Mode Delay Research Articles

Weakly guiding graded-index ring-core fiber supporting 16-channel long distance mode division multiplexing systems based on OAM modes with low MIMO-DSP complexity.

We propose a weakly guiding graded-index ring-core fiber (RCF) with trench-assisted structure. The simulation analysis indicates that such a special fiber design is able to support 8 orbital angular momentum (OAM) mode groups (MGs) with low inter-group crosstalk (< -25 dB/km) and low intra-group differential mode delay (DMD) (< 125 ps/km) for higher order OAM MGs with topological charge |l| = 4, 5, 6, 7. The designed RCF also shows favorable tolerance characteristics to ellipticity and bending. Moreover, stable and distinguished broadband performance of proposed RCF is verified over the whole C band ranging from 1530 nm to 1565 nm. This kind of fiber design could be employed in small-scale multiple-input multiple-output digital signal processing (MIMO-DSP) intra-group modes multiplexing transmission combined with MIMO-free inter-group mode multiplexing transmission. The simulated results of the designed RCF show its great potential of the 16-channel long-distance mode division multiplexing (MDM) transmission with low MIMO-DSP complexity.

Differential mode delay and modal bandwidth measurements of multimode fibers using frequency-domain method

• A frequency-domain method is developed to measure the DMD of multimode fibers. • Vector network analyzer is used to measure the complex transfer functions. • The time-domain output pulses can be calculated from CTF with proper procedures. • Frequency-domain method yields DMD results equivalent to the time domain method. • The frequency domain method can conduct DMD measurements at very low optical power. We report a frequency-domain method for measuring the differential mode delay (DMD) and bandwidth of multimode fibers (MMFs). Using a frequency domain instrument, vector network analyzer (VNA), the method measures the complex transfer functions (CTFs) of multimode fibers for a given set of launch conditions. As a result of the fiber length, which is long relative to sampling points used in VNA, the frequency sampling is under-sampled and the measured CTF is aliased. Aliased CTF behaves very differently from fully sampled CTF with dependence on the sampling frequency step. With proper procedures, the CTF can be transformed to local time frame centered around DMD into a modified CTF. The time-domain output pulses can be further recovered through an inverse Fourier transform. By recovering output pulses using complex transfer functions of a multimode fiber at controlled launch offsets, one can subsequently follow the same procedures of existing time domain methods to determine the effective modal bandwidth of the multimode fiber under test (FUT). As a result of the method, DMD and modal bandwidth measurements can be undertaken using frequency domain instruments rather than time domain instruments in a mathematically equivalent manner for multimode fibers. The measurement method utilizes CW light sources that are readily available in a wide range of wavelengths, thus providing greater flexibility for measuring the modal bandwidth of MMFs at different wavelengths, including WDM applications other than 850 nm. The very high sensitivity of the VNA allows the measurement at much lower optical power compared to the time domain instrument. Several measurements at 850 nm have been conducted using the frequency domain method and validated by comparison with the results from the time domain method. The method is suitable for measuring MMFs from a short length of a few hundred meters to a very long length close to 20 km. We have also measured an MMF at 910 nm using the method to demonstrate its flexibility in adopting different wavelengths.

Coherent Communication Over Multi Mode Fibers for Intra-Datacenter Ultra-High Speed Links

Multimode fibers (MMFs) links using vertical cavity surface-emitting lasers (VCSELs) are still the solution of choice for today’s data center shorter distances thanks to their low cost and robustness. Currently, the market is moving towards 400G-capable systems using multiple lanes at 50 Gbps per lane, based on intensity modulation (IM) and direct detection (DD). A technology switch will probably be required to overcome the 100 Gbps per lane limit that will likely be the bottleneck of future IM-DD MMF-based links. In this manuscript we propose an intra-data center system based on coherent detection and MMF, analyzing experimentally and analytically the performance of polarization multiplexed coherent communication. We show that the advantages enabled by the coherent technology can be fully exploited in an MMF-based link when central launch is ensured. In particular, we study in detail the effect of lateral offsets introduced by the connectors at the interface between two MMF facets, in terms of net optical loss and signal-to-noise ratio (SNR) degradation. A statistical analysis is performed analytically exploiting a large database of OM3 and OM4 fibers modal delays and results are presented for various combinations of fiber length, type and number of MMF-to-MMF connections along the link. We show quantitative results on the maximum acceptable lateral offsets in the MMF connectors, highlighting that in practical conditions average offsets of up to 3 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> m can be tolerable.

Simulation Study on the Influence of Sampling Delay on the Accuracy of Energy Metabolism Measurement

Indirect energy metabolism measurement is the gold standard for providing nutritional support for critical illness. The accuracy of the measurement data directly affects the outcome of the disease. In order to study the influence of sampling delay on the accuracy of energy metabolism measurement under mechanical ventilation, the Matlab/Simulink platform and respiratory electrical model were used for simulation and quantitative analysis. The results show that the error of indirect energy metabolism measurement increases with the increase of sampling delay, the error of sampling delay in mechanical ventilation mode is larger than that of spontaneous breathing, and the error of sampling delay in PCV mode of mechanical ventilation is larger than that in VCV mode. Therefore, there should be different sampling delay compensation strategies under severe mechanical ventilation and its different control modes.

High-speed performance evaluation of ultra-flexible polymer waveguides supporting meter-scale optical interconnects.

We demonstrate bandwidth measurement and high-speed data transmission of meter-scale connectorized ultra-flexible multimode waveguide links with a maximum length of 180 cm. The pulses propagating through the waveguides broadened linearly with the increase of the length from 20 cm to 240 cm and the estimated mode delay from the pulse broadening was 0.093 ps/cm. The corresponding waveguide bandwidth decreased inversely with the increase of waveguide length, leading to a bandwidth-length product of 42 GHz·m. Degradation in bandwidth due to the introduction of bending or twisting was small when the samples were bent with a bending radius as small as 1 mm for 3 turns or twisted for 4 full turns, respectively. Error-free transmission of 30 Gb/s non-return-to-zero (NRZ) signal was achieved with a record link length up to 140 cm to the best of our knowledge. Our results show that the demonstrated flexible waveguides have both excellent optical and mechanical properties and are ideal for high-speed optical interconnects application especially those have a strict requirement on flexibility.

Cyclic silicon waveguide four-mode converter for mode division multiplexing transmission.

In this paper, a novel cyclic mode converter (CMC) is proposed and fabricated to implement cyclic mode permutation (CMP) on-chip for differential mode delay and mode-dependent loss elimination in the mode division multiplexing (MDM) transmission system. Cascaded by three optimally designed mode converters that do not affect the non-target modes, the proposed CMC can realize the conversion of any input mode among the TE0/TE1/TM0/TM1 modes. The three-dimensional finite-difference time-domain (3D-FDTD) simulation results show that the insertion loss of our device is less than 0.59 dB, and the crosstalk of each mode is lower than -15 dB under the range of 1500-1600 nm. The flat spectral response of this CMC is maintained even in the presence of fabrication errors up to±10 nm, showing great robustness. The experimental results also prove that at the center wavelength of 1550 nm the measured insertion loss of each mode is below 2.22 dB, and the crosstalk of each mode is lower than -15 dB. The proposed CMC provides a new idea for effectively reducing link damage in the MDM transmission system.

Intravascular polarization-sensitive optical coherence tomography based on polarization mode delay

Intravascular polarization-sensitive optical coherence tomography (IV-PSOCT) provides depth-resolved tissue birefringence which can be used to evaluate the mechanical stability of a plaque. In our previous study, we reported a new strategy to construct polarization-sensitive optical coherence tomography in a microscope platform. Here, we demonstrated that this technology can be implemented in an endoscope platform, which has many clinical applications. A conventional intravascular OCT system can be modified for IV-PSOCT by introducing a 12-m polarization-maintaining fiber-based imaging probe. Its two polarization modes separately produce OCT images of polarization detection channels spatially distinguished by an image separation of 2.7 mm. We experimentally validated our IV-PSOCT with chicken tendon, chicken breast, and coronary artery as the image samples. We found that the birefringent properties can be successfully visualized by our IV-PSOCT.

Design of ultra-dispersion flattened M-type few-mode fiber for weakly-coupled mode division multiplexing transmission

In this work, we present an ultra-dispersion flattened few-mode (UDF-FMF) fiber design that can support ten linearly polarized modes in the C-band. The proposed fiber has an M-type refractive index profile with 13.5% GeO2 doped original core, and fused silica cladding. A high-index ring is inserted in the cladding, to increase the number of modes with low mode coupling. A trench in the cladding and a depression in the original core are added to manage the chromatic dispersion parameter and to reduce the bending loss. The fiber exhibits non-zero dispersion at 1.55 µm for the fundamental LP01 mode to satisfy the ITU-G.655 standard and yields a minimum dispersion flatness of ~0.18 ps/nm/km over the C-band for the first time according to our knowledge. The modal characteristics of the UDF M-type FMF have been systematically analyzed through the finite element method-based COMSOL software. The fiber parameters and the dopants concentration are systematically chosen through simulations to guide ten LP modes with large mode separation (max∆neff≅5×10−3), optical loss in the range of 10-10 to 10-12, minimum differential mode delay of 0.09ps/m, nonlinear coefficient lower than 2 × 10-3 km−1 W−1, and large effective mode-area of 385 µm2 across the C-band. We believe the proposed fiber design can be a potential contender for new-generation optical communication using mode-division multiplexing.

Design of ultra-flattened dispersion weakly coupled few-mode photonic crystal fiber with low confinement loss

We present a unique design of weakly coupled few-mode photonic crystal fiber (FM-PCF), which can support six vector modes (HE11a,HE11b,TM01,HE21a,HE21b, and TE01) with ultra-flattened chromatic dispersion over the C wavelength band. We investigate the impact of fiber parameters on chromatic dispersion, minimum effective refractive index difference (minΔneff), confinement loss, bending loss, and differential mode delay using the finite element method. To achieve ultra-flattened chromatic dispersion and large minΔneff, an extra small elliptical defected hole is introduced in the fiber core. The circular holes in the first ring are replaced by elliptical holes to further obtain flattened-chromatic dispersion. The simulated results show that the designed weakly coupled FM-PCF can obtain an ultra-flattened average dispersion of 0.011 ns/nm/km with a small dispersion slope (<1.5 × 10 − 5 ns / km / nm2) in the wavelength range of 1520 to 1570 nm. And the proposed weakly coupled FM-PCF has large minΔneff (>1 × 10 − 3), low confinement loss (<10 − 4 dB / km), and good bending resistance. In summary, the proposed weakly coupled FM-PCF has potential applications for large-capacity MDM communication systems.

Effect of Quadrature Control Mode on ZRO Drift of MEMS Gyroscope and Online Compensation Method.

The quadrature coupling error is an important factor that affects the detection output of microelectromechanical system (MEMS) gyroscopes. In this study, two quadrature error control methods, quadrature force-to-rebalance control (Mode I) and quadrature stiffness control (Mode II) were analyzed. We obtained the main factors affecting the zero-rate output (ZRO) under force-to-rebalance (FTR) closed-loop detection. The analysis results showed that the circuit phase delay in Mode I caused the quadrature channel to leak into the in-phase channel. However, in Mode II, the quadrature coupling stiffness was corrected in real time, which effectively improved the stability of the ZRO. The changes in the vibration displacement and Q-factor were the main factors for the ZRO drift in Mode II. Therefore, we propose an online compensation method for ZRO drift based on multiparameter fusion. The experimental results on a cobweb-like disk resonator gyroscope (CDRG) with a 340 k Q-factor showed that the bias instability (BI) of Mode II was significantly better than that of Mode I. After online compensation, the BI reached 0.23°/h, and the bias repeatability reached 3.15°/h at room temperature.

Octagonal polarization-maintaining supermode fiber for mode division multiplexing system

We present a new type of polarization-maintaining supermode fiber which can separate adjacent modes from each other. The proposed polarization-maintaining supermode fiber features an octagonal core composed of multiple high-refractive-index circular holes. By using high refractive index cores and setting the angle subtly between the cores, the fiber proposed can support 22 modes with different polarization states under two parameters in the entire C-band. Through the finite element method simulation, we conducted simulation study to analyze the influence of the angle between the cores and the core diameter on the performance of the optical fiber. In addition, we analyzed effective refractive index difference (Δneff) and effective modal area (Aeff) of the fiber for each characteristic mode. The differential mode delay (DMD) under different cores angle is also calculated. Numerical results present that the minimum Δ neff of the octagonal polarization-maintaining supermode fiber in the entire C-band under the two parameters is greater than 1.1 × 10−4. It was measured to have good tolerance under the condition of unsatisfactory structure. These results indicate that the proposed fiber is superior candidate for improving the optical transmission capacity in the transmission of the mode division multiplexing system.

Multicore raised cosine fibers for next generation space division multiplexing systems

Space division multiplexing (SDM) is a promising solution for improving the transmission capacity and increasing the spectral efficiency. SDM over few mode multicore fibers (FM-MCFs) is an attractive approach that observes increasing interest. In this work, after reviewing the basic guidelines for FM-MCFs design, we address, for the first time, the Raised Cosine (RC) profile to multicore fibers context. We optimize the single core RC profile in order to support exactly 6 linearly polarized (LP) modes with large effective mode area (min Aeff = 96 μm2), with low differential mode delay (DMD) (max DMD = 33 ps⧹km) and high intermodal separation (⩾2×10−4). Once achieved, we investigate the induced crosstalk between twin RC cores and twin trenched RC (TRC) cores. We then propose four 6 modes 7 cores RC⧹TRC fibers. Their crosstalk and their relative core multiplicity are analysed and compared with those reported in recently graded index-FM-MCFs. The selected designs could be promising candidates for short and medium haul interconnects.

Design of weakly coupled 20-eigenmode bow-tie rectangular dual-step fiber for short-haul communication in O band

We present a weakly coupled bow-tie rectangular dual-step few-mode fiber supporting 20 eigenmodes for short-haul communication systems across the O band. The rectangular dual-step core and bow-tie stress-applying area are introduced to effectively split adjacent eigenmodes. We evaluate the impact of parameters on modal mode effective refractive index difference (MERID) Δneff, min Δneff, min Aeff, Bm, and bending loss at a wavelength of 1310 nm. Broadband performance of the entire O band, including neff, MERID Δneff, differential mode delay, and dispersion, is also analyzed. Results indicate that the 20 eigenmodes supported by the designed fiber are completely separated with MERID Δneff between adjacent modes larger than 2.319 × 10 − 4 over the whole O band. The designed fiber can be used for short-haul multiple-input multiple-output-free eigenmode-division multiplexing systems to improve transmission capacity and expand bandwidth.

Differential mode delay diagnostics for LP modes traversing a few-mode fiber.

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.

Влияние соединения опорных проводников на разложение сверхкороткого импульса в модальном фильтре на двухсторонней печатной плате.

The location of the reference conductor in a modal filter (MF) on a double-sided printed circuit board (PCB) could affect the decomposition of an acting ultrashort pulse (USP) in the MF. The paper considers two ways of connecting the reference conductors: at the ends of the MF and along the entire MF length. The effect of the filter cross-sectional parameters on the decomposition of USPs is also discussed. The results showed that for two ways of connecting the reference conductors, the difference in per-unit-length mode delays increases with decreasing h and increasing w and s. This, in turn, leads to the increase in the MF attenuation factor. It was revealed that the difference in per-unit-length mode delays is slightly larger in the case of connecting the reference conductors at the end for all values of the parameters. It was also found that if the reference conductors are connected only at the ends, 3 pulses arrive at the MF output (despite the 5 propagating modes in the line). And when the conductors are located along the entire length there are 2 pulses. Accordingly, the decomposition of the input action into 3 pulses allows achieving a larger attenuation of the USP (3.2 times relative to half of the e.m.f.).

Asymmetry core effects in multimode fibers for space-division multiplexing

Here we report a detailed numerical investigation into the effects of asymmetric cores on the modal properties in multimode fibers (MMFs). Three asymmetric core shapes combine with three core structures, respectively, forming nine kinds of common asymmetric cores in our simulation. The discussed modal properties include mode number, birefringence, effective index, power confinement factor, fiber loss, effective mode area, and differential mode delay. An evaluation factor called mode-NSD is proposed to integratedly judge the nonlinearity and compatibility ability in the MMF. Finally, the manufacturing tolerance with the size variation up to 5% is also discussed for practical needs. These numerical results are beneficial for the comprehensive assessment of the space-division-multiplexing optical fibers with asymmetric cores.

Demonstration of QPSK data correlation and equalization using a tunable optical tapped delay line based on orbital angular momentum mode delays

We demonstrate a tunable optical tapped delay line (OTDL) using delays based on orbital angular momentum (OAM) modes to perform data correlation and equalization for a quadrature phase-shift-keyed (QPSK) signal. The system: (i) creates N signal replicas as N taps on different OAM modes through mode multicasting, (ii) tunes the complex tap weights (i.e., amplitude and phase of the modes), (iii) applies a tunable mode-dependent delay to each replica, and (iv) coherently combines the taps in order to realize the OTDL functions of correlation and equalization. The experiment results: (i) identify the correlation occurrence of a sequence of 2 or 3 symbols in an incoming 10 or 20 Gbaud QPSK signal, and (ii) equalize the distortion caused by chromatic dispersion for a 20-Gbaud QPSK data signal and reduce error vector magnitude (EVM) from ∼25.4 to ∼12.9%.

Design of a side-hole-assisted weakly coupled rectangular ring-core multimode fiber for mode-division-multiplexing networks.

We present a side-hole-assisted weakly coupled polarization-maintaining rectangular ring-core multimode fiber supporting 68 eigenmodes. The rectangular ring-core and side-hole structures are introduced to effectively split eigenmodes. The impact of parameters on mode utilization rate η and mode number is evaluated at the wavelength of 1550 nm. We also analyze bending loss and broadband performance of the entire C band, including neff, Δneff, Aeff, nonlinearity, and differential mode delay. By optimizing the design parameters, the 68 eigenmodes are completely separated with Δneff between adjacent modes larger than 10-4 over the whole C band. The designed fiber can be used for eigenmode-division multiplexing networks to improve transmission capacity and spectral utilization.

Mode analysis of orbital angular momentum modes carrying multi-mode ring-core fibers

We discuss the mode properties for orbital angular momentum (OAM) modes supporting multi-mode ring-core fiber (MM-RCF). For strongly-guiding MM-RCF, by introducing one more layer to the ring-core, a two-layer ring-core fiber (TL-RCF) is proposed. It is proven that this TL-RCF can increase the separation degree between the vector eigenmodes and meanwhile weaken the spin–orbit coupling. For mode-group supporting MM-RCF, the maximum mode number is limited by the thickness of ring-core and the cut-off of radial higher-order mode. We also present the tradeoff relationship between the mode group effective index difference and inter-eigenmode differential mode delay in one mode group. The discussion in this paper can give guidance for the design of MM-RCF.

Design of steering wheel-type ring depressed-core 10-mode fiber with fully improved mode spacing.

We present a steering wheel-type ring depressed-core few-mode fiber (SWTR-DC-FMF) that features a central depressed step-index core and a novel SWTR structure consisted of two symmetrical high-index parts and low-index parts, respectively. The DC and SWTR make great contribution to separate the non-degenerated LP modes and spatial modes in the circular symmetry core, resulting in fully improved mode spacing. The designed fiber is able to support 10 spatial modes with the minimum effective index difference (Min Δneff) between adjacent spatial modes larger than 1.93 × 10-4 and the Min Δneff between adjacent LP modes above 1.51 × 10-3 at the same time, facilitating potential fiber spatial mode multiplexing transmission with less multiple-input multiple-output (MIMO-less) digital signal processing technique. The broadband performance including neff, Δneff, effective mode area (Aeff) and differential mode delay (DMD) is comprehensively investigated over the whole C and L band. Moreover, the birefringence and fabrication tolerance are discussed. The designed fiber targets emerging applications in short-reach weakly coupled space-division multiplexing (SDM) optical networking to increase transmission capacity and spectral efficiency and further reduce the system complexity effectively.