode conversion which degrade transmission quality [16, 17].
3. Fiber design
3.1 Zero-DMD TMF (zTMF)
Figure 3 shows our proposed refractive index profile of TMF, which consists of a graded index (GI) core and a depressed inner cladding around the core. The fiber is characterized by four parameters, the normalized frequency T, Rd which is defined as the ratio of the relative-index difference of the depressed inner cladding Δ- to the relative-index difference of the core Δ+, Ra which is defined as the ratio of GI core radius a-W to the outer radius a where W is width of the depressed inner cladding and index profile parameter α. The normalized frequency T is defined as follows
Figure 4 shows the calculated DMD for different Ra as a function of normalized frequency T at the wavelength of 1550 nm. Since the normalized cutoff frequency of third mode (LP21 or LP02) was obtained to be around T = 4.5, two mode propagation region is T ≤ 4.5. It is confirmed from Fig. 4 that low DMD slope against T can be obtained when Ra is less than 0.6 and T is between 3.8 and 4.5. It means that DMD sensitivity due to a small change of fiber parameters is small. Since DMD results in Fig. 4 converge at Ra = 0.5, we determined to set Ra = 0.5.
Figure 5 shows the calculated SDMD_λ for different Rd and α as a function of normalized frequency T at the wavelength of 1550 nm. It is confirmed from Fig. 5 that SDMD_λ varies with Rd and zero SDMD_λ can be obtained by Rd = 0.3 and T = 4.1. Moreover, SDMD_λ is nearly independent of α in the region of 1.7 ≤ α ≤ 2.0. Figures 6 (a) and (b) show respective the effective area (Aeff) and the calculated DMD as a function of SDMD_λ for various α when Rd = 0.3 and λ = 1550 nm. The dashed line in Fig. 6 shows the T = 4.1. DMD increases with increase in α and T. From Fig. 6, TMF with zero-DMD and zero- SDMD_λ can be designed by Rd = 0.3, T = 4.1 and α = 1.82.
3.2 Positive-DMD TMF and negative-DMD TMF
pTMF and nTMF can be designed by using Fig. 6. The sign of DMD can be controlled by adjusting α. In addition, zero SDMD_λ can be obtained by T ≈4.1 in Rd = 0.3 as well as zTMF. Moreover, effective areas for LP01 and LP11 modes do not nearly depend on α in the region of 1.7 ≤ α ≤ 2.0. Therefore, pTMF and nTMF can be designed to have almost the same effective area for LP01 and LP11 modes while keeping on the sign of DMD and minimally low SDMD_λ. We determined that the fiber parameters for pTMF were T = 4.01, Rd = 0.3 and α = 1.95, and those for nTMF were T = 4.24, Rd = 0.3 and α = 1.71, respectively.
4. Characteristics of fabricated fibers
4.1 Zero-DMD TMF
We fabricated zTMF with a length of 26.2 km according to our fiber design. Table 1 summarizes the optical properties of zTMF. The calculated values were obtained by the measured refractive index profile and finite element method . From Table 1, the C + L band was confirmed to be the two mode propagation region from the measured cutoff wavelengths. The bending loss of LP11 mode satisfied with the G.654 bending loss requirement of less than 0.5 dB/100 turns at the bending radius of 30 mm. Figure 7 shows the measured OTDR traces for LP01 and LP11 modes at the wavelength of 1550 nm by using mode-multiplexer . The transmission losses for LP01 and LP11modes were less than 0.20 dB/km.
DMD was measured by the sweep frequency method [11, 20, 21]. Figure 8 shows the experimental setup for DMD measurement. The measurement system consists of a vector network analyzer, a tunable laser source (TLS), an optical modulator, and a Photo Detector (PD) including the multi mode fiber. the SMF was used as the launched fiber and it was offset-connected to the test fiber in order to excite LP01 and LP11 modes. Figure 9 shows the measured DMD as a function of wavelength. It is seen from Fig. 9 that the DMD is below 15 ps/km in the C band.
4.2 Positive-DMD TMF and negative-DMD TMF
We also fabricated the pTMF and the nTMF according to our fiber design. Table 2 summarizes the optical properties of the fabricated fibers. Similar to zTMF, it was confirmed that these fibers had the two mode propagation region in the C + L band and the bending loss of LP11 modes for these fibers were satisfied with the G.654 bending loss requirement. In addition, all fibers exhibited the same degree of effective area for both LP01 and LP11 modes as just our designed. Figure 10 shows the measured OTDR traces. The transmission losses of both modes were less than 0.21 dB/km for all fabricated TMFs. Figure 11 shows the measured DMD for each TMF as a function of wavelength. The solid lines show the best fitted to the measured values. The sign of DMD for the nTM3 was opposite to those for the pTMF1 and the pTMF2 and SDMD_λ of all fibers were below 0.15 ps/km/nm. All fibers with small SDMD_λ were fabricated just as our designed.
5. Experimental results for DMD compensation line
5.1 DMD property
We constructed a DMD compensation line composed of pTMF1, pTMF2, and nTMF3. The average splice loss of LP01 mode between pTMF1 and nTMF3 at 1550 nm was 0.03 dB and that between nTMF3 and pTMF2 was measured to be less than 0.01 dB by using the bidirectional OTDR. The DMD of the constructed compensation line was evaluated by changing the length of pTMF2 while keeping the lengths of both pTMF1 and nTMF3. Since the resolution of the DMD measurement system is about 2 ps/km when fiber length is about 100 km, the DMD of the constructed line was measured by changing the fiber length with larger DMD than the resolution. Figure 12 shows the measured and calculated DMD plotted as a function of wavelength for the DMD compensation lines with different lengths. Dashed lines show the calculated values which are obtained by using the measured DMD and the length of each TMF. It was confirmed from Fig. 12 that measured DMD for each compensation line was in good agreement with calculated one. Then, it is seen that the DMD of the compensation line with a length of 102.6 km is below 4.0 ps/km in the C + L band. Moreover, it is estimated from the calculated results that the transmission line at the length of 101.4 km can achieve the DMD of below 0.5 ps/km in the C band.
5.2 Mode conversion at the splice point
Mode conversions at splice points of the DMD compensation line were evaluated by impulse response obtained by the inverse fast Fourier transform (IFFT) of measured frequency domain data by sweep frequency method . Figure 13 shows the measured impulse response signals when nTMF were connected to pTMF1 and pTMF2. The pulses which generate due to the mode conversion at the splice points were observed in addition to LP01 and LP11 mode pulses. From Figs. 13(a) and 13(b), mode conversion power ratio at the splice point (Cs) between nTMF3 and pTMF2 was about −35 dB and Cs between pTMF1 and nTMF3 was about −38 dB respectively. Therefore, it confirmed that we succeeded in fabrication of the DMD compensation line that has the excellent properties of not only the low DMD in the C + L band but also the low mode conversion at the splice points.
We proposed TMFs with low SDMD_λ which is of great benefit for compensating the total DMD in wide wavelength range. We designed and fabricated three different kinds of TMF, zTMF, pTMF and nTMF with a graded index core and a depressed inner cladding which can realize minimally low SDMD_λ. All fabricated TMFs have low attenuation, low bending loss, same degree of effective area and low SDMD_λ. We achieved low DMD of below 15 ps/km in the C band by the fabricated zTMF. Moreover, a constructed DMD compensation line composed of the fabricated pTMF and nTMF achieved not only DMD of below 0.5 ps/km in the C band but also Cs of less than −30 dB. Our proposed TMF could realize to reduce MIMO complexity substantially in WDM-MIMO systems.
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