· Tu2G.4.pdf OFC 2016 © OSA 2016 Requirements and Results for Practical VCSEL Transmission using...
Transcript of · Tu2G.4.pdf OFC 2016 © OSA 2016 Requirements and Results for Practical VCSEL Transmission using...
Tu2G.4.pdf OFC 2016 © OSA 2016
Requirements and Results for Practical VCSEL Transmission using PAM-4 over MMF
GaTech: Justin Lavrencik, Shriharsha Kota Pavan, Aliro Melgar, Varghese A Thomas
GaTech Research Support: GaTech Terabit Consortium; Adva Optical Networks, Avago, Inphi, OFS, Keysight, Harris, Picometrix, Synopsys
Slides: Balemarthy, Bhoja, Cunningham, Giovane, Kolesar, Kuchta, Lingle, Owens, Tatum
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Outline
Evolution of VCSEL Links Impairments and Noise of VCSEL/MMF Links Simulation and Modeling tools VCSELs Fiber Noise
RIN MPN MPN Revisited
Recent PAM-4 Transmission Results OM4 Wideband Fiber
Summary
2 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
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MMF Ethernet Standards
IEEE 802.3ae 10Gb/s (2002) 10GBase SR 300m on OM3 10GBase-LX4 300m on OM3
IEEE 802.3aq 10Gb/s (2007) 10GBase LRM 220m on OM2
IEEE 802.3ba 40 Gb/s and 100 Gb/s (2010) Introduced 4 x 25 Gb/s as fundamental building block 40GBase SR4 150m on OM4 (8 fibers duplex) 100GBase SR10 150m on OM4 (20 fibers duplex)
IEEE 802.3bm 40 Gb/s and 100 Gb/s (2015) 100GBase SR4 100m on OM4 (8 fibers duplex) Read-Solomon FEC Uncorrected BER ~5x10-5 Single mode variant: CWDM w/ 2 fibers
IEEE 802.3bs 400 GbE (planned 2017) At least 100 m over OM4 Baseline 100GBase SR16 Re-use of 100GBASE-SR4 specifications
Uncorrected BER ~2x10-4
3 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
http://www.ethernetalliance.org/roadmap/
Core data rates are now 25Gbps and moving to 50Gbps
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The Ethernet Alliance roadmap shows the evolution of data rates
• Client Optics – needed soon to connect IP routers to 400G DWDM gear for long haul transport
• Switch Ports – 100G data
center switches deployed in 2016 in hyper-scale, but 40G will remain common in enterprise
• Server I/O – planning for 50G,
deploying 25G servers now, though 10G has high volume still
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 4
Slide Courtesy: Robert Lingle Jr.
Moving to Terabit
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400G: Prospects for 50 Gb/s per laser w/MMF
100G MMF links have 100m reach using 4 fibers x 25G 400G requires16 fibers x 25 Gb/s (32 distinct fibers for duplex)
Alternatives for 8 x 50 Gb/s per fiber 400G solution NRZ: Much faster VCSELs and/or strong pre emphasis PAM-4: increases RIN and MPN requirements Shortwave WDM requires wideband MMF fiber
Challenges for both NRZ and PAM-4 RIN: Continue improvement of VCSEL RIN MPN: Much better understanding of mode
partition noise and characterization Higher speed VCSELs at new wavelengths
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Clear roadmap forming(ed) within IEEE for 50GbE, 200GbE and 400GbE
Scalability: Eyes on 1 Terabit
Paul Kolesar,– CommScope IEEE 802.3 50G & NGOATH Study Group January 2016, Atlanta GA
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Deployment Opportunities
DCs optimized for cloud computing require more interconnections and redundancy
6 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
SMF < 2km
MMF <500m
Cu Cable <5m
DC Architecture for Cloud Computing
Standards Based Building Wiring Link Lengths
LAN Architecture
Number of DCs world wide will continue to grow exponentially Data Centers are a key part of Web 2.0 networks Data Centers provide two key functions:
Content Storage and Computing
Data Centers and High Performance Computing require high data rate short distance links
100 m reach covers >80% of data center cabling
Cisco Global Cloud Index: Forecast and Methodology, 2014–2019
25% CAGR 2014 - 2019
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Early Optical Demonstrations
Experimental demonstration of 4-ASK over 225 SSMF (1997) S. Walklin, J. Conradi, "A 10 Gb/s 4-ary ASK lightwave system," in Integrated Optics and Optical Fibre
Communications, 11th International Conference on, and 23rd European Conference on Optical Communications (Conf. Publ. No.: 448) , vol. 3, pp. 255-258 Sep. 1997
Multilevel Signaling and Equalization over Multimode Fiber at 10 Gbit/s (2003) C. Pelard, E. Gebara, A. J. Kim, M. Vrazel, E. J. Peddi, V. M. Hietala, S. Bajekal, S. E. Ralph, and J. Laskar
Gallium Arsenide Integrated Circuit (GaAs IC) Symposium, 25th Ann. Tech. Digest 2003. IEEE , 9-12 Nov. 2003 Experimental demonstration of analog FFE using PAM-4 in OM2 MMF using VCSEL10 Gbps,150 m MMF
Experimental sensitivity analysis of PAM4/VCSEL/MMF links 100 m 5 Gbps (2005) J. E. Cunningham, D. Beckman, D. Huang, T. Sze, K. Cai, and A.V. Krishnamoorthy, "PAM-4 signaling over
VCSELs using 0.13 μm CMOS," in Information Photonics, 2005. OSA Topical Meeting, 6-8 June 2005
2 µm GaAs HBT 5 Gsym/s w/o FFE 150m OM2 5 Gsym/s w/ FFE 150m OM2
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VCSEL Data Rates
8
IBM OOK 71Gb/s, 7m 64Gb/s, 57m 62Gb/s, 7m
Chalmers PAM-4 70Gb/s, btb Offline equalization
OFS PAM-4 51.56Gb/s, 150m, 850nm
Georgia Tech PAM-4 51.56Gb/s,100m
IBM Chalmers
IBM OFS
PAM-4 w/DSP
850nm OOK w/DSP
850nm OOK w/o DSP
GT
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Evolution in PAM-4 Transceivers
9
[1] R. Farjad-Rad et al., “A 0.3-µm CMOS 8-Gb/s 4-PAM Serial Link Transceiver," in Solid-State Circuits, IEEE Journal of, May 2000
[2] J. T. Stonick et al., "An adaptive PAM-4 5-Gb/s backplane transceiver in 0.25-μm CMOS," in Solid-State Circuits, IEEE Journal of, Mar. 2003
[3] J. L. Zerbe et al., "Equalization and clock recovery for a 2.5-10-Gb/s 2-PAM/4-PAM backplane transceiver cell," in Solid-State Circuits, IEEE Journal of, Dec. 2003
[4] T. Toifl et al., "A 22-Gb/s PAM-4 receiver in 90-nm CMOS SOI technology," in Solid-State Circuits, IEEE Journal of, April 2006
[5] J. Lee et al., "Design and Comparison of Three 20-Gb/s Backplane Transceivers for Duobinary, PAM4, and NRZ Data," in Solid-State Circuits, IEEE Journal of, Sept. 2008
[6] Broadcom unveils 40G/50G PAM-4 physical layer chip, (http://www.lightwaveonline.com/articles/2014/12/broadcom-unveils-40g-50g-pam-4-physical-layer-chip.html), Dec. 2014
[7] P. Khandelwal et al., "100Gbps Dual-channel PAM-4 transmission over Datacenter Interconnects," DesignCon, Jan. 2016
Complete Tx and Rx Transceivers All employed SiCMOS as the material platform 5 Gb/s
250 nm [2]
10 Gb/s 130 nm [3]
22 Gb/s 90 nm [4]
20 Gb/s 90 nm [5]
50 Gb/s 28 nm [6]
56 Gb/s (dual channel) 28 nm [7]
8 Gb/s 300 nm [1]
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
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PAM-4 Transceiver Architectures
Transmitter Binary or gray mapping Precoder implements a 1/(1+D) filter to reduce DFE
burst-error length 3-tap FIR filter & line driver
10 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
Courtesy: Pulkit Khandelwal, InPhi)
Dual 56Gbaud PAM-4 transceivers are
commercially available
Receiver Continuous-Time Linear Equalizer (CTLE) 7-bit ADC at 28GSamples/s Digital FFE for equalization 1-tap Decision Feedback Equalizer Inverse of Tx Precoder
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Impairments and Noise of VCSEL/MMF Links
Quantifying and Minimizing
11 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
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Impairments
PAM-4 Waveform
Source Driver
VCSEL
TIA
PIN
PAM-4 Receiver
MMF
Tx Limited bandwidth of
transmitter o Components not scaling w/ bit rate
Tx nonlinearity o Driver and VCSEL
Finite extinction ratio (ER)
Fiber Fiber attenuation and
connector losses Chromatic Dispersion
(CD) o VCSEL RMS spectrum
(~0.5nm) determines spectral content
Modal dispersion (DMD) Multi-Path Interference
(MPI) o Multiple optical reflections
Rx Baseline Wander
o AC-coupling induces pattern dependent “dc” point
Limited Bandwidth of the receiver o Components not scaling w/ bit
rate
Rx nonlinearity
Optical Coupling
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Noise
PAM-4 Waveform
Source Driver
VCSEL
TIA
PIN
PAM-4 Receiver
Tx Relative Intensity Noise (RIN)
o Random amplitude fluctuations at the output of VCSEL
Fiber Mode partition noise (MPN)
o Different delay values for different modes resulting in timing jitter
Modal noise (MN) o Different fiber modes have
different attenuation (fiber DMA or connectors) resulting in amplitude noise
Rx Receiver noise
o Thermal noise o Shot noise
All noise is evaluated at the receiver
Jitter o Clock recovery
MMF
Optical Coupling
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End-to-end MMF-VCSEL Physical link model
Complete link model including computation of fibers mode profiles and group velocities, coupling optics, RIN and MPN Transmits bit stream and counts errors Cj(λi): Coupling coefficient of ith VCSEL mode into jth fiber mode group δτj(λi): Modal and Chromatic Delays of jth fiber mode group with wavelength λi
15 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
MMF Optical Link Simulation Model
MPN factor kmpn
Random variables generated:
{a1(λ1), a2(λ2), a3(λ3),…} (∑ 𝑎𝑖𝑛
𝑖=1 = 1)
x
λ1 λ2 λn
a1(λ1)
I1(r), λ1
an(λn)
MM VCSEL
RIN
time
VCSEL output (No RIN)
time
VCSEL output (with RIN)
Fiber illuminating lens assembly
In(r), λn x
MMF Model C1(λ1), δτ1(λ1)
CK(λ1), δτK(λ1)
GT MMF Mode Solver
GT MMF Mode Solver
C1(λ1), δτ1(λn)
CK(λ1), δτK(λn)
Order of mode {l, m}, Mode field radius (MFR)
Order of mode {l, m}, Mode field radius (MFR)
VCSEL Spectrum
I1(r), λ1
In(r), λn
(1xK)
(1xK)
Collection lens assembly
K. Balemarthy, et al., J. Lightwave Technol., V24, pp4885-4894, 2006.
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End-to-end link analytic model: Overview
Analytic model calculates BER directly from 𝑄 factor:
𝑸 =𝑹𝑷𝒐𝒐𝒐
𝝈𝑹𝑹𝟐 + 𝑹𝒓𝒐𝒎𝒎𝑷𝒐𝒐𝒐
𝟐 𝑬𝑹𝑬𝑹 − 𝟏
𝟐+ 𝑹𝒓𝑹𝑹𝑹𝑷𝒐𝒐𝒐
𝟐 𝑬𝑹𝑬𝑹 − 𝟏
𝟐+ 𝝈𝑹𝑹
𝟐 + 𝑹𝒓𝒐𝒎𝒎𝑷𝒐𝒐𝒐𝟐 𝑬𝑹𝑬𝑹 − 𝟏
𝟐+ 𝑹𝒓𝑹𝑹𝑹𝑷𝒐𝒐𝒐
𝟐 𝟏𝑬𝑹 − 𝟏
𝟐
𝑬𝑹: Extinction Ratio (linear units)
𝒓𝑹𝑹𝑹: Normalized std dev. due to RIN {𝑟𝑅𝑅𝑅 = Δ𝑓 ∗ 10(𝑅𝑅𝑅𝑑𝑑/𝐻𝐻10 )}
𝒓𝒐𝒎𝒎: Normalized std dev. due to MPN 2 {𝑟𝑚𝑚𝑚 = 𝑘2
(1 − 𝑒−𝜋𝜋𝜋𝜋σλ2)}
𝑷𝒐𝒐𝒐: Optical Power OMA reduced by ISI eye closure (Watts)
Extended to PAM-4 Noise variances equivalent to the IEEE 802.3bm link budget model
𝑸 =𝑹𝑷𝒐𝒐𝒐𝝈𝟏 + 𝝈𝟎
𝝈𝑹𝑹: Receiver noise std. dev. in Amps (Thermal, Shot etc.,) 𝑹: Responsivity of photodiode (A/W)
𝑷𝒐𝒐𝒐 includes all ISI effects: Laser and receiver bandwidths Chromatic Dispersion (CD) Modal Dispersion (DMD) Baseline wander (BLW) Any additional ISI causing effects
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 16
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12.5 Gbps (6.25 GBaud), PRBS7 Tx with 3-tap FFE
PAM-4 at Rx
Simulated Tx Waveform to AWG
Compare simulation with measurement
Keysight ADS 2016.01 Channel Simulation Tx Rx
DUT
AWG Tx with FFE PAM-4 at DCA Rx
AWG
QSFP28 3m DUT
PAM-4 Test and Measurement
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ADS PAM-4 Channel Simulator DesignCon 2016 Keysight Technologies
17
Slide courtesy Keith Owens, Keysight
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Simulation Model - Analytic Model
Link Parameters Tx
10Gbit/s, PRBS-7, ER=3.5dB, RIN=-133dB/Hz
Δλrms ~ 0.55nm, λ0 ~ 849nm Inset depicts simulated Gaussian
VCSEL spectrum
Fiber D = -117ps/(nm.km); EMBc~10GHz.km Ogawa - Agarwal MPN model
Rx NF = 4dB BWRx = 34GHz Responsivity = 0.4A/W Tx filter LCF = 40KHz (for BLW effect)
Simulation results match very well with IEEE based analytic model results at 10Gbit/s
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 18
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25Gbit/s: Simulation Model - Analytic Model(No MPN)
25Gbit/s PRBS-7, ER = 4.5dB,
RIN = -140dB/Hz
D=-117ps/(nm.km); EMBc~6GHz.km
Δλrms ~ 0.45nm, λ0 ~ 849nm
No MPN
Receiver specifications used NF = 4dB
Temp = 300K BWrx = 28GHz Responsivity = 0.38A/W
L-MMF performs 0.5dB better than the R-MMF: MCDI impact is noticeable at 25Gbit/s
IEEE 802.3 based analytic model slightly overestimates the fiber ISI penalty
Performance depends on the exact alpha profile of the fiber used
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0
5
10
15
20
25
30
35
1991 1996 2001 2006 2011 2016
Ban
dwid
th (G
Hz)
Year
VCSEL Bandwidth Evolution
21
Chalmers, Tokyo Inst. of Technol.
Chalmers
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Volume Manufacturing of High-Speed VCSELs
22 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
Volume Manufacturing of 25-28Gb/s VCSELs has been enabled by developing a robust InGaAs QW based process
High Bandwidth VCSELs with well behaved frequency response are essential to generate quality PAM-4 waveforms
Figure Courtesy Laura Giovane, Avago
Tu3D.5. High Speed Transmitters (5:30pm) Volume Manufacturable High speed 850nm VCSEL for 100G Ethernet and Beyond Laura Giovane; Jingyi Wang; MV Ramana Murty; Ann Lehman Harren; Hsu-Hao Chang; Charlie Wang; David Hui; Zheng-Wen Feng; Thomas Fanning; Aaditya Sridhara; Sumitro-Joyo Taslim; Jason Ch
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1D VCSEL Rate Equations
1D VCSEL model Coupled carrier and photon rate equations
Can be modified to include polarization effects Requires electric field rather than power
Can be modified to support transverse modes Requires a 2D model to support spatial overlaps
See “A Simple Rate-Equation-Based Thermal VCSEL Model” by P.V Mena for example rate equations
VCSEL nonlinearities Significant overshoot and ringing Not often measured experimentally
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 23
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1D VCSEL Rate Equations
Fabry-Perot lasers exhibit large ringing consistent with 1D rate equations
Measured Transients of 25G 850nm VCSEL
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
Application Note: Modulating VCSELs – Finisar, 2007
Multiple transverse modes give rise to extra features in the power transients
1D VCSEL rate equations do not capture the full effects of VCSELs at 25G
24
2D Laser Model with Multiple Transverse Modes are needed to simulate VCSEL more accurately
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Amplitude and Timing Penalty
25 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
Amplitude Penalty HPAM4 ≅
13*HOOK
PAM-M amplitude penalty = M-1 PAM-4 eye closure penalty ~ 4.77 dB
compared to OOK Optical sensitivity penalty may be less
due to the reduced electrical bandwidth
Timing Penalty Expect: WPAM4 ≈2*WOOK
Observe: WPAM4 < 2*WOOK
Reason: 12TPAM4< WPAM4 <
23TPAM4
Additional transitions narrow eye width: 8 (OOK), 64 (PAM 4)
y
TOOK
WOOK
HOOK
TPAM4
Time (s)
y
-2
2
Time (s)2.04e-9 2.1975e-9
S1
WPAM4
HPAM4
Timing Penalty Cannot be Dismissed
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Transmitter Signal Quality
Generating and maintaining high quality PAM-4 signals Electrical noise figure Impedance mismatch: Driver-VCSEL VCSEL nonlinearities
26 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
25.78 Gbaud
No pre-emphasis With pre-emphasis
Q-Factor ~ 9.5 Q-Factor ~ 8.7
Vmax,pp= ~600mV
PAM-4 Waveform
Source Driver
VCSEL
Electrical Optical
Pre-emphasis is essential
Tu2G.4.pdf OFC 2016 © OSA 2016
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27 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
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Fiber: Short Wavelength Regime
Fiber loss o Ethernet standard is <3.5 dB/km @
850nm o Typical is <2.5 dB/km @850nm
Dispersion
o ~100 ps/nm-km @850nm o Prior to 25G symbol rates, dispersion
in the 850 regime has not been a significant impairment
Chromatic dispersion limited reach o Source limited spectral content o ∆λ~ 0.4nm RMS o @850nm 0.1nm = 37GHz
28 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
Chromatic Dispersion is a primary impairment for symbol rates >10Gbps
760 800 840 880 920 960 1000 1040 1080-160
-140
-120
-100
-80
-60
-40
-20
0
Atte
nuat
ion
[dB/
km]
Ethe
rnet
Disp
ersio
n [p
s/nm
-km
]
Wavelength [nm]
0
1
2
3
4
5
6
Typical
IEEE standard
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Modal Dispersion in Graded Index MMF
Effective Modal Bandwidth – Calculated (EMBc) Standardized VCSEL flux distributions weight a sum of DMD impulse responses Method standardized by the Telecommunications Industry Association (TIA)
10 VCSEL Radial power distributions
Measured Fiber DMD
-3dB
f
H
f3dB Impulse Response
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 29
FOTP-220 Differential Mode Delay Measurement of Multimode Fiber in the Time Domain”, TIA-455-220-A, Jan. 2003.
MMF
Differential Modal Delay (DMD) Measure impulse response for a range of launch offset conditions DMD metric: delay between 25% of trailing edge of slowest pulse
and 25% of leading edge of fastest pulse
SMF
EMBc = worst case f3dB
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Differential Mode Delay (DMD)
Current MMF manufacturing techniques allow precise control of the index profile yielding near optimum profile and excellent DMD
Fiber Type
Wavelength (nm)
Max Loss (dB/km)
Minimum Bandwidth
(MHz-km)
OFL EMBc
62.5µm (OM1)
850 1300
3.5 1.5
200 500
-
50µm (OM2)
850 1300
3.5 1.5
500 500
-
50µm (OM3)
850 1300
3.5 1.5
1500 500
2000
50µm (OM4)
850 1300
3.5 1.5
3500 500
4700
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 30
Evaluate link performance on multiple examples of the same class of fiber
DMD=22ps
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Impact of DMD
51.56Gbs PAM-4 OM4 100m With Pre emphasis 3 Tap T-spaced
FFE
DMD results in measurable penalty
10 GHz-km: ISI penalty ~1.5dB 6 GHz-km:, ISI penalty ~1.9dB
S. Kota Pavan et. al., ECOC Cannes, France
Sept. 22-25, 2014
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 31
Inherent back-to-back penalty arises primarily from impedance mismatch between driver and laser For unpackaged devices it is best to compare results against back-to-back
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Mode Spectral Bias
VCSEL transverse modes have increasing power away from center
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 32
Mode Spectral Bias Longer wavelengths couple predominantly to lower order
fiber modes
Transverse modes have decreasing wavelength with increase mode
VCSEL modes couple to MMF modes with similar mode spatial patterns: higher VCSEL modes couple to higher fiber modes
Two polarizations each
LP01
LP11
LP02
LP21
LP31
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Modal and Chromatic Dispersion Interaction (MCDI)
Ideal GI fiber profiles α = αopt Least delay between lowest and highest order modes Performs best in the absence of CD
L-MMF (over-compensated) α < αopt Higher order modes arrive before lower order modes Compensates for CD (Since higher-order VCSEL modes
couple mostly into higher-order fiber modes) Performs the best in presence of CD
R-MMF (under-compensated) α > αopt Higher order modes arrive after lower order modes Performs the worst in presence of CD
MCDI: Chromatic dispersion (λ<1300nm) always results in delays for
the shorter λ (lowest-order modes) with respect to longer λ (higher-order modes)
CD and hence interaction depends on VCSEL spectral content
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 33
CD and DMD effects may either add or subtract
L-MMF
R-MMF
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Left and Right Fiber
All EMBc is Not Equal
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 34
EMBc GHz-km
DMD slope
ISI penalty
4.8 L 2.3
5.6 R 2.4
6.0 N 1.9
10.0 N 1.5
Left Sloped DMD compensates CD
51.56Gbs PAM-4 OM4 100m With Pre emphasis 3 Tap T-spaced FFE
S. K. Pavan, J. Lavrencik, S.E. Ralph, "Experimental demonstration of 51.56 Gbit/s PAM-4 at 905nm and impact of level dependent RIN," in Optical Communication (ECOC), 21-25 Sept. 2014
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OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 35
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PAM-4 and RIN
Effect of RIN Imposes power penalty at lower power Results in BER floor
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
Captures all laser intensity noise Fundamental Spontaneous emission Shot noise Mixing of spontaneous emission with
the lasing field Environmental Electrical noise Back reflections Vibrations
Varies with Bias i.e. laser power Frequency
Strongly connected with MPN
RIN parameter Simulation Parameters Ith = 2.2x10-6Amp; Responsivity = 0.4A/W Extinction Ratio (ER) = 6dB 25.78 Gbaud
2
210 log /avg s
RIN dB HzP fσ
=
Effective RIN should be <140 dB/Hz 36
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Relative Intensity Noise (RIN)-Bias Dependence
RIN exhibits strong bias and frequency dependence
RIN penalty (IEEE)
𝑃𝑅𝑅𝑅 = 10 log 1
1− 𝑄∙𝜎𝑅𝑅𝑅𝑅𝐼𝑅𝑟
2
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 37
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L-I-RIN
Increasing output power decreases average RIN RIN decreases by ~ 2 dB/Hz per 1mA Relaxation oscillation freq and hence modulation bandwidth also increase with
power
IEEE model currently uses single fixed RIN Proper Effective RIN allows good predictions for OOK Effective RIN for PAM-4, presumes unequal levels and may have unknown
cross terms
Average RIN vs bias
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 38
S. K. Pavan, J. Lavrencik, S.E. Ralph, "Experimental demonstration of 51.56 Gbit/s PAM-4 at 905nm and impact of level dependent RIN," in Optical Communication (ECOC), 21-25 Sept. 2014
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Variable RIN for PAM-4, 50Gbit/s
Using separately measured RIN for each PAM-4 level yields better modeling than use of average fixed RIN which under estimates RIN penalty Back-to-back (btb): ~0.5dB OM4: 0.6dB Higher RIN yields larger discrepancy
OM4 (10 GHz-km), 100m: ISI penalty ~1.5dB
RIN is not a fixed parameter
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 39
S. K. Pavan, J. Lavrencik, S.E. Ralph, "Experimental demonstration of 51.56 Gbit/s PAM-4 at 905nm and impact of level dependent RIN," in Optical Communication (ECOC), 21-25 Sept. 2014
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OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 40
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Mode Partition Noise and Modal Noise
Mode partition noise Time-varying mode power distribution
of laser sources Differential path delay
VCSEL mode power fluctuates among different modes which couple to different fiber modes
MPN is phase jitter, appearing as amplitude noise, due to variation in group velocities for each VCSEL mode group
Modal noise Time-varying mode power distribution in optical sources
and mode selective losses in the link High-speed VCSELS (>10Gbps)
may exhibit chaotic behavior Differential path attenuation Combination of VCSEL mode power fluctuation and mode
selective losses in the link
Fraction of power reaching receiver is time dependent
Arrival time of energy is dependent on current
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 41
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Mode Partition Noise
The delay among the VCSEL spectra is Where D = dispersion, L = fiber length Typical value is 5ps for 100m and 0.5nm rms
Relating this to an amplitude noise requires many assumptions
Basic Idea of Ogawa-Agrawal model used in IEEE 802.3 standards
Modes are strictly anti-correlated
Developed for FP lasers with longitudinal modes that share the same gain region Not appropriate for VCSELs with multiple transverse modes
RMSD Lτ λ∆ = ⋅ ⋅ ∆
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 42
If one mode experiences an increase in power, the other modes decrease in power
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MPN: Ogawa - Agrawal
Ogawa-Agrawal model assumptions: (1) No RIN: ∑ ai
Ni=1 = 1 (assumes RIN and MPN are separable)
(2) Any two modes exhibit the same constant correlation
Covariance is strictly negative: a decrease in one mode is exacly balanced by increases in other modes
Covariance varies between 0 and -1 γcc varies between 1 and 0, 1=>no variation
(3) MPD ai is constant for entire bit duration
Using the IEEE model, we determine a kmpn from mode noise
measurements using these assumptions, which we use to calculate an MPN penalty in end-to-end models
43 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
,covariance1 = for all i jγ
−− = ≠i j i j i j
cci j i j
a a a a
a a a a
Strongly constrains fluctuation statistics of the VCSEL modes
Not true for VCSEL transverse modes
Not true in general
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MPN
The variance of the ith mode is
Noise variance can be determined, using additional assumptions of the IEEE modeling efforts Raised cosine pulse shape at receiver Temporal delay results exclusively from CD i.e. single mode fiber Continuous Gaussian spectrum
The amplitude variance is approximately given by
kmpn is a scaling metric that depends on the specific power variation and correlations among the VCSEL modes
Calculated heuristically var(ai) = k𝟐mpn(< ai> −< ai > 2)
var(ai) = (1 −𝛾cc)(< ai> −< ai > 2)
22 2
2 12
λπ σ− = − mpn BLD
mpn
kr e
B = bit rate L = transmission length D = Dispersion σλ = rms spectral width
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 44
Exponential Increase with Fiber length Dispersion Baudrate
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Mode Partition Noise Penalty
-10 -5 014131211109 8 7
6
5
4
3
2
Pave(dBm)
-log(
BER
)
BER Vs Rx Power
Rx Thermal Limit0m25m50m75m100m
Kmpn = 0.3
Impact of MPN Creates noise floor Imposes significant power penalty
-10 -5 014131211109 8 7
6
5
4
3
2
Pave(dBm)
-log(
BER
)
BER Vs Rx Power
Rx Thermal Limit0m25m50m75m100m125m150m
Kmpn = 0.1
IEEE standards require link performance with KMPN = 0.3
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 45
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MPN Limited Reach
MPN is a limiting penalty for VCSEL-MMF links Kmpn = 0.3 limits PAM 4 links to <100m 25G VCSELs are better than IEEE assumptions
Figure Courtesy David Cunningham, Avago
Kmpn=0.3, with 3 Tap T spaced FFE OM4 fiber @ 850nm
Isolated MPN penalty OM4 fiber @ 850nm
Realistic Assessment of VCSEL MPN is Needed
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 46
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Direct Assessment of kMPN
Directly measure mode correlations real-time 1) MMF efficiently coupled into spectrometer: matched f/# 2) Grating spatially separates mode sets Grating chosen to minimize polarization sensitivity 3) Modes spatially separated and individually collimated
RF cable VCSEL Lensed Fiber
probe Bias-tee SHF 12124A 30G
BPG
Spectrometer Triax 550
+5.00 dBm
1.40 dBm
SHF 827
1
2 3
Mirror MMF
Shorter λ
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 48
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Direct Assessment of kMPN
Inphi TIA
SHF 807
50Ω Termination
Inphi TIA
LeCroy Real-Time Scope
SHF 807
50Ω Termination
LeCroy Real-Time Scope
GaTech Custom InGaAs MMF Receivers
28GHz BW Top-Illuminated PDs 20μm diameter
Lensed fiber
Lensed fiber
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 49
Filtering VCSEL spatial modes retains all spectral components
Unfiltered VCSEL spectrum (black) Individual filtered mode sets (colors)
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kmpn
Mode separation enables the direct assessment of the variance and power of each mode and the covariance between each mode pair
Continuing with the Ogawa-Agrawal theory we can determine kmpn with two methods:
Two-mode correlation Single mode variance
𝑘𝑚𝑚𝑛 𝜏 = −𝑅𝑖𝑖 𝜏𝜎𝑖𝜎𝑗𝑎𝑖 𝑎𝑗
= 1 − 𝛾𝑐𝑐 𝑘𝑚𝑚𝑛 = ( 𝑎𝑖2 − 𝑎𝑖 2)( 𝑎𝑖 − 𝑎𝑖 2)
where, 𝑅𝑖𝑖 𝜏 =𝑎𝑖(𝑡)𝑎𝑗(𝑡+𝜏) − 𝑎𝑖 𝑎𝑗
𝜎𝑖𝜎𝑗=
𝑐𝑐𝑐𝑖𝑗(𝜏)𝜎𝑖𝜎𝑗
Where kmpn is now in terms of the measured parameters
If the assumptions of the Ogawa-Agarwal model hold, specifically assumption (2),
then these two methods will yield the same results
Reference: J. Lavrencik, et al., "Direct Measurement of Transverse Mode Correlation and MPN using 900nm VCSELs," Optical Fiber Communication Conference, paper W2A.55, 2015.
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 50
The covariance and kmpn depend on the relative delay between the VCSEL modes
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Kmpn for Modulated Signals
Partial spectral filtering significantly increases kmpn VCSEL modes are mode sets
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 51
Critical to capture entire VCSEL spectra
Single mode determination of kmpn allows evaluation of modulated signals
Mode 2: Average kmpn ~ 0.06
Pattern: 0011011000100111 8mA bias
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Directly Measured kmpn
Measured kmpn consistently < 0.1 For both static and modulated
VCSELs
Single mode method and two mode method yield similar but not identical results Demonstrates limits of Ogawa-
Agarwal model
kmpn is not a fixed parameter
Unmodulated signals
Two-Mode Correlation
Single Mode Variance
VCSEL Mode Pairs kmpn Mode kmpn
3.5mA 1,2 0.042 1 0.045 2,3 0.047 2 0.04 - - 3 0.034
8mA 1,2 0.053 1 0.022 2,3 0.039 2 0.059 - - 3 0.043
10mA
1,2 0.035 1 0.031 2,3 0.015 2 0.029 3,4 0.018 3 0.016 - 4 0.012
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 52
Reference: J. Lavrencik, et al., "Direct Measurement of Transverse Mode Correlation and MPN using 900nm VCSELs," Optical Fiber Communication Conference, paper W2A.55, 2015.
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Direct Measurement of Mode Correlation
Cross correlation Rij versus delay Modes are correlated for less than ~500ps Longer than symbol duration Maybe shorter than delay due to dispersion
Adjacent mode pairs strongly anti-correlated Mode pair 1, 3 is positively correlation Contradicts Ogawa-Agarwal model assumptions
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
Reference: J. Lavrencik, et al., "Direct Measurement of Transverse Mode Correlation and MPN using 900nm VCSELs," Optical Fiber Communication Conference, paper W2A.55, 2015.
54
𝑅𝑖𝑖(𝜏) =𝑃𝑖(𝑡)𝑃𝑖(𝑡 + 𝜏) − 𝑃𝑖 𝑃𝑖
𝜎𝑖𝜎𝑖
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RIN Enhancement Through Fiber
The aggregate RIN depends on the degree of correlation among VCSEL modes at the receiver Received RIN depends on the measured variances and cross-correlations and
hence delay τ: The RIN coefficient RIN[dB/Hz] is
10𝑅𝑅𝑅 [𝑑𝜋 𝐻𝐻]⁄
10 ∙ ∆𝑓 = �𝜎𝑎𝑖2
𝑅
𝑖=1
+ ��𝜎𝑎𝑖𝜎𝑎𝑗𝑅𝑖𝑖𝑖≠𝑖
𝜏
where 𝜎𝑎𝑖
2 is the variance of mode i normalized to the mode power, ∑ 𝑎𝑖 = 1 The lasing transverse modes are orthogonal to each other Noise variance is measured over bandwidth ∆f which is limited by the receiver The noise is white and Gaussian
J. Lavrencik, et al., "Direct Measurement of Transverse Mode Correlation and Fiber-Enhanced RIN through MMF using 850nm VCSELs," Optical Fiber Communication Conference, 2016. Th3G.1
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 55
22
2
σσ =i
ia
ia
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RIN Enhancement Through Fiber
Fiber dispersion increases the received RIN regardless of modulation by reducing the cross-correlations between modes, e.g.
lim𝑅𝑖𝑗→0,
��𝜎𝑖𝜎𝑖𝑅𝑖𝑖𝑖≠𝑖
𝜏 = 0
The effect is observed as a higher RIN induced noise floor in R-MMF fiber which exhibits larger total dispersion compared to L-MMF
(a) Measured RIN Parameter of back-to-back vs.100m MMF; (b) 34 Gbps OOK link BER analytic model vs. experiment; (c) Eye diagrams of 100m L-MMF and 100m R-MMF
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 56
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57 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
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MPN: New Model
Mode fluctuation statistics completely described by a single Covariance matrix:
COV ai =
var1 cov12 . .
cov1Mcov21
var2 . . cov2M
.
.covM1
covM2 . . varM
where vari = <ai2> − <ai>2 and covij = <aiaj> − <ai><aj>
For instance, ∑ aiMi=1 ≠ 1 though Σ<ai> = 1
Captures both RIN and MPN while retaining their independence
Composite power fluctuations measured as RIN Correlation in fluctuations define extent of MPN
We derive vari and covij from the VCSEL physical dynamics
Formalism explicitly allows for both positive and negative cross−correlations
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 58
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Closed-Form Expressions for VCSEL Mode Correlations: Time Domain
Equivalent time-domain expressions VCSEL-specific parameters 𝜶, 𝜞𝒎, and 𝒌𝒎 defined over the measurement bandwidth
Composite RIN for the VCSEL derived as
Variance due to MPN derived as
rik is the normalized received waveform at the optimum sampling instance
𝑣𝑎𝑟𝑖 = 𝜶𝟐 ai�
cov𝑖𝑖 = ai�aj� 𝜞𝒎𝟐 − 𝐶𝑖𝑖𝑖𝒌𝒎𝟐
𝑅𝑅𝑅𝑐𝑐𝑚𝑚,𝑎𝑐𝑖 =1
2𝜋Δ𝑓� vari
𝑀
𝑖=1
+ �� covij
𝑀
𝑖≠𝑖
σMPN2 = 𝛂2 ∑ rik2 − 1 a𝑖� M
i=1 + ∑∑ {rikrjk𝑖≠𝑖 − 1} {𝜞𝒎𝟐 − 𝒌𝒎𝟐𝐶𝑖𝑖𝑖}a𝑖� a𝑖�
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 59
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Simulation Results: Individual Mode RIN and CSD
Average RIN in a single VCSEL mode, 𝑹𝑹𝑹𝒊,𝒐𝒂𝒂 vs. 𝑨i 𝑴
Average Cross spectral density, 𝑹𝑹𝑹𝒊𝒊,𝒐𝒂𝒂vs.𝑪𝒊𝒊𝒂
Cross-correlation coefficient, 𝑹𝒊𝒊(𝟎) vs.𝑪𝒊𝒊𝒂
(a): 𝑅𝑅𝑅𝑖 ω� =𝑣𝑎𝑟𝑖 ω�
ai�2
(b): 𝑅𝑅𝑅𝑖𝑖 ω� =cov𝑖𝑖 ω�
ai� aj�
(c): Rij(τ = 0) = 𝑐𝑐𝑐𝑖𝑗 0𝑐𝑎𝑣𝑖(0)𝑐𝑎𝑣𝑗(0)
(a)
(b)
(c)
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 60
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Features of the new MPN model
Robust and accurate Allows for a customized COV matrix that is measured directly for a VCSEL Can be readily included in the IEEE spreadsheet model Representation of RIN and MPN requires 3 VCSEL-specific parameters
New MPN model includes VCSEL relevant features not found in the standard O-A model VCSEL mode correlation statistics depend on the spatial overlap integral 𝑪𝒊𝒊𝒂 Mode pairs may have positive cross-correlations
Direct measurements on mode fluctuations of VCSELs validate the new model
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 61
S. K. Pavan, J. Lavrencik, S.E. Ralph, “New Model for Mode Partition Noise in VCSEL-MMF Links Based on Langevin-driven Spatio-Temporal Rate Equations,” Submitted to JLT
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Comparison with OOK modulation
Measured sensitivity at BER=10-12 , theoretical sensitivity at BER=10-9
and measured sensitivity at BER=1.8 × 10-4 , with data rates reduced by the 7% FEC overhead, measured using 100 m of fiber
K. Szczerba, P. Westbergh, E. Agrell, M. Karlsson, P. A. Andrekson, and A. Larsson, "Comparison of Intersymbol Interference Power Penalties for OOK and 4-PAM in Short-Range Optical Links," in Lightwave Technology, Journal of , vol. 31, no. 22, pp. 3525-3534, Nov.15, 2013
16 GHz VCSEL 100 m OM4 fiber Photoreceiver with 10 GHz -3dB
bandwidth
At higher bit rates the sensitivity of PAM 4 is better than OOK
The cross over is due to limited link bandwidth
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 63
Tu2G.4.pdf OFC 2016 © OSA 2016
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80 Gbps PAM-4
64
80 Gb/s over 3 m of OM4 Separate coding for LSB and
MSB Effective bit rate of 70 Gb/s
Offline 5 tap FIR equalization Component bandwidths
VCSEL: 25 GHz Photoreceiver: 22 GHz
K. Szczerba, P. Westbergh, M. Karlsson, P. A. Andrekson, and A. Larsson., "70 Gbps 4-PAM and 56 Gbps 8-PAM Using an 850 nm VCSEL," in Lightwave Technology, Journal of , vol. 33, no. 7, pp. 1395-1401, April1, 2015
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
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PAM-4: 850nm @51.56Gbps
Error-free performance demonstrated for variety of 100m OM4 fibers
Near error free demonstrated for OM3 Pre-emphasis required ISI penalties with pre-emphasis
All fibers 100m OM4 fibers ~ 0.8dB OM3 fibers ~ 1.4 to 2.2dB
No measurable influence of MPN Noise/ISI metrics in analytic model
Noise Eq Curr Ith = 2.2x10-6Amp Responsivity = 0.3A/W Extinction Ratio (ER)
6dB RIN < -150dB/Hz
PAM-4 ISI penalties: OM4 fibers ~ 0.8dB
OM3-1 ~ 1.4dB, OM3-2 ~ 2.2dB OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 65
Tu2G.4.pdf OFC 2016 © OSA 2016
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VCSEL Data Rates
66 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
IBM OOK 71Gb/s, 7m 64Gb/s, 57m 62Gb/s, 7m
Chalmers PAM-4 70Gb/s, btb Offline equalization
OFS PAM-4 51.56Gb/s, 150m, 850 nm
Georgia Tech PAM-4 51.56Gb/s,100m
IBM Chalmers
IBM OFS
PAM-4 w/DSP
850nm OOK w/DSP
850nm OOK w/o DSP
GT 880nm-1100nm w/DSP
GT
IBM OOK 71Gb/s, 7m 64Gb/s, 57m 62Gb/s, 7m
Chalmers PAM-4 70Gb/s, btb Offline equalization
OFS PAM-4 51.56Gb/s, 150m 850nm-940nm CWDM four λ @ 51Gbps each
Georgia Tech PAM-4 51.56 Gb/s, 100m 50Gb/s, 200m 62 Gb/s, 100m
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VCSEL MMF links: Speed vs. Reach
Filled markers indicate error-free performance achieved without FEC correction
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 67
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OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 68
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Wideband MMF
OM4 performance is possible over a wide range of wavelengths
Standard graded index MMF is not wideband due to wavelength dependence of index and dispersion n = n(λ) |dn/dλ| >0
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 69
Figure Courtesy Y. Sun, OFS
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WDM in Wideband MMF
70
51.56 Gb/s per wavelength, 4 channels, 150 m fiber BER below the KP4 FEC threshold (2 ×10-4)
Without linear equalization With linear equalization (4 taps and 1 precursor)
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
Figure Courtesy Y. Sun, OFS
Y. Sun, R. Lingle, R. Shubochkin1, K. Balemarthy, D. Braganza, T. Gray, W. J. Fan, K. Wade, D. Gazula, and J. Tatum, "51.56 Gb/s SWDM PAM4 Transmission over Next Generation Wide Band Multimode Optical Fiber, " Optical Fiber Communications Conference, Tuesday, 22nd March, 2:45pm-3pm
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50Gbps 1060nm PAM-4
Wideband fiber capacity Robust error free performance beyond 150m Beyond 300m with low latency FEC
“wideband”
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 71
IBM has demonstrated 1530 nm VCSELs at 56 Gb/s OOK ECOC 2015 PDP Figure courtesy Dan Kuchta, IBM
S. K. Pavan, J. Lavrencik, R. Shubochkin, Y. Sun, J. Kim, D. Vaidya, R. Lingle, T. Kise, and S.E. Ralph, "50Gbit/s PAM-4 MMF transmission using 1060nm VCSELs with reach beyond 200m," in Optical Fiber Communications Conference and Exhibition (OFC), 2014, 9-13 Mar. 2014
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PAM-4, 50Gbit/s at 1060nm: OM3 and OM4
72
OM3, 100m 2.86 GHz-km: ISI penalty ~2.1dB 2.05 GHz-km: ISI penalty ~2.6dB
OM3, 200m
2.86GHz-kmz: ISI penalty ~4.2dB
OM3, 150m
2.05GHz-km: ISI penalty ~4.2dB
OM4, 100m 5.6 GHz-km: ISI penalty ~0.8dB 10 GHz-km: ISI penalty ~0.8dB
Noise/ISI metrics RIN < -150dB/Hz MPN k < 0.1
ISI penalties 100m OM3 (2.86GHz-km) ~ 2.1dB
100m OM4 ~ 0.8dB
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
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PAM-4, > 31GBaud, 1060nm: Wideband Fiber
31GBd btb ISI penalty ~1.5dB
31GBd 100m ISI penalty ~2.2dB
33GBd btb ISI penalty ~2.2dB
Noise/ISI metrics RIN < -150dB/Hz kmpn < 0.1
~ 1. 5dB
~ 2.2dB
OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph 73
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Summary
Components and test/measurement tools are available to support wide deployment of VCSEL-MMF based links employing PAM-4 signaling High capacity, low power, SiCMOS transceivers with digital and analog filtering High speed VCSELs Low DMD OM4 fiber
MPN of current generation InGaAs based VCSELs exhibit low noise so that MPN is not a limitation up to and beyond 100m High bandwidth low RIN VCSELs are moving to large scale production
Multimode VCSEL-based technology (850-1100 nm) will likely continue to be the lowest cost and lowest power solution for short reach links
PAM-4 modulation allows links to maintain reach to 100m and beyond
Wideband MMF together with PAM-4 modulation enables deployment of short wavelength WDM systems that support 400G and higher connections
74 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
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GaTech Terabit Optical Networking Group
75 OFC 2016 Tutorial - PAM-4 and VCSEL MMF Links S. E. Ralph
Back Row: Siddharth Varughese, Pierre Isautier, Jerrod Langston, Edward Tan, Justin Lavrencik Front Row: Mike Pratt, Antony Thomas, Stephen Ralph, Aliro Melgar
Thanks to my team at GaTech