Polarisation Mode Dispersion in Highspeed Transmission Systems

1
Polarisation Mode Dispersionin High-speed
Transmission Systems

• Michael Cahill

2
Presentation Overview

• Origins of PMD
• why PMD is a problem for high-speed systems
• descriptions of first order (PMD1) and higher
  order (e.g. PMD2)
• influence of environment of PMD evolution
• System degradation due to PMD
• analyse impact of PMD1 only, as well as all PMD
  orders
• PMD Compensation
• PMD1 compensation and its limitations
• techniques for high-order compensation
• experimental demonstrations of high-speed
  transmission with compensation

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Pulse Dispersion in Optical Fibre

• Minimise all forms of pulse dispersion to
  maximise rate of signal transmission through
  fibre
• History of dispersion minimisation in optical
  fibre systems
• modal dispersion è singlemode fibre
• chromatic dispersion è non-zero dispersion
  shifted fibre and dispersion compensating fibre
• polarisation mode dispersion (PMD) è ?
• PMD exhibits fundamental differences to other
  system impairments (like chromatic dispersion,
  Kerr effect) since it is stochastic by nature
• varies with optical frequency and time
• difficult to minimise, since compensation
  (probably) needs to be active

4
Polarisation Mode Dispersion

• PMD originates from the inherent weak
  birefringence in optical fibres(due to core
  ellipticity, fibre stresses due to manufacturing
  or layout)
• Origins can be understood through analogy with
  birefringent crystals 1,2
• consider a weakly birefringent telecom fibre as a
  concatenation of many randomly orientated
  birefringent waveplates
• Distribution of optical energy from each axis of
  one waveplate into some combination of the axes
  of the next - mode coupling

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Polarisation Sensitivity ofLight Transmission
Through Fibre

• Light emerging from the fibre is the
  superposition of pulses split between the fast
  and slow axes of each of the waveplates, and its
  temporal characteristics are highly
  wavelength-dependent
• However, there exist orthogonal input states of
  polarisation (SOPs) for which the output states
  are orthogonal and wavelength independent 2-
  principle states of polarisation (PSPs)
• Propagation delay difference, , between
  light propagation along these PSPs - differential
  group delay (DGD) - modelled as Maxwellian distr.
  3
• Light injected into the fibre can then be
  considered as a superposition of energy between
  the two input PSPs
• to 1st order, not true when there is
  polarisation-dependent loss (PDL) 4

6
Polarisation-induced Group Delay

• When pulsed light is launched in both PSPs, to
  1st order, the output is a linear superposition
  of 2 orthogonal pulses 2
• delay between pulses equal to the DGD
• power of each pulse dependent on the input
  polarisation
• average DGD over frequency range referred to as
  1st order PMD (PMD1)
• Impact on transmission performance
• maximum - equal distribution of energy in each
  input PSP
• minimum - input light aligned to one input PSP

Input PSPs
Output PSPs
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Other Polarisation Effects

• In reality, pulsed light comprises a range of
  frequencies
• DGD is frequency dependent
• PSPs are also frequency dependent
• both are stochastic by nature
• This frequency dependence is referred to as
  higher order PMD 4,5
• increases with increasing PMD1
• 2nd order PMD (PMD2) is most important for
  telecomms applications
• All PMD orders change over time, which makes PMD
  difficult to analyse and minimise
• temperature, acoustic vibrations, splice movement

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Analytical Model for PMD, 1st Order PMD

• PMD can be completely described by the
  polarisation dispersion vector (PDV), ,
  defined as 4-6
• is the DGD at frequency
• is the fast-output PSP at the same
  frequency
• the magnitude of PDV is equal to the DGD, and
  therefore also PMD1 4, i.e.
• Note that at a given time and frequency, the DGD
  can be more ore less than PMD1, since PMD1
  represents the average delay between PSPs

9
2nd Order PMD (I)

• PMD2 represents the frequency-dependence of the
  fibres polarisation dispersion, and is defined
  as 4
• the subscript refers to the functions
  derivative with respect to
• the constant scales the sqrt so that PMD2
  can be expressed in the same units as chromatic
  dispersion (ps/nm)
• The derivative of PDV is also a vector, but now
  has 2 components 4,7

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2nd Order PMD (II)

• Thankfully, the PDV derivative can be explained
  intuitively
• change in DGD with respect to frequency for that
  specific PSP, commonly referred to as
  polarisation-dependent chromatic dispersion (PCD)
  5
• change in PSP with frequency, commonly referred
  to as signal depolarisation
• PMD2 is further enhanced by chromatic dispersion
• PMD2 is sometimes misrepresented as simply
  related to the average derivative of DGD versus
  wavelength, but this is only half true (PCD)
• Depolarisation has been shown, both theoretically
  and experimentally, to dominate over PCD, with a
  ratio of 91 4,6

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2nd Order PMD (III)

• Measured components of PMD2 across 40 nm around
  1560 nm 6
• Orthogonal and parallel values for are
  relative to , so PCD is the parallel comp.
  (dots), whereas depolarisation is the orthogonal
  comp. (thin line), and total PMD2 is solid line
• Depolarisation dominates over PCD, as predicted

12
Dependence of PMD on Fibre Length

• When the length of fibre is much greater than the
  polarisation coupling length (i.e. the length of
  each randomly-orientated waveplate)
• PMD1 increases with the sqrt of the length
• since the arrangement of the waveplates axes is
  random, the increase in the DGD will represent a
  random walk 7
• PMD2 increases linearly with the fibre length
• the DGD slope increases with sqrt(L), more
  frequencies appear as the length increases,
  another sqrt (L), so PCD increases with L 4
• For long lengths of fibre (I.e. strong mode
  coupling), there PMD1 and PMD2 are intrinsically
  related

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Environmental Influences on PMD

• PMD is strongly affected by environmental
  fluctuations, esp. temperature variations and
  fibre vibrations
• PMD sensitivity to temperature is related to the
  fibres location, e.g. PMD for an aerial cable
  8, right, and PMD vs wavelength for 6.5 km of
  lab fibre 1, centre, and 50 km of installed
  fibre (50 km) 1, left
• Note - PMD fluctuations can occur in time
  intervals down to msec 1,9

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System Degradation Due to PMD

• Many early evaluations of PMD-induced degradation
  only considered PMD1, but for higher bit rate
  systems, PMD2 is just as important
• At lower speeds (e.g. 2.5 Gbps), PMD1 dominates,
  resulting in eye closure and time drift 10
• eye closure results in a reduction in Q, and
  hence a power penalty
• time drift, if caused by changes in PMD due to
  temperature fluctuations, can be accomodated by
  the receiver clock recovery cct
• At higher speeds, the average PMD penalty is
  determined by PMD1, but PMD2 causes an additional
  fluctuation of the penalty 11
• a good measure of the impact of PMD2 is
  Pr(outage), where outage is defined as a time
  interval where the BER is above a specified value
  12

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Examples of Pulse Degradation due to PMD

• 40 Gbps transmission through 186 km of fully
  compensated installed fibre 1,13
• PMD1 highlighted by pulse splitting and received
  pulse shape depends heavily on input SOP

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PMD1 Compensation (I)

• A pulse under the influence of PMD1 exists fibre
  in two orthogonal modes (according to the output
  PSPs), differentially delayed by the fibres DGD
• This can be completely compensated by using a
  polarisation-based interferometer, where the
  orthogonal pulses are delayed, with the pulse in
  the fast PSP delayed by the DGD, then recombined
  14,15
• i.e. functionally the same as many PMD1 emulators
• requires active feedback to delay mechanism

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PMD1 Compensation (II)

• PMD1 can be minimised by aligning the input light
  to one PSP 1,13,15 using a polarisation
  controller (PC)
• this minimises polarisation-induced dispersion
  only to 1st order
• requires feedback path from receiver to
  transmitter to track changes in PSP over time
  (unrealistic)
• E.g. 40 Gbps transmissionpreviously mentioned
  1,13
• Residual penalty due tohigher-order PMD
• Performance heavilydependent on accuracyof
  input SOP alignment

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Limitations to PMD1 Compensation

• As more PMD1 compensation is required in a link,
  the more sensitive the system becomes to PMD2,
  since PMD2 is proportional to PMD12
• Numerical calculations used to determine
  Pr(outage), equal to Pr (BER) gt 10-12 in this
  case, for a system with a 2 dB (PMD 0) margin
  14
• Without compensation10 eye closure, mainly due
  toPMD1, can be tolerated
• With compensation40 PMD1 eye closure can
  beremoved, but PMD2 causesBER fluctuation

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Higher-order Dispersion Compensation

• Requires concatenation of DGD fibre sections,
  with polarisation transformers between each
• degree of compensation depends on number of
  sections
• can be realised using a number of techniques
• polarisation controllers located along the
  transmission fibre length 13
• polarisation controllers or waveplates 15-17,
  or ferroelectric liquid crystals 15, located
  between section(s) of polarisation maintaining
  fibre (PMF) before the receiver
• distributed equaliser using PMF-twist sections
  15 before the receiver
• PCs and waveplates may be too slow to compensate
  for some PMD-induced signal fluctuations
• liquid crystals require fibre coupling, and do
  not have proven reliability

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Higher Order Compensation - PCs in Fibre Path

• Experimental set-up similar to the one discussed
  on P17 1,13
• PCs located at fibre input, and mid-span of
  fibre (corresponding to equal amounts of PMD1
  before and after)
• PC2 optimised, then PC1used to align input to
  PSPof complete light path
• Impact of PMD2 is reduced,but not eliminated

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Higher Order Compensation - PMF sectionswith PMD
monitors

• Experimental demonstrations of compensation at 40
  Gbps using PMF sections and polarisation
  transformers, coupled with novel polarisation
  state monitors 15-17
• Detect electrical power of sub-harmonics
• power proportional to sin2(K.fSH.DGD)
• detect a number of sub-harmonics, fSH,for
  unambiguous measure of DGD
• choice of sub-harmonics depend onRZ or NRZ
  waveform (different electrical spectral content)
• example of 40 Gbps NRZ detection 16

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Higher Order Compensation - Distributed Equaliser

• Length of PMF fed through a cascade of fibre
  twisters 25
• minimal insertion loss, since no fibre cuts
  required
• many degrees of freedom, limited only by number
  of twisters
• Promises best PMD compensation, may require
  significant computation to avoid trapping in
  local minima

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Conclusion

• PMD is a significant problem for long-distance
  transmission systems operating at 10 Gbps and
  higher
• PMD1 can be minimised using relatively simple
  delay line techniques
• Compensation of higher-order PMD requires more
  complex equalisation techniques
• Monitoring of polarisation dependent dispersion
  is required for all compensation schemes, due to
  the time-varying nature of PMD
• Initial experimental demonstrations of PMD
  compensation act on a per-channel basis, due to
  strong wavelength dependence of PMD

24
References

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