Mode-dependent Loss Research Articles

All-fiber spatial and wavelength gain-flattening of few-mode EDFA via mode selective coupler

The mode division multiplexing (MDM) technique together with wavelength division multiplexing (WDM) shows the great prospect to solve the capacity crunch of current standard single mode fiber (SSMF) transmission system. However, the modal and wavelength gain fluctuation fundamentally limit both the capacity and the reach of hybrid MDM-WDM transmission system. Here, we propose an all-fiber few-mode gain-flattening filter (FM-GFF) based on mode selective coupler (MSC), to effectively mitigate the gain fluctuation of few-mode erbium doped fiber amplifier (FM-EDFA) in both spatial and wavelength dimensions. With the help of genetic algorithm (GA), variable mode dependent loss spectra of cascaded MSCs can be efficiently obtained, according to the gain profile of the used FM-EDFA. Consequently, gain-flattening among all guided linearly polarized (LP) mode groups over the C-band can be realized. Simulation results reveal that, as for the spatial and wavelength gain flattening among 4/6-LP mode groups, only 5/7 cascaded MSCs are good enough to mitigate the modal and wavelength gain fluctuation from 9.89 dB and 11.79-dB to less than 0.38 dB and 0.46 dB over the C-band. Finally, we carry out experimental verification based on 2-LP mode groups gain flattening over C-band. When 3 cascaded MSCs are involved, the gain fluctuation of FM-EDFA over the C-band can be flattened from 2.46 dB to less than 0.96 dB.

Compact and efficient photonic lanterns through multi-stage tapering.

Photonic lanterns (PLs) have been recently used in mode-division multiplexed systems with a low insertion loss, a low mode-dependent loss (MDL), and a wide bandwidth. However, the cross talk (XT) performance of the PLs requires further enhancement within a short taper length. In this Letter, a multi-stage cascaded scheme for short PLs is proposed to further improve the performance on losses and XT. The XT of the optimized 6-mode 3-stage PL is below -23.4 dB, while the total length is only 6 cm. To the best of our knowledge, this is the first quantitative optimization of a 3-stage tapered PL, resulting in a compact structure and excellent performance. Furthermore, we experimentally validate the feasibility of the 3-stage tapering process.

Free-standing microscale photonic lantern spatial mode (De-)multiplexer fabricated using 3D nanoprinting

Photonic lantern (PL) spatial multiplexers show great promise for a range of applications, such as future high-capacity mode division multiplexing (MDM) optical communication networks and free-space optical communication. They enable efficient conversion between multiple single-mode (SM) sources and a multimode (MM) waveguide of the same dimension. PL multiplexers operate by facilitating adiabatic transitions between the SM arrayed space and the single MM space. However, current fabrication methods are forcing the size of these devices to multi-millimeters, making integration with micro-scale photonic systems quite challenging. The advent of 3D micro and nano printing techniques enables the fabrication of freestanding photonic structures with a high refractive index contrast (photopolymer-air). In this work we present the design, fabrication, and characterization of a 6-mode mixing, 375 µm long PL that enables the conversion between six single-mode inputs and a single six-mode waveguide. The PL was designed using a genetic algorithm based inverse design approach and fabricated directly on a 7-core fiber using a commercial two-photon polymerization-based 3D printer and a photopolymer. Although the waveguides exhibit high index contrast, low insertion loss (−2.6 dB), polarization dependent (−0.2 dB) and mode dependent loss (−4.4 dB) were measured.

Study on joint effects of modal dispersion, mode-dependent loss and noise by unified density-matrix formalism

We generalize the density-matrix formalism to provide a simple and unified framework for the study of modal dispersion (MD), mode-dependent loss (MDL) and noise in mode-division-multiplexing communication systems. Fundamental concepts and formulas in the original formalism are generalized, while new elements and associated equations are introduced and/or derived. Due to the ability of the density operator to characterize partially-coherent fields, the generalized density-matrix formalism is particularly useful for analyzing the field propagation in presence of noise. Combining the unified density-matrix formalism and the stochastic-process theory, we conduct detailed numerical simulation and analysis on the modal properties of a randomly-perturbed 6-mode fiber with loss and noise. We find that although the MDL only slightly affects the statistics of the group delays, it can cause significant non-orthogonality among the principal modes, which might induce extra crosstalk and temporal spreading in the signal pulses. Furthermore, with the coherency of fields in the fiber being reduced by the noise, the MDL can induce substantial fluctuation in the field coherency even though it does not significantly affect the averaged field coherency.

Mapping-varied modulation with labeling optimization for secure transmission in mode-division-multiplexed fiber-optic systems

To improve the physical-layer security of mode-division multiplexing (MDM) systems, a simple security scheme named mapping-varied modulation (MVM) is proposed in this paper by combining cryptographic and information-theoretic security. Specifically, on top of the information-theoretic security provided by the less-conditioned wiretap channel due to the larger mode-dependent loss induced by fiber-bend tapping, the proposed MVM security method varies the mapping rules of the adopted constellations for the subchannels (one subchannel corresponds to one mode) by using the inherently time-varying random channel state information (CSI) of the MDM fiber, under the assumption that an eavesdropper does not know the exact instantaneous CSI of the legitimate link. To maximize the difference among the binary labels of the constellation points in the same position for each subchannel, a labeling optimization method is proposed as well. Numerical results demonstrate the effectiveness of the proposed MVM method via bit-error ratio performance and secrecy rate, showing a potential way to improve the security of the MDM link for high-speed data transmission.

Co-planar arbitrary ratio optical power splitter based on cascaded hybrid-core vertical directional couplers for arbitrary guide modes

We propose a co-planar optical power splitter based on cascaded hybrid-core vertical directional couplers, which serves to split arbitrary ratio power of arbitrary guide modes. We fabricate the optical power splitter using micro-fabrication facilities. Our fabricated chip demonstrates power splitting for the E11, E21 and E12 modes between two few-mode waveguides. The experimental device shows that optical power splitting ranges can be larger than 11.0 dB, 12.1 dB and 11.3 dB for the E11, E21 and E12 modes, respectively, over the C + L band and beyond. The proposed optical power splitter could be used in the mode division-multiplexing systems where power splitting for arbitrary guide modes in few-mode waveguide is required in the ultra-broadband wavelength range for mode manipulating, such as mode power distribution, mode dependent loss equalization and all-optical MIMO signal processes.

Post-FEC performance evaluation of optical SDM systems with mode-dependent loss

This work is focused on the bit error rate (BER) performance of spatial division multiplexing (SDM) systems over an optical channel with mode-dependent loss or gain (collectively referred to in this paper as MDL). When the latter is non-negligible, the BER has a random nature that introduces the outage probability as an important performance metric for the system design and also impacts on the selection of a forward-error correction (FEC) scheme. In MDL-impaired SDM systems, the pre-FEC BER is a random variable whose probability density function (PDF) and coding gain depend on the signal-to-noise ratio (SNR) at the receiver input. Hence, the common and simple approach of adding a coding gain factor to the pre-FEC BER to obtain the post-FEC BER is not adequate, and numerical simulations are needed. In this paper, we simulate and analyze the performance in terms of post-FEC BER for two proposals of applying low-density parity check (LDPC) FEC encoder/decoder in a SDM system MDL-impaired and an optimal linear multiple input multiple output (MIMO) receiver. In the first one, the LDPC is applied independently to each mode, and in the second one, the LDPC is applied among all SDM modes. Simulation results indicate that the first proposal outperforms the second. Simplifications in the log-likelihood ratio (LLR) computations have also been considered.

Broadband design of silica-PLC mode-dependent-loss equalizer for 2LP-mode transmission systems.

A new configuration of mode-dependent-loss (MDL) equalizer for two linearly-polarized mode transmission systems using the silica planar lightwave circuit platform is proposed. This device acts as an LP01-mode attenuator (precisely, LP01/LP21 mode converter) to adjust the MDL keeping a high transmission of the LP11 modes. Almost all components constructing the device are based on the adiabatic mode conversion, which brings broadband operation. Especially, a newly proposed E12/E22 mode converter plays a key role in broadband MDL equalization. It is numerically revealed that the flattened spectra with designated transmission can be obtained for the wavelength from 1200 nm to 1650 nm.

Variable Mode-Dependent-Loss equalizer based on Silica-PLC for Three-Mode transmission

We present a low-loss and compact silica-based planar lightwave circuit (PLC) mode-dependent loss (MDL) equalizer for three-mode transmission with a variable range of 2.5 dB. The proposed device utilizes a Mach-Zehnder interferometer (MZI) structure to selectively attenuate the LP01 mode while maintaining low insertion loss for the LP11a,b modes. We demonstrate that the device effectively reduces differential modal gain (DMG) in a three-mode transmission system. Additionally, we successfully equalize the pump-power dependence of the DMG in a two-LP mode erbium-doped fiber amplifier (EDFA) to less than 0.5 dB over the entire C-band. We also show that the variable range has a tradeoff relationship with the wavelength bandwidth, where too large a variable range results in non-negligible wavelength dependencies. Consequently, fixed equalizers are advantageous when large MDL compensation is required, while variable equalizers are effective for fine-tuning MDL of less than 1.2 dB.

BER analysis of an optimum MIMO linear receiver in optical SDM systems with mode-dependent loss.

Multiple-input multiple-output (MIMO) receivers designed to optimize the minimum mean square error (MMSE) are a common choice in coherent optical communication systems based on spatial division multiplexing (SDM). This kind of receivers naturally integrate both MIMO equalization and matched filtering functions. However, when the optical channel exhibits significant mode-dependent loss (MDL) and/or mode-dependent gain (MDG), the impact of inter-symbol interference (ISI) and crosstalk that arise, even using an ideal MIMO MMSE linear receiver, is barely analyzed. Moreover, due to the random nature of the MDL/MDG model, the resulting ISI, crosstalk, and bit error rate (BER) also become random variables and, hence the system performance is more unpredictable. In this paper, we first evaluate the residual distortion (ISI and crosstalk) after the MIMO receiver and then we study the validity of assuming it as an additional Gaussian noise term independent of the channel noise. Next, the probability density distribution (PDF) of the BER is analyzed, from both an analytical perspective and numerical simulations. For the latter, we use a single-carrier 2-PAM (pulse amplitude modulation) system, with pulse shaping, and the MIMO MMSE receiver implementation by means of a MIMO fractionally-spaced equalizer (FSE). We carry out simulations of the system under different conditions of MDL/MDG level and signal to noise ratio (SNR), measured at the receiver input. Additionally, we address possible fits of the BER PDF to known closed-form distributions, among which the Generalized Extreme Value (GEV) family of distributions is selected, and polynomial functions are proposed that relate the system parameters with the GEV PDF parameters. Finally, we present contour maps of BER according to a giving target of system outage probability (OP) that depend on the MDL/MDG and SNR conditions.

Design mode filtering interferometer using etched double clad fiber

Abstract Mode filtering technique is one of the most desired techniques in optical fiber communication systems, especially for multiple input multiple output (MIMO) coherent optical communications that have mode-dependent losses in communication channels. In this work, a special type of optical fiber sensing head was used, where it utilizes DCF13 that is made by Thorlabs and has two numerical apertures (NA’s). One is for core and 1st cladding region, while the 2nd relates the 1st cladding to the 2nd cladding. Etching process using 40 % hydro-fluoric (HF) acid was performed on the DCF13 with variable time in minutes. Investigation of the correlation between the degree of etching and the refractive index (RI) profile of double-clad fibers for low order linearly polarized (LP) modes is the focus of this work research. The used software programs to simulate the effect of etching are Comsol Multi-Physics V6 and Optigrating V4.2.2. It is seen that the optimum case that gave highest cladding power to core power ratio is the case of etching for 10 min, which can be used for detection applications. This ratio greatly affects the sensitivity of the system.

Compact implementation of high-dimensional mutually partially unbiased bases protocol

Transverse spatial mode of light is crucial in high-dimensional quantum key distribution (QKD). However, applications in realistic scenarios suffer from mode-dependent loss and the complexity of system, making it impractical to achieve higher-dimensional, longer-distance and low-cost communications. A mutually partially unbiased bases (MPUBs) protocol has been proposed to fundamentally eliminate the effects induced by mode-dependent loss for long propagation distances and limited sizes of apertures. Here, we demonstrate the first implementation of the MPUBs protocol in dimensions of and 6. By performing a controlled unitary transformation, we can actively switch the measurement basis and enable a compact measurement system. In consequence, a higher encoding dimension is available under finite system resources, resulting in higher key rates and stronger noise resistance. Our work enhances the practicability of MPUBs protocol, and may promote the applications of high-dimensional QKD in quantum networks.

Transverse Mode Instability in Raman Fiber Amplifiers

Hybrid ytterbium-Raman fiber amplifiers have reached multi-kW levels in recent years, showing great promise for kW powers at new wavelengths. Many applications need diffraction-limited output which is limited by transverse mode instability (TMI). In this work, we extended our 3D amplifier model for studying TMI in ytterbium fiber amplifiers to include Raman gain and used this new model to study TMI in two Raman fiber amplifiers: a hybrid ytterbium-Raman fiber amplifier and a passive Raman fiber amplifier. Our previous study shows that gain saturation effect in ytterbium fiber amplifiers plays a significant role in suppressing TMI in kW ytterbium fiber amplifiers. This new study shows that in a Raman fiber amplifier in the absence of similar connection between local Raman gain and local Stokes wave, TMI is not much affected by seed power, fiber length or core diameter in the absence of mode-dependent loss. Mode-dependent loss is a key factor for increasing the TMI threshold in this case.

Bandwidth-Decomposed Analysis of Spatial-Mode Dispersion of Coupled 2-Core Fiber Employing Linear Optical Sampling

The complex impulse responses of two types of coupled 2-core fibers, with homogeneous and heterogeneous cores, were measured by using a measurement system based on linear optical sampling. The measurements were performed over a bandwidth of 20 nm (∼2.5 THz), and the spatial-mode dispersion (SMD) was analyzed. Several lengths of both homogeneous and heterogeneous core fibers were prepared to investigate the length dependence of SMD. The SMDs for divided frequency bands were examined by numerically analyzing the measured broadband impulse response. Consequently, the power impulse response at each subband was obtained, and the variation in the SMDs was examined. In addition, the statistical distribution of the SMD was revealed to be different for each type of the 2-core fiber. The SMD observed at a specific band is handled by the receiver in space-division multiplexing transmission systems. Finally, we present a measurement of mode dependent loss (MDL) of a 2-core fiber, and discuss the impact of time axis inaccuracy to the MDL measurement. These analyses performed are expected to be beneficial for designing such systems.

Long-distance modal power equalization with hybrid pumped FM-EDFA

In a few-mode fiber-based mode division multiplexing system, the different modes as distinct channels suffer from discrepant mode-dependent loss, leading to an intensive channel power imbalance and large bit error. The few-mode erbium-doped fiber amplifier (FM-EDFA) enables mode power regulation to ensure high-quality long-distance transmission. In this paper, we propose an FM-EDFA for long-haul equalization with a core and cladding hybrid pump structure. The particle swarm optimization is applied to determine the multilayered erbium ions doping profile. Based on the profile, targeted compensation for high-order modes with high loss is realized to mitigate the power difference in long-distance transmission. Compared with the single pump selection, the differential modal gain reduces from 6.553 dB to 1.239 dB in the hybrid pump with a 1000 km multistage amplification and transmission. We provide new ideas for loss compensation and power balance in long-distance transmission. This method has the ability of dynamic power adjustment while keeping the design simple.

Long-Haul WDM/SDM Transmission Over Coupled 4-Core Fibers Installed in Submarine Cable

We demonstrated long-haul transmissions over coupled four-core fibers (C4CFs) installed in a 15-km-long submarine cable. A small propagation-loss coefficient of 0.16 dB/km and spatial-mode dispersion coefficient of 5.1 ps/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\sqrt{\mathbf{km}}}$</tex-math></inline-formula> were confirmed after cabling. A recirculating loop consisting of two spans of a 60-km C4CF were constructed using eight C4CFs installed in the submarine cable. 16-channel wavelength-division multiplexed (WDM) and 4-core space-division multiplexed (SDM) 32-Gbaud polarization-division-multiplexed quadrature phase shift keying signals were transmitted. By using adaptive multi-layer filters that compensate for mode coupling as well as in-phase and quadrature impairments in transmitters and receivers, we confirmed that error-free transmission after forward error correction was obtained up to 6000 km. We also evaluated the transmission performance during long-term measurement and the characteristics of mode dependent loss (MDL). The root-mean square MDL averaged over frequency within a WDM channel was estimated to be 0.8 dB per two-span loop and temporally fluctuated after long-haul transmission. These results indicate that C4CFs are viable for long-haul submarine application and that MDL should be further suppressed for a longer distance and more stable performance. We also evaluated a WDM/SDM transmission of probabilistic-constellation-shaped 16-quadrature amplitude modulation signals. Depending on the information rate from 3.2 to 1.2 b per symbol per mode, error-free transmission was achieved up to 2160 and 6600 km.

Securing Data in Multimode Fibers by Exploiting Mode-Dependent Light Propagation Effects.

Multimode fibers hold great promise to advance data rates in optical communications but come with the challenge to compensate for modal crosstalk and mode-dependent losses, resulting in strong distortions. The holographic measurement of the transmission matrix enables not only correcting distortions but also harnessing these effects for creating a confidential data connection between legitimate communication parties, Alice and Bob. The feasibility of this physical-layer-security-based approach is demonstrated experimentally for the first time on a multimode fiber link to which the eavesdropper Eve is physically coupled. Once the proper structured light field is launched at Alice's side, the message can be delivered to Bob, and, simultaneously, the decipherment for an illegitimate wiretapper Eve is destroyed. Within a real communication scenario, we implement wiretap codes and demonstrate confidentiality by quantifying the level of secrecy. Compared to an uncoded data transmission, the amount of securely exchanged data is enhanced by a factor of 538. The complex light transportation phenomena that have long been considered limiting and have restricted the widespread use of multimode fiber are exploited for opening new perspectives on information security in spatial multiplexing communication systems.

In-line mode-dependent loss equalizer with femtosecond laser induced refractive index modification.

We demonstrate an in-line all-fiber mode-dependent loss (MDL) equalizer with femtosecond laser induced refractive index (RI) modification. By inscribing an RI-modified structure into the core of a few-mode fiber (FMF), a differential mode attenuation (DMA) can be achieved for LP01 and LP11 modes. The DMA can serve as an in-line MDL equalizer for the long-haul mode-division multiplexing transmission system. Through numerical simulations, we identify that the LP01 mode has a larger attenuation than that of higher-order modes, where the sign of DMA is contrary to that of the conventional FMF links and devices. Finally, a proof-of-concept experiment is implemented by inscribing an RI modified region with a width of 4 µm, a height of 13 µm, and a length of 200 µm into the FMF core. An average additional attenuation of 8.4 dB and 3 dB can be applied to the LP01 and LP11 modes over the C-band, respectively, leading to an MDL equalization range of 5.4 dB. Meanwhile, the average polarization dependent loss (PDL) of the LP01 and LP11 modes induced by the in-line MDL equalizer is approximately 0.3 dB over the C-band. Power matrix measurement indicates that the in-line MDL equalizer has a negligible mode coupling. The proposed in-line MDL equalizer with a wider range and low insertion loss is feasible by precise manipulation of femtosecond laser inscription.

Randomly-Coupled Multi-Core Fiber Technology

Randomly-coupled multi-core fiber (MCF) technology has come to attract lots of attention because of its strong applicability to long-haul transmission systems. Compared with weakly-coupled MCFs with independent cores, it can simultaneously realize higher spatial channel density and ultralow transmission loss using existing ultralow-loss single-mode fiber (SMF) core designs. The strong mode coupling characteristics of randomly-coupled MCFs can provide favorable optical properties, such as suppressed accumulation of modal dispersion (MD), mode-dependent loss (MDL), and nonlinear impairments. This article gives an overview of randomly-coupled MCF technology advancements. First, we describe the classification and design of randomly-coupled MCFs and explain what the randomly-coupled MCFs are and how they are designed. State-of-the-art randomly-coupled MCFs can accommodate four, seven, or 12 cores in a standard 125- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> cladding while achieving ultralow transmission loss and/or small MD, which are very promising for long-haul transmission media. Next, we present the methods to characterize the optical properties of randomly-coupled MCFs and the difference compared to conventional SMF measurements. We also show the low-loss low-MDL connectivity of this type of MCF and the cabling that can suppress MD. A field-deployed randomly-coupled MCF cable testbed is also presented, which confirmed the favorable optical properties of randomly-coupled MCFs after deployment. Then, multi-core amplifier technologies are briefly summarized, and finally, we discuss the performance improvements in the transmissions over randomly-coupled MCFs and suitable application areas.

Compact cyclic fiber three-mode converter based on mechanical fiber grating.

In this Letter, a compact cyclic mode converter (CMC) based on a mechanical fiber grating is proposed and fabricated to eliminate differential mode group delay and mode-dependent loss in the mode division multiplexing (MDM) transmission system. The proposed CMC can realize cyclical interchange of any input mode among the LP01/LP11a/LP11b modes, which requires only one mechanical grating. The mode conversion is evaluated by observing the mode field patterns of the fiber output. The experimental results prove that the introduction of CMC does not significantly degrade the transmission performance of the photonic lanterns back-to-back system. The insertion loss and the average cross talk of the whole system are lower than 5 dB and -11.3 dB, respectively. The proposed CMC provides a new method for reducing link damage in the MDM transmission system.