opticalfiber characteristics

7/31/2019 OpticalFiber Characteristics

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Copyright Jouko Kurki, 1996-2004 Optical Fiber Charactersitics1 (36)

INTRODUCTION TO OPTICAL FIBERS

Light guidance in optical fibers Types of optical fibers and their main characteristics

Step-Index Fiber

Single-Mode fiber

Graded-Index Fiber

Attenuation in optical fibers Dispersion and bandwidth calculation

Multimode fiber bandwidth

Multimode fiber standards

Single-mode fiber dispersion

Single-mode fibers standards (SM-fiber, DS-fiber) Fiber reliability and lifetime

Bibligraphy


2/36


LIGHT GUIDANCE IN OPTICAL FIBERS

Refraction: Light ray is bend out from normal of the surface when coming

to a media with lower refractive index (n2)

Snells law states:

n1 sin1 = n2 sin2

All the light is reflected at the interface when the angle 1 reaches somecritical value c (then 2 = 90o). This is called total internal reflection.

c = arc sin (n2/n1)

Optical fiber is formed by having a circular core area of higher refractive

index material (n1) than the cladding area (n2). Side view:


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The external maximum coupling angle i = arc sin (n12- n2

2) can be

calculated from the critical angle using Snells law and assuming the

refractive index of n0 = 1 in the air. Light rays coupled to the optical

fiber experience total internal reflection if the incoming angle of the ray

is within an acceptance cone defined by the numerical aperture of the

fiber

NA = sin max = (n12- n2

2) = n1

( 2 )1/2,

where the relative index difference

= n1 -n2 / n1

The absolute refractive index is defined as:

n = n1.

For single-mode fiber cladding n2=1.465 , core n1=1.470; m=arcsin(1.465/1.470) = 85o. Max acceptance angle to the fiber is = 90o - m(=5

oin this case). For multimode fibers NA is typically 0.2 and m =

12o. From above n = 0.5.103, typical for single-mode fibers. becomes

0.0034 = 0.34 % ( is usually expressed in %).

Coupled power to a fiber from a

Lambertian (e.g. surface emitting

LED) source:

P = P0 * (NA2 ), where P0 is

source total output power.

For NA = 0.2 typical for

multimode fiber, P/P0 ~ 4 %


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BASIC TYPES OF OPTICAL FIBERS

n(r)

2a

2a

2a = 50-400 m

2a = 50 m

2a

2a = 6-9 m

T

T

T

r

r

r

n(r)

n(r)

T

T

T

Fiber type Cross section n(r) Input pulse Light propag. Output

Step-indexmultimode fiber

Graded-index

multimode fiber

Single-mode

fiber

In Step-Index fibers, different flight times of rays (several hundred

thousands) limit the bandwidth to some 10-20 MHz.km

Dispersion compensation in Graded-Index fibers can be understoodqualitatively by using speed of light in nondispersive bulk media v = c

/n(r,), graded-index fiber compensates the different velocities of thevarious modes. Bandwidth around 1 GHz.km

In Single-Mode fibers there is no difference between traveling times of

rays /modes, but there is still some amount of pulse broadening due tomaterial dispersion and waveguide dispersion. Bandwidth around 100

GHz.km of much more depending of laser (> 1000 GHz.km achieved).


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STEP INDEX FIBER

In ray analogy there are two types of rays in a step index optical fiber:1)Meridional rays passing through the core center 2) Skew rays rotating

around the fiber axis.

o

Propagation characteristics of the step Index fiber can be solved by solvingthe Maxwells equations for a cylindrical waveguide. The field solutions are

Bessel functions in the core characterizing light propagation. Due toboundary conditions , only certain propagation constants (corresponding to

certain propagation angles) and associated fields are possible. These are

obtained from the complex eigenvalue equations.In the weakly guiding

approximation (small refractive index difference) the eigenvalue equation

reduces to

Where J(ua) is Bessel function of the first kind and K(wa) is modified

Hankel function. Parameters u and v are related to the propagation constant as

Defining the normalized frequency parameter V = 2 (a / ) * NA =

2 (a / ) * [ n12

-n22

]

1/2

; it is easy to show that V

2

= (ua)

2

+ (wa)

2

Meridional

rays

Skew rays


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The eigenvalue equation can be solved e.g. computer simulation or

graphically (below an example with V= 12.5)

Here we draw both sides of the eigenvalue equation with ua as parameter. Since

both sides need to be the same, the only allowed solutions are the intersection

points. This gives the values for the allowed ua, from which propagation constant b

can be easily calculated using equations above.

A mode is cut-off when w=0. This would correspond to /k0 = n2, and the mode isno longer bound to the fiber core (escapes from the potential well with quantum

mechanics analogy).

/k0

n2

n1123

/k0

n2

n1123

The allowed range of propagation constant /

free space wave vector k0 is /k0 = n2 n1.

In quantum mechanics analogy the refractive

index (when turned upside down) is a

potential well and the propagation constants

correspond to the quantizised particle

energies. In fact the wave equation and the

Schrdinger in equation in quantum

mechanics in steady state have similar form !


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At cut-off wavelength (or frequency) the mode is not able to propagate ( /k0must be lager than n2). The propagation areas for a few low order modes are given

below.

Here the normalized frequency V = 2 (a / ) * NA = 2 (a / ) * [ n12

-n22

]1/2

The total number of modes in the step-index fiber is N = V2

/ 2

E.g. for a step-index fiber operated at 0.85 m wavelength and having corediameter 62.5 mm, and NA=0.29 (maximum coupling angle = arc sin(0.29) =

16.8o

); V = 2 [ (62.5/2) / ] * NA = 67. The total number of modes is N

= V

2

/ 2 2245.


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Modal dispersion in Step-Index (SI) Multimode fiber

In step index fiber the speed is the same for all propagating rays but the angleof propagation is different. We can estimate the modal pulse broadening a

difference in flight time of the ray having zero angle to the fiber axis and themost oblique ray having the critical angle (Sibley)

tmin = L / (c/Ng1); tmax = L / sinc(c/Ng1) = L / [(n2/n1) (c/Ng1)]

So d/L = mod, SI = [ tmax - tmin ] / L=( Ng1 /c n2) n

E.g. a SI-fiber, a = 25 mm, = 1 % (n = 1.5 *0.01*100 = 0.015). mod, SI =50 ns correesponding to a bandwidth of 0.44 / = 8.8 MHz.km. More

elaborate treatment gives following equation for the step index fiberdispersion (Cherin p. 115-117)

m = (L/c) n1 n2 * (1/V)

So this adds a small correction. With that pulse broadening becomes 45 ns,

only a 10 % difference to the simple estimate.

In any case the modal dispersion is a very severe limitation to the bandwidth,

and therefore SI-fiber is not used in any high speed communications over

long distances.


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SINGLE-MODE FIBER

In Single mode fiber, only propagating mode is the fundamental mode isHE11 mode, also called LP01 mode. LP comes from Linearly Polarized, that is

an approximation to the exact HE11 field solution. Single mode operation is

possible if

V = 2 (A / ) * NA = 2 (A / ) * [ N12-N2

2]

1/2 < 2.405

Single-mode fiber design curve:V < 2.405 implies restriction to core size and refractive index

difference according to a design curve below (fiber design needs to beon the curve or left from the curve to meet the single-mode criteria).


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V-parameter is related to wavelength and there is a critical wavelength called cut-off

wavelength, c (in Finnish: Raja-aallonpituus) above which the fiber works as asingle-mode fiber:

c > 2.6 a (n12

n22

) = 2.6 * a * NA

Typically in SM-fiber NA 0.1, so c = 2.6 * 4.5 um * 0.1 1.2 m

The cut-off wavelength specified to a single-mode fiber is typically around 0.1 mshorter than the above theoretical cut-off wavelength (this is due to the measurement

practice that measures c as approx. 20 dB attenuation of the LP11 mode as

compared to the LP01 mode.

Single mode fiber dispersion

In single mode fibers the dispersion is due to material and waveguide dispersions

(modal dispersion is not present because there is only on possible mode !). Pulse

broadening due to material dispersion in the SM-fiber is given as:

= (nm).fiber(ps/nm.km)

.Lfiber(km), where is the source

rms spectral width ( /2.35 for Gaussian shape distribution; is

the half width of the spectral distribution of the source).

fiber(ps/nm.km) = mat + wg (Total dispersion)

Thematerial dispersion coefficient in the fiber is:

mat = dmat / d = - ( /c) * dn2/d2 [expressed in ps/nm.km]

This is negative till until around 1.3 mm, and thereafter postive in normal

silica fiber.

Waveguide dispersion is due to the fact that the wavelength/core diameter ratio

varies for different wavelengths and thus the mode sees the waveguide in a different

way. The effect causes dispersion. Waveguide dispersion can be calculated

starting from the definition of group delay =1/ vg = d/d . After lengthycalculations , the delay tw = can be expressed with parameter Dw in the drawingbelow as follows (Miller, Chynoweth, pp. 104-105). Here n1 core index, and n2 is

cladding index

Dtw / d = ( L / c ) (n1-n2) Dw(V)


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Sign of the waveguide dispersion is negative, so it can used to offset the material

dispersion above 1.3 m, and works as basis for the dispersion shifted fiber.Parameters and examples are given below. Note that to achieve dispersion shifting a

small core size, high delta, and low cut-off are required.

Standard SM-fiber dispersion

characteristics: 2a = 8.2 m,Dispersion shifted SM-fiber

dispersion characteristics: 2a

Waveguide dispersion

parameter Dw


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SINGLE-MODE FIBER PARAMETERS

When optical fiber core diameter and refractive index diffrence are made

small enough, there is room only for one fundamental mode (LP01) topropagate. The wavelength above wich the fiber works as a single-mode

fiber is c. From Maxwells equations the condition for this to happen isas follows (c given below is theoretical cut-off being around 75-200nm higher than measured cut-off depending of structure of the SM-fber).

V a n= ( / )*2 21* * < 2. 405

c = 2.715 * 2a * ()1/2

Where: c= Cut-off wavelength

V = Normalized frequency (V-parameter)

a = Core radius

= Wavelength

n1 = Core refracitive index

n2 = Cladding index

= Relative index difference = (n1-n2)/n1

Practical conditions for single-mode operation are: 2a=8-9 m and =0.3-0.37 %). Numerically the condition for single-mode operation is as

follows: 2a < (0.368 * ) / ()1/2


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In single-mode fibers only about 75 % of the power propagates in the

core of the fiber and the power distribution is nearly Gaussian in shape

(see above). Instead of using core diameter, Mode Field Diameter

(MFD) is used to describe the size of the power distribution. MFD is the

width of the power distribution at level 13.5 % (=1/e2) from the bottom.

MFD depends on the cut-off wavelength and core diameter as follows

(For G.652 SM-fiber the MFD is defined at 1.30 m)

MFD= 2a * (0.65 + 0.434*(/c)1.5 + 0.0149*(/c)6 )

Approx. MFD=1.081.(/c)

.2a -> approx. 1.1

.2a

E.g.. 2a = 8.3 m, cut-off 1.25 m; MFD=1.13*2a = 9.4 m. The MFDof the same fiber at 1.55 m is 10.4 m, i.e. the electric field extends

further away from the core.


15/36


GRADED-INDEX FIBER

Graded-index fiber refractive index profile is normally characterized with profile

of the form:

Several fiber types can be described with the -profile as indicated. In typical GI-fiber 2, so the profile is nearly parabolic. Graded index fiber theory (see e.g.Cherin) shows that each mode (ray) propagates between two turning points

within the profile,. For meridional rays turning points are intersections of b and

profile, for skew rays rotational paths depicted below are obtained.


16/36


The bandwidth of a graded-index fiber is optimized when the profile exponent is

This forms the basis for profile optimization of a GI-fiber. The optimum profile

depends on the derivatives of the refractive index and can be optimized at one

wavelength only in the general case.

Below are curves of the optimum profile as a function of wavelength for two

material compositions. Unfortunately the phosphorus (P2O5) doped combination is

not suitable due to manufacturing constraints.

Optimum profile parameter 0 as a function of wavelength for several glasscompositions

Total dispersion the graded index fiber is due to modal dispersion and chromatic

dispersion (composed of material and waveguide dispersions). These add as shown

below. In normal cases in GI-fiber, waveguide dispersion is insignificant as

compared to other mechanisms.


17/36


OPTICAL ATTENUATION

Intrinsic optical fiber attenuation can be expressed as follows:

() = A /4 + uv + IR + B + OH + imp

A /4 Rayleigh scattering; A 0.9 for SM- and 1.2 dB/km.m4for 50/125 GI-fiber

uv and IR are UV-an IR- absorptions; B is imperfection loss 0-0.2dB/km

OH and imp are absorptions due to water (OH-ion) and impurities inthe glass

The theoretical minimum intrinsic attenuations for various types of

optical fibers (dB/km)

Standard-SM Pure-silica Dispersion 50/125 0.20 NA

fiber core shifted MM-fiber

_______________________________________________________

0.85 m - - - 2.30

1.31 m 0.32 0.30 0.36 0.50

1.55 m 0.18 0.16 0.195 0.25


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BENDING INDUCED LOSSES IN SINGLE-MODE FIBER

Micro- and macrobending effects can increase optical attenuation ofsingle-mode fibers especially at 1550 nm region

Micro and macrobending loss effects

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1 1.1 1.2 1.3 1.4 1.5 1.6

Wavelenght (nm)

Attenuation(dB/km)

Normal

With microbending

With macrobending

Microbending induced loss:

Very small periodic local curvatures with 0.1.. 1 mm longitudinaldistance cause increase of attenuation when light escapes from core to

cladding.

Microbending loss is in practice only seen at 1.55 m wavelength, but itcan slightly increase attenuation also at 1.3 m region.

In single-mode fibers microbending induced loss MFD2n, where n=2-3.

Macrobending induced loss:

Macrobending is attenuation appearing when single-mode fiber is bent to20-50 mm radius. This kind of curvature radii are met e.g. splicing boxes

and optical distribution frames.

Macrobending loss is seen only at 1.55 m wavelength region.


19/36


Macrobending loss increases where quickly when a critical wavelength isexceeded at a given bend radius or when fiber is bend on a too small

radius.

The critical bend radius is given as

R c = 20 * ( /(n )1.5 ) . (2.748 -0.996 ( /c )-3

Macrobending induced attenuation depends on fiber parameters(Mode Field Diameter, MFD; and fiber cut-off wavelength, c). LowMFD and high cut-off values give better bend loss performance

(recommendation: MFD < 9.5 m and c >1.18 m). Current

specifications for the allowed macrobending loss are:

ITU-T G.652: 100 turns of fiber loosely wound on 37.5 mm

radius (approx. 23 m of fiber), allowed attenuation max. 1 dB

ETSI I-ETS 300 227: 100 turns of fiber loosely wound on 30

mm radius (approx. 19 m of fiber), allowed attenuation max.

0.2 dB

Typical manufacturers specifications are max. 0.1 dB for 37.5 mmbend radius. Typical results obtained at 30 mm bend radius are alsobelow the ETSI-specification limit of 0.2 dB, but margin to the

specification is not high.


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Attenuation vs. temperature:

Different operators have varying requirements for the max. change ofattenuation (1.31/1.55 m)

lower temperature limit -60 .... -40 oC

upper temperature limit +60 .... +85oC

allowed max. change at the temperature interval 0.05 ... 0.1 dB/km

Typical supplier specification -60...+85oC

Max. change 0.1 dB/km; change typically below 0.05 dB/km

At tenuat ion changes wi th temperature

Tem per a t u r e ( C )

Changefroms

tart(dB/km

- 0 . 0 2

0

0 . 0 2

0 . 0 4

0 . 0 6

0 . 0 8

0 . 1

20

-20

-40

-50

-60

85

20

-60

85

20

-60

85

20

-60

85

20

-60

20

1 5 5 01 9 . 3 . 9 4 G 4 0 1 3 A 5 3 2 B


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SPLICING LOSSES

Splicing fibers can cause additional losses due to geometric errors Splicing loss due to MFD-mismatch is almost negligible in practical

cases

Fiber cleave angle should be good (


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FIBER CURL

Optical fibres exhibit some degree of curvature when stripped from theircoating.

Large curvature can cause problems in mass fusion splicing of especiallyribbon fibers (see below)

Matrix material

Primary coating, two layers

Color layer

Glass

x

y

Curvature can be expressed:

Max curvature in 3 mm distance (describes splicing machine); onesupplier specification 2.25 m

Minimum radius on which the fiber is curved. 2 m corresponds to abovedefinition. Bellcore specification proposal 1.3 m (more loose than

above)


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DISPERSION AND BANDWIDTH CACULATION

During propagation the (narrow) transmitted pulse is broadened in the

fiber. The pulse broadening is due to fiber dispersion and source spectralcharacteristics

Below are equations to calculate the bitrate and bandwidth of the fiberonce dispersion and source properties are known. Here we assuming very

small input pulse, so that pulse width of that does not need to be taken

into account. Output pulse from fiber:

t

Output pulse from fiber

Average arrival time, t0

t0 = (1/S0)

.

t.

S(t) dt, where S0 = S(t) dt (first moment ofdistribution)

Spread of arrival time = Root mean square (rms) dispersion ( )

= [(1/S0) t2.

S(t) dt - t02]

0.5(second moment of distribution)

For Gaussian shape (only !) pulses = t / 2.35 (t = pulse width at50 % level)

3 dB optical bandwidth ( 6 dB electrical bandwidth) of the fiber is B =0.44 /t = 0.18 /. However, the more useful definition is 3 dBelectrical bandwidth calculated as follows (Sibley, p. 36):

B-3dBelec = 0.13 /= 0.31 /t

Maximum bitrate (Non Return to Zero= NRZ signaling) with approx. 1

dB power penalty due to dispersion (Ref:J.Gowar, Optical Communication Systems,

Prentice-Hall, 1984, ISBN 0-13-638056 5, p. 65)

R = 1 / (4 ) (for Gaussian pulses only R = 0.58 /t)


24/36


DISPERSION EFFECTS IN OPTICAL FIBERS

1. Modal dispersion (difference in flight time of the different rays)

Significant in multimode fibers

2. Material dispersion

Source wavelength is the key issue

Affects single-mode links and multimode systems with sources having

large spectral width

3. Waveguide dispersion

Limiting bandwidth in single-mode fibers, not significant inmultimode fibers

Wavelength (m)

Refract ive index

Pulse delay (ns/km)

Delay spread or

Material dispersion(ps/nm.km)

t m = (1/c) [ n - dn/d) ]

(1/L) dtm

/d = - (1/c) (d2n/d2) ]

MATERIAL DISPERSION IN

OPTICAL FIBER


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MATERIAL DISPERSION

If the carrier wave carries a signal that modulates e.g. the intensity of the

carrier, the modulation of the signal is not (usually) the as phase velocity inbulk media. It can be shown (Sibley), that

Phase velocity (velocity of carrier phase is:

Group velocity (velocity of signal):

We can calculate the delay / unit length in the fiber = 1 / vg:

1 / v g = (1/c) x [ n (dn/d ) ] = Ng / c

Material dispersion is the wavelength dependence of the group delay:

Dmat = d / d = - ( /c) x dn2/d2

A plot of material dispersion in silica based optical fiber glass is given

below (Miller, Chyoweth) for various glass materials

Material dispersion in undoped silica

(solid line), corresponding closely to

single-mode fiber and

13 % Ge doped silica (dashed line)

corresponding to Graded-Index fiber


26/36


MULTIMODE FIBER BANDWIDTH

In multimode fibers the total dispersion () is composed of material and

modal dispersions, mat and mod as follows: = [ mat

2 + mod2

]0.5

Modal dispersion is measured from the fiber with a narrowband laser

source. Material dispersion (only important in graded-index MM-fibers

when using LEDs at 0.85 m wavelength) is

mat = (nm). mat (ps/nm.km)

.Lfiber (km); where is the source rms

spectral width (= /2.35 for Gaussian shape distribution; is the half width

of the spectral distribution of the source)

Multimode graded-index fibre bandwidth for a long fiber (B) is:

B = Bl * (L/Ll )- , where B is bandwidth of L km long fiber(MHz.km), Bl is bandwidth of Ll km long fiber and isbandwidth concatenation exponent

Value of

is typically 0.7-0.8 (min value 0.5, max. value 1.0). Safe

(pessimistic) way in calculating link budget = 1.

The bandwidth of multimode fibers is at its best only about 1 Ghz.kmand dispersion can limit transmission bitrate already at 34 MBit/s.

Single-mode fiber is always advisable for bandwidth critical applications

(bandwidth on the order of 100 GHz.km).

Multimode fiber bandwidth is optimum only at one wavelenght at a time,

e.g. at 0.85 m or at 1.30 m (optimised by the shape of the refractiveindex profile).


27/36


Graded-index fiber bandwidth as a function of wavelength

(typical behaviour)

0

200

400

600

800

1000

1200

1400

800 1000 1200 1400 1600

Wavelength (nm)

Bandwidth(MHz.km) Optimised for 1.3 m

Optimised for 0.85 m


28/36


IMPORTANT TYPES OF MULTIMODE FIBERS

Multimode fibers have a large core and high numerical aperture and thus

low cost transmitter and connector components can be used.

50/125 m; 0.20 NA (ITU-T G.651, IEC 793-2 A1a)

Reasonable bandwidth (1-2 GHz.km @1.31 m) and attenuation

(0.5-1 dB/km @1.31 m)

Applications: high speed LAN, military applications etc.

62.5/125 m; 0.26- 0.29 NA (IEC 793-2 A1b)

Bandwidth approx. 0.2-1 GHz.km; attenuation 0.7-2 dB/km

@1.31 m

Applications: LAN (most important LAN-fiber), various

automation and machine applications etc.

In addition to above there is a large number of multimode fibers withvarying core size, NA, primary coatings, etc. for many applications in

data and light transmission (e.g. endoscopes).

For cable standards, please, refer also to:IEC 794-1 Test methods

IEC 794-2 Requirements of indoor cables

SESKO 56-88 in Finland, based on IEC 794-2


29/36


SINGLE-MODE FIBER DISPERSION

In single-mode fibers there is no delay spread due to different modes

Single-mode fiber dispersion is called chromatic dispersion and iscomposed ofmaterial and waveguide dispersions

In standard Single-mode fiber (ITU-T G.652) waveguide dispersion isrelatively small and dispersion is dominated by the material dispersion.

The zero dispersion wavelength is around 1.35 mm.

Waveguide dispersion is negative and can be used to compensatematerial dispersion. This requires special structure for the core (high

refractive index difference and small core size).


30/36


TYPES OF SINGLE-MODE FIBERS

Standard single-mode fiber, ITU-T G.652

Zero dispersion wavelength in 1310 nm region Most common type of fiber, suitable for up to 100-500 km links at 2.5 Gb/s Dispersion cases problems at higher bitrates when suing 1.55 m

wavelength

Dispersion shifted single-mode fiber, ITU-T G.653 This fiber is no longer installed due to problems with WDM systems Zero dispersion wavelength in 1550 nm region Dispersion shifting obtained with high ( 1 %) and triangular shape

profile, slightly higher attenuation than with G.652 fiber Attenuation optimised single-mode fiber, ITU-T G.654

Zero dispersion wavelength in 1310 nm region, higher dispersion at 1550 nmthan with G.652 fiber; Not common (Japan)

G.655 (Non-Zero Dispersion Dispersion-Shifted Fibre)

Low but not zero dispersion at Optical fiber amplifier (EDFA, OFA)transmission band 1530...1565 nm

State of the art Single-mode fiber for long transmission distances and highbit rate (10 GB/s), optimized for EDFAs and Wavelength Division

Multiplexing (WDM); replaces G.653 fiber.

Fiber for submarine links and very high bit rate long distance terrestial links


31/36


DISPERSION PROPERTIES OF SINGLE-MODE FIBERS

For standard single-mode fiber (G.652) the dispersion zero wavelenght

0 is around 1310 nm; for dispersion shifted fiber (G.653) 0 is around1550 nm.

The dispersion [ D() ] at wavelenght is calculated for G.652 SM-fibers from the ITU-T dispersion formula (according to G.650

specification) using the parameters from the dispersion measurement

(zero dispersion wavelength, 0 and dispersion slope, S0, at the zerodispersion wavelenghth).

D() = (S0 /4) * ( - 04 /3 )

Dispersion characteristics of various Single-mode fibers

-15

-10

-5

0

5

10

15

20

1200 1300 1400 1500 1600 1700

Wavelength [nm]

Dispersion[ps/nm

.km]

SM, G.652

SM-DS, G.653

NZ-DS, G.655

OFA band


32/36


Once fiber dispersion is known, total dispersion and bitrate can becalculated:

= (nm).fiber(ps/nm.km)

.Lfiber(km), where is the source rms spectral

width (= /2.35 for Gaussian shape distribution; is the half width of the

spectral distribution of the source)

The achievable bitrate is depends on the allowed dispersion power

penalty, a typical estimate can be obtained from

R=1/4

With typical values for 80 km standard SM-fiber and directly modulatedDFB-lasers (laser having = 0.07 nm; corresponding to a laser

wavelength distribution half width of 0.16 nm)

R= 1 / 4.( 0.07 nm

.18 (ps/nm.km)

.80 km ) = 2.5 GBit /s


33/36


POLARISATION MODE DISPERSION (PMD)

The single-mode fiber propagates actually two orthogonal polarisation

modes.

In asymmetric fibers (geometrical or stress anisotropy), the polarisation

modes may have different propagation delay causing dispersion called

polarisation mode dispersion (PMD). PMD is added to chromatic

dispersion by square law.

The phenomenon causes problems in multichannel analog cable-TV

systems and high bitrate long transmission distance systems (10 Gbit/s).

PMD is expressed in ps/km0.5. The PMD of L km long fiber is:

PMD = PMD fiber(ps/(km)0.5 ).(Lfiber )0.5

E.g. PMD = 0.5 ps /(km)0.5 (Typical cable specification today). PMD of100 km fiber is (0.5 ps / km0.5 )

.(100 km)0.5= 5 ps. According to

ITU-T G.691, the value of total PMD for the link should be < 10 % of

the bit period, e.g. < 10 ps for 10 Gb/s system.

The maximum PMD for digital systems is 0.5 ps /(km)0.5 for 10 Gbit/sand 400 km. For 2.5 Gbit/s the requirement for 400 km link is 2 ps

/(km)0.5 which is easy even with old cables.

Optical components may also have high PMD values.


34/36


FIBER LIFETIME AND RELIABILITY

The breakage strength of todays high quality 125 m OD silica fiber isapproximately 4.5 GPa (corresponding force F=4.5.109

N/m2.

((0.125)2/4 mm2)) = 55 N = 5.6 kg

Permanent stresses much below this value may cause reduction ofstrength and fiber breakage in extreme cases.

To guarantee a certain minimum strength, every meter of fiber has beentested for strength in the factory. Typical proof-test load is 9.3 N (0.74

GPa) corresponding to 1 % elongation of the fiber ( 6.1 mm bend radius).

Bending the fiber also causes a permanent stress on the fiber

During lifetime the permanent stress must be less than about 20 % of theproof-test load in good conditions. This means max. 1.9 N pulling

tension or 30 mm bending radius.

Coating and its stickeness on the fiber are very important for thereliability of the fiber. In bad conditions (high temperature and relative

humidity) stress levels have to be relaxed: Max. temperature of the fiber

is around 70oC, there must be no condensing humidity on the fiber;

since these can quickly reduce the strength (in weeks).


35/36


LIFETIME EVALUATION

Predicted fiber lifetime with full Nokia model

1.00E+00

1.00E+02

1.00E+04

1.00E+06

1.00E+08

1.00E+10

1.00E+12

1.00E+14

0.00 0.20 0.40 0.60 0.80 1.00

Applied stress divided by proof test stress

Applicationtime(s

n=20

25 years

1 % failure probability for 1000 km of fib

Applied stress / Proof-test stress vs. lifetime of fiber

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

0 10 20 30

Fiber lifetime (years)

Applidstress/proof-test

stress

Series1

Series2

n = 20 (good conditions)

n = 15 (bad conditions)


36/36

STRENGTH CONVERSION FACTORS

Strain: = f / (SE)

Youngs modulus (Ref. 1) E = E0 (1 + 3 )Stress = f / S

Equivalent stress nt = n t

Bending strain vs radius tmax = r ( R + r + t )

where

f load (N)

S cross sectional area (m2)

E0 72 GPa for fused silica

n static fatigue parameter

t stressing time

r radius of fiber

t thickness of coating

1 kg = 0.799 GPa = 116 ksi = 116 psi

Strain, % Load, kg Stress, GPa Eqv. bend radius, mm

____________________________________________________________________

0.5 0.46 0.37 12.4

0.7 0.64 0.51 8.8

1 0.93 0.74 6.1

2 1.91 1.53 3.0

3 2.95 2.35 2.0

4 4.04 3.23 1.4

Bibligraphy:

Allen H. Cherin, Introduction to optical Fibers, McGraw-Hill, 1983, ISBN 0-07-010703-3(when ordering use 0-07-Y66222-3), 326 p.

Ajoy Ghatak, K.Thyagarajan, Introduction to Fiber Optics, Cambridge University Press,

Cambridge, UK, 1998, ISBN 0-521-57785-3, 565 p.

M.J.N. Sibley, Optical Communications, Macmillan Education Ltd., London, 1990, ISBN 0-

333-47513-5, 152 p.

5.Miller, A.G. Chyweth (Eds.), Optical fiber telecommunications, Academic Press, New

York, 1979, 705 p.

opticalfiber characteristics

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