FIBER CONFIGURATIONS

STEP INDEX FIBERS

• Refractive Index Profile

• Ray transmission and Mode density

• Power flow in Core and Cladding

GRADED INDEX FIBERS

• Refractive Index Profile

• Ray transmission and mode density

SINGLE MODE FIBERS

• SM Operation parameters

• SM Designs

Step Index Fibers

Fiber with a core of constant refractive index n1 and a cladding

of slightly lower refractive index n2 .

• Refractive index profile makes a step change at the core-cladding interface

The refractive index profile and ray transmission

in step index fibers: (a) multimode step index

fiber. (b) single-mode step index fiber.

Refractive index profile

n1 r<a (core)n(r) =

n2 r a (cladding)

• Multimode Step Index

• Single mode Step Index

Single mode SI fiber has a distinct advantage of low intermodal

dispersion (broadening), as only one mode is transmitted, whereas

with multimode SI fiber considerable dispersion may occur due to

the differing group velocities of the propagating modes.

For lower BW applications MMFs have several advantages over

single mode fibers.

Use of spatially incoherent sources (LEDs), which cannot

be coupled to single mode fibers;

Larger NA, as well as core diameters, facilitating easier

coupling to optical sources;

Lower tolerance requirements on fiber connectors;

This restricts the maximum bandwidth attainable with multimode SI

fibers, when compared with single mode fibers.

Modes in SI Fibers

• MM SI fibers allow the propagation of a finite number of

guided modes along the channel.

Number of guided modes is dependent upon the physical parameters ; a,

of fibers and wavelength of the transmitted light – included in V-number

• The total number of guided modes or mode volume Ms for SI

fiber is related to V-number for the fiber by approximate

expression (G Gloge,1971, Weakly guided fibers)

Ms V2/2

Allows an estimate of number of guided modes propagating in a

particular MM SI fiber.

For example: A MM SI fiber of core diameter 80m, core refractive index 1.48,

relative index difference of 1.5% and operating at 850nm supports 2873 guided

modes.

Power flow in Step-Index Fibers

• Another quantity of interest in fibers is the fractional power

flow in the core and cladding for a given mode.

• Thus EM energy of a guided mode is

carried partly in the core and partly in the

cladding.

• The farther away the mode is from its cutoff

frequency the more concentrated its energy

in the core.

• As cutoff is approached, the field penetrate

further into the cladding region and a

greater percentage of energy travels in the

cladding.Four possible TE and TM fields and the

intensity distribution for the LP11 mode.

The EM field for a given mode does not go to zero at the core-cladding

interface, but changes from oscillating form in the core to an exponential

decay in the cladding (Evanescent Field).

Fractional power flow in the cladding of a

SI fiber as a function of V.

• Under weakly guided mode

approximation;

Gloge et al, has determined the

relative powers in core and

cladding for a particular modes as

P

P1

P

P coreclad

• Plots of fractional powers Pcore/P

and Pclad/p for various LPlm modes

The relative amount of power flowing in the core and cladding

can be obtained by intergating Poynting vector in the axial

direction over the fiber cross-section.

Sz= ½Re(EH*).ez

• Far from the cutoff the average power in the cladding has been

derived for the fibers in which many modes can propagate.

Because of this large number of modes, those few modes

that are appreciably close to cutoff can be ignored to a

reasonable approximation.

The total average cladding power is thus approximated by

21

M3

4

P

P

total

clad

Here M is the total number of modes

entering the fiber

Since M is proportional to V2, the power flow in the cladding is

inversely proportional to V Pclad decreases as V increases.

For V = 1; 70% of power flow in cladding

For V = 2.405; 20% of power flow in cladding.

Graded Index Fiber Structure

• GI fibers do not have a constant refractive index in the core, but a

decreasing core index n(r) with radial distance from a maximum

value of n1 at the axis to a constant value n2 beyond the core

radius ‘a’ in the cladding

Inhomogeneous core fibers

The refractive index profile and ray transmission in a multimode

graded index fiber.

Possible fiber refractive index profiles for

different values of

= ; Step index profile

= 2; Parabolic profile

=1; Triangular profile

Index variation is represented as

where, ‘’ is relative refractive index difference and ‘’ is the profile

parameter which gives the characteristic RI profile of the fiber core.

A helical skew ray path within a graded index fiber

Skew ray Propagation

An expanded ray diagram showing refraction at the

various high to low index interfacial within a graded

index fiber, giving an overall curved ray path.

• Gradual decrease in RI from

the centre of the core creates

many refractions of the rays

effectively from large number

of high to low index interfaces

• Ray is gradually curved with

an ever-increasing angle of

incidence, until conditions of

TIR are met.

Graded Index Fiber Parameters

Local numerical aperture

Axial numerical aperture

• The parameters defined for SI fibers ( NA, , V) may be applied to GI

fibers and give comparison between two.

• However, in GI fibers situation is more complicated because of radial

variation of RI of core from the axis, NA is also function of radial distance.

• Number of bound modes in graded index fiber is

2

V

2)kan(

2M

22

1g

• For parabolic profile core ( =2),

Mg=V2/4 , which is half the number

supported by a SI fiber with sane V

value

Single-Mode Fiber (SMF)

Signal dispersion caused by delay differences between different modes in a MMF may be avoided by designing fibers which allow only one mode to propagate within an optical fiber.

Step-Index type with very small core radius.

Most common design: 8-10 /125m , NA ~ 0.1-0.15, Small (< 1%)

SM propagation of LP01 mode within range 0V<2.405 with cutoff for LP11

mode at Vc=2.405.

n

r

1.4651.460

SM-Graded Index Fibers

• GI fibers may also be designed for single-mode operation.

• Some specialist fiber designs do adopt such non-step index profiles.

• Cutoff value of normalized frequency ‘Vc’ to support a single GI fiber

Vc=2.405(1+2/)½

2 2

3

• Possible to determine fiber parameters for SM operation

• For parabolic profile core, Vc = 2.4 ; increase by a factor of on SI case.

This gives a core diameter increased by similar factor with equivalent core RI

and same .

• Choosing triangular profile ( =1), a factor of can be achieved over

comparable SI fiber and hence larger core diameter SMFs may be produced

utilizing this index profile.

SMF- Cladding

Another problem with SMFs with low and low V values

EM field associated with LP01 mode extends appreciably into the cladding.

For V<1.4, over half the modal power propagates in the cladding.

Exponentially decaying evanescent field may extend significant

distance into the cladding.

Essential that cladding be of suitable thickness, and has low absorption

and scattering loses in order to reduce attenuation of the mode.

Estimates show that the necessary cladding thickness is of the order of

50m to avoid prohibitive losses in SMFs.

Thus, total fiber cross section for SMFs is of a comparable size to

MMFs, which is 125 m.

Single mode W-Fiber

Another approach to SMF design which allows the V value to

be increased above 2.405 is the W-fiber

Refractive index profile for a single-

mode W fiber

RI profile with two cladding regions.

• Two step cladding allows the loss

threshold between the desirable and

undesirable modes to be substantially

increased.

• The fundamental mode is fully supported

with small cladding loss with in the

range kn3< <kn1

• If the undesirable modes which are excited to have values of <kn3, they will

leak through the barrier layer between a1 and a2 into the outer cladding region n3.

Consequently loose power by radiation into the lousy surrounding

• W-design can provide SMFs with larger core diameters; proves useful for easing

joint difficulties – reduced losses at bends.

Importance of SMFs Although SMFs have emerged only since 1983, they have quickly

become the dominant and the most widely used fibers within

Telecom sector. Major reasons for this situation are;

• They currently exhibit the greatest transmission bandwidths and the lowest

losses of the fiber transmission media.

• They have a superior transmission quality over other fiber types because of

the absence of modal noise

• They offer a substantial upgrade capability (i.e. future proofing) for future

wide bandwidth services using either faster optical transmitters and receivers

or advanced transmission techniques (e.g. coherent technology).

• They are compatible with the developing integrated optics technology.

• The above features provide a confidence that the installation of SMFs will

provide a transmission medium which will have adequate performance such

that it will not require replacement over its twenty-plus-year anticipated

lifetime.

Dispersion Optimized SMFs

In the conventional MC fibers, the region external to the core has a constant

uniform refractive index, which is slightly lower than the core region. A mode-

field diameter (MFD) of 10 m is typical for MC fibers with relative refractive

index differences of around 0.3%.

In the DC fibers the cladding region immediately adjacent to the core is of a

lower refractive index than that of an outer cladding region. A typical MFD of a

DC fiber is 9 m with positive and negative relative refractive index

differences of 0.25% and 0.12%.

Most commonly used SMFs employ a SI profile and are dispersion optimized

for operation in the 1300nm wavelength region. These are either of a matched-

cladding (MC) or a depressed-cladding (DC) design.

More recent experimental MC fiber design employs a segmented core. Such a

structure provide conventional single-mode dispersion optimized performance

at wavelengths around 1.3 m but is multimoded with a few modes (two or

three) in shorter wavelengths. Helps to relax the tight tolerances involved

when coupled to LEDs and their connectorization.

Dispersion Optimized Designs

Single-mode fiber step index profiles optimized for operation at a wavelength

of 1.3 m: (a) conventional matched-cladding design; (b) segmented core

matched-cladding design; (c) depressed-cladding design; (d) profile

specifications of a depressed-cladding fiber.

Cutoff Wavelength

• SM operation only above a theoretical cutoff wavelength, c:

21

2V

na2

c

1c

c is the wavelength above which a particular fiber becomes single-moded

c

c

V

V

Further, we can obtain :

For SI fiber, Vc=2.405, the cutoff wavelength is

405.2

Vc

Power distribution:

• At V=2.405: 80% of mode’s power in core

• At V=1: only 30% power in core;

• Do not want V too small, design compromise: 2<VSM SI<2.405

• MFD an important parameter for characterizing SMF

properties. It takes into account the wavelength

dependent field penetration into the fiber cladding.

• For single mode fibers better to measure the geometric

distribution of light in the propagating mode(MFD)

rather than the core diameter or the NA.

• For SI and near parabolic profiles, field distribution is

almost Gaussian and MFD is generally taken as

distance between the opposite 1/e field amplitude or

1/e2

power points.

MFD = 2W0 ; W0 is mode-field radius

Mode-field diameter (MFD)

For real fibers and those with arbitrary RI profiles,

the radial field distribution is not strictly Gaussian

and hence alternative techniques have been proposed

Petermann Definitions

Effective Refractive Index

Convenient to define an effective refractive index for SMF, sometimes

referred to as a phase index or normalized phase change coefficient,

neff = /k ; ratio of propagation constant of the fundamental mode to that of the vacuum propagation constant

Hence, wavelength of the fundamental mode’01’ is smaller than the vacuum wavelength ’’ by the factor 1/neff i.e

01 = / neff

Rate of change of phase of fundamental LP01 mode propagating along a straight

fiber is determined by phase propagation constant , which is directly related to

the wavelength of the LP01 mode 01 by the factor 2.

01 = 2 or 01 = 2/

It should be noted that the fundamental mode propagate in a medium with a refractive

index n(r) which is dependent on the distance r from the fiber axis. The effective

refractive index can therefore be considered as an average over the refractive index of

this medium.

Effective Refractive Index

At long wavelength (small V values), the MFD is large compared to the core

diameter and hence electric field extends far into cladding region.

The propagation constant n2k (cladding wave number) and effective

index will be similar to refractive index of the cladding n2. Physically,

most of the power is transmitted in the cladding material.

At short wavelength, the field is concentrated in the core region and

approximate to the maximum wave number n1k

As the propagation constant for single mode fiber varies over the

interval n2k< <n1k, hence, the effective refractive index will

vary over the range n2< neff <n1

Within normally clad fiber

Effective Refractive Index & Normalized

Propagation constant (b)

22

2

22

1

22

2

2

2

2

2

1

2

2

2

knkn

kn

nn

nk/b

Normalized propagation constant is

or

knknknkn

knknb

2121

22

Taking the fact that n1k, 21

2

21

2

nn

nk

knkn

knb

Finally, as neff is equal to /k, therefore,

21

2eff

nn

nnb

Dependence of b on V

The dimensionless parameter ‘b’ which varies between 0 and 1 is

particularly useful in theory of SMFs because ‘’ is very small

giving only a small range for .

• Moreover, it allows a simple graphical

representation of results to be

presented by the characteristic curve of

normalized phase constant of as a

function of normalized frequency V in

a SI fiber.

• Note that b(V) is a universal function,

which does not depend explicitly on

other fiber parameters.Normalized propagation constant (b) of

the fundamental mode in a SI fiber as a

function of normalized frequency (V)

Group delay and Mode delay factor

The transit time or group delay ‘g’ for a light pulse propagating along a unit

length of fiber is the inverse of the group velocity ‘vg’ .

dk

d

c

1

d

d

v

1

g

g

The group index of uniform plane wave propagating

in a homogeneous medium has been determined as; g

gv

cN

For SMFs, it is usual to define an effective group index Nge by:

where Vg considered to be group velocity of fundamental fiber mode g

gev

cN

Hence, specific group delay for the

fundamental fiber mode becomes; c

Nge

g

Moreover, the effective group index may be written in terms of the effective

refractive index ‘neff’ as

d

dnnN eff

effge • Same form of relation as for

planar guide

Mode delay factor & V

‘’ can be expressed in terms of and b by approx. expression

b1knnbnnk 2

2

2

2

2

2

1

21

Further approximating, (n1-n2)/n2 for weakly guiding fiber where <<1,

we can use

2g

2g1g

2

21

N

NN

n

nn

Ng1 and Ng2 are group indices for fiber core

and cladding.

Substituting for and using approx. expression for , we obtain group delay

per unit distance as

dV

)Vb(d)NN(N

c

1

dk

d

c

12g1g2gg

Since, dispersive properties of fiber core and cladding are almost

same, therefore the wavelength dependence of can be ignored

Variation of Mode delay factor with V

Hence, the group delay is

dV

)Vb(dnN

c

122gg

The Ist term gives the dependence of group delay on wavelength caused when uniform

plane wave is propagating in an infinitely extended medium with a refractive index

which is equivalent to that of the fiber cladding.

The 2nd term results from the waveguiding

properties of fiber only and is determined by the

mode delay factor d(Vb)/dV, which describes the

change in group delay caused by the changes in

power distribution between fiber core and

cladding.

Mode delay factor for fundamental

mode in SI fiber as a function of V

Mode delay factor is another universal

parameter which plays a major part in

the theory of SMFs.