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    Prof. Lian K Chen Part I. Fibers 1

    IEG 4030 Optical Communications

    Part I. Fibers

    Professor Lian K. Chen

    Department of Information Engineering

    The Chinese University of Hong Kong

    [email protected]

    [For slide with * sign: supplemental material]

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    Prof. Lian K Chen Part I. Fibers 2

    Ref: [Keiser Ch2.1-2.3, 2.4*, 2.8*, 3.1, 3.2, 3.5.2-3 ][Agrawal Ch2.1-2.3 2.4*, 2.5]

    Outline

    Fiber basics

    Fiber types

    Ray theory

    Basic EM wave theory Propagation mode

    Single-mode and multimode fiber

    Fiber attenuation

    Signal distortion in fiber

    Dispersion

    Transmission system capacity

    Fiber manufacturing

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    Prof. Lian K Chen Part I. Fibers 3

    IEEE Spectrum Feb. 2001

    The hidden Hazard of Aging AircraftWiring

    Pros and cons of fiber

    Advantages:

    low cost

    small size, weight, flexibility

    immunity to interference : no short circuit and crosstalk security

    high bandwidth

    low loss

    stress and heat resistant

    hazardous environment resistant

    Disadvantage: difficult to tap light out

    difficult to make connection

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    Prof. Lian K Chen Part I. Fibers 5

    Fiber Types

    By refractive index profile

    step-index fiber : the refractive index profile of fiber core is a step function

    graded-index fiber : the refractive index of fiber core depends on the

    radius distance.

    By sustainable propagation mode

    single-mode fiber : support only single propagation mode.

    multi-mode fiber : support multiple propagation mode.

    By dispersion characteristics non-dispersion-shifted fiber(NDSF) : standard single-mode fiber with zero

    dispersion at 1.3m. [ITU-T G.652]

    dispersion-shifted fiber(DSF) : zero dispersion at 1.55m. [ITU-T G.653]

    non-zero dispersion shifted fiber(NZDSF) : small but non-zero dispersion

    at 1.55m. [ITU-T G.655]

    By polarization characteristics

    polarization maintaining fiber : polarization preserved fiber

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    Prof. Lian K Chen Part I. Fibers 6

    Single-Mode Fiber Spool Multi-Mode Fiber Spool

    Multi-Mode FiberPatchcord (Jumper)

    Single-Mode FiberPatchcord (Jumper)

    Fiber Types - 2

    Notice the color difference!

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    Prof. Lian K Chen Part I. Fibers 7

    Fiber Types other specialty fibers

    Photonic crystal fiber (PCF)

    inculdephotonic-bandgap fiber(PCFs that confine light

    by band gap effects), holey fiber(PCFs using air holes in

    their cross-sections), hole-assisted fiber(PCFs guiding

    light by a conventional higher-index core modified by thepresence of air holes), and Bragg fiber(photonic-bandgap

    fiber formed by concentric rings of multilayer film).

    Plastic optical fiber (POF)

    larger core

    much higher attenuation

    easier for termination and splicing processing

    Rare-earth doped fiber

    e.g. for EDFA amplifiers

    http://en.wikipedia.org/wiki/Photonic_crystal_fiber

    http://en.wikipedia.org/wiki/Plastic_optical_fiber

    http://en.wikipedia.org/wiki/Erbium-doped_fiber_amplifier

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    Prof. Lian K Chen Part I. Fibers 8

    Step Index

    Pulse spreading in fibers

    Graded Index

    (1). multi-mode, step index fiber (2) multi-mode, graded index (3). single-mode, step index fiber

    core

    cladding

    n1

    n2

    refractive

    in

    dex

    core

    cladding

    n1

    n2

    refractive

    in

    dex

    Step-index and Graded-index fiber

    http://media.corning.com/flash/opticalfiber/2008/fiber101/fiber101.html

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    Prof. Lian K Chen Part I. Fibers 9

    Snells Law :

    Note: if we increase1 to c such that

    2

    =90o

    Ray theory valid if

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    Prof. Lian K Chen Part I. Fibers 10

    c=Set , then

    2

    12

    2

    2

    12

    1

    2

    1

    21

    2

    1

    2

    1 )())(1()sin1( nnnnnn c ==

    =in sin0

    N.A.

    1

    21 )(

    n

    nn =Defined fractional index change

    1/ 2

    1N .A . (2 )n Larger N.A. more light collected.

    But usually is chosen to be quite small,

    ~ 0.002 weakly guided

    2

    1

    2112

    1

    21212

    12

    2

    2

    1 )](2[)]()([)( nnnnnnnnn +==for n1~n2

    Ray Theory - 2

    2

    1

    2

    11110 )sin1(cos)2

    (sinsinsin

    ==== nnnnn ri

    loss (leaky and unguided)

    ir

    n2

    n1Acceptance

    angle

    O.K.

    core

    cladding

    n0

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    Prof. Lian K Chen Part I. Fibers 11

    Ray Theory - 3

    Q. Whats wrong with strong guiding?

    different arrival time

    Large large N.A.

    Large

    large NAMultipathArray of

    angles

    wider acceptance angle

    support an array of rays with different incident angles

    multiple modes/ multipath

    path length difference + different modes travel at different speeds

    intermodal dispersion

    signal pulse broadening

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    Prof. Lian K Chen Part I. Fibers 12

    Concept of an electric field E

    If an electric fieldE exists in a certain region of space ,then every point (x,y,z) within the region is associatedwith a vector field E(x,y,z) such that when a test charge e

    is brought to the point (x,y,z), it will experience a force

    F = eE(x,y,z).

    Concept of a magnetic f ield B

    Similarly, if a region is associated with a magnetic fieldB, then a test charge in motion with velocity v will

    experience a force F=evB(x,y,z) at every point (x,y,z)within .

    The Lorentz force equation F=e(E+v B) describes thecombined effect of an electromagnetic field on a test

    charge e.

    e

    F

    E(x,y,z)

    eF

    B(x,y,z)v

    Basic Electromagnetic Theory*

    (bold face: a vector)

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    Prof. Lian K Chen Part I. Fibers 13

    Importance of the field concept

    The electromagnetic phenomena arise from the interaction of charges.

    With the concept of electromagnetic fields, one can study many

    electromagnetic phenomena (such as the propagation of

    electromagnetic waves) without having to worry about how they are

    generated.

    Unification of electricity and magnetism

    Historically, electricity and magnetism were two different phenomena

    in which many empirical relations had been discovered experimentally.

    Maxwell unified them by introducing the concept of displacement

    current to resolve the inconsistency in the equation of continuity. The

    set of equations resulted is known as Maxwells equations.

    Filed concept and unification of B and E*

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    Prof. Lian K Chen Part I. Fibers 14

    0

    t

    j

    t

    =

    = =

    = +

    D

    BB

    E

    DH

    E and Hare the electric and magnetic field intensityD and B are the electric and magnetic flux density

    D=E and B=H

    andj are the charge density and current density.

    and are thepermittivity andpermeability characterizing the electric and magnetic

    properties of the medium. For isotropic media, and are scalars. In some

    anisotropic media, and are tensors, denoted by and

    Ref:

    Ch4, Fiber-Optic Communications Technology D.K. Mynbaev and L.L. Scheiner, Prenctice Hall

    Maxwells Equations (MKS Differential

    Form)-1*

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    Prof. Lian K Chen Part I. Fibers 15

    Maxwells Equations (MKS Differential

    Form)-2* In general, there are an infinite number of solutions to Maxwellsequations for any geometry and boundary conditions.

    Under certain circumstances, the boundary conditions and the initial

    field distribution may uniquely determine the EM field.

    We usually consider only a few classes of solutions that represent

    physical phenomena we are interested in. For example, in a

    waveguide, we may be only interested in some of the propagating

    modes.

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    Prof. Lian K Chen Part I. Fibers 16

    From Maxwells equation, one can derive the wave equations forlinear, isotropic and homogeneous medium:

    Representation of a single-frequency wave and phase velocity

    a general wave motion can be represented by sin(t-kz) or

    is the temporal frequency andkis the spatial frequency (or propagation

    vector, wave vector, wave number...)

    temporal frequency denotes the number of repetitions of a wave per unittime

    spatial frequency denotes the number of repetitions of a wave per unit

    distance

    The /kis known as the phase velocity; it is the velocity of anyconstant-phase point of a wave

    2 22 2 2

    2 2 2 2

    1 1 10; 0; where c

    c t c t

    E HE H

    = = =

    ( )i t k ze

    EM Wave equation in isotropic,

    homogeneous medium*

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    Prof. Lian K Chen Part I. Fibers 17

    The E field and H field of an EM wave are always orthogonal, either

    component completely determines the other.

    An EM wave propagates by exchanging energy between its E field and

    H field (analogous to an LC oscillator). If E field is at the maximum, the

    H field will vanish (and vice versa).

    There are two independent polarizations for each monochromatic wave

    with the same wave vector k because of the two spatial dimensions (xand y). When the phase difference between the two polarizations is

    0o - the EM wave is plane-polarized

    90o - the EM wave is circularly polarized

    arbitrary - the EM wave is elliptically polarized

    Reflection and refraction occur at the boundary interfaces - a result of

    boundary condition for EM field.

    Properties of electromagnetic waves

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    Prof. Lian K Chen Part I. Fibers 18

    +=

    =

    )cos(

    )cos(

    ztaE

    ztaE

    yy

    xx

    yExEyxE yx +=),(With

    ztA =Let

    =

    =

    +=

    =

    sinsincoscos

    cos

    )cos(

    cos

    AAa

    E

    Aa

    E

    AaE

    AaE

    y

    y

    x

    x

    yy

    xx

    2

    22

    22

    22

    22

    2

    22

    2

    sincos2

    sinsincos2cos

    sin1cos

    sin1cos

    =

    +

    =

    +

    =

    =

    yx

    yx

    y

    y

    x

    x

    x

    x

    yx

    yx

    y

    y

    x

    x

    x

    x

    y

    y

    x

    x

    x

    x

    x

    x

    y

    y

    aa

    EE

    a

    E

    a

    E

    a

    E

    aa

    EE

    a

    E

    a

    E

    a

    E

    a

    E

    a

    E

    aE

    aE

    a

    E

    Polarization Ellipse

    Polarization of Light

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    Prof. Lian K Chen Part I. Fibers 19

    Polarization of Light -2

    222

    sincos2 =

    +

    yx

    yx

    y

    y

    x

    x

    aa

    EE

    a

    E

    a

    EPolarization Ellipse:

    Consider when =/2, gives 1

    22

    =

    +

    y

    y

    x

    x

    a

    E

    a

    E

    If ax=ay=a, the locus of the resultantE(x,y)will be a circle.

    ),( yxE

    x

    y

    Circularly polarized/Circular polarization

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    Prof. Lian K Chen Part I. Fibers 20

    Circular Polarization

    Polarization of Light - 3

    See also http://webphysics.davidson.edu/physlet_resources/dav_optics/Examples/polarization.html

    for some animation of polarization

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    Prof. Lian K Chen Part I. Fibers 21

    Polarizer in Photography

    Use the Circular Polarizer or Linear Polarizer to block some of the

    unwanted light

    Also see http://www.geocities.com/COKINFILTERSYSTEM/polarizer.htm

    Ref: National Geographic Photography Field Guide, ISBN 986-7680-46-4

    with polarizer

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    Prof. Lian K Chen Part I. Fibers 22

    Whether a mode can be supported by the fiber described by two

    parameters

    : normalized propagation constant

    If , these modes will not be supported cut off If

    : normalized frequency

    Note that a is the fiber core radius and where s thewavelength of the light.

    2 2

    2 2

    2 2

    1 2 1 2

    ( / ) /, for

    12 2 2

    1 2 1

    2( ) ( ) 2V ka n n an

    =

    2 /k =

    Propagation mode supported in Fiber

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    Prof. Lian K Chen Part I. Fibers 23

    Completely

    cut off at b=0

    guidedtightly

    nn 1

    Example: For a multimode fiber with n1=1.5, a=25 m, and =5x10-3, V is 18 for asource wavelength at 1.3 m. It will support ~ 162 modes.

    2

    ~2

    V

    To have a single-mode

    operation, V should be

    2.405.

    Note: large V large support more modes; and

    the number of modes is

    Supported propagation modes in fiber

    Q: Why does fiber only support discrete modes?

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    Prof. Lian K Chen Part I. Fibers 24

    Comparison of Single- and multi-mode

    fiberMulti-mode fiber (MMF) : larger core area easier for power coupling between source and

    fiber or fiber to fiber.

    can use LEDs as the light source; LED are easy to make, lessexpensive, require simpler circuitry, and have longer life time; but

    bandwidth is limited.

    Q: what are the cons?

    Single-mode fiber (SMF) :

    allows only one propagation mode no intermodal dispersion

    (intermodal dispersion is caused by different propagation velocity for

    different modes)

    Note: Recent research on MMF has made high-speed communication

    on MMF possible. We will come back to this later.

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    Prof. Lian K Chen Part I. Fibers 25

    Attenuation in Optical Fibers

    Attenuation is measured in dB/km:

    =

    out

    in

    P

    P

    L10log

    10

    wherePin and Pout are the optical power into and out of the optical fiber,andL is the total length of fiber in km.

    a

    e

    Attenuation spec. of Corning SMF-28 fiberThe ITU has specified six transmissionbands for fiber optic transmissions.

    The six bands are theO-Band (1,260nm to 1,310nm),E-Band (1,360nm to 1,460nm),S-Band (1,460nm to 1,530nm),C-Band (1,530nm to 1,565nm),L-Band (1,565nm to 1,625nm),U-Band (1,625nm to 1,675nm).

    A seventh band, not defined by the ITU, butused in private networks, runs around850nm.

    In new fibers (Lucent All-Wave or Corning SMF-28e), OHabsorption peak around 1.4m has been largely suppressed.

    We want to transmit signal at the

    wavelength with small attenuation

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    Prof. Lian K Chen Part I. Fibers 26

    Causes of Fiber Attenuation

    1. Material absorption: Silica (Intrinsic) and Impurities (Extrinsic) For SiO2, intrinsic absorption results from electronic absorption band in UV

    ( 7m) Impurities : Fe, Cu, Co, Ni, Cr. absorption

    OH ions absorption at 2.7m. Harmonic tones occur at 1.4m, 0.95m,and 0.725m. Need to keep it below 1ppb.

    2. Rayleigh scattering: Silica molecules move randomly in the molten state.

    density fluctuations (~) cause Rayleigh scattering with scattering loss:

    R=C/4 (C~0.7-0.9dB/km-m4)~ 0.12-0.16 dB/km at 1.55m

    3. Waveguide Imperfections: Core radius variations scattering very small Bend loss can be high ~ e-R/Rc

    R = radius of the fiber; Rc=a/(n12-n2

    2);

    For SMF, Rc=0.2-0.4mm. R>5mm.microbend

    core

    cladding

    cladding

    Density fluctuations

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    Prof. Lian K Chen Part I. Fibers 27

    Optical signal is distorted as it propagates along the fiber waveguide.

    The distortion is due to intermodal dispersion, intramodal dispersion,

    and polarization mode-dispersion .

    All effects lead to ISI (inter-symbol interference) caused by pulsespreading, and subsequently limit the system transmission capacity.

    t=0

    t=t1

    t=2t1

    t=3t1

    Evolution of pulse broadening

    (Assume after t1, pulse width increases by

    20% and pulse height reduces by 20%)

    Signal distortion in optical waveguide

    distance

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    Prof. Lian K Chen Part I. Fibers 28

    Intramodal dispersion

    Intramodal dispersion

    Intramodal dispersion or chromatic dispersion is the pulse spreading

    occurs in a single propagation mode.

    The pulse spreading is due to group velocity dispersion - signal atdifferent wavelength has different group velocity.

    Intramodal dispersion consists of Material dispersion : caused by

    the wavelength-dependence of

    refractive index

    Waveguide dispersion : causedby cladding mode (~20% for SM

    fiber) which travels faster.

    30

    20

    10

    0

    -10

    -20

    -301.1 1.2 1.3 1.4 1.5 1.6 1.7

    Wavelength (m)

    DM

    DW

    Dispersion

    [ps/(km

    nm)]

    ZD

    Dtotal

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    Prof. Lian K Chen Part I. Fibers 29

    20

    10

    0

    -10

    -20

    1.1 1.2 1.3 1.4 1.5 1.6 1.7Wavelength (m)

    standard fiber

    dispersion f latten fiber

    dispersion shif ted fiberDispersion

    [ps/(km

    nm)]

    Dispersion-shifted fiber

    For silica fiber,

    Dmat (material dispersion) is a monotonically increasing function of .

    Dwg (waveguide dispersion) is always

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    Prof. Lian K Chen Part I. Fibers 30

    Material dispersion (due to the frequency-dependent of the silica

    fibers refractive index n)

    2

    2matd nD

    c d

    =

    Material Dispersion

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    Prof. Lian K Chen Part I. Fibers 31

    2

    2

    2

    1 ( )wg

    n d VbD V

    c dV

    =

    [Gloge Diagram]

    LPjm modes

    Waveguide Dispersion*

    The effect of waveguide dispersion can be approximated by assuming

    that the refractive index of the materials is independent of wavelength.

    Dwg depends on the V parameter of the fiber

    d(Vb)/d

    V

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    Prof. Lian K Chen Part I. Fibers 32

    (c) triangular dispersion

    shifted

    (d) quadruple-clad

    dispersion-flattened

    (a) matched cladding

    1300nm-optimized (b) depressed cladding

    1300nm-optimized

    Dispersion adjustment by refractive index

    profile Various Refractive Index Profile to manipulate the fibers dispersion:

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    Prof. Lian K Chen Part I. Fibers 33

    Various fiber with different dispersions

    Material dispersion can be changed by changing fiber glass doping

    concentration

    Waveguide dispersion can be changed by changing waveguide

    geometry

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    Prof. Lian K Chen Part I. Fibers 34

    (Multipath dispersion)

    The lights (rays) that enter the fiber at different angles will traverse

    different distances inside the fiber.

    The propagation time difference between the longest and shortest

    paths is the Intermodal dispersion.

    For step-index fiber :

    c: critical angle

    21 1

    2c sin c

    n L L nT L

    c n = =

    Modal dispersion

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    Prof. Lian K Chen Part I. Fibers 35

    Birefringence: f y xB n n=

    Two modes propagate at different speeds.

    PMD (polarization mode dispersion) occurs.

    Birefringence

    Even for single-mode fiber, there are two independent, degenerated

    propagation modes.

    These two modes are orthogonal in polarization.

    In regular fiber, due to some imperfections (e.g. asymmetrical lateral

    stress, noncircular core, or variations in refractive index), the refractive

    indices for x and y direction are different .

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    Prof. Lian K Chen Part I. Fibers 36

    - Well defined, frequency independent eigenstates

    - Deterministic, frequency independent Differential Group Delay (DGD)

    - DGD scales linearly with fiber length

    1st-order PMD

    Ideal Practical

    Core

    Cladding

    Cross-section of optical fiber

    Fast axis

    Slow axis

    Fast

    Slow

    : Differential Group Delay (DGD)

    Ref: Kazuo Yamane, Fujitsu

    Polarization mode dispersion (PMD)

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    Prof. Lian K Chen Part I. Fibers 37

    Polarization mode dispersion (PMD)

    PMD is caused by Fiber birefringence (difference in refractive indices

    of two principle polarization states).

    The fluctuation of PMD is due to the fluctuation of

    signals principle states of polarization (PSP) or

    differential group delay (DGD). (the delay difference between two

    orthogonal mode of polarizations)

    The mean PMD can be calculated by

    where DPMD is the average PMD parameter measured in ps/(km)0.5 .

    Typical DPMD ranges from 0.1 to 1 ps/(km)0.5

    .

    LDT PMDPMD

    Ex

    Ey

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    Prof. Lian K Chen Part I. Fibers 38

    Polarization mode dispersion (PMD)

    PMD is an important factor for high speed (>10 Gb/s) systems.

    Optical fibre cables covered by ITUG.652 recommendation generally have

    a DPMD below 0.5 ps/km1/2.

    This corresponds to a PMD-limited transmission distance of about 400 km

    for STM-64 (10Gb/s) systems

    For STM-256(40Gb/s), this distance is reduced to ~ 25 km!

    PMD varies along the fiber and depends on the temperature.

    PMD also depends on the fiber cable installation.

    For example, in one experiment, the PMDs measured for a 36-km

    spooled fiber, a 48.8-km buried cable, and a 48.8-km aerial cable

    were 0.028, 0.29, and 1.28 ps/(km)0.5, respectively.

    (Assume tolerable PMD is 10% of pulsewidth)

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    Prof. Lian K Chen Part I. Fibers 39

    group velocity vg :

    group delayg :

    Since the group velocity depends on the wavelength, a pulse that

    contains different spectral components will spread out during

    propagation.

    Assume the is the spectral width of the pulse, the extent of pulsebroadening (T) for a fiber with length L is given by

    where is known as GVD (group velocity dispersion) parameter.

    11

    =

    dk

    dcd

    dvg

    fiber)oflength:(

    2

    2

    LL

    d

    d

    cdk

    d

    c

    L

    v

    L

    g

    g

    ===

    ==

    ==

    22

    2

    Ld

    dL

    v

    L

    d

    d

    d

    dTT

    g

    2

    2

    2

    d

    d

    Group velocity dispersion

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    Prof. Lian K Chen Part I. Fibers 40

    More commonly, the spectral width is expressed in(unit: nm).

    (Conversion ofand) Using or

    the pulse spreading for an optical source with a spectral width isgiving by

    where the dispersion parameterD is defined as

    Note:As D can be positive or negative, we take the absolute value of Dto calculate the pulse spreading .

    = ,)/2(

    2 = c

    g

    dT d LT D Ld d v

    = = =

    i i

    .1

    gvd

    dD

    Group velocity dispersion (contd.)

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    Prof. Lian K Chen Part I. Fibers 41

    Assume infinitely extended dielectric medium with refractive index n()Then the propagation constant is given by

    From the previous equation of the group delay g , the material dispersion(or group delay) can be derived as

    Then the pulse spreadmat is given by

    where2

    2mat

    d nD

    c d

    =

    ( )2 n

    =

    mat g

    g

    L L dn

    nv c d

    = = =

    2

    2( )mat

    mat mat

    d L d nL D

    d c d

    = =

    Material Dispersion Derivation

    (Note: pulse spectral width is also expressed as)

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    Prof. Lian K Chen Part I. Fibers 42

    Since all light sources have non-zero spectral width , the dispersioncannot be zero for all wavelength within .

    The effective dispersion is D=S where is the dispersion

    slope, differential dispersion parameter, or second-order dispersionparameter( note : Some people use D=0.5S )

    From D, S can be derived as

    Typical parameters of some commercial single-mode fibers

    2 2 3

    3 2(2 / ) (4 / )S c c = +

    N.A. =(n1-n2)/n2(%)

    2w(m)

    ZD(m)

    S[ps/(km-nm

    2)]

    Corning SMF-28

    AT&T Matched-Clad

    0.13

    0.12

    0.36

    0.33

    9.3

    9.3

    1.312

    1.312

    0.090

    0.088

    Corning SMF-DS

    AT&T True Wave

    0.17

    0.16

    0.90

    0.75

    8.1

    8.4

    1.550

    1.530

    0.075

    0.095

    d

    dDS

    Higher order dispersion*

    where ( / )m mm

    d d =

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    Prof. Lian K Chen Part I. Fibers 43

    (ITU-T G.652)

    The maximum chromatic dispersion coefficient shall be specified by:

    the allowed range of the zero-dispersion wavelength between 0min =1300 nm and

    0max

    = 1324 nm; the maximum value S0max= 0.093 ps/(nm2 km) of the dispersion slope at

    zero dispersion wavelength. (shown as -0.093 in the standard document)

    The chromatic dispersion coefficient limits for any wavelength within

    the range 1260-1360 nm shall be calculated as:

    ( )4

    0min0max1 34

    SD

    =

    Dispersion specification of SM Fiber-1*

    For a set of fibers with certain manufacturing tolerance:

    ( )4

    0max0max2 34

    SD

    =

    ( )4

    0 034

    SD

    =

    If specific values (rather than a range

    of values) of S0 and 0 are given,then D is in the form of :

    (check corning SMF-28e spec sheet)

    Di i ifi ti f SM Fib 2*

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    Prof. Lian K Chen Part I. Fibers 44

    The dispersion at 1500-1600nm for for a dispersion-shifted fiber

    (Class IVb fiber specified in EIA) (or when is close to0)

    The asumption is that the dispersion slope is constant around 0

    ( ) 0 0( )D S =

    Dispersion specification of SM Fiber-2*

    T i i t it

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    Prof. Lian K Chen Part I. Fibers 45

    For Gaussian input pulse, the output pulse width after passing through

    a fiber is

    where 0

    is the r.m.s. pulse width of input Gaussian pulse and D

    is

    the pulse broadening due to fiber dispersion.

    A commonly used criterion for the pulse broadening is

    where TB is the bit period =1/Br and Bris the Bit rate (not bandwidth) of

    the system.

    Assume negligible initial pulse width, then

    (For detail derivation under various conditions, see [Agrawal])

    ,)( 2/1220 D +=

    ,4/BT

    )4/(1or4/1 DLBDLB rr

    DLD=

    -- bit-rate - distance product

    Transmission system capacity

    E l

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    Prof. Lian K Chen Part I. Fibers 46

    Example:

    S t Si *

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    Prof. Lian K Chen Part I. Fibers 47

    For single mode fiber, the intensity distribution of the propagation

    mode is important for characterizing the performance.

    Ex can be approximated by a Gaussian distribution *.

    [Agrawal]

    By analytical fitting,

    22

    o

    o

    exp(- / )exp( ), where

    - field radius = spot size

    2 = mode filed diameter (MFD)

    x oE A r w i z

    w

    w

    =

    -3/ 2 -6

    o / 0.65 1.619 2.879w a V V + +

    (* One of the various approximations.)

    r=0

    Spot Size*

    Fiber drawing

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    Prof. Lian K Chen Part I. Fibers 48

    Fiber drawing

    Various techniques for producing

    optical fiber

    Outside Vapor-Phase Deposition

    (OVPD)

    Vapor-Phase Axial Deposition (VAD) Modified Chemical Vapor

    Deposition(MCVD)

    Plasma-Activated Chemical Vapor

    Deposition (PCVD)(see Kaiser)

    Also seeCoring Fiber Manufacturing Demohttp://www.corning.com/cms/FlashVideoPlayer.aspx?id=39

    597&ydistance=312

    Preform feed

    Furnace2000

    C

    Thicknessmonitoring gauge

    Take-up drum

    Polymer coater

    Ultraviolet light orfurnace for curing

    Capstan

    Schematic illustration of a

    fiber drawing tower. 1999 S.O. Kasap,Optoelectronics(Prentice Hall)

    Outside vapor deposition

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    Prof. Lian K Chen Part I. Fibers 49

    Outside vapor deposition

    Vapors: SiCl4+ GeCl4+O2

    Rotate mandrel

    (a)

    Deposited soot

    Burner

    Fuel: H2

    Target rod

    Deposited Ge doped SiO2

    (b)

    Furnace

    Porous sootpreform with hole

    Clear solidglass preform

    Drying gases

    (c)

    Furnace

    Drawn fiber

    Preform

    Schematic illustration of OVD and the preform preparation for fiber drawing. (a)

    Reaction of gases in the burner flame produces glass soot that deposits on to theoutside surface of the mandrel. (b) The mandrel is removed and the hollow porous soot

    preform is consolidated; the soot particles are sintered, fused, together to form a clear

    glass rod. (c) The consolidated glass rod is used as a preform in fiber drawing.

    1999 S.O. Kasap, Optoelectronics (Prentice Hall)

    Fiber Cable

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    Prof. Lian K Chen Part I. Fibers 50

    For practical application, fiber needs to be

    encapsulated in cable for better protection.

    Outer Sheath

    Yarn strength

    member

    Buffer strength

    member

    Paper/Plastic

    Binding Tape

    Basic Fiber building

    block

    Insulator Copper

    Conductor

    Polyurethane/PVC

    Jacket

    Six-fiber cable

    (See Coring Fiber Manufacturing Demo)

    Fiber Cable

    ITU T Recommendations

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    Prof. Lian K Chen Part I. Fibers 51

    ITU-T Recommendations

    G.650 - Definition and test methods for the relevant parameters ofsingle-mode fibres

    G.651 - Characteristics of a 50/125 m multimode graded index

    optical fibre cable

    G.652 - Characteristics of a single-mode optical fibre cable

    G.653 - Characteristics of a dispersion-shifted single-mode optical

    fibre cable

    G.654 - Characteristics of a cut-off shifted single-mode optical fibrecable

    G.655 - Characteristics of a non-zero dispersion shifted single-mode

    optical fibre cable

    Case Study flexible optical fiber

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    Prof. Lian K Chen Part I. Fibers 52

    Case Study flexible optical fiber

    Question:

    Fiber is made of glass. Can we make it very flexible for home cabling?

    Solution: special fiber (e.g. Photonic Crystal Fiber or fiber with special

    coating)

    NTT - Fiber to the Home(FTTH) Project

    Also see Corningsshowhttp://www.corning.com/optica

    lfiber/library/videos.aspx

    Photonic Crystal Fiber (Holey Fiber)*

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    Prof. Lian K Chen Part I. Fibers 53

    Photonic Crystal Fiber (Holey Fiber)

    Applications

    Dispersion compensation

    White light (supercontinuum)

    sources

    Wavelength converters Hollow transmission fibers

    Multi-core fiber couplers

    Pulse shapers

    Chemical sensors with long

    interaction lengths

    Temperature-insensitive PM

    pigtails

    Gyroscope fibers--athermal, and

    highly birefringent

    Pressure and temperature sensors

    High Aeff and PM fibers for single-

    mode interconnects

    Mode converters http://www.blazephotonics.com/

    Reading the Data Sheet

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    Prof. Lian K Chen Part I. Fibers 54

    Reading the Data Sheet

    Corning SMF-28e+ optical fiberhttp://www.corning.com/WorkArea/showcontent.aspx?id=41261

    Other interesting sites

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    Prof. Lian K Chen Part I. Fibers 55

    http://www.corning.com/opticalfiber/ (Corning Optical Fiber)

    http://www.arcelect.com/fibercable.htm (The Basics of Fiber Optic

    Cables: A tutorial)

    http://www.sff.net/people/Jeff.Hecht/history.html (A short history offiber optics) and http://www.sff.net/people/Jeff.Hecht/chron.html (A

    Fiber-Optic Chronology )

    Other interesting sites