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We propose a transmission distance-independent technique for modal dispersion compensation over few-mode fiber that uses a single-input multiple-output configuration and adaptive equalization. Our technique can compensate for the modal dispersion of a signal with 1-tap FIR filters regardless of the amount of modal delay difference, and enables us to utilize fiber with a large core and few modes as a long-haul transmission line. We also show numerically the advantage of few-mode photonic crystal fiber (PCF) for realizing a larger effective area (Aeff), and finally we report a transmission over a large-core two-mode PCF with Aeff>280 μm2.
©2011 Optical Society of America
1. Introduction
The rapid growth of Internet traffic has led to a huge demand for increased transmission capacity. To meet this exponential demand, large capacity transmission using multiplexing technologies and advanced modulation formats has been intensively investigated. Although high-speed transmission exceeding 100 Tb/s has been realized by employing dense WDM and complex modulation formats such as OFDM [1], a nonlinear effect in optical fiber severely restricts the input signal power and makes it difficult to realize high-capacity long-haul transmission [2].
Enlarging the effective area (Aeff) of optical fibers is a practical way of reducing fiber nonlinearity. It has been reported that photonic crystal fiber (PCF) can realize an Aeff of 220 μm2 with both single-mode operation and a low bending loss [3]. However, it is difficult to enlarge the Aeff further because of the trade-off relationship between cut-off wavelength and bending loss.
Using multi-mode fiber and adaptive equalization [4,5] is another way to greatly enlarge Aeff. It is well known that electrical equalization using an FIR filter can mitigate linear fiber impairments such as a chromatic dispersion or polarization mode dispersion. In addition, we can also compensate for modal dispersion with an FIR filter. The required tap number in the FIR filter is proportional to the group delay difference between the fundamental and higher-order modes at the receiver, and an adaptive algorithm can be used to determine the tap coefficients to compensate effectively for the modal dispersion. However, the computation needed to determine the tap coefficients becomes more complex as the tap number increases, and this restricts the transmission distance to less than tens of kilometers to obtain a realistic computation time.
In this paper, we propose a modal dispersion compensation technique that is independent of transmission distance over a few-mode fiber with a single-input multiple-output (SIMO) configuration. We can compensate for the modal dispersion of the signals with 1-tap FIR filters regardless of the amount of group delay difference, and can utilize a large-core few-mode fiber as a transmission line to reduce fiber nonlinearity [6]. Furthermore, we show numerically the advantage of a few-mode PCF for realizing a larger Aeff, and finally we report a transmission over a large-core two-mode PCF with Aeff>280 μm2.
2. Modal dispersion compensation with SIMO configuration
In our proposed technique, we use a 1 × n SIMO configuration (1 transmitter and n receivers) over few-mode fiber within n propagation modes. Figure 1 shows a schematic block diagram of the configuration when n = 2. An input signal ETR is launched into a two-mode fiber and coupled with fundamental and higher-order modes with the ratio aFM:aHOM. At the fiber end, the signal is degraded by modal dispersion and includes two pulses passing through the fiber in the fundamental mode EFM and higher-order mode EHOM when we assume there is no modal crosstalk in the fiber. The transmitted signals are then divided into two ports at a splitter. If we assume that the splitter has a different splitting ratio for each mode (e.g. b1:b2 and c1:c2 for the fundamental and higher-order modes), we can recover the ETR by estimating the inverse coupling matrix S and multiplying it by the column vector of the received signals (ER1 ER2) as shown in Fig. 1. This technique is signal format transparent because the coherent detection is employed at the receiver and the signal amplitude and phase information are utilized for the compensation. A fiber-fused splitter can be utilized as the splitting device because the splitting ratio differs from mode to mode owing to the difference in the propagation constant. Therefore, this technique requires FIR filters with only 1 tap to recover the signals regardless of the transmission distance unlike the conventional technique.
Adaptive equalization using the least mean square or recursive least squares (RLS) algorithm can be utilized to estimate the matrix. Another advantage of our technique is that it can be used even when the transmission fiber has several modes. As the number of propagation modes increases, higher-order mode propagation is inevitable, and it becomes difficult to transmit the signal via central launching on the input side or mode filtering techniques at the receiver [7]. However, we can also recover the signal simply by using a 1 × n configuration and estimating the n × n matrix S based-on the n received signals of ER1, ER2,∙∙∙ERn. Although the system cost increases as the mode number increases because at least n receivers must be deployed, the Aeff of the fiber can be further enlarged in accordance with the increase of the mode number. It should be also noted that we must design the fiber carefully for preventing the inter-modal crosstalk between all propagation modes when we consider the fiber with 3 or greater number of modes. This technique can also be adapted to polarization multiplexing by employing a 2 × 2n configuration and polarization diversity coherent detection at the receivers.
3. Design and fabrication of large-core few-mode PCF
Our proposed SIMO system enables us to transmit a signal correctly despite the existence of large modal dispersion in the fiber. This means the effective area of the fiber can be further enlarged because single-mode operation is no longer required. Here, we targeted the use of a PCF as a transmission fiber owing to its suitability for designing a large Aeff [8], and we calculated the maximum Aeff of the PCF allowing up to three-mode operation to realize a low nonlinear fiber.
In our calculation, we assumed the use of a 1450~1625 nm telecommunication band and set the permissible bending loss αBL of the fundamental mode at less than 0.5 dB/100 turn at R = 30 mm, which is compatible with ITU-T G.655. Figure 2 shows the PCF structural parameters that satisfy the requirements calculated with the full vector finite element method. The calculated PCF has 36 air holes, and the structural parameters d and Λ denote the air-hole diameter and pitch, respectively, as shown in the inset of the figure. The solid and dashed lines in the figure show the structures that satisfy αBL = 0.5 dB/100 turns and αCL = 1 dB/m at each higher-order mode, respectively. We assumed the higher-order mode radiated when αCL>1 dB/m in the fiber design. Although Λ is limited to less than 12.4 μm with single-mode operation, it can be extended to 19.5 and 22.6 μm by allowing two- and three-mode operation, respectively. The maximum effective area of the PCF as a function of mode number is shown in Fig. 3 . The Aeff of step-index fiber (SIF) is also shown in the figure for comparison. Although the SIF can achieve an Aeff of more than 200 μm2 for two-mode operation, the Aeff does not increase even when we allow three-mode operation because LP21 and LP02 have the same cut-off wavelength. On the other hand, the PCF can realize an Aeff of 329 and 411 μm2, respectively, with two- and three-mode operation. Thus, fiber nonlinearity can be reduced greatly by using a large-core few-mode PCF as a transmission line with the SIMO configuration.
We next fabricated a few-mode PCF with a large effective area. The fabricated PCF was designed to have at most two propagation modes in the 1450~1625 nm wavelength range on the premise of using a transmission system with a 1 × 2 configuration as shown in Fig. 1. The measured structural parameters and optical properties of the PCF are listed in Table 1 . The PCF parameters satisfy the structural requirements for two-mode operation. Here, the propagation losses of the PCFs at 1550 nm were measured by the cut-back method when we spliced standard single-mode fiber on the input side of the PCF. Figure 4 shows the measured bending loss characteristics of the PCF. The solid, dashed and dotted curves correspond to λ = 1450, 1550 and 1625 nm, respectively. The symbols represent measured values, and the three curves represent fitted curves that were exponentially approximated. Here, the bending losses were measured when we spliced 50 μm-core graded-index multi-mode fiber on the input side of the PCF, and bent the fiber by 1 turn at each bending radius. We confirmed that the PCF also satisfied the bending loss requirement of less than 0.5 dB/100 turns in the 1450~1625 nm band.
Table 1. Structural parameters of fabricated PCF
We then evaluated the effective area of the fabricated PCF. Figure 5(a) shows a microscope image of a cross-section of the PCF and Fig. 5(b) shows the electrical fields of a fundamental mode that was calculated based on the cross-sectional image. We achieved an Aeff of 288 μm2 with the fundamental mode at 1550 nm, which was an improvement in Aeff of more than 30% compared with the value obtained for large core single-mode PCF reported in Ref [3]. Our PCF has the Aeff of more than 280 μm2 in the 1450~1625 nm wavelength range and that makes it possible to reduce the fiber nonlinearity over a wide wavelength range.
We also measured the impulse responses of the PCF to confirm higher-order mode propagation in the fiber. We launched pulses with a 100 ps duration and a 100 ns interval at 1550 nm, and we spliced a 50 μm-core graded index fiber on the input side of the PCF to excite the higher-order mode. The measured pulses included two pulses within the period that were expected to be EFM and EHOM as shown in Fig. 6 . There were no noticeable pulses except for EFM and EHOM, which indicates that there was negligible modal crosstalk between the fundamental and higher-order modes in the fiber. Although each pulse consists of multiple degenerate fiber modes, they can be treated as one mode as long as they arrive with the same group delay at the receivers even if the mode coupling is occurred within the degenerate modes. Thus, the modal dispersion that occurred in the PCF can be compensated with a 1 × 2 configuration by using 1-tap FIR filters.
4. Experimental setup with 1 × 2 configuration
Figure 7 shows the experimental setup we used for 1 × 2 SIMO transmission over two-mode fibers. We firstly transmitted signals over a 20 km-long two-mode SIF to confirm that our compensation technique performed properly even when the fiber had a large amount of modal delay. The SIF had a core diameter of 14 μm and a relative index difference of 0.4% (LP01 and LP11 modes can propagate at 1550 nm). A CW light at 1550 nm was modulated into a 10-Gb/s BPSK signal at a BPSK modulator and a linearly polarized wave was launched into the fiber. The transmitted signals were then divided into two ports at a fiber-fused multi-mode splitter and observed by coherent detection at the two receivers. The coherent receivers including 90° hybrids and balanced receivers are the single mode devises. The 90° hybrids we used had 2 × 4 ports with polarization diversity, and we used only the x-pol. outputs at each receiver. The signals were received at an oscilloscope, and then digital signal processing was carried out to compensate for the modal dispersion. Figure 8 shows the constellation maps of the received BPSK signals without compensation. Although the higher-order mode was expected to be partially filtered out between the multi-mode splitter and single mode devises, we can see that the input signals were distorted by the modal dispersion after the transmission, and different constellation maps were measured at each receiver.
We also measured the impulse responses of the two-mode SIF and the multi-mode splitter to confirm the splitting ratio diversity of the splitter as shown in Fig. 9 . The pulse width and repetition rate were 100 ps and 100 ns, respectively. We observed only two pulses in addition to the result, which we obtained by using the two-mode PCF. Therefore, there was also negligible modal crosstalk between the fundamental and higher-order modes even when we transmitted the signals over a 20 km-long SIF. Moreover, the splitter exhibited various splitting ratios for each mode because each pulse between receivers 1 and 2 had a different intensity. Each polarization controller installed in front of the 90° hybrids was adjusted to maximize the EFM in this experiment.
Figure 10(a) shows the constellation of the 5000 bit PRBS data signals after compensating for modal dispersion using a single-input single-output (SISO) configuration (using only signals from receiver 1 for compensation). We used adaptive equalization based on an RLS algorithm for the compensation, and estimated the coupling matrix S from 1000 training symbols. Although modal dispersion can be compensated for slightly by the SISO configuration, the tap number Ntap required for the FIR filter becomes large (Ntap = 423 in this case) because the group delay difference is 21 bits/km at 1550 nm for a 10-Gb/s signal. We then used the signals from both receivers 1 and 2 for the compensation. The number of training symbols and data were 100 and 500000 bits, respectively. Here, the recovered signals passed through a decision feedback equalizer (DFE) with 1 feedback tap after passing through the FIR filters to equalize the pulse distortion that occurred in the BPSK modulator (the DFE made no contribution to the modal dispersion compensation). We successfully recovered the signal with almost the same quality as the input signal using only an FIR filter with Ntap = 1 at each receiver as shown in Fig. 10(b), thus revealing that by using our technique we can transmit and effectively recover a signal with a 1-tap FIR filter regardless of the transmission distance and with low computational complexity.
We next used the large-core PCF as a transmission line and evaluated the recovered signal quality. The constellations of the received signals over PCF were also distorted by the modal dispersion and the signals were successfully recovered by using a 1-tap FIR filter as shown in Fig. 11 .
Fig. 11 Received signals at receiver 1 or 2 and recovered signals after compensation for signals transmitted over two-mode PCF.
Figure 12 shows the measured BER data as a function of the received power. The circles and squares show the results for a back-to-back transmission and for a signal transmitted over the PCF. The figure also shows the result of a transmission using the SIF. Here, the received power was the sum of the powers at the two receivers and was adjusted by the attenuators installed in front of the two receivers. The attenuation coefficient of the two attenuators was aligned with the same value in each BER measurement. We measured 500000 symbols at each point in Fig. 12 for the BER evaluation, and we confirmed that the signals were successfully transmitted without any noticeable error floor, and the power penalties were small. Therefore, we can construct a long-haul transmission line with low fiber nonlinearity by using a SIMO configuration and a few-mode PCF with a large Aeff.
5. Conclusion
We proposed a modal dispersion compensation technique that was independent of transmission distance that uses few-mode fiber and adaptive equalization with a SIMO configuration. This technique enables us to compensate for the modal dispersion of the signals regardless of fiber length by employing a 1 × n configuration when the transmission fiber has n modes. We can enlarge the effective area of the fiber and reduce the fiber nonlinearity by using this technique because single-mode operation is no longer required. Furthermore, we showed numerically the advantage of a few-mode PCF for realizing a larger Aeff, and finally achieved a transmission over two-mode PCF with Aeff>280 μm2. We expect the Aeff of the PCF to be extended beyond 400 μm2 by allowing three-mode operation.
Acknowledgments
We thank Y. Sakuyama for his continuous encouragement.
References and links
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