Broadband mode multiplexers – Alternative solution for telecommunications and research
There is a perception that the transmission capacity of a fiber optic line during signal transmission using time-division multiplexing and wavelength-division multiplexing has reached its limit . However, the method of spatial division of channels is still not fully implemented. Two popular approaches are Space division multiplexing (SDM) (Fig. 1), implemented based on multi-core fibers (e. g., by OFS) and Mode Division multiplexing (MDM) (Fig. 2).
In the second case, a few-mode fiber (FMF) with a core, where several polarization or spatial modes propagate, is used [3, 4]. These methods can potentially increase the line capacity by almost an order of magnitude and, apparently, are promising solutions for overcoming the limitation imposed by the nonlinear effect in the DWDM systems.
OPERATION PRINCIPLE OF THE SELECTIVE MODE MULTIPLEXER
The authors of  suggested the structure and basic principles of the spatial mode multiplexer. A multiplexer is a structure of few-mode and single-mode fiber, polished from the side and fixed next to each other in quartz with a similar refractive index (Fig. 3). When the propagation constant and, therefore, the refractive index (neff) for the guided modes in the SM fiber coincides with the propagating modes in the FM fiber, an efficient coupling occurs between these modes in the evanescent fields screening field. Perfect coupling in few-mode fibers is impossible due to phase mistiming dissynchronism. Almost perfect coupling is possible with the isolation of higher modes, as in experiments [5, 6]. The key parameter is the phase matching of the coupling modes.
DETERMINATION OF THE REFRACTIVE INDEX (RI)
Measuring RI for the modes is important for manufacturing a coupler. The measurement is made through a prism, as shown in Fig. 4. The evanescent fields of the flowing modes in the region of polished fibers leak penetrates the prism, and depending on the angle deviation we can determine neff
where np is the refractive index of the prism. In Fig. 4b, the measured graph of the intensity of the emitted light versus screen height (h) for modes in an FM fiber at a wavelength of 1550 nm.
Fig. 5 shows graphs of the measured RI for various modes depending on the wavelength (1515–1590 nm) and the fibers used. As can be seen in Fig. 5 (top), the dependence of neff on the wavelength is almost linear, but with different slopes for different modes. In the ideal case, three different SM fibers should be used, which have corresponding RI values consistent with the characteristics of higher-order modes in the FM fiber in a wide range of wavelengths. In practice, SM fiber is used, but with a larger numerical aperture (NA). In this case, the dependence of the wavelength on the RI (d neff / dλ) is preserved.
As an example, Fig. 5 (bottom) shows the RI dependence on the wavelength for the LP02 mode in the FM fiber (red line) as compared with the resulting mode in the SM fiber (dark blue line), showing good coincidence level. For comparison, the values are shown for matching in a standard SM fiber, where a large discrepancy can be seen (green line).
The fibers in the experiment had nominal NA in the range of 0.2–0.3. The narrowing of the fibers was carried out by heating and stretching (tapering), which reduces neff . The correct diameter of the taper was calculated by numerical simulation of mode propagation in the SM fiber . The optimum diameter of the taper was determined after the experiment.
MODE COUPLING EFFICIENCY
Mode coupling between higher order modes (HOM) in a few-mode fiber (FMF) and LP01 modes in a single-mode fiber (SMF) describes the theory of mode coupling :
where Pin and Pout are the input power and output power, respectively, κ is the coupling constant, z is the interaction length, and δ = Δ / 2β is the wave propagation constant (β) between the modes in the FM and SM fibers. According to equation 2, the difference in neff between the target mode in a few-mode fiber and the LP01 mode in a single-mode fiber should be minimized to increase the interaction power. For example, when the value of z is 1.6 mm (which corresponds to our case), and κz = π / 2 at 1550 nm, the value of δ should be less than 2.2 Ч 10–4, thus the coupling coefficient will be 80%. In this paper, the efficiency of the coupling (Ce) is determined by the ratio of the output power of the mode in the FM fiber and the output power of the LP01 mode in the SM fiber.
The rest of input power fell on the unwanted LP21 mode (8.2%), loss at the splice points (nominally 6–10%) and some of the remaining modes in SMF (~1%). The measurements were carried out as follows. The input power was measured using a power meter. The total output power of the FM fiber, which was also measured with a power meter, may contain signals from unwanted modes. A loop was formed to measure bending losses on the output modeless fiber. The results showed that with a fiber bend diameter of 20 mm, the loss is 20 dB for the LP02 mode without significant influence on other modes. In the case of the LP21 mode, bending losses are less than 0.1 dB with a diameter of 20 mm and 17 dB with a required bending diameter of 6 mm. Bending loss values for modes LP01 and LP11 were insignificant. The degradation of Ce in the L-range in Fig. 6 (b) is calculated from the finite spectral bandwidth of the splitter’s shielding field, i. e. imperfect matching of RI.
MODE DIVISION MULTIPLEXER
The four-mode multiplexers (MDM) by KS Photonics are designed by cascading three mode multiplexers (MSC), as shown in Fig. 6. To prevent losses at the splice points, a continuous chain of FM fibers was used for all three MSC. Four-mode input ports are equipped with standard single-mode pigtails to make them compatible with communications systems. To cut off the unwanted optical signal in the LP02 mode, connected to the LP21 MSC, a mode filter was installed between the LP21 and LP02, made by bending a fiber with a diameter of 20 mm. However, the presence of the filter did not allow to measure the coupling of the LP21 or LP02 modes, which is believed to be associated with a large separation of the RI between the LP11 mode and higher-order modes.
The extinction ratio of the RE MSC is an important parameter and is determined by the formula:
where Ptarget is the optical power of the coupling with the selected (desired) mode, Pother is the optical power of the coupling with the unwanted modes.
The RE measurement for modes LP01 and LP11 must be made during the manufacturing process of the MSC, since after assembly the measurement of the extinction ratio becomes impossible. To determine the RE, radiation is applied to one input port, the optical power is measured at the output port before and after the unwanted modes, as described in the previous section. Mode separation was performed by bending the fiber or using a liquid with a similar RI on the coupler halves after measuring each MSC. To this end, the MSC were assembled in the following mode order: LP11, LP21 and LP02. It was confirmed that the assembly process of the LP21 and LP02 MSC did not cause additional losses for the LP01 and LP11 modes.
CHARACTERISTICS OF THE SIX–MODE MULTIPLEXER
The six-mode multiplexer is similar to the structure shown in Fig. 7. In order to match the RI for the LP01 mode in a single-mode fiber with the higher-order modes in the SM fiber, the SM fiber was tapered. Germanium-doped FM fiber with a step refractive index was used to transmit six modes of LP01, LP11a / 11b, LP21a / 21b, and LP02. Each fiber is enclosed in a quartz unit, and the fiber cladding is partially polished. The standard efficient coupling of the LP11, LP21, and LP02 modes were 80%, 70%, and 80% in the C-band. The complete structure is shown in Fig. 8.
A scanning interferometer was used to measure the characteristics. It measured the matrix of the transmissibility of amplitude and phase between input and output. The mode loss (MDL) was analyzed by decomposing the singular values from the measured matrix. The measurement scheme is shown in Fig. 9.
EXPERIMENTAL SETUP. DATA TRANSFER
Fig. 10 shows an experimental setup for data transmission using the mode channel separation method. Thirty channels with a pitch of 100 GHz in the C-band (1534.25–1557.36 nm) were generated by distributed feedback (DFB) lasers. A wavelength selective switch was used to equalize the optical power in all channels. Each channel group was amplified by an erbium amplifier, and then directed to an IQ modulator. Both IQ modulators were controlled by independent bit sequences of 216 characters in length generated by digital analog converter of 60 Giga-samples / s (DAC). The modulators were with fiber outputs. The signals arrive at the polarization separation multiplexing stage, where two polarization separations are delayed by 382 ns. The resulting polarized quadrature phase shift (120 Gbit / s (DP-QPSK)) was divided into six copies with relative delays of 0, 50, 100, 150, 200 and 250 ns. Six decorrelated signals were connected to the fiber inputs of a 6-mode multiplexer.
6-mode multiplexed signals were fed into the circulation loop. An acousto-optic switch (AOS) was used to transmit signals through multi-turn cycles. Optical components such as AOS, lenses and beam splitters (BS) were installed to support the propagation of several modes.
All four ports of the loop were with fiber with a RI stepped profile supporting approximately 15 / 9 modes. Then these fibers are tapered (stretch up to 1 m), which gave us 6 modal fibers. This extension was aimed at reducing the number of modes transmitting the signal.
The transmission line was 58.5 km long with a gain in MM-EDFA. MM-EDFA, (c), was used as a linear amplifier to compensate for losses in the fiber and other optical components in the line. The signals were sent through a polarization splitter (BS), and then demultiplexed into 6 modes. The test channel wavelength was filtered using a unit (WB). Six coherent polarization diversity receivers (PD-CRx) were used to detect signals. A total of twenty-four electrical signals in the time interval of 100 µs were simultaneously transmitted to a modular digital oscilloscope operating at a sampling rate of 40 GHz / s and a bandwidth of 20 GHz.
Also, the BER parameter was measured for the line, which made the data transmission mode LP01 less than 2 · 10–5 over the entire wavelength range.
The paper demonstrates the operation principle of a fiber mode multiplexer based on cascaded mode selective couplers with a broad bandwidth. The coupling efficiency over the entire wavelength range from 1 515 to 1 590 nm varied from 87% for the LP01 mode, in the worst case – more than 55% for the LP21 mode. Significantly improved performance was achieved by comparing neff over the operating wavelength for few-mode and single-mode fibers. This device may be useful for the further development of multiplexed communication systems with high bandwidth. The experiment showed that the transfer of information by the method of multiplexing modes is possible. It can also be expected that the performance of the multiplexer can be improved by efficiently multiplexing degenerative asymmetric modes.