Crosstalk Power Research Articles

A Numerical Assessment of the Effect of Concatenating Arbitrary Uncoupled Multicore Fiber Segments on Intercore Crosstalk in Long-Haul Communication Links

Random core dependent loss (CDL) has been shown to increase the direct average intercore crosstalk (ICXT) power in long-haul uncoupled multicore fiber (MCF) links. Longer links are composed of multiple MCF segments, and random CDL may arise on these links from manufacturing imperfections. During link implementation, other random effects may arise and enhance the ICXT power. In this work, the effect of concatenating MCF segments with random characteristics on the direct average ICXT power in long-haul links is assessed numerically by studying the influence of the randomness of segment length, coupling coefficient, and random CDL on the mean, standard deviation, relative spread, and excess kurtosis of the ICXT power. The numerical results show that the segment length randomness marginally affects the ICXT power. For 2000 km long links and a 6 dB maximum random variation of the coupling coefficients, the mean almost doubles and the standard deviation almost triples, relative to considering only random CDL. However, the effect of the coupling coefficients randomness on the relative spread and excess kurtosis is reduced, not affecting significantly the nearly Gaussian distribution of the direct average ICXT power and the excess of direct average ICXT power (less than a 0.26 dB increase relative to considering only random CDL).

Analysis and Compensation of Vibration Induced Beat Frequency Shift in OFDR Based Fiber-Optic Distributed Acoustic Sensor

Optical frequency domain reflectometry (OFDR) is an attractive locating technology for distributed acoustic sensor (DAS) due to its high spatial resolution, but the detectable bandwidth of vibration is very limited up to date, because high frequency vibration will induce time-variant beat frequency shift within the probe, which can deteriorate or even invalidate the demodulation algorithm. In this work, the influence of vibration induced beat frequency shift in OFDR is analyzed and assessed by the crosstalk power spectral density (PSD). Then an adaptive two-dimensional cross-correlation algorithm is proposed for beat frequency shift compensation, in which the instantaneous beat frequency shift within the probe is estimated and compensated for precise strain demodulation. In the experiment, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$18 \text{-}kHz$</tex-math></inline-formula> vibration signal is successfully detected with spatial resolution of 12 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\rm cm$</tex-math></inline-formula> and strain resolution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$594\;\rm p\varepsilon/\sqrt{Hz}$</tex-math></inline-formula> , whose frequency is an order of magnitude higher than previous works. The proposed beat frequency shift compensation algorithm is evaluated in different conditions, and a suppression of crosstalk PSD up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$40.5\rm \ dB$</tex-math></inline-formula> is proved.

Analytical expressions for the crosstalk of super-modes in the tightly bounded multicore fibers.

In this paper, an analytical approach for the super-modes in the tightly bounded multicore fibers is proposed. The method considers deterministic and random inter-core coupling, and the analytical analysis is based on the ordinary differential equations (ODEs), which are derived from the stochastic differential equations (SDEs). It is theoretically found that the crosstalk level is directly proportional to the square of the ratio for the random inter-core coupling strength over the deterministic coupling strength, and is inversely proportional to the random coupling correlation length. The ODEs for the variance and the super-mode power correlations are also provided to further facilitate the analysis for the tightly bounded multicore fibers. Simple and explicit formulas for the super-mode crosstalk power and power covariance evaluation are provided in the weak super-mode crosstalk scenario.

Hybrid buffer and AWG based add-drop optical packet switch

Abstract Optical packet switching (OPS) exhibits the ability to be utilized as a data transmission technique for next-generation. The core router/switch plays a significant role in packet routing and buffering in OPS. Arrayed waveguide grating (AWG) is realized as a promising core element for fast optical switching, with its intrinsic capacity to achieve wavelength routing of different wavelengths in parallel. This paper proposes an AWG-based add-drop optical packet switch, including a hybrid buffer, to resolve contention among packets. In a hybrid buffer, both optical and electronic buffers are used for the buffering of contending packets. AWGs are affected by crosstalk that can significantly impair system operation. The physical layer analysis is discussed in the presence of crosstalk, and the performance of the switch is evaluated in terms of bit error rate. The desired minimum input power is calculated for the switch’s correct operation for both optical buffer and electronic buffer. Finally, the packet loss probability (PLP) of the hybrid buffer is examined under various buffering conditions. Results reveal that with the increase in the optical power of the input signal, crosstalk power increases linearly for optical and electronic buffers. The increased crosstalk power is higher for electronic buffers than the optical buffer. The use of electronic memory in the hybrid buffer allows the hybrid buffer to increase its buffer size thus, reducing the PLP.

BER performance limitations due to inter-core crosstalk in a multi-core fiber-optic transmission system

An analytical approach is developed to evaluate the amount of crosstalk due to inter-core coupling and its limitations on the Bit Error Rate (BER) performance of a fiber link length of 1000 m with a homogeneous multi-core optical fiber (MCF) with a direct detection receiver. Coupling coefficients due to inter-core coupling in 9, 7 and 3 core MCF are evaluated numerically for different core pitch. Crosstalk power, Signal to Crosstalk plus Noise Ratio (SCNR) and BER at any output core with light launched into other core of the MCF are determined numerically. Crosstalk is found to be more pronounced in 9 core and 7 core MCF compared to 3 core. It is found that there is significant deterioration in BER performance due to inter-core coupling induced crosstalk. Power penalty due to inter-core crosstalk at a BER of 10−9for a link length of 1000 m are found to be 2.5 dB, 1.50 dB and 0.5 dB for 9, 7 and 3 core MCF respectively. There is a minimum attainable BER corresponding to a given pitch and number of cores.

Design and analysis of hybrid optical distribution network for worst-case scenario of E2-class symmetric coexistence 80 Gbps TWDM NG-PON2 architecture for FTTX access networks

In this paper, we investigated the cost-effective design and validation of E2-class coexistence 80 Gbps symmetric 8 × 8 Time and Wavelength Division Multiplexing (TWDM) NG-PON2 optical access network considering worst-case scenario for the deployment of Fiber-to-the-X (FTTX) access network using hybrid optical distribution network (ODN). Full-service access network (FASN) unanimously agreed and ITU-T G.989.2 described recommendations for TWDM PON NG-PON2 technology to cater to the need of ever-increasing demand for higher bandwidth and data speed beyond 10 Gbps per user through access networks. Wavelength select (WS) and wavelength-routed (WR) ODN for downstream (D/S) and upstream (U/S) channels symmetric coexistence functionality supporting 80 Gbps accommodating GPON and XGS-PON legacy channels i.e.4-TWDM and 4 point-to-point (PtP) WDM channels operating at 1.25/2.5/10 Gbps respectively in D/S and U/S direction with error free higher splitter configuration of 2304 at 20 km, 640 at 40 km, 576 at 60 km. Precise calculations are done to ensure 11 dBm and 9 dBm ODN launch power (PTODN) to implement worst-case scenario for symmetric E2-class TWDM NG-PON2 network. Calculated inter-channel cross-talk (Cc) is -33.57 dB/-34.74 dB and corresponding cross-talk power penalty (Pc) is 0 dB for D/s and U/S channels respectively. Simulation results demonstrated and verified with the recommendations made in ITU-T G.989.2 confirmed that the proposed network configuration supports extended to reach upto 60 km in D/S and 80 km in U/S direction delivering incremental receiver sensitivity (Rxs) as -34.40/-34.40/42.21 dBm and -34.11/-37.25/-33.37 dBm, ODN path loss 29.40 dB.

New Expression for Evaluating the Mean Crosstalk Power in Weakly-Coupled Multi-Core Fibers

A closed-form expression is proposed for evaluating the mean inter-core crosstalk (ICXT) power in weakly-coupled multi-core fibers (WC-MCFs), with cores’ propagation constants perturbed by bending, twist, and random structure fluctuations. This expression generalizes the expression proposed by Koshiba et al. by taking the dependence of the propagation constants on the longitudinal coordinate of the fiber (induced by constant bending and twist along the MCF) into account in a more rigorous way. We provide a physical interpretation of the proposed expression as the convolution of the spectrum of the $z$ -dependent component of the propagation constant induced by the bending and the spectrum of the perturbation induced by the structure fluctuation. The accuracy of the proposed closed-form expression is assessed by comparing simulation results of the coupled-mode equations with the theoretical predictions from the proposed expression. Very good agreement of the mean ICXT power estimates is shown in the whole range of tested bending radius, difference of intrinsic effective refractive indexes of cores, twisting period and correlation length, for fiber lengths longer than one half of the twisting period and five times the correlation length. We show that the proposed expression enables evaluating the mean ICXT power in WC-MCFs with improved accuracy relative to Koshiba's expression: remarkable differences of mean ICXT power, that may exceed $\text{6}\;\text{d}\text{B}$ , can occur between the estimates provided by the Koshiba's expression and the closed-form expression derived in this article, particularly for high correlation length and twisting rate. Differently from the expression proposed by Koshiba et al. , the proposed closed-form expression predicts that the twisting period may have a significant influence on the mean ICXT power, in qualitative agreement with experimental results reported by other authors.

A Hybrid Algorithm for Multi-Beam Steering of LCOS-Based Wavelength Selective Switch

Iterative Fourier transform algorithm (IFTA) has been widely applied to achieve holograms in diffractive optical elements, however it is insufficient for designing holograms uploaded on liquid crystal on silicon (LCOS) to steer multi-beams in a wavelength selective switch (WSS). In this paper, a three-step hybrid algorithm including IFTA, Symmetrical IFTA with both phase and amplitude freedoms (SIFTA-2) and Genetic algorithm (GA) is developed to optimize the multi-casting hologram and experimentally demonstrated the multi-casting function of WSS. The reconstructed output field not only has max 128 fan-out patterns with flexible power ratio, but also can be adjusted to balance multi-indicators like reconstructed root mean square error (RMSE), diffraction efficiency and crosstalk power by setting flexible weightings of fitness functions in GA.

Stochastic Properties and Outage in Crosstalk-Impaired OOK-DD Weakly-Coupled MCF Applications With Low and High Skew×Bit-Rate

Intercore crosstalk (ICXT) impaired weakly-coupled multicore fiber (MCF) systems using on-off keying (OOK) and direct-detection (DD) are experimentally assessed. The stochastic properties of the received bit amplitudes that depend on the relative propagation delay (skew) between two cores of the MCF and on the OOK bit-rate are discussed. For low skew×bit-rate ( $ 1): (i) the received amplitude of bits 0 or 1 of the interfered core are mainly characterized by two possible levels; (ii) when the short-term average crosstalk (STAXT) power increases (decreases), the fluctuations of the received amplitudes of bits 1 and 0 become larger (lower). For high skew×bit-rate ( $>>$ 1): (i) the received amplitudes of bits 0 and 1 present a noise-like behaviour; (ii) larger fluctuations of the received amplitudes of the OOK signal may not occur only for high STAXT powers. For both low and high skew×bit-rate, it is shown that the histogram of the received amplitudes of bits 1 or 0, and the histogram of the mean and variance of these amplitudes are reasonably well characterized by Gaussian distributions. Experimental results suggest that the rule of thumb to design emerging MCF applications with higher ICXT tolerance is to use cores with skew much longer than the symbol period.

Crosstalk-Induced System Outage in Intensity-Modulated Direct-Detection Multi-Core Fiber Transmission

Crosstalk-power in homogenous single-mode multi-core fibers can vary by more than 20 dB over time and frequency. The extend of these fluctuations depends on the interacting cores’ propagation parameters and the transmitted modulation format. Furthermore, the polarizations of signal and crosstalk can change randomly during transmission. In this paper, we describe the effect of random crosstalk-power variations and the relative signal-crosstalk polarization fluctuations when transmitting single-polarization, intensity-modulated signals such as on-off-keying. We show experimentally that the polarization of a signal fluctuates slower than the polarization of crosstalk, indicating uncorrelated processes. We further investigate the system impact of both, crosstalk-power fluctuations and the relative signal-crosstalk polarization variations on a 10 Gb/s on-off-keying transmission system employing a 10.1 km 19-core multi-core fiber. We show that the two-dimensional space of random fluctuations that is spanned by crosstalk power and relative signal-crosstalk polarization can vary the system's bit error rate by more than five orders of magnitude.

Crosstalk Limitations due to Intercore Coupling on the BER Performance of an Optical Communication System with Homogeneous Multi-core Fiber

Abstract The effect of crosstalk due to inter-core coupling on the bit error rate (BER) performance of a fiber optic communication link with a homogeneous multi-core optical fiber (MCF) and a direct detection receiver with optical preamplifier is analytically evaluated and presented in this paper. Coupling coefficients due to inter-core coupling in a 7-core MCF is evaluated numerically with as a function of core-to-core distance (pitch) and relative refractive index contrast. Coupling length is determined against various index contrasts and at different core pitches. Crosstalk power, Signal to Crosstalk plus Noise Ratio (SCNR), BER and power penalty at any output core with light launched into other core of a 7-core MCF are determined analytically. The results show that there is mentionable deterioration in BER performance due to coupling induced crosstalk, and system suffers distinct power penalty at a given BER. For example, power penalty at BER of 10e-9 is found to be 4.0 dB and 4.3 dB for a MCF link of 10 km corresponding to relative refractive index difference of 0.0036 and 0.0030, respectively, for a pitch value of 30 µm and core radius of 4.5 µm.

Probability Distribution of Intercore Crosstalk in Weakly Coupled MCFs With Multiple Interferers

The statistical behavior of the intercore crosstalk (ICXT) power in weakly coupled multicore fibers (MCFs) with multiple interfering cores is experimentally assessed. The histograms with multiple interfering cores are compared with the probability density function (pdf) of the quadratic form corresponding to the ICXT power considering different correlation coefficients between the in-phase and quadrature Gaussian ICXT field components of the orthogonal polarizations. A very good fitting between experimental histograms and the numerical pdf of the quadratic form occurs when the ICXT field components are modeled as uncorrelated random processes. These results demonstrate that the ICXT power can, with a very low error, be described by a chi-square distribution with 4 degrees of freedom not only with a single interfering core but also with multiple interfering cores. This means that the ICXT contributions induced by different cores of the MCF are uncorrelated.

Decorrelation Bandwidth of Intercore Crosstalk in Weakly Coupled Multicore Fibers With Multiple Interfering Cores

The decorrelation bandwidth of the intercore crosstalk (ICXT) power generated in a weakly coupled multicore fiber (MCF) with multiple interfering cores is studied. For the first time, this is accomplished using a closed-form expression of the equivalent autocovariance function of the ICXT power that enables evaluating the correlation between the ICXT power generated at two different frequencies using a theoretical model to describe the stochastic evolution of the ICXT over time. It provides fast and reliable estimates of the decorrelation bandwidth of the ICXT induced by multiple interfering cores with arbitrary relative time delays (skews) between cores, which represents a crucial tool to assist the design of new MCF systems. Validation of the autocovariance and decorrelation bandwidth expressions by numerical simulation and with experimental results published by other authors is accomplished. In contrast to the single interfering case, the equivalent autocovariance of the ICXT induced by multiple interferers may present several inflexion points along the frequency lag due to the different core contributions that may be characterized by different skews. For MCFs with similar skews between cores, the equivalent autocovariance has, approximately, a sinc-squared shape with the decorrelation bandwidth, defined as the first zero of equivalent autocovariance, occurring at the frequency lag, in Hz, given by the inverse of the skew. When the decorrelation bandwidth of the ICXT induced by multiple interfering cores is much lower or much higher than the signal bandwidth, the ICXT mechanism can be considered as uncorrelated noise or as a static coupling component, respectively. When the decorrelation bandwidth is similar to the signal bandwidth, the ICXT mechanism should be treated as correlated noise.

Cascaded versus parallel architectures of two‐stage optical crossbar switches with an extra set of inputs and outputs

Two principal two-stage switch architectures (cascaded and parallel), both of which are composed of two identical optical crossbar switches with an extra set of inputs and outputs, are compared in terms of their number of crosspoints, switch control complexities, and key optical performances, such as insertion loss and crosstalk power, through theoretical analysis. The authors begin by briefly introducing a known N × N cascaded optical crossbar switch with N 2/2 crosspoints, where N is the switch size, and present a new functional perspective based on quasi-bitonic sorting. Subsequently, the authors derive two types of two-stage parallel optical crossbar switches with reduced crosspoints from a conventional single-stage parallel crossbar switch with N 2 + 2N crosspoints. The first type uses two N/2 × N asymmetric switches in parallel, both of which are embedded in a single N/2 × N/2 crossbar switch. It has (N 2 + 2N)/2 crosspoints and suffers from a complex switch control of O(N 2). The second type is equivalent to a three-stage Benes network and exploits bidirectional transmission to reduce the number of switching stages. It requires (N 2 + 3N)/2 crosspoints, but has a dramatically reduced switch control complexity of O(N), and significantly improved optical performance.

Intercore crosstalk in direct-detection homogeneous multicore fiber systems impaired by laser phase noise

The impact of the laser phase noise on the photodetected intercore crosstalk and performance of direct-detection orthogonal frequency division multiplexing multicore fiber systems is experimentally investigated. A new solution to overcome the performance fluctuations over time induced by the combined effect of laser phaser noise and intercore crosstalk is proposed. The solution uses adaptive modulation with extended time memory to estimate the bit loading scheme of each subcarrier from the mean and maximum error vector magnitude evaluated over the last ten blocks of transmitted training symbols. During measurements of up to 90 hours, intercore crosstalk power variation induced by fast laser phase noise variations exceeded 20 dB in both time and frequency, and error vector magnitude fluctuations of 4 dB were observed on a sub-second timescale. It is shown that direct-detection orthogonal frequency division multiplexing multicore fiber based systems employing a typical adaptive modulation solution, in which the bit loading scheme is evaluated from a single set of training symbols, suffer from unacceptable outage probabilities and are unable to counteract the fast power variations of intercore crosstalk and phase noise induced impairments. By extending the system memory used to estimate the bit loading scheme employed by the adaptive technique, an outage probability reduction by one order of magnitude is achieved. This reduction is attained by using the mean of the error vector magnitude evaluated over the last ten blocks of training symbols to estimate the bit loading scheme of subcarriers. Further reduction of the outage probability by four orders of magnitude is also demonstrated using a more conservative approach to estimate the bit loading scheme of the subcarriers. However, this conservative approach, based on the maximum error vector magnitude, may lead to additional loss of the average throughput.

Outage probability of WDM free‐space optical systems affected by turbulence‐accentuated interchannel crosstalk

Massive deployment of free space optical (FSO) communication systems in future optical access networks will use wavelength division multiplexing (WDM) technology to leverage extended reach and enhanced user capacity. An analytical framework for the estimation of outage probability in a turbulence-affected WDM FSO system is presented in this study. The authors derive simplified expressions of the probability of outage in the presence of turbulence-accentuated interchannel crosstalk, and show how design parameters such as the FSO link length, demultiplexer adjacent channel rejection and receiver aperture diameter affect the performance of the system. Numerical results show that the outage probability due to irradiance fluctuation is worsened in WDM FSO systems by the effects of turbulence-affected interchannel crosstalk signals. Specifically, the average crosstalk power and the degree of irradiance fluctuations on the crosstalk set a limit on the outage probability performance of the system which appears in the form of outage floors.

Crosstalk dynamics in multi-core fibers.

Inter-core crosstalk is a potential limitation on the achievable data-rates in optical fiber transmission systems using multi-core fibers. Crosstalk arises from unwanted coupling between cores of a homogenous multi-core fiber and it's average power has been observed to vary over time by 10s of decibels, potentially requiring an additional performance margin to achieve acceptable outage probability. Most investigations of crosstalk have so far only considered continuous wave laser light or amplified spontaneous emission as sources of crosstalk. In this paper, we theoretically and experimentally investigate the time-dependence of inter-core crosstalk in a homogeneous multi-core fiber when considering signals with various modulation formats and symbol rates. We find that crosstalk power fluctuations depend on the symbol rate, modulation and skew between cores. For carrier-free signals, such as quadrature amplitude modulation, the crosstalk power is nearly constant for expected conditions of multi-core transmission systems. However, carrier-supported signals, such as OOK, always induce time-varying crosstalk powers.

Bit Error Rate Performance Limitations Due to Raman Amplifier Induced Crosstalk in a WDM Transmission System

AbstractAnalysis is carried out for a single span wavelength division multiplexing (WDM) transmission system with distributed Raman amplification to find the effect of amplifier induced crosstalk on the bit error rate (BER) with different system parameters. The results are evaluated in terms of crosstalk power induced in a WDM channel due to Raman amplification, optical signal to crosstalk ratio (OSCR) and BER at any distance for different pump power and number of WDM channels. The results show that the WDM system suffers power penalty due to crosstalk which is significant at higher pump power, higher channel separation and number of WDM channel. It is noticed that at a BER 10

Crosstalk Penalty in Microring-Based Silicon Photonic Interconnect Systems

We examine inter-channel and intra-channel crosstalk power penalties between non-return-to-zero on-off keying (NRZ-OOK) wavelength-division-multiplexing (WDM) channels for microring-based silicon photonic interconnects. We first propose a new model that relates the crosstalk power penalty to the interfering signals power, the extinction ratio of the non-return-to-zero, OOK modulated “victim” channel, and finally the bit-error-ratio that the power penalty is referenced to. As for inter-channel crosstalk, the proposed model agrees well with our recent experimental measurements. We leverage this model to quantify crosstalk induced power penalties in a microring based WDM receiver. We also propose an optimization procedure to equilibrate the power penalty across channels. We then compare our model with intra-channel crosstalk measurements, where two NRZ channels are at the same wavelength and are simultaneously routed to different paths by two cascaded ring resonators. We remark that intra-channel crosstalk is very sensitive to the data rate of NRZ channels. As data rate increases, the observed disturbances exceed what models predict. Based on these observations, we propose an empirical modification of the original model for estimating intra-channel crosstalk power penalties in high ( $>$ 20 Gb/s) data rate situations.

Crosstalk in SOI Microring Resonator-Based Filters

We experimentally investigate the interchannel and intrachannel crosstalk of first- and second-order microring resonator (MRR) filters fabricated on a silicon-on-insulator platform. We find that there is an MRR radius that maximizes the wavelength division multiplexing channel count given a waveguide geometry, a maximum tolerable insertion loss, and a minimum permissible adjacent channel isolation. The measured power penalties due to interchannel crosstalk of two-channel demultiplexers based on first-order and series-coupled MRR filters are presented as functions of channel spacing and adjacent channel isolation. Next, we compare the intrachannel crosstalk of first-order, cascaded, and series-coupled MRR add-drop filters. Our results show that first-order MRR devices are unsuitable for simultaneous add-drop operation at high data rates and small channel spacings. Intrachannel crosstalk of cascaded and series-coupled designs are measured as functions of the data rate and the level of detuning between the MRRs. Low intrachannel crosstalk power penalties are demonstrated for cascaded and series-coupled MRR filters for data rates up to 20 Gb/s. Based on the measured results, we present requirements for the input-to-through response of add-drop filters that will ensure low intrachannel crosstalk.