Fiber-Optic Temperature Sensor Using Differential LP-Mode Delay Measurement in Weakly-Coupled FMFs

We provide differential mode delay (DMD) diagnostics for linearly polarized (LP) modes traversing a few-mode fiber (FMF). We employ a modal interferometer method with a butt coupling mechanism to measure the DMD between any two modes guided in FMFs with step-index (SI) and depressed-cladding profiles. The measurement principle is based on investigating a transmitted spectrum through temporal decomposition by means of a Fourier transform. At least four different temporal waveforms are needed for an FMF supporting four LP modes to estimate the DMD between two different LP modes. A butt coupling mechanism with an air gap between an FMF and a dispersion-shifted fiber is employed for simultaneous DMD measurement. The present diagnostics requires some knowledge of the bending loss characteristics of the FMFs and the butt coupling properties of the circular symmetry modes or circular asymmetry modes in their electric fields. The DMD diagnostics are realized taking the bending loss and butt coupling characteristics into consideration. We present experimental results for the DMD and DMD slope as a function of the wavelength in a 1450-1625 nm telecommunication band.

We investigate the graded-index few-mode fiber (GI-FMF) to realize a 4-LP-mode (i.e. LP01, LP11, LP21, and LP02) fiber for mode-division-multiplexed transmission. This study optimizes the GI-FMF for both, first, for large effective indices differences (Δneff), and second, for low differential mode delay (DMD) between any two LP modes, for different optimized parameters. Thus, it shows that GI-FMF is suitable for both weakly-coupled few-mode fiber (WC-FMF) as well as strongly-coupled few-mode fiber (SC-FMF) via adjusting the profile parameter (α), refractive index difference between core and cladding (nco - nclad), and core radius (a). We report the optimized parameters for WC-GI-FMF with large effective indices difference (Δneff) of 0.6 × 10-3 and low |DMD| of 5.4 ns/km while the minimum effective mode area (Min.|Aeff|) is 80 µm2 and bending loss (BL) of the highest order mode is 0.005 dB/turn (much lower than 10 dB/turn) at a 10 mm bend radius. Here, we could break down the degeneracy between LP21 and LP02 mode, which remains a challenging task in GI-FMF. To the best of our knowledge, this is the lowest DMD (5.4 ns/km) ever reported for such a weakly-coupled (Δneff = 0.6 × 10-3) 4-LP-mode FMF. Similarly, we optimized the parameters for SC-GI-FMF with Δneff of 0.1 × 10-3 and the lowest DMD of 0.9 ns/km while Min.|Aeff| is ≫ 100 µm2 and BL of higher order mode is 6 dB/turn (< 10 dB/turn) at 10 mm bend radius. Further, we investigate narrow air trench-assisted SC-GI-FMF to reduce the DMD and achieve the lowest DMD of 16 ps/km for a 4-LP-mode GI-FMF with a minimum Δneff of 0.7 × 10-5.

Weakly-coupled mode division multiplexing (MDM) technique is a promising candidate for capacity enhancement of short-reach optical interconnections, for which the multiple-ring-core few-mode fiber (MRC-FMF) has been proven to be an effective design method to suppress distributed modal crosstalk. Similar to low chromatic-dispersion (CD) O-band transmission based on single-mode fibers (SMF), all the mode channels in a weakly-coupled FMF for short-reach applications should achieve low CD to support intensity-modulation/direct-detection (IM/DD) transmission. In this paper, we propose, for the first time to the best of our knowledge, an index perturbation method to adjust both effective index and CD of each mode in an MRC-FMF. Firstly, an accurate modeling method to model the relationship between SiO2-GeO2 material index and the germanium concentration at different wavelengths is proposed by analyzing the index characteristics of 4 kinds of germanium-doped fused silica SMFs at the same fabrication processing, which could be utilized to calculate the CD characteristics for an MRC-FMF with perturbed index profile. Then, based on the perturbation method considering the influences on both effective index and CD, a weakly-coupled low-CD MRC-FMF supporting 4 linearly-polarized (LP) modes is designed and fabricated. The measured minimum effective index difference min|Δneff| among all modes is larger than 1.3 × 10-3, and the CD values of all the modes lie between -6 and +6 ps/km/nm ranging from 1280 to 1320 nm, which agree well with the design. The 2-km transmission experiment indicates that the fabricated MRC-FMF could support stable digital-signal-processing (DSP)-free IM/DD transmission for all the 4 LP modes. This work is beneficial to the application of short-reach weakly-coupled MDM systems.

We propose a novel mode multiplexer based on phase plates followed by a Mach-Zehnder interferometer (MZI) with image inversion. After the higher-order modes are selectively converted from fundamental linear-polarized (LP) modes by the phase plates, the converted modes are coupled without fundamental loss using MZI with image inversion, in which the original spatial pattern and inverted pattern of the optical signal are interfered. Our scheme is also applicable to the coupling of degenerated LP modes such as LP(11a) and LP(11b). First, we numerically and experimentally evaluate the performance of the mode converter based on phase plates. The mode converter is suitable as long as the five LP modes such as LP(01), LP(11ab) and LP(21ab) are sustained in a few-mode fiber (FMF), although the crosstalk due to excitation of undesirable modes is unavoidable when the higher-order modes over LP(02) are sustained in FMF. Next, we develop and characterize the proposed mode multiplexers based on phase plates and MZIs with image inversion. The insertion loss is suppressed to around 3 dB for mode multiplexing of LP(11a) and LP(11b). Using a fabricated mode multiplexer for LP(31a) and LP(31b), we measure the bit-error rate performance of single-polarization mode-multiplexed quadrature-phase shift keying optical signals.

A proposal for a temperature and strain sensor, based on OAM interference in few-mode fibers

New transmission techniques for short-reach optical transmission applications especially datacenter interconnections are highly expected to break current bandwidth bottleneck, among which mode division multiplexing (MDM) based on few-mode fiber (FMF) is promising by exploring different linearly-polarized (LP) modes or mode groups as spatial transmission channels. However, it has been a great challenge to deal with degenerate modes in FMFs. In this paper, a FMF design utilizing multiple ring perturbations in fiber core to suppress modal crosstalk during fiber transmission is firstly proposed and a 6-LP-mode double-ring-core (DRC) FMF is fabricated with a high minimum refractive index difference (min|neff|) of 1.4910-3 among all the modes. Secondly, a novel degenerate-mode-selective coupler (DMSC) converting each degenerate LPmn mode into the LP11 mode in a two-mode fiber is proposed. Then intensity-modulation/direct-detection (IM/DD) MDM transmission scheme without any digital signal processing (DSP) can be realized utilizing mode multiplexer/demultiplexer (MUX/DEMUX) consisting of cascaded mode-selective couplers (MSC) and DMSCs, in which each degenerate or non-degenerate LP mode is considered as an independent transmission channel. Then based on the proposed DRC-FMF and mode MUX/DEMUX, we demonstrate a 4-LP-mode prototype system using commercial single-mode 10 Gbps SFP + modules and 4K video transceivers without any hardware or software modifications. Finally, the intra-LP-mode dispersion (ILMD) effect in a weakly-coupled FMF is analyzed and a modified fixed-analyzer method is proposed for its measurement. Experimental results show that it may be one of the major impairments for IM/DD MDM transmission.

Increasing demand for high data transmission rates and bandwidth availability driven by the rapid development of the broadband services becomes challenging in the context of constraints imposed by nowadays exploited telecommunication optical fibers. Based on single-mode fibers and multiplexing in the wavelength domain (wavelength division multiplexing, WDM), the current technology seems to have reached its fundamental limits. At present, two promising technologies are a subject of intensive research. One of them is the increase of the data transmission through multiplying the number of fiber cores, thus implementing the concept of Multi-Core Fibers (MCF), where each core is used as a separate data transmission channel. The second widely investigated technique is based on the idea of mode division multiplexing (MDM), where different transverse modes of a Few-Mode Fiber (FMF) can be used as different carriers for data channels. In this work, we demonstrate the results of R&D works and the comprehensive tests of the few-mode fibers developed within the project NMKM+. Developed few-mode fibers (both passive and active) and their commercially available counterparts have been tested with respect of transmission parameters and applicability to the real telecom systems. In particular, guided mode profiles, numerical apertures, OTDR, and dispersion characteristics for the passive fibers have been recorded and compared. Also, methods of selective excitation and detection of singular modes have been discussed and partially verified. The results of data transmission experiments have been performed and discussed with respect to the quality of transmitted signals. These have been complemented by the amplification experiments with the use of erbium-doped few-mode fibers in “classical” and microstructural geometry. The results were studied and analyzed, showing the potential for future optimization. Acknowledgement: This work has received support from the National Centre for Research and Development through project NMKM+ (TECHMATSTRATEG1/348438/16/NCBR/2018).

Design and optimization of 3-mode×12-core dual-ring structured few-mode multi-core fiber

Few-mode fibers (FMFs) have garnered significant attention in mode-division multiplexing (MDM) systems due to their parallel mode transmission capability. To achieve efficient mode control and characterization of FMFs, we present an adaptive spatial light modulation (SLM) system based on the genetic algorithm (GA) by combing the digital holography (DH). Single exposure DH technology can achieve precise decomposition of fiber modes, laying the foundation for subsequent precise mode control. The implementation of GA optimization can effectively select the phase distribution loaded onto SLM corresponds to the expected mode field in FMFs. Through closed-loop optimization of output mode fields via a SLM, this methodology achieves high-purity linearly polarized (LP) mode generation by solely monitoring the output intensity distribution. The experimental results show that in FMFs with 5.3 µm and 8.2 µm core diameters, LP mode excitation with purity approaching 90% is demonstrated. Simultaneous excitation of composite LP mode superposition fields generates customized intensity profiles showing similarity indices nearing 0.9. This self-adaptive mode control approach eliminates complex coupling requirements while overcoming static encoding limitations, providing critical technical support for advancing MDM systems.

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 (A(eff)), and finally we report a transmission over a large-core two-mode PCF with A(eff)>280 μm(2).

Multicore fibers and few-mode fibers have potential application in realizing dense-space-division multiplexing systems. However, there are some tradeoff requirements for designing the fibers. In this paper, the tradeoff requirements such as spatial channel count, crosstalk, differential mode delay, and cladding diameter are discussed. Further, the design concept and transmission characteristics of high-core-count single-mode multicore fibers are discussed. A heterogeneous multicore fiber with 30 cores and quasi-single-mode multi-core fibers with 31 cores are developed.

Stimulated Brillouin scattering (SBS) in a few-mode fiber (FMF) is of significance for the distributed temperature and strain sensing. An FMF with M-shaped refractive index distribution (M-FMF) is proposed in order to improve the performance of simultaneous temperature and strain sensing based on SBS. Propagation of four optical modes is supported by the M-FMF, so that the Brillouin gain spectrum (BGS) can be obtained by both intra-mode and inter-mode SBS. The BGSs produced by the interactions of LP&lt;sub&gt;01&lt;/sub&gt;-LP&lt;sub&gt;01&lt;/sub&gt; mode pair, LP&lt;sub&gt;01&lt;/sub&gt;-LP&lt;sub&gt;11&lt;/sub&gt; mode pair, and LP&lt;sub&gt;11&lt;/sub&gt;-LP&lt;sub&gt;11&lt;/sub&gt; mode pair are analyzed, respectively. Meanwhile, the temperature and strain sensing performance based on the BGS of LP&lt;sub&gt;01&lt;/sub&gt;-LP&lt;sub&gt;11&lt;/sub&gt; mode pair are studied in detail. Considering a common step-index FMF, only one obvious scattering peak is usually present in the BGS obtained from the interaction between different optical mode pairs, therefore, it is inconvenient to achieve multi-parameter sensing measurement. In this paper, the BGS of LP&lt;sub&gt;01&lt;/sub&gt;-LP&lt;sub&gt;11&lt;/sub&gt; mode pair has two scattering peaks, which are contributed by the acousto-optic coupling between the acoustic modes L&lt;sub&gt;1&lt;i&gt;n &lt;/i&gt;&lt;/sub&gt;(&lt;i&gt;n&lt;/i&gt; = 1, 2) and the optical modes LP&lt;sub&gt;01&lt;/sub&gt; and LP&lt;sub&gt;11&lt;/sub&gt;. The two Brillouin scattering peaks have large gain values of 0.1004 m&lt;sup&gt;–1&lt;/sup&gt;·W&lt;sup&gt;–1&lt;/sup&gt; and 0.0463 m&lt;sup&gt;–1&lt;/sup&gt;·W&lt;sup&gt;–1&lt;/sup&gt;, respectively. More importantly, the gain difference between two Brillouin scattering peaks is small, and the frequency interval is 75 MHz, which can be applied to simultaneous temperature and strain sensing. The influences of the refractive index and the fiber core radius on the BGS of LP&lt;sub&gt;01&lt;/sub&gt;-LP&lt;sub&gt;11&lt;/sub&gt; mode pair are studied. By selecting the optimal structure parameters, we discuss the effect of temperature and strain on the BGS of LP&lt;sub&gt;01&lt;/sub&gt;-LP&lt;sub&gt;11&lt;/sub&gt; mode pair. The errors for simultaneous temperature and strain measurement are reduced to 0.23 ℃ and 5.67 με. Compared with other reported results, our obtained temperature and strain sensitivity are high and sensing errors are low in the considered M-FMF. In other words, based on the BGS of LP&lt;sub&gt;01&lt;/sub&gt;-LP&lt;sub&gt;11&lt;/sub&gt; mode pair, the performance of temperature and strain sensing are improved in the M-FMF. This work is of great significance for studying intra-mode and inter-mode SBS in an FMF. Moreover, the results also provide a guideline for further improving the performance of simultaneous temperature and strain sensing.

Modal dispersion characterization of few-mode fiber based on electrical spectral interferometry with optical frequency comb

The few-mode fiber (FMF) based Brillouin sensing operated in quasi-single mode (QSM) has been reported to achieve the distributed curvature measurement by monitoring the bend-induced strain variation. However, its practicality is limited by the inherent temperature-strain cross-sensitivity of Brillouin sensors. Here we proposed and experimentally demonstrated an approach for simultaneously distributed curvature and temperature sensing, which exploits a hybrid QSM operated Raman-Brillouin system in FMFs. Thanks to the larger spot size of the fundamental mode in the FMF, the Brillouin frequency shift change of the FMF is used for curvature estimation while the temperature variation is alleviated through Raman signals with the enhanced signal-to-noise ratio (SNR). Within 2 minutes measuring time, a 1.5 m spatial resolution is achieved along a 2 km FMF. The worst resolution of the square of fiber curvature is 0.333 cm-2 while the temperature resolution is 1.301 °C at the end of fiber.

For several decades silica-based optical fibres have been used for telecommunication and sensor purposes. The single-mode fibre is frequently employed in long-distance networks, whereas the multi-mode fibre is the preferred means of signal transport in campus and in-building networks. Because of the huge bandwidth of optical fibres in comparison to its electrical wireless and copper-based counterparts, the demand for optical fibres keeps increasing. In a competitive market, fibre manufacturers aim to produce ever better fibres that are as cheap and easy to employ as possible. As fibre research, development and manufacturing is a mature discipline, improvements in fibre design can only be achieved through the construction of robust, accurate and efficient numerical fibre models for the computation of those quantities that determine the behaviour of the fibre. We have developed a modular software code, based on Maxwell’s equations, to compute these quantities in a vectorial full-wave way for both single-mode and multi-mode optical fibres. Key is the refractive-index profile, or, more specifically, the dopant profile, as it defines the propagation, splicing and bending-loss characteristics of the fibre. For the single-mode fibre, the fibre quantities that we have concentrated on are dispersion, dispersion slope, mode-field diameter, effective area, bending loss, effective and theoretical cut-off wavelength and MAC-value. We highlight one fibre quantity in particular, viz. the computation of the bending loss in a single-mode fibre. Many approximate modelling techniques have been developed to estimate this loss in a fast way. Our numerical scheme, however, is the first rigorous one, as we have performed a vectorial full-wave analysis of the bent optical fibre. In this context, triple integrals involving products of Bessel functions with large, complex order and argument appear. Due to cancellations in the pertaining computation, a high relative accuracy is needed for the computation of each product. As a result, it takes weeks on a contemporary computer to compute the bending loss as a function of the radius of curvature. We have used the vectorial full-wave bending-loss results to determine the most appropriate approximate method. Subsequently, we have extended that approximate method to compute the bending losses of higher-order modes, since the required effective cut-off wavelength depends on the bending loss of the first higher-order mode. The selected approximate method has been used in the ensuing bending-loss calculations. Since the fibre properties are often conflicting, it is a challenging task to adapt the radial dopant profile to meet a set of predefined design goals. A design goal is a combination of desired values for (some of) the aforementioned fibre quantities, and can mathematically be translated into a cost function. The minimisation of this cost function provides us with the optimal dopant profile for that specific set. For the single-mode fibre, we have performed this minimisation for piecewise-linear profiles, by employing various global and gradient-based local optimisation strategies to speed up the design step considerably. Frequently,these optimisation strategies lead to counter-intuitive dopant profile designs that could not have been contrived otherwise. We have selected a deliberate mix of several optimisation routines and have compared their performances. Perhaps the most important conclusion is that there still appears to be room for improvement in the design of the radial dopant profile of commercially available fibres. For the multi-mode fibre, vectorial full-wave optimisation is not feasible yet because of the long computation times for the large number of propagating modes. Still, our numerical scheme allows for a manual fine-tuning of the popular power-law profile to minimise differential mode delay. Further, we have included mode coupling and differential mode attenuation in our model to obtain intensity patterns that match closely with measurements. We have also analysed the influence of profile variations, e.g. on-axis dips and kinks, on the intensity pattern. A selective excitation of different mode groups in a multi-mode fibre, offers the possibility to create several independent transmission channels, and thus a higher information capacity. Recently, the feasibility of this so-called mode group diversity multiplexing technique has been demonstrated. Simulations provide us with a means to better understand its operation and possibly increase its efficiency. The channel separation may be enhanced by employing a lens between the fibre and the detector, which is called mode-selective spatial filtering. Our numerical simulations of a mode group diversity multiplexing link, with and without mode-selective spatial filtering, are in agreement with the measurements. The above discussion makes clear that the developed software code has a wide range of applicability. Moreover, it is built in a modular way and thus extensions, like the inclusion of more fibre quantities or different profile dopants, are straightforward.