US20190260470A1 - Methods for Estimating Modal Bandwidth Spectral Dependence - Google Patents

Methods for Estimating Modal Bandwidth Spectral Dependence Download PDF

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US20190260470A1
US20190260470A1 US16/341,536 US201716341536A US2019260470A1 US 20190260470 A1 US20190260470 A1 US 20190260470A1 US 201716341536 A US201716341536 A US 201716341536A US 2019260470 A1 US2019260470 A1 US 2019260470A1
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wavelength
emb
dmd
wavelengths
mmf
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Jose M. Castro
Richard J. Pimpinella
Bulent Kose
Brett Lane
Yu Huang
Asher S. Novick
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Panduit Corp
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/07—Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems
    • H04B10/073—Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems using an out-of-service signal
    • H04B10/0731—Testing or characterisation of optical devices, e.g. amplifiers
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M11/00—Testing of optical apparatus; Testing structures by optical methods not otherwise provided for
    • G01M11/30—Testing of optical devices, constituted by fibre optics or optical waveguides
    • G01M11/33—Testing of optical devices, constituted by fibre optics or optical waveguides with a light emitter being disposed at one fibre or waveguide end-face, and a light receiver at the other end-face
    • G01M11/338—Testing of optical devices, constituted by fibre optics or optical waveguides with a light emitter being disposed at one fibre or waveguide end-face, and a light receiver at the other end-face by measuring dispersion other than PMD, e.g. chromatic dispersion
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/07—Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems
    • H04B10/075—Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems using an in-service signal
    • H04B10/079—Arrangements for monitoring or testing transmission systems; Arrangements for fault measurement of transmission systems using an in-service signal using measurements of the data signal
    • H04B10/0795—Performance monitoring; Measurement of transmission parameters
    • H04B10/07951—Monitoring or measuring chromatic dispersion or PMD
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/25—Arrangements specific to fibre transmission
    • H04B10/2581—Multimode transmission

Definitions

  • the present invention relates in general to the field of optical fibers and more specifically, to multimode fibers (MMF) designed for operation at multiple wavelengths.
  • MMF multimode fibers
  • the present invention also relates to the field of modeling, designing, production, sorting and testing of MMFs. More specifically it relates to the estimation of the MMF EMB at multiple wavelengths.
  • the invention is also related to modal and chromatic dispersion compensation in Vertical Cavity Surface Emitting Laser (VCSEL) based MMF channels [1].
  • VCSEL Vertical Cavity Surface Emitting Laser
  • the methods described here can provide an estimation of the skew in radial DMD pulse waveforms (tilt) at different wavelengths which is critical in the field of modal-chromatic dispersion compensation.
  • MMF single-mode fiber
  • SWDM Short Wavelength Division Multiplexing
  • SWDM Concept is similar to the Coarse Wavelength Division Multiplexing (CWDM), already used for SMF channels operating in the 1310 nm spectral region.
  • SWDM requires the specification of the minimum EMB at the wavelengths limits of the operating spectrum (e.g. 850 nm and 953 nm).
  • the EMB is computed from DMD pulse measurements.
  • the DMD test method specified within standards organizations [2], describes a procedure for launching a temporally short and spectrally narrow pulse (reference pulse) from a SMF into the core of a MMF at several radial offsets [5]. After propagating through the MMF under test, the pulses are received by a fast photodetector which captures all the MMF core power.
  • the EMB is estimated by the Fourier domain deconvolution of the input pulse from a weighted sum of the received signals for each radial offset launch. The set of weight values utilized in the computation belong to a set of ten representative VCSELs described elsewhere [2].
  • FIG. 1 shows a simulation of EMB vs wavelength 100 for a MMF fiber compliant to the OM4 standard.
  • the EMB 105 has a peak value at ⁇ P 120 .
  • the labels 115 and 125 show the measured and predicted wavelengths, ⁇ M and ⁇ S , respectively.
  • the range 110 shows the spectral window in which the fiber can maintain an EMB higher than a specified value, i.e. 4700 MHz ⁇ km for OM4.
  • FIG. 2 shows simulated MMFs with identical EMB at ⁇ M 200 , but different EMB spectral dependence. Peaks 205 , 210 , 205 are different and uncorrelated with 200 . Moreover, since the spectral windows 220 , 225 and 230 are different, an estimation of the EMB at ⁇ S 240 is not possible.
  • FIG. 3 Shown in FIG. 3 . is the EMB at 850 nm and 953 nm for a large number of simulated fibers, represented using rectangle markers 300 with random variations in their refractive index core.
  • a subset of these fibers that meet the TIA-492AAAD OM4 EMB specification are represented by diamonds markers 305 . This figure shows the lack of correlation among EMBs at 850 nm and 953 nm.
  • This simulation which was extended for a large range of wavelengths from 800 nm to 1100 nm, clearly shows that there is no direct relationship between the fiber's EMB at a specified wavelength, ⁇ S , and the EMB at a measured wavelength, ⁇ M , when ⁇ S ⁇ M .
  • a method that enables the prediction of the EMB at an arbitrary wavelength based on measurements at another wavelength is desirable to reduce testing time and cost of a MMF.
  • EMB Effective Modal Bandwidth
  • MMF laser optimized Multimode Fiber
  • the present invention discloses novel methods to estimate the EMB of a MMF at a desired wavelength, from measurements performed at another wavelength.
  • the first method, Method 1 can be used to predict the EMB at an arbitrary wavelength, ⁇ S , based on an EMB measurement at a different wavelength, ⁇ M .
  • the second method can be used to evaluate if the EMB at an arbitrary wavelength, ⁇ S , is equal of greater than a minimum specified threshold.
  • Each method provides different degree of complexity and accuracy.
  • FIGS. 4 and 5 Refractive index profiles for two types of MMF are shown in FIGS. 4 and 5 .
  • FIG. 4 a traditional MMF refractive index profile is shown.
  • the profile 400 does not present any abrupt discontinuity inside the core or inside the cladding.
  • the propagating mode groups of this fiber are shown in 410 .
  • the refractive index profile 500 abruptly changes in the cladding due to the refractive index trench 520 introduced to provide lower bending loss.
  • Labels 510 and 515 shows some of the propagating and leaking mode groups respectively.
  • Waveguide theory for alpha-profile fibers has been well developed [ref].
  • the theory can enable the modeling of fiber DMD behavior over a broad range of wavelengths, when the profiles and dopants concentrations are known.
  • the designed “optimum” refractive index profile is distorted deterministically and randomly.
  • Very small alterations in 400 or 500 basically change the way the mode groups 410 , 510 interact with the variations in refractive index, which destroys or reduces the correlations among DMDs at different wavelengths as it was showed in FIG. 3 .
  • This method can be used to predict the EMB at an arbitrary wavelength, ⁇ S , based on an EMB measurement at a different wavelength, ⁇ M .
  • the method was developed based on the inventors' realization that in order to increase the correlation among EMB measurements at ⁇ M , and a second wavelength, ⁇ S , a new approach that fully utilizes the information provided by the measured DMD waveforms is required.
  • the method proposed here uses the DMD pulse waveform information at ⁇ M , such as centroids, peak position, width, shapes, energy per radial offset, and skews, to predict the EMB at a second wavelength.
  • FIGS. 6 and 7 show the block diagrams for the training and estimation processes respectively. For illustrative purposes, we use an example to describe both methods.
  • the populations of TIA-492AAAD standards compliant OM4 fibers from two suppliers (A and B), which use different manufacturing processes are selected. It is understood that the population used here is only an example and is not restricted to any specific number of fiber suppliers.
  • FIGS. 8( a ) and 8( b ) show the DMD radial pulses for three MMF from each population at 850 nm (dark trace) and 953 nm (lighter trace).
  • FIGS. 8( a ) and 8( b ) show that most of the fibers have similar DMD pulses at low radial offset for both wavelengths.
  • the DMD pulse shapes are very different at larger radial offset for the two wavelengths.
  • the EMBs computed from the measured DMD pulses for the A and B populations at 850 nm and 953 nm are shown in FIG. 9 . These measurements agree with simulation results showed in FIG. 3 , which indicates that EMBs at different wavelengths are uncorrelated.
  • step 606 of FIG. 6 the main features of the DMD pulses at each wavelength are extracted.
  • This process captures the main characteristics required to describe the DMD pulses at each radial offset and each wavelength for post-processing and analysis.
  • the centroid feature is computed using,
  • r is the radial offset index that relates the position of the single-mode launch fiber to the MMF core center axis during the DMD measurement
  • t is the discrete length normalized temporal
  • k is the time index.
  • the variable t and k are related to the number of temporal samples simulated or acquired from the oscilloscope during DMD measurements at a given wavelength.
  • the mean power is computed by,
  • the peak power is computed using,
  • max t (.) is a function that finds the maximum of the DMD pulses for each radial offset and for each wavelength. The peak position is computed using.
  • find_peak is a function that finds the maximum value of the DMD pulses for each radial offset and for each wavelength.
  • the RMS width of the pulse for each radial offset is computed
  • T REF is the RMS width of the reference pulse used for the measurement.
  • the features extracted from DMD measurements at ⁇ M are used to predict features at ⁇ S , based on the model described in equations (6-8).
  • C r, ⁇ S , and C t, ⁇ M represent the centroids per radial offset at ⁇ M and ⁇ S
  • I C (.,.),F C (.,.),G C (.) is the set of polynomial functions that describe the relationship between centroids at those wavelengths.
  • P r, ⁇ S , and P r, ⁇ M represent the centroids per radial offset at ⁇ M and ⁇ S
  • I P (.,.), F P (.,.),G P (.) is the set of polynomial functions that describe the relationship between peak positions at those wavelengths.
  • W r, ⁇ S (1 +I W ( r )) W r, ⁇ M +F W ( ⁇ M , ⁇ S ) G W ( r ) (8)
  • W r, ⁇ S , and W r, ⁇ M represent the centroids per radial offset at ⁇ M and ⁇ S , I W (.,.),F, W (.,.),G W (.) is the set of polynomial functions that describe the relationship between widths at those wavelengths.
  • the F(.,.) functions are solely dependent on the measured and targeted wavelength. These functions accommodate for chromatic effects in the refractive index and material.
  • the G(.) functions are solely dependent on radial offsets and accommodate for relationships between the group velocity of DMD pulses at different radial offset in the fiber core.
  • the I(.) functions dependent on the radial offset, accommodates for mode transition due to the change of wavelengths.
  • step 608 the features extracted from the measured DMD pulses at the two wavelengths are used to find the coefficients of the polynomial functions described above (6-8). Standard curve fitting techniques are applied as described in [3].
  • FIGS. 10( a ) and ( b ) show the centroid features for 850 nm and 953 nm for radial offsets from 1 to 24 microns for the two fiber populations A (red) and B (blue).
  • FIGS. 11( a ) and ( b ) show the peak positions for 850 nm and 953 nm for radial offsets from 1 to 24 microns for the two fiber populations.
  • F(850,953) was 16 ps/ ⁇ m/km for population A and 13.3 ps/ ⁇ m/km for population B.
  • the functions G C (.,.) and G P (.,.) for a cubic polynomial curve fitting is shown in FIGS. 12( a ) and 12( b ) for fiber populations A and B respectively.
  • curves for the other features described above (1-5) are obtained.
  • the correlations among the features i.e. the ones shown in FIGS. 1-12 are evaluated. If they are higher than a determined threshold, e.g., 80%, the model is ready to use and the process end in 615 . If not, in 612 the signal to noise ratio (SNR) of all DMD measurements are evaluated. If the noise of the measurements is higher than a pre-determine threshold, the measurements need to be repeated. If the SNR is high, but the correlations are low, it is possible that the samples do not represent the fiber population and a new set of samples will be required.
  • a determined threshold e.g., 80%
  • the method for the DMD mapping and estimation shown in FIG. 7 , is ready to use.
  • the fibers that require EMB estimation are selected.
  • the DMD at ⁇ M is measured.
  • the features are extracted from the DMD pulse centroids at ⁇ M using equations (1-5).
  • the DMD pulses are estimated at ⁇ S .
  • Equation (6-8) the model described in equations (6-8) is used to estimate the features C r, ⁇ S , P r, ⁇ S ,W r, ⁇ S , Ymax r, ⁇ S Ymean r, ⁇ S at ⁇ S .
  • the parameter P r, ⁇ S is used to reposition each of the DMD pulses using,
  • y P (.,.,.) array represents the estimated DMD pulses after the peak position correction.
  • the parameter ⁇ is used to estimate the new width and skew of the DMD pulses at ⁇ S .
  • ⁇ S > ⁇ M the DMD pulse width tends to increase.
  • ⁇ S ⁇ M the width tends to decrease.
  • the changes in skew and width are corrected using a linear filter as shown,
  • y W (.,.,.) represents the estimated DMD after equalization
  • i is the equalizer tap index
  • Ntaps the number of taps
  • a i represents the tap coefficient
  • K is a scaling factor
  • Ntaps For each fiber, the optimum values of Ntaps, A i , and K, are found by numerically searching.
  • the constraint conditions or equations for this search are the estimated mean, peak, and the values shown in table I.
  • the algorithm evaluates if the conditions shown above can be maintained below a pre-determined threshold, e.g., 60% of the estimated constraint' values. If that is not achieved, in 712 the SNR of the DMD measurement is evaluated. Depending on this, the DMD may need to be measured again 704 . Otherwise, in 717 it is indicated that the estimation failed. If the conditions compared in 710 are achieved, the algorithm provides the DMD corrected pulses and the estimated EMB is obtained.
  • a pre-determined threshold e.g. 60% of the estimated constraint' values.
  • FIG. 13 shows the corrected DMD results for populations A and B.
  • This method can be used to predict if the EMB at an arbitrary second wavelength, ⁇ S , is equal or greater than a specified threshold, EMB th , based on a DMD measurement at a different wavelength, ⁇ M .
  • this method utilizes features of the DMD pulse waveforms at ⁇ M , such as centroids, peak position, width, shapes, energy per radial offset, and skews.
  • the average centroid for positions R t _ start -R t _ end is defined using,
  • the average centroid for positions RB —start -RB —end is defined using,
  • k is the index that represent the selected radial offset regions
  • the k index can take values from 1 to N k where N k ⁇ 25 r of radial offsets, i.e. 25.
  • N k the number of radial offsets
  • the training method which is described below, utilize machine learning techniques to find the radial-offset regions that maximize the difference between parameters such as P_shift, P_slopes and M_widths for two or more population of fibers.
  • One population of fiber will have EMB>EMB th at ⁇ S and other populations will not satisfy this constraint.
  • the estimation method simply evaluates if the extracted features from MMF under test belong to the regions found during training that satisfy the condition, EMB>EMB th at ⁇ S based on the DMD measurements at ⁇ M .
  • the training process is identical to the one shown in FIG. 6 , with exception of steps 606 and 608 .
  • steps 606 and 608 We use the same example, starting from 606 of FIG. 6 , to illustrate the training method.
  • step 606 the main features of the DMD pulses at ⁇ M , are extracted. Note the differences with the first method which require the computation of the features at each wavelength, ⁇ M and ⁇ S .
  • the extracted features are C r, ⁇ M , P r, ⁇ M and W r, ⁇ M (centroid, peak and width) using equations (1-5).
  • the training is performed.
  • the training is an iterative process that has the goal to maximize a metric or a series of metrics that represents the differences in features of two groups of fibers.
  • One group, Group 1 are composed by the MMFs that have EMB>EMB th at ⁇ S and the other group, Group 2 by MMFs that have EMB ⁇ EMB th at ⁇ S .
  • the utilized metric is a function implemented in C, Python, or Matlab, which computes p-norm distances in the mentioned space, among the MMFs that belong to the groups Group 1 and Group 2.
  • a 1,k , A 2,k are weight parameters to quantify the relative importance of each features and/or radial offset regions.
  • the coordinate axes are modified by changing the values of ⁇ R B _ start , R B _ end ⁇ , ⁇ R T _ start ,R T _ end ⁇ , and the set of k parameters ⁇ R_start k ,R_end k ⁇ .
  • the norm parameter p and the weights can be also optimized in each iteration.
  • the values can be changed at random, or in deterministic ways. For example, using the random search algorithms or using gradient methods.
  • the features are recomputed using (12-17) for each new set of regions.
  • the MMFs are mapped in the new space and the utilized metric, i.e. equation (18) is computed. The process continue until the metric is maximized, or until an exhaustive search is produced.
  • FIG. 15 shows initial mapping of the population for one to 8000 iterations.
  • the square markers represent MMF from Group 1 and the circle markers represents MMFs from Group 2. It can be observed that for the initial iterations 1-5000, FIGS. 15( a ), ( b ), ( c ), ( d ) and ( e ) it is not possible to differentiate between both populations.
  • the optimum regions were 2 to 3 microns for C_Top and 18-24 microns for the C_Bottom
  • the training using the disclosed algorithm demonstrates that the MMFs for Group 1 and Group 2 have distinctive features that can be observed when the optimum set of radial regions to represent them are selected. These results demonstrate a method to predict if EMB>EMB th at ⁇ S based on the DMD measurements at ⁇ M .
  • the optimum radial-offset regions to extract the features that optimally represent MMFs that have EMB S >EMB th at ⁇ S were found.
  • the Groups of MMFs that have the desired characteristics can be separated by a line or in general by a polynomial that isolate two regions one for Group 1 and another for Group 2.
  • the features of a MMF are extracted from DMD measurements at ⁇ M and mapped in the feature-space. If the MMF belongs to the desired regions that produce EMB>EMB th at ⁇ S (see FIG. 17 the fiber is accepted. Otherwise the fiber is rejected.

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