Optical Fiber Communications

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Optical Fiber Communications (121102) Chris
Roeloffzen
Chair Telecommunication engineering (EWI) Floor
8 HOGEKAMP EL/TN building (north) Telephone 489
2804 E-mail c.g.h.roeloffzen_at_el.utwente.nl
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Chapter 14 System noise
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Contents

• Intensity noise of the light source
• Competition noise
• Partition noise
• Modal noise
• The SNR due to system noise receiver noise

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Introduction

• Importance of the subject
• Noise considerations in Chapter 12 and 13
  referred to noise produced in the receiver
• More noise sources are present in OFC systems
• Sometimes system noise is not the limiting factor
  but generally it is (especially in analog
  systems).
• System noise originates in the system components
  and cominations of the system components

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Intensity noise of the light source

• Intensity noise in LEDs
• Photons are generated due to the recombination of
  electrons and holes injected by the forward
  current
• Causes
• The number of recombinations varies within a
  certain length of time
• The energy per photon varies
• The stochastic process that describes the LED is
  modeled as a Gaussian bandpass process (see
  slides of chapter 8)
• where ?c 2??, ?c/?
• x(t) and y(t) are real independent stochastic
  processes with random phase
• The random fluctuations of the emitted power of
  an LED is called beat noise.

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Intensity noise of the light source

• The signal-to-noise ratio due to the beat noise
  is given by
• where
• B0 bandwidth of the optical spectrum of the
  source
• B electrical bandwidth of the receiver
• V factor the depends on the shape of the
  optical spectrum and shape of the electrical
  transfer function of the receiver
• Special case
• ideal rectangular bandpass optical spectrum
• ideal rectangular low-pass filter electrical
  receiver
• Then the factor V becomes
• for an LED B0 gtgt B ? V?1 (also for non
  rectangular band limitations)
• The S/N becomes very large ? for an LED this
  noise source is not important

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Intensity noise of the light source
Intensity noise in semiconductor lasers Intensity
noise in incoherent laser light same conditions
that were reached for the LED apply Intensity
noise in coherent laser light is treated in
Chapter 9 (RIN). This is important in analog
optical systems or coherent systems
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Competition noise

• Competition noise occurs when a laser that
  oscillates in different lateral (transversal)
  modes is used
• photon 1 contributes to lateral mode 1
• photon 2 contributes to lateral mode 2
• The different laser modes are thus in competition
  for any emitted photon
• Fixed laser current ? fixed optical power ?
  fluctuating power per lateral mode
• Coupling from laser to fiber spatial filtering
  ? selective mode attenuation ? competition noise
  in the power coupled into the fiber
• No competition noise when
• all the light is coupled into the fiber
• all the modi are attenuated equally
• laser with only one lateral mode (Gaussian shape)

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Partition noise

• Partition noise occurs when a laser oscillates in
  different longitudinal modes (multiple spectral
  lines)
• Fixed laser current ? fixed optical power ?
  fluctuating power per longitudinal mode
• Optical fiber with chromatic dispersion
• delay is wavelength dependent
• Longitudinal modes experience different delays
• ak power of the kth spectral line (or laser
  mode)
• m(t) input signal to the laser
• ?k delay of the kth mode
• The coefficients ak are stochastic variables

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Partition noise

• Using the following assumptions
• Although the amplitudes ak of the various modes
  can differ from pulse to pulse, the total optical
  power is constant and is assumed to be unity
• The optical laser spectrum has a Gaussian shape
• ?c is the central wavelength
• p(a1,,aN) is the N-dimensional joint probability
  density function of the set ak
• ?k is the wavelength of the kth spectral line
• ?S(?)??(?- ?k) is the lasers optical spectrum
• ? is the half root mean square (r.m.s.) width of
  the envelope of this spectrum

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Partition noise

• Using the following assumptions
• The pulses received consist of raised cosines in
  the time domain
• with T0ltT (1/T is the bitrate)
• None of these assumptions means any loss of
  generality for the method described, but they
  only serve to simplify the calculations
• The differential delay between the kth laser mode
  with wavelength ?k and the center mode with
  wavelength ?c is denoted by ??k.
• Let us suppose that the pulses received are
  nominally sampled at the peak of the waveform, if
  the pulse is sampled by the center mode
• The amplitude fluctuation ?k at this nominal
  sampling moment, when the pulse is shifted in
  time due to transmission by laser mode k, becomes

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Partition noise

• for ??k ltlt ?0

The signaling waveform sp(t) transmitted by the
center wavelength (solid line) and by laser mode
k (broken line).
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Partition noise
The total amplitude fluctuation with respect to
the nominal pulse is found From this expression
the noise power ?pn2 due to this fluctuation is
found to be See book for further calculation is
calculated from the laser spectrum we need to
know the joint probability density function
p(a1,,aN) , which is generally not known. The
maximum can be calculated which occurs
when This condition can be interpreted as the
situation where the laser modes are mutually
exclusive (each data pulse consists of a single
dominant longitudinal laser mode, whose
wavelength may vary from pulse to pulse).
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Partition noise
Using this worst case scenario The
signal-to-partition-noise ratio is defined as the
mean square of the signal value divided by the
variance of the partition noise In order to
simplify the calculations, the spectrum of the
laser is best described by a continuous Gaussian
function
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Partition noise
??k can be expanded into a Tailor series where
I is the length of the fiber, and ? are
respectively the second and third derivatives of
the propagation constant ? with ?g the
specific group delay of the fiber where and
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Partition noise
A very important conclusion the
signal-to-partition-noise ratio depends on the
width ? of the laser spectrum and the dispersion
parameters A1 and A2 of the fiber, but is
independent of the signal power. This means that
the SNR cannot be improved by increasing the
transmitting power. SNR ?? when bitrate ? For
systems operating at the wavelength of minimum
dispersion, the parameter A1 vanishes Far from
the minimum dispersion
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Partition noise

• We shall now drop the assumption that the laser
  modes within each pulse are mutually exclusive.
  We can now write the variance of the received
  signal as
• with
• k is a constant, and thus equal for any mode i
  and can be measured from a single mode by
• numerator (variance of the ith mode) RMS
  voltmeter
• denominator avg(ai) DC voltmeter
• The mode partition coefficient k may vary from 0
  (no partition noise) to 1 (full mode partition)
  (in k 0.17 0.7)
• No partition noise for an LED or single-mode
  laser

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Modal noise

• Modal noise can only occur in multimode fibers
• The beam of light can reflect at different angles
  ? at the core cladding boundary
• For a consistent wave pattern the extended
  wavefronts of a certain ray should coincide with
  the wavefronts of that same ray after two
  successive reflections
• This is only possible for discrete values of ??
  and thus a discrete number of modes

A meridional ray in a multimode step index fiber
with its corresponding wavefronts (broken lines),
forming a consistent wave pattern.
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Modal noise
For modal noise the number of modes in a fiber is
one of the crucial parameters. Number of modes
for a step index fiber Number of modes for a
graded index fiber where v is the normalized
frequency of the monochromatic light source a
radius of the core of the fiber (for graded index
see eq. 6.58) ?0 wavelength in vacuum n1
refractive index of the core n2 refractive
index of the cladding
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Modal noise

• Different modes ? different delay times
• Modes interfere a the end-face of the fiber ?
  speckle pattern
• Example two modes
• pattern of maxima and minima are dependent of the
  position of the cross-section
• Multiple modes in a fiber ? irregular speckle
  pattern

Two possible light rays in a step index fiber,
with corresponding wavefronts and interference
patterns at z1 and z2
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Modal noise
Filtering of the speckle pattern in a connector.
(a) Radial misalignment of the fibers. (b) end
separation of the fibers.
Number of degrees of freedom in the speckle
pattern number of excited modes
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Modal noise

• The phase difference between two interfering
  modes depends on the differential delay (can be
  multiple of 2??) and can fluctuate due to
• changes in the wavelength (due to back-reflection
  into the laser)
• mechanical vibration
• fluctuation in the launching condition
• A moving speckle pattern acts as a noise source
  where a part of the speckle pattern is filtered
  out, such as
• connectors
• splices
• mode mixers
• coupling to a photodiode

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Modal noise

• In order to estimate the modal noise we assume
• all the modes are excited
• all by the same amount
• Coherence time of the source gt pulse broadening
  of the fiberif pulse broadening gt coherence
  time ? no speckle pattern (modes not coherent),
  so a splice close to the laser causes more modal
  noise
• speckle pattern is stationary over the
  cross-section of the fiber
• number of modes much greater than one
• power carried by a specific mode- completely
  passes through the connector- or is completely
  removed at the connector

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Modal noise
Now the problem reduces to a binomial
distribution, namely the selection of an average
number of n modes (or speckles) from a set of Nf
modes (or speckles) The probability that a
speckle is inside the circle (see fig )
equals which is the efficiency of the
coupling Assume xnumber of speckles inside the
circle (random variable) and its variance
is giving the SNR SNR does not depend on the
optical power!! The coupling efficiency ?? is
determined by de mode-selective loss (not the
mode-independent loss)
L in dB
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Modal noise

• How to prevent or removes modal noise
• Modal noise occurs when
• coherent source
• and multimode fiber
• and mode-selective loss
• Condition 1 Due to the bandwidth requirements it
  is not always possible to use an LED
• Condition 2 Single-mode fiber ? non modal noise
  (if fiber operates far enough from its cut-off
  wavelength)
• Condition 3 Coherent source multimode fiber ?
  minimize the mode-selective loss (especially
  losses that occur near the source)

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Modal noise
Modal noise in a link with several lossy
devices The book gives an analysis of the modal
noise when multiple mode-selective components are
used Two case will be dealt with a) no mode
coupling in the fibers between two successive
devices ? the series connection behaves as though
the total mode-selective loss ?t is concentrated
into a single device b) Full mode coupling in
the fiber ? SNR is larger than in a)
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Modal noise
see the book for this example
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SNR due to system receiver noise
System receiver can be seen as two noisy
systems with individual SNRs Assume a
constant transfer ?? between the systems do
not use dB!!! The constant transfer ? does not
influence the SNR at the end of the series
connection It should be borne in mind that only
the noise inside the information band has to be
considered
Series connection of two systems that are
disturbed by noise.
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END