Weakly-coupled Multi-core Fibers Research Articles

Numerical Estimation of Inter-Core Crosstalk Affected by Stimulated Raman Scattering in Weakly Coupled Multicore Fiber

Numerical Estimation of Inter-Core Crosstalk Affected by Stimulated Raman Scattering in Weakly Coupled Multicore Fiber

Demonstration of an 800G CDM-SDM coherent PON utilizing weakly coupled multicore fibers with CDM tributary manipulation

In this Letter, we present an experimental demonstration of downstream signaling in a 16 × 50 Gbit/s coherent passive optical network (CPON) using the code and space division multiplexing (CDM-SDM) approach. We realize optical SDM through the utilization of a 4-core weakly coupled multicore fiber (WC-MCF), enhancing the total available optical launch power at the optical line terminal (OLT). This enhancement significantly improves the power budget for CPONs that connect with a large number of optical network units (ONUs). At the second stage of the CPON, four CDM-assigned ONUs are connected to individual cores of the WC-MCF, thereby supporting the connectivity of up to 16 ONUs. Through experiments, we have noted substantial disparities in the downstream signaling performance among individual CDM-assigned ONUs, particularly as the capacity is increased to 800 Gbit/s. To address this issue, we have employed an innovative approach by leveraging space–time coding techniques to manipulate the CDM tributaries, to achieve a balanced reception performance for all ONUs within the CPON. We believe that the proposed CDM-SDM CPON scheme, complemented by the advanced DSP flow chart, holds significant promise for future PON systems characterized by substantial capacity and extensive connectivity.

Polarization Misalignment Between Signal and Crosstalk in Direct Detection WC-MCF Systems

The impact of the polarization misalignment between the signal and the intercore crosstalk (ICXT) on the performance of direct detection (DD) weakly coupled multicore fiber (WC-MCF) systems is investigated by numerical simulation. It is shown that the bit-error ratio (BER) is not maximized for all time when the signal field polarization is aligned with the polarized component of the ICXT. However, this is the scenario in which higher levels of bit-error ratio (BER) occur more frequently along time. For the same outage probability, these higher BER levels lead to an incremental requirement of the ICXT level between 1 dB and 2 dB when compared with the scenario of independent polarizations of the signal and ICXT fields. These conclusions are valid for on-off-keying DD WC-MCF short-reach systems operating with arbitrary product between the skew (i. e., the relative propagation time delay between two cores) and the bit rate.

Theoretical investigations of weakly- and strongly-coupled multi-core fibers for the applications of optical submarine communications under power and fiber count limits.

The practical cable design for optical submarine communications has a limited fiber pair count due to the mechanical considerations of cable weight and size. Consequently, multi-core fibers (MCFs) could exhibit higher capacity than conventional single-mode fibers (SMFs) thanks to space division multiplexing (SDM). That is because the power supply to a submarine cable is fed by the voltage difference between shores. Under the power-limited condition, SDM improves the cable capacity by using more paths which outperforms the SMF link whose capacity approximately complies with a logarithmic relationship to optical power. At the same time, fiber nonlinearity can be alleviated by the reduced power density of transmitted light in MCFs, due to the increased spatial diversity and mode coupling among coupled cores. In this work, we theoretically investigate the potentials of MCFs including weakly-coupled multicore fiber (WC-MCF) and strongly-coupled multicore fiber (SC-MCF) as the propagation media for submarine communications across the Atlantic and the Pacific. To fairly compare the performances of SMFs- and MCFs-based submarine cables, the Gaussian noise (GN) model for SDM links is employed to optimize the systematic settings including spatial multiplicity and single span length. Then, we develop an SDM and wavelength division multiplexing (WDM) fiber transmission model based on coupled nonlinear Schrodinger equations (CNSE) to investigate the optical filed coupling effect in MCFs-based cables. The developed transmission model has been self-examined by measuring the inter-core crosstalk (IC-XT) and spatial mode dispersion (SMD), referring to the set values. As indicated by the theoretical analysis, the WC-MCFs cable exhibits a larger capacity than the SMFs cable, when the fiber pair count is limited below 32. Moreover, the SC-MCFs cable outperforms the WC-MCFs cable thanks to the reduced fiber nonlinearity due to the random mode coupling and the assistance of multiple-input and multiple-output digital signal processing (MIMO-DSP). At last, the marginal influences of IC-XT, SMD, and insertion loss of Fan-in and Fan-out couplers are also analyzed for the MCFs cable.

Mitigating the Inter-Core Crosstalk of Multicore Fiber Transmission by Orthogonal Filtering

We for the first time proposed to utilize the orthogonal filtering technique to suppress the inter-core crosstalk (IC-XT) in multicore fiber (MCF) transmission. It could simplify the implementation of weakly-coupled MCF (WC-MCF) signal reception without multiple-input and multiple-output (MIMO) digital signal processing, by extracting the individual lanes separately. Effective IC-XT mitigation using a pair of orthogonal filters are demonstrated for MIMO-free 2-core MCF transmitted signal receptions. 600-Gbps 64-QAM (quadrature amplitude modulation) signal transmission over 100-km MCF is emulated by constructing a concrete transmission model based on coupled nonlinear Schrodinger equations. Maximum Q factor improvement of 6 dB can be achieved using orthogonal matching filters to suppress IC-XT at −10dB. The effect of spatial mode dispersion on the filter orthogonality performance is also analyzed.

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.

Power-Over-Fiber in Support of 5G NR Fronthaul: Space Division Multiplexing Versus Wavelength Division Multiplexing

We investigatethe potential of space division multiplexing (SDM) for the power-over-fiber (PWoF) technique, in terms of weakly-coupled multicore fiber (WC-MCF) design and experimental verification. Our simulation results indicate that, the SDM-enabled PWoF scheme is superior to the wavelength division multiplexing (WDM) enabled counterpart, due to the scalability of the energy light delivery and the save of wavelength division multiplexers. Then, we experimentally demonstrate the co-transmission of optically carried fifth generation new radio (5G NR) signals at 1550-nm and the 60-W energy light at 1064-nm over the 1-km weakly-coupled seven-core fiber (WC-7CF) fronthaul link. Since the optical power delivery characteristic per the WC-MCF core is similar to that of the standard single-mode fiber (SSMF), the SDM-enabled PWoF scheme can evenly distribute the high-power energy light into multiple spatial channels, to maximize the efficiency of the optical power transition efficiency (OPTE). Consequently, the total collected optical power of the energy light over the 1-km WC-7CF is 4.6 times higher than that of the 1-km SSMF, mainly due to the insertion loss of the fan-in and fan-out (FIFO) devices. Meanwhile, the error-vector magnitude (EVM) of 1.5-Gbit/s 5G NR signal is 0.28%, when the received electrical signal power is −25 dBm. The EVM value of the co-transmitted 5G NR signal with the 60-W energy light only has a fluctuation of 0.01% over six hours. The SDM-enabled PWoF is useful for the optically powered 5G pico-cells, with the capability of high-speed access and centralized management.

Optically powered 5G WDM fronthaul network with weakly-coupled multicore fiber.

The number of base stations (BSs) for the fifth generation (5G) wireless network is substantially increased, as each coverage is greatly reduced. Therefore, both the miniaturization and the densification of BSs suffer from the challenges of electrical power supply and deployment cost. Here, we present an optically powered 5G fronthaul network, in support of the co-propagation of spatial-division-multiplexing (SDM) energy light and wavelength-division-multiplexing (WDM) 5G new radio (NR) signals over the weakly-coupled multicore fiber (WC-MCF). When the 60-W energy light at 1064.8-nm is equally distributed among the outer six cores, and the 9-Gbit/s 5G NR WDM signals are transmitted over the central core of 1-km WC seven-core fiber (WC-7CF), we can collect total 11.9-W electrical power at the remote node, for the purpose of optically powered small cells. Meanwhile, the error-vector magnitude (EVM) values of 1.5-Gbit/s 5G NR 64-level quadrature amplitude modulation orthogonal frequency division multiplexing (64QAM-OFDM) signals at the central frequency of 3.5 GHz fluctuate within a range of 0.3%∼0.39%, under a received electrical power of -25 dBm, for all six-wavelength channels. Six optically powered small cells are equipped with the characteristics of centralized management and flexible access-rate.

High Sensitivity Strain Sensors Using Four-Core Fibers through a Corner-Core Excitation.

A weakly-coupled multicore fiber can generate supermodes when the multi-cores are closer to enter the evanescent power coupling region. The high sensitivity strain sensors using tapered four-core fibers (FCFs) were demonstrated. The fan-in and fan-out couplers were used to carry out light coupling between singlemode fibers and the individual core of the FCFs. A broadband lightsource from superlumminescent diodes (SLDs) was launched into one of the four cores arranged in a rectangular configuration. When the FCF was substantially tapered, the asymmetric supermodes were produced to generate interferences through this corner-core excitation scheme. During tapering, the supermodes were excited based on a tri-core structure initially and then transited to a rectangular quadruple-core structure gradually to reach the sensitivity of 185.18 pm/μԑ under a tapered diameter of 3 μm. The asymmetric evanescent wave distribution due to the corner-core excitation scheme is helpful to increase the optical path difference (OPD) between supermodes for improving the strain sensitivity.

DD-OOK Multicore Fiber Systems Impaired by Intercore Crosstalk and Laser Phase Noise

Direct-detection on-off keying (DD-OOK) weakly-coupled multicore fiber (WC-MCF) systems impaired by intercore crosstalk (ICXT) and laser phase noise are investigated numerically and experimentally. This is performed for systems with a product between the bit rate and the absolute value of the skew between cores much larger than one. It is shown that the phase noise increases the instantaneous ICXT power fluctuations. The standard deviation of the short-term average ICXT (STAXT) power induced by the phase noise depends on the product between the laser linewidth and the absolute value of the skew between cores (linewidth &#x00D7;<inline-formula><tex-math notation="LaTeX">$|$</tex-math></inline-formula> skew<inline-formula><tex-math notation="LaTeX">$|$</tex-math></inline-formula>). When linewidth &#x00D7;<inline-formula><tex-math notation="LaTeX">$|$</tex-math></inline-formula> skew<inline-formula><tex-math notation="LaTeX">$|$</tex-math></inline-formula><inline-formula><tex-math notation="LaTeX">$\gg$</tex-math></inline-formula>1, typical of distributed feedback (DFB) lasers (linewidth in the few MHz range) and MCFs with skew in the <inline-formula><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula>s range, the decrease of the standard deviation of the STAXT power induced by the phase noise is 5 dB per decade of linewidth &#x00D7;<inline-formula><tex-math notation="LaTeX">$|$</tex-math></inline-formula> skew<inline-formula><tex-math notation="LaTeX">$|$</tex-math></inline-formula> increase. For linewidth &#x00D7;<inline-formula><tex-math notation="LaTeX">$|$</tex-math></inline-formula> skew<inline-formula><tex-math notation="LaTeX">$|$</tex-math></inline-formula><inline-formula><tex-math notation="LaTeX">$\ll$</tex-math></inline-formula>1, typical of external cavity lasers (ECLs) and DFB lasers, and MCFs with skew of a few ns, the standard deviation of the STAXT power remains almost unaffected by the phase noise. Experimental results show that, compared with low linewidth ECLs, 10 Gb/s DD-OOK WC-MCF systems using DFB lasers as optical sources in the interfering cores and skew in the range between 2.4 ns and 5.4 ns, may require an additional ICXT margin up to 8 dB for a given outage probability. The additional ICXT margin and the lower amplitude of the STAXT power fluctuations observed experimentally for DFB lasers suggest that the level of the fluctuations of the STAXT power may be an inadequate system performance indicator. The dependence of the outage probability on the interfering core count is also investigated experimentally. It is shown that, for systems with bit rate &#x00D7;<inline-formula><tex-math notation="LaTeX">$|$</tex-math></inline-formula> skew<inline-formula><tex-math notation="LaTeX">$|$</tex-math></inline-formula><inline-formula><tex-math notation="LaTeX">$\gg$</tex-math></inline-formula>1, the outage probability only depends on the total ICXT power and not on the interfering core count.

Correlation and Power Distribution of Intercore Crosstalk Field Components of Polarization-Coupled Weakly Coupled Single-Mode Multicore Fibres

The correlation and power distribution of intercore crosstalk (ICXT) field components of weakly coupled multicore fibers (WC-MCFs) are important properties that determine the statistics of the ICXT and ultimately impact the performance of WC-MCF optical communication systems. Using intensive numerical simulation of the coupled mode equations describing ICXT of a single-mode WC-MCF with intracore birefringence and linear propagation, we assess the mean, correlation, and power distribution of the four ICXT field components of unmodulated polarization-coupled homogeneous and quasi-homogeneous WC-MCFs with a single interfering core in a wide range of birefringence conditions and power distribution among the field components at the interfering core input. It is shown that, for homogeneous and quasi-homogeneous WC-MCFs, zero mean uncorrelated ICXT field components with similar power levels are observed for birefringence correlation length and birefringence beat length in the ranges of 0.5m,10m and 0.1m,10m, respectively, regardless of the distribution of power between the four field components at the interfering core input.

Outage Probability Due to Intercore Crosstalk From Multiple Cores in Short-Reach Networks

The outage probability (OP) due to intercore crosstalk (ICXT) arising from multiple interfering cores in short-reach binary intensity modulation-direct detection optical links supported by homogeneous weakly-coupled multicore fibers is assessed through numerical simulation. The maximum acceptable ICXT level for a given OP is extracted from simulation results, for low and high skew-bit rate products (SBRPs). (i) For high SBRP, a 3 dB reduction of the maximum acceptable ICXT level per core for a given OP is observed when the number of interfering cores doubles. In this case, as a very large number (≫1) of bits of each interfering core is contributing to ICXT, the total detected ICXT tends to a Gaussian distribution that makes the maximum acceptable total ICXT level independent of the interfering core count. (ii) For low SBRP, the number of bits contributing to ICXT is similar to the interfering core count and the total detected ICXT assumes a set of discrete amplitudes, which deviates it from the Gaussian distribution. Hence, the reduction of the maximum acceptable ICXT level per core, when the number of interfering cores is doubled, is about 2 dB, and the maximum acceptable total ICXT level increases with the interfering core count, by around 3 dB, when the interfering core count increases from 1 to 8.

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.

Analysis of Inter-Core Crosstalk in Weakly-Coupled Multi-Core Fiber Coherent Systems

The influence of the inter-core crosstalk (ICXT) on the performance of weakly-coupled multi-core fiber (WC-MCF) systems with coherent detection and arbitrary inter-core skew is studied numerically and analytically. We analyze the evolution of the instantaneous ICXT power, induced by polarization division multiplexed quadrature amplitude modulation signals, short term average crosstalk (STAXT), and detected ICXT components along the time to get insight on how the ICXT affects the coherent system performance. Numerical results show that, with low skew-symbol rate product (4:1), the STAXT can have large fluctuations along the time and the variance of the detected ICXT can also have large fluctuations along the time, causing large variations of the bit error rate (BER) along time. With large skew-symbol rate product (≫1), the STAXT is almost constant along the time and, although the detected ICXT varies along time, the detected ICXT variance is almost constant along time leading to very small fluctuations of BER along time. Analytical expressions for the variance of the coherently detected ICXT, average BER and optical signal-to-noise ratio (OSNR) penalty are proposed and shown to agree with Monte-Carlo simulation results for arbitrary skew, modulation format order, and roll-off factor of the transmitted signals. Numerical results show that the maximum allowable ICXT level for 1 dB OSNR penalty increases when the skew augments and can reach 1.3 dB for a roll-off factor of 1. For most cases of interest of low roll-off factor, the increase of the maximum allowable ICXT level is very small. It is shown that the OSNR penalty estimates agree quite well with other authors' experimental results (with nearly zero roll-off factor).

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.

Role of polarization-mode coupling in the crosstalk between cores of weakly-coupled multi-core fibers.

We develop a theory of crosstalk in weakly-coupled multi-core fibers that accounts for the effect of intra-core polarization-mode coupling. We show that random polarization-mode coupling plays a critical role, just like other polarization-independent effects such as fiber bending and twist, in explaining the observed incoherent crosstalk in weakly-coupled multi-core fibers.

Machine Learning Assisted Optimization of Dynamic Crosstalk-Aware Spectrally-Spatially Flexible Optical Networks

We focus on optimization of dynamic spectrally-spatially flexible optical networks (SS-FONs), in which distance-adaptive, spectral super-channel (SCh) transmission is realized over weakly-coupled multi-core fibers (MCFs). In such networks, the inter-core crosstalk (XT) effect in MCFs impairs the quality of transmission (QoT) of optical signals, which has a negative impact on overall network performance. In this context, a key issue is the selection of a modulation format (MF) for a particular lightpath, since each MF offers a different tradeoff between spectral efficiency (number of occupied frequency slices) and transmission reach, and both these elements are in a close relation with the experienced XT. In fact, it is difficult to quantify the impact of the MFs used in a given network on the deterioration in QoT due to the XT effect and on overall network performance, as the levels of XT experienced by particular lightpaths depend directly on the ongoing transmissions in neighbor MCF cores, and those (i.e., established lightpaths) are subject to stochastic changes in dynamic SS-FONs. Therefore, in this article, we propose an approach that selects a MF for a lightpath based only on the transmission distance, i.e., length of the applied routing path. In particular, for each considered MF, we define a Modulation format Distance Limit (MDL) parameter that is used to select the MF for a lightpath by a simple comparison of the considered routing path length against the MDL parameter. To facilitate the very complex process of determining the best values of the MDL parameter, we propose a machine learning (ML) approach, namely, supervised learning regression method, with the overall goal to optimize network performance in terms of bandwidth blocking probability (BBP). Extensive simulation experiments performed in different network scenarios show that the proposed method ML allows to achieve performance gains when compared to various reference approaches, including a more computationally expensive method that is based on dynamic (flexible) selection of MFs.

Carrier Beating Impairment in Weakly Coupled Multicore Fiber-Based IM/DD Systems

Weakly coupled multicore fiber (WC-MCF) is promising for use in short-reach fiber telecommunication systems in the near future. Intercore crosstalk (XT) plays an important role in WC-MCF-based short-reach intensity-modulation/direct-detection (IM/DD) systems, because XT can significantly degrade system performance. For the first time, the combined effect of intercore XT and the frequency offset between optical carriers, which is defined as the carrier beating impairment (CBI), is measured and characterized by experiments and numerical simulations. The experimental results show that the CBI causes large fluctuations in the signal-to-noise ratio (SNR) with a normally tolerable XT level. Such SNR fluctuations can additionally reduce the system’s XT tolerance (at worst 1-dB SNR degradation) by as much as 20 dB for 4-level pulse amplitude modulation (PAM-4) transmission. The simulation results show that the CBI is mainly affected by the specific properties of the laser source and the modulation depth of the transmitted signals. These results suggest that the XT should be designed to be much smaller for WC-MCF-based short-reach IM/DD systems when there is the CBI.

Outage Probability Due to Intercore Crosstalk in Dual-Core Fiber Links With Direct-Detection

The outage probability (OP) in short-haul direct-detection (DD) optical links supported by weakly-coupled multicore fiber (MCF) impaired by intercore crosstalk (ICXT) and using ON–OFF keying signaling is assessed theoretically and through simulation. A closed-form expression for the OP is proposed for a single interfering core. This expression is useful to provide fast and reliable performance estimates in preliminary studies of weakly-coupled MCF-based systems where the ICXT is highly correlated along the signal bandwidth, i.e., when the skew-bit rate product is small. Particularly, the results for a 20-km-long link at 10 Gbit/s and walk-off below 1 ps/km are detailed. For high skew-bit rate products, i.e., when the ICXT is decorrelated along the signal bandwidth, the simulation results show that for a typical OP of 10−4, the tolerance to ICXT increases above 4 dB, when compared with low skew-bit rate products. It is also shown that the DD links with finite extinction ratio are more robust to outage induced by the ICXT than those with an ideal extinction ratio.

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.