Measurement and Estimation of the
Mode Partition Coefficient k
Rick Pimpinella and Jose Castro
IEEE P802.3bm 40 Gb/s and 100 Gb/s Fiber Optic Task Force
November 2012, San Antonio, TX
Background & Objective
Background:
Mode Partition Noise in MMF channel links is caused by pulse-to-pulse
power fluctuations among VCSEL modes and differential delay due to
dispersion in the fiber (Power independent penalty)
“k” is an index used to describe the degree of mode fluctuations and takes
on a value between 0 and 1, called the mode partition coefficient [1,2]
Currently the IEEE link model assumes k = 0.3
It has been discussed that a new link model requires validation of k
The measurement & estimation of k is challenging due to several
conditions:
Low sensitivity of detectors at 850nm
The presence of additional noise components in VCSEL-MMF channels (RIN,
MN, Jitter – intensity fluctuations, reflection noise, thermal noise, …)
Differences in VCSEL designs
Objective:
Provide an experimental estimate of the value of k for VCSELs
Additional work in progress
2
MPN Theory
Originally derived for Fabry-Perot lasers and SMF [3]
Assumptions:
Total power of all modes carried by each pulse is constant
Power fluctuations among modes are anti-correlated
Mechanism:
When modes (different wavelengths) travel at the same speed their fluctuations
remain anti-correlated and the resultant pulse-to-pulse noise is zero.
When modes travel in a dispersive medium the modes undergo different delays
resulting in pulse distortions and a noise penalty.
Example: Two VCSEL modes transmitted in a SMF undergoing chromatic dispersion:
START
END
START
t
Optical Waveform @ Detector
With mode power fluctuations
END
Decision Region
Shorter
Wavelength
Time
(arrival)
slope 
Longer
Wavelength
t
 DL

Time
(arrival)
3
Time (arrival)
Example of Intensity Fluctuation
among VCSEL modes
MPN can be observed using an Optical Spectrum Analyzer (OSA).
Measurements require a detector with high sensitivity and high bandwidth,
and a means of isolating other noise components.
The Figure below shows the optical spectrum of a 16GFC transceiver
Green traces are 100 VCSEL spectral measurements at ~2 second intervals
Black trace is the average spectrum
Noise can be observed but a slow detector does not provide a means of estimating the
magnitude
0
Intensity fluctuations among
VCSEL wavelengths
Power (dBm)
-10
Integration time 3.8ms
Duration 200 seconds
-20
-30
-40
Counts
-50
-60
843
843.5
844
844.5
845
845.5
846
846.5
847
847.5
Wavelength, (nm)
- High Resolution OSA (0.005nm)
- Low Sensitivity
- Linear amplitude
- 3.8ms integration time (min)
- Two VCSEL “Mode Sets”
Wavelength (nm)
4
848
Measurement Methods
Two methods used to measure k:
1. Monochromator and APD measurements (equivalent to OSA)
High sensitivity
Bandwidth limited by APD
Fast transceivers were modulated at lower rates
Could not measure MPN for response rates >2.5Gbps
Short length used (5m) to avoid dispersion effects
2. Temporal measurements in the spectral domain – specific data
patterns measured at 16G data rates
Useful for evaluating noise dependence on transmitted pattern [4,5]
Fast detector – enables measurements at high bit rates (i.e. 14.025Gbps
for 16GFC)
Short lengths used (5m) to avoid dispersion effects
Lower sensitivity must be compensated by increasing measurement time
i.e., sample size
Need to estimate the noise introduced by other noise components
5
Method 1: Monochromator–APD measurement
Signal measured using an APD (M > 40).
Modulation rate limited to <2.5Gbps due to APD bandwidth (180ps rise time).
VCSEL spectra separated into VCSEL Mode Sets (MS’s). In practice only 4 MS’s could
be measured due to low power levels
Light from the transceiver was filtered using a tunable monochromator with a spectral
resolution between 0.2nm–0.5nm
Oscilloscope used to obtain the signal histogram for specific bits in the sequence
Monochromator spectral window
Pattern Generator
0
3
-10
APD + TIA Rx
1
4
Power (a.u.)
Eval. Brd & Transceiver
Monochromator
2
-20
5
-30
-40
-50
-60
Oscilloscope
851
852
853
854
Wavelength(nm)
(nm)
Wavelength
6
855
856
Method 1: Monochromator–APD measurement
Used PRBS 27-1 bit pattern
For consistency only the zero and one bits shown in red in the
following sequence were measured. “…100111001... “
Measured signal level histogram away from pulse edges
Pattern Generator
Measured “1”
Eval. Brd & Transceiver
Monochromator
APD + TIA Rx
Measured “0”
Oscilloscope
Time scale: 500ps/div
Y-axis in mV
7
Method 1: Monochromator–APD Calculation
Computation Example
Computation using [2]:
 
a  a 
ai  ai
2
k
MS
1
2
3
4
2
2
i
i
MEAN (mV) SD (mV)
~0.000
0.850
26.017
2.500
26.910
3.200
9.214
1.570
SD ai
~0.000
0.038
0.050
0.021
ai
~0.000
0.419
0.433
0.148
Total Power (Vrms) = 62.14mV
for any mode set i
k
--0.077
0.100
0.060
Max. k = 0.1
Maximum k for each transceiver
0.25
2
0.20
k-value
Where ai and ai are the normalized mean
powers of each peak (measured as rms
voltage) and the rms variation respectively,
after subtracting the background noise SD
(0.89mV).
All OMA measurements limited to <2.5Gbps
due to APD bandwidth limitations
0.15
0.10
0.05
0.00
0
2
4
6
8
Transceiver #
8
10
12
Method 1: Measurement Issues
Limited APD bandwidth (2.5Gbps) might result in a lower value for k
(filters high frequency noise).
Are the 16G transceivers operating properly at 2.5Gbps, or are we
introducing additional noise?
Is a correction required to extrapolate to 14Gbps?
Based on theory [2] the noise variance should be scaled.
However, in order to apply scaling, we must assume how the
MPN spectrum behaves above the cutoff frequency.
It is challenging to use the laser rate equations to predict the noise
spectrum above cutoff for the individual transceivers measured.
All these questions indicate an alternative method in which the
transceivers operate at the specified line rate is required.
9
Method 2: Temporal-Spectral characterization
using a fast detector and post processing
Procedure
The transceiver is modulated with a specific bit pattern
Resultant waveforms measured for 5m to 1km lengths with and without monochromator
The measurements reported here are for 5m
Sampling Oscilloscope with high bandwidth optical plug-in
The oscilloscope acquired the waveforms and sent them to a computer for processing
0
Pattern Generator
3
-10
2
1
4
Power (a.u.)
-20
5
-30
Eval. Brd & Transceiver
-40
-50
-60
Monochromator
851
852
853
854
855
856
Wavelength (nm)
1
VCSEL mode 0-1
VCSEL mode 2
VCSEL mode 3-4
Total
0.9
Receiver
Optical Power, A.U
0.8
Oscilloscope
0.7
0.6
0.5
3
0.4
2
1
0.3
0.2
Offline post processing
0.1
0
10
200
400
600
800
1000 1200
Time, ps
1400
Example for a 10G signal
1600
1800
Method 2: Signal acquisition
Test Equipment Characteristics
Sources: 16GFC Transceivers (clock 14.025GHz)
Linear Receiver: DCA plug-in,12GHz BW
Sampling Oscilloscope DCA 861000, temporal resolution = 0.5ps
Acquisition Procedure
The chromatic unfiltered signal (black trace) was measured
The signals for 4 VCSEL mode sets were acquired using the
monochromator (colored traces)
Signals were compensated for measurement noise and monochromator
loss
800
700
MS_2
MG_2
MG_1
MS_1
MS_3
MG_3
MS_4
MG_4
Total
TotalSignal
Signal
Opt. Power, (μW)
600
500
400
300
200
100
0
-1000
-500
0
Time, (ns)
11
500
1000
Method 2: Procedure
45
Noise Computation Procedure
 
a  a 
ai  ai
2
k
2
2
i
i
MG_1
MS_1
MG_2
MS_2
MG_3
MS_3
MG_4
MS_4
Total
Total Noise
Signal
40
Optical Power, (μW)
35
SD
30
25
20
15
10
5
0
-1000
-500
0
500
1000
Time, (ps)
800
700
Optical Power, (μW)
>500 signal waveforms were captured for
each MS
The standard deviation (SD) for each MS
signal was computed every 0.5ps
The SD of the total signal (black trace in
Top Fig.) is less than the noise in any one
VCSEL MS signal
This is attributed to the high degree of anticorrelation among VCSEL modes [2]
There are other noise components in the
total noise including thermal, jitter-intensity
fluctuations, RIN, …
Using this measurement method the
maximum k is ~0.22
Example of processed Measurements
MG_2
MS_2
MG_1
MS_1
MG_3
MS_3
MS_4
MG_4
Total Signal
Signal
Total
600
500
400
300
200
100
0
-1000
12
-500
0
Time,
Time, (ps)
(ns)
500
1000
Method 2: Noise considerations
The Random and Deterministic Jitter was measured, used RJ for noise calculations.
The signal waveform and measured jitter was used to calculate the jitter-intensity
noise (red trace). Method to be published.
It can be observed that the jitter-intensity noise matches the total noise at the pulse
edges.
The magnitude of the noise contributions due to RIN and other noise components
can be obtained by subtracting the jitter-intensity noise (red trace) from the total noise
(black trace). The difference is indicated by the double arrow.
Close inspection of the jitter-intensity noise and the total noise suggests the remainder
of noise is proportional to signal intensity.
800
Noise Optical Power, (μW)
Total Noise
Jitter Int. Noise
Total Signal
20
700
600
500
15
400
300
10
200
100
5
Signal Optical Power (mW)
25
0
0
-1000
-500
0
Time, (ps)
13
500
-100
1000
Conclusions
Two methods where used to measure k:
Measurements made at 2.5Gbps and 14Gbps
Both methods yield similar values for k
Method 1, monochromator and APD:
The maximum value for k was measured to be 0.20
Method 2, Temporal-Spectral characterization:
The maximum value for k was measured to be 0.22
The current value for k (0.3) is reasonable, but might be
conservative
A value 0.25 could be more accurate
Additional work underway
Larger transceiver sample set
MPN over long lengths
Effect of modal-chromatic dispersion and spectral mode coupling [6]
14
References
[1] K. Ogawa, “Analysis of Mode Partition Noise in Laser Transmission Systems, IEEE
J. Quantum Electron., vol. QE-18, no. 5, May 1982.
[2] K. Ogawa and R.S. Vodhanel, “Measurements of Mode Partition Noise of Laser Diodes,”
IEEE J. Quantum Electron., vol. QE-18, No. 7, July 1982.
[3] G. Agrawal, P. Anthony, and T. Shen, “Dispersion Penalty for 1.3-mm Lightwave Systems
with Multimode Semiconductor Lasers,” J. Lightwave Technol., vol. 6, no. 5, May 1988.
[4] P. Pepeljugoski, “Dynamic Behavior of Mode Partition Noise in Multimode Fiber Links,”
IEEE J. Lightwave Technol., vol. 30, no. 15, August 2012.
[5] J. Castro, R. Pimpinella, B. Kose, and B. Lane, “The Interaction of Modal and Chromatic
Dispersion in VCSEL based Multimode Fiber Channel Links and its Effect on Mode
Partition Noise,” Proceedings of the 61 IWCS 2012.
[6] J. Castro, R. Pimpinella, B. Kose, and B. Lane, “Investigation of the Interaction of Modal
and Chromatic Dispersion in VCSEL-MMF Channels,” J. Lightwave Technol., vol. 30,
no. 15, August 2012
15