We report successful transmission of dual-LP11 mode (LP11a and LP11b), dual-polarization coherent optical orthogonal frequency division multiplexing (CO-OFDM) signals over two-mode fibers (TMF) using all-fiber mode converters. Mode converters based on mechanically induced long-period grating with better than 20 dB extinction ratios are realized and used for interfacing single-mode fiber transmitters and receivers to the TMF. We demonstrate that by using 4x4 MIMO-OFDM processing, the random coupling of the two LP11 spatial modes can be successfully tracked and equalized with a one-tap frequency-domain equalizer. We achieve successful transmission of a 35.3-Gb/s CO-OFDM signal over 26-km two-mode fiber with less than 3 dB penalty.
©2011 Optical Society of America
Single-channel data transmission rate over 100 Gb/s has become a commercial reality, thanks to reemergence of coherent detection technologies in combination with high-speed electronic digital-to-analog and analog-to-digital converter (DAC/ADC) and digital signal processing (DSP). Together with wavelength-division multiplexing (WDM), polarization-division multiplexing (PDM) and high-order modulation schemes, the highest reported single optical fiber data transmission speed has reached over 100 Tb/s . However, there is a need to continue enhancing the total data transmission capacity while keeping the signals within the available optical spectrum of the conventional Erbium doped fiber amplifier (EDFA), which translates into the requirement for increased spectral efficiency (SE, expressed in b/s/Hz). Although Shannon’s theory predicts SE to increase with higher received SNR as a result of increased transmission power, fiber nonlinearity poses a hard limit on improving channel capacity much beyond the state-of-the-art and the achievable SE rather decreases with increasing optical power after a certain transmission power level [2,3].
In order to explore avenues of further increasing data transmission capacity, the research community has therefore focused on either fibers with large core to improve nonlinear tolerance, or fibers with multiple cores, or fibers that support multiple spatial modes. Even though the first approach is convenient because it is compatible with existing single-mode fiber (SMF) components [4,5], it is either limited to a certain enlargement of effective area within the single-mode condition, or need careful design to avoid modal mixing induced crosstalk. Multi-core fiber has recently been actively explored [6,7], and also can be made compatible with SMF components with tapered multi-core couplers, but needs be precisely designed to sufficiently suppress the crosstalk among the cores. The third approach is to use multiple spatial modes of a single-core fiber, which has been predicted to increase the total capacity [8,9]. Recently a number of groups have demonstrated this approach of spatial mode division multiplexing (MDM) of LP01 and LP11 modes [10,11] and LP01 and two degenerate LP11 modes [12,13]. In addition to increased capacity or SE and higher possible tolerance to fiber nonlinearity, MDM allows the possibility of using spatial modes as an additional degree of freedom for information coding, whereby the forward error correction (FEC) codes can be made further efficient .
The biggest challenge in MDM is the efficient combining and splitting of higher-order spatial modes from and to the fundamental LP01 mode of SMF components. Early proposals of MDM [8,9] focused on using multimode fiber (MMF) with core diameters of 50-62.5 µm for short distances. However, these fibers may support 100 or more modes which couple with each other during transmission of even moderate distance in a random manner due to environmental perturbation, therefore practical demonstrations of MDM in MMF is limited to using a limited number of modes and using some form of spatial filtering, such as using donut-shaped photodiodes , MMF fused couplers , butt-coupling  or spatial light modulators (SLM) . However, it is more practical to limit the number of supported modes to very small numbers, hence the name of few-mode fiber (FMF). It has been demonstrated that by using two-mode fibers (TMF) that support only the LP01 and two degenerate LP11 modes, well controlled coupling to SMF is achievable [10–13,19]. FMF has the potential to provide high mode selectivity, well understood modal dispersions and stable, broadband transmission performance. For example, by designing the differential modal dispersion (DMD) to be large, inter-modal mixing between the LP01 and LP11 modes in the TMF can be minimized , and no complex algorithm to separate the channels are required [10,11]. In addition, by combining the powerful multiple-input, multiple-output (MIMO) digital signal processing (DSP) techniques, modal and polarization mixing can be tracked and the dispersion can be equalized, as demonstrated in [12,13].
The reports in [12,13] relied on free-space mode conversion with the use of phase masks which may be bulky to realize in a practical system. In this paper, we demonstrate the application of all-fiber-based mode converters to multiplexing and demultiplexing of the two-degenerate LP11 modes (LP11a and LP11b). We also demonstrate the transmission over 26-km TMF where we apply 4x4 MIMO processing along with coherent optical orthogonal frequency-division multiplexing (CO-OFDM). CO-OFDM has the advantage of fast channel estimation by using only a few training symbols at the beginning of data frame. Together with heterodyne detection scheme that reduces the number of required ADCs, we have achieved transmission of a 35.3-Gb/s CO-OFDM signal in a bandwidth of only 5.5 GHz.
2. All-fiber LP01-LP11 mode converter and LP11 mode multiplexer
The 26-km custom designed TMF used in this work has the same parameters as the 4.5-km TMF used in [11,19], which are summarized in Table 1 . The TMF is designed to provide a high DMD value of 3 ps/m between LP01-LP11 to minimize coupling probability during transmission. The mode beat length LB = 2π/(β0-β1) is estimated to be 520 µm. By employing a metallic V-groove with pitch equal to LB to create a mechanical pressure grating along the TMF length, we can build a LP01-LP11 mode converter (MC) with low-loss, high conversion efficiency, without the requirement for coupling out to free-space bulk optics . Because the index grating changes only in the direction of the applied pressure, the input LP01 light couples predominately to the LP11 mode oriented in that direction. The schematic diagram of the mode conversion and multiplexing of the two orthogonal LP11 modes is shown in Fig. 1(a) and the picture of the corresponding setup is shown in Fig. 1(b). We have utilized precision-tooled steel-made v-grooves with pitch closely matched to the beating length LB and having only 20 periods, which provides the advantage of compact size and low polarization dependence. In order to prevent damage to the TMF fiber itself, 0.9-mm loose tube jacket is used as a buffer. With this simple design, the mode extinction ratio of better than 20 dB is achieved for all the 4 MCs used in the MDM transmission experiment, two for the transmitter to convert incoming signal from SMF to LP11a or LP11b, and the remaining two at the receiver to convert LP11a or LP11b back to LP01 for SMF coherent detector setup, respectively. The MCs are assisted by mode strippers (MS) to prevent unwanted LP11 mode before MC at the transmitter and after MC at the receiver. The MSs are realized by tight bending the 0.9 mm jacketed TMF fiber over 8 mm posts of about 10 rounds. The insets of Fig. 1(a) show the two orthogonal LP11 modes, (hereafter we denote LP11a and LP11b) viewed by a beam-profiler.
Because it is not easy to know beforehand the axial orientation of the TMF prior to applying the V-groove, we utilize rotation of an adjustable keyed FC connector to enable rotational correction of the two LP11 modes to be orthogonal (orientation 90° rotated) to each other during mode multiplexing and demultiplexing, in the same manner as axial alignment of polarization maintaining fiber (PMF). In order to enable coupling and splitting the LP11a and LP11b mode components in the absence of fiber-based options for this demonstration, we chose to use free-space beam splitters along with collimating lenses with numerical aperture (NA) of 0.25. In future, a fused TMF or micro-optic coupler could be utilized in order to fabricate a compact and low loss orthogonal LP11 mode multiplexer.
3. Dual-LP11-mode transmission experimental setup
In this work we focus on the demonstration of the MDM transmission feasibility instead of high data rates using the proposed transmission method, which will be targeted in future works. The end-to-end transmission experiment setup is depicted in Fig. 2 . In order to maintain simplicity in the receiver setup, we have chosen to adopt heterodyne polarization and mode-diversity coherent detection condition so that only 4 sets of photodetectors (PD) and a real-time oscilloscope with 4-channels of ADC are sufficient to realize the 4 MIMO receivers. Similarly at the transmitter, we use a single optical OFDM generator consisting two DACs of an arbitrary waveform generator (AWG), and then optically subdivide and recombine it twice to emulate the 4 MIMO transmitters. This is schematically depicted in Fig. 3(a) . First the laser output from an external cavity laser is modulated with an optical IQ modulator to generate OFDM signal employing 4 training symbol (TS) slots, of which only the first slot is populated with 1 TS and the remaining 3 are empty. When the signal is split and recombined on orthogonal polarizations with one OFDM symbol delay between them, dual-polarization transmitter is emulated . Then the signal is again split with a 3-dB SMF coupler and the two branches are delayed by two OFDM symbols length to de-correlate them and adjust the location of the TS so that all the 4 tributaries have an orthogonal set of TSs, which can be utilized to compute the 4x4 MIMO channel matrix. The offline DSP processing steps at the OFDM transmitter are shown in Fig. 4(a) . The two branches of PDM OFDM signal are then transferred from SMF to the LP11a and LP11b modes of the transmission TMF by utilizing the mode multiplexer shown in Fig. 1. After the TMF transmission, the mode demultiplexer splits the randomly oriented incoming mode patterns to two orthogonal LP11 modes by using beam-splitter, and converts them back to SMF components by using MCs. Any residual LP01 mode components excited during mode multiplexing or fusion splicing on the TMF are eliminated, as the MCs convert them to LP11 and then subsequent MSs strip them off. After this the two PDM tributaries are further split to orthogonal polarizations by PBS. The 4 tributaries are mixed with 4 LO branches using 3-dB couplers into 4 PDs with trans-impedance amplifiers. RF spectrum of one of the 4 receivers is depicted in Fig. 3(b).The signal-signal intermixing products falling on the lower frequency regions are avoided by inserting a frequency guard band between the signal and the LO in the heterodyne scheme. The 4 channel RF signals on an intermediate frequency (IF) of around 7.7 GHz are then directly sampled by 50 GSa/s ADCs and digitally down-converted and filtered into baseband 4 OFDM tributaries. The 4x4 MIMO-OFDM receiver processing steps are shown in Fig. 4(b), which include frequency estimation and phase-noise compensation by RF pilot-tone method , timing synchronization and MIMO-channel estimation based on zero-forcing algorithm using TS. After estimating the 4x4 channel matrices for each subcarrier, channel equalization, demodulation and bit error rate (BER) evaluation processes follow.
Because the two LP11 modes of the TMF have relatively low DMD between them, even very small environmental perturbation causes the signal to rotate and couple between them. Then as the MCs at the receiver are mode-selective, this would cause power fading if we only used one of the LP11 modes. For dual-LP11 mode transmission, we solve this problem by orthogonal LP11 mode demultiplexing and MIMO channel tracking, as also reported in [12,13]. However, in contrast to previous approaches of employing long memory finite impulse response (FIR) filters, the use of MIMO-OFDM gives the advantage of simplicity in channel equalization employing one-tap equalizer. In order to periodically update channel estimation, we use TS after every 2.5 µs. We measure a channel delay spread of 10ns in our 26 km TMF (corresponding to 0.38 ps/m). Because the DMD between LP11 and LP01 much larger than this value (ref. Table 1), we conclude this to be caused by residual DMD between the two LP11 modes. We will investigate the cause of relative large DMD between the two degenerate LP11 modes in our prototype TMF in future works. In this work we minimize the effect of the channel delay spread by inserting cyclic prefix of 12.8 ns as guard interval to prevent inter-symbol interference from DMD.
4. Dual-LP11 mode, 4x4 MIMO-OFDM transmission experiment results
After building the mode multiplexing and demultiplexing subsystem, we record the achieved end-to-end transmission losses among the PDM transmitters (Tx1 and Tx2) and PDM receivers (Rx1 and Rx2), because of lack of a suitable TMF amplifier, the transmission distance will be limited if the mode conversion loss is too high. The MCs are each estimated to cause only a combined excess loss between 2.8 to 4 dB. The loss of the MC and free-space couplers can be avoided partially by realizing efficient all-fiber mode couplers . However, this will require specialized fusion splicing or evanescent coupling methods. Even though the excess losses are relatively high at this early stage of TMF development, because of the short distance and increased effective area the transmission power can be increased and the received OSNR is still above 30 dB in our case. Therefore, power loss due to mode conversion is not the fundamental limitation transmission over such moderate distances of TMF. Next we proceed to measure the back-to-back 4x4 MIMO-OFDM transmission performance without the long TMF, but including the two transmitters and two receivers with mode conversion (we call this TMF “B2B” and use as a benchmark for evaluating transmission impairments). Because of heterodyning and direct ADC sampling, in order to avoid the influence of signal-signal intermixing products in the low-frequency regions, we used increased LO-signal ratio of 20 dB and optimize the frequency guard band. We find a large delay spread for the 26-km TMF and increased spatial mode coupling, therefore we use a longer symbol length of 115.2 ns with 1/8 CP length to verify the feasibility of overcoming DMD and penalty in dual-LP11 mode transmission over 26-km TMF. We chose QPSK modulation for all subcarriers. The total data rate is 35.3 Gb/s, taking into consideration CP and TS overheads. Figure 5 (a) shows the performance of the 26-km TMF transmission as compared to TMF B2B. For B2B, the required optical signal-to-noise ratio (OSNR) to achieve a BER of 1 × 10−3 is found to be 11.5 dB, with 2 dB of variations among tributaries. Increased BER variation may have been caused by channel estimation error due to using long symbols; however this variation further increases to almost 4 dB after 26 km transmission. This is also evident in the constellations of Fig. 5 (b), where LP11b components showed poorer performance and also from the BER-vs-OSNR plots in Fig. 5 (a) after 26 km transmission. Together with the influence of DMD, the polarization dependent loss and the power imbalance in the two transmitter side MC may be playing a role in BER variation, and we will investigate ways to mitigate this by power pre-emphasis and optimization of MC in future works. On average the required OSNR penalty after 26-km TMF transmission is 3 dB. Therefore we conclude that by using OFDM signals with longer CP, the spatial mode mixing and random rotations are still correctable in a 4x4 MIMO transmission on LP11a/b modes in relatively long TMF spans. This indicates that spatial mode diversity among the degenerate LP11 modes in TMF can be harnessed to double the capacity compared to SMF. It is also noteworthy that the LP01-LP11 mode converters required to interface TMF with SMF components can be realized based on fiber-based compact with low complexity. As the data bandwidth is only 5.5 GHz, even after considering 7% overhead for FEC, the achieved net SE is 5.9 b/s/Hz, which is only possible for QPSK through the use of the two spatial modes.
We report successful mode-multiplexed dual-polarization transmission on two degenerate LP11 modes of a two-mode fiber using all-fiber based LP01-LP11 mode converter. Mechanically induced fiber gratings show stable mode conversion between LP01-LP11 with extinction ratios over 20 dB. Using free-space coupling of the two LP11 modes, we have realized 4x4 MIMO CO-OFDM transmission over up to 26-km of a two-mode fiber. After mode- and polarization-diversity heterodyne detection, we have successfully demonstrated transmission of a 35.3-Gb/s CO-OFDM signal over 26-km TMF fiber with QPSK modulation, with less than 3-dB penalty compared to TMF back-to-back detection.
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