3 Propagation Fibre

Dublin Institute of Technology

Dr. Gerald Farrell

Optical Communications Systems

School of Electronic and Communications Engineering

Unauthorised usage or reproduction strictly prohibitedCopyright 2002, Dr. Gerald Farrell, Dublin Institute of Technology

Propagation in Fibre

18/03/02 1.3 Propagation in Fibre.prz

Optical Communications Systems, Dr. Gerald Farrell, School of Electronic and Communications Engineering

Unauthorised usage or reproduction strictly prohibited, Copyright 2002, Dr. Gerald Farrell, Dublin Institute of Technology

How many light rays??

Range of angles over which light will

be transmitted

Range of angles over which light will not be transmitted

Recall that only light rays which enter the core with an angle less than the acceptance angle will propagate

There are an infinite number of possible ray angles, all less than acceptance angle

In theory then there are an infinite number of light rays?

Source: Master 2_1




Observing Modes Experimentally

Visible light is used as a source, typically HeNe laser (Red, 670 nm)

Output from a fibre is projected onto a reflective surface, such as a white card in a darkened room

Output from singlemode fibre, HE11 mode

Output from a multimode fibre, a so-called speckle pattern

Output from a fibre supporting two modes

Source: Master 2_1




Electromagnetic Modes in Fibre

To obtain an improved model for propagation in a fibre, EM wave theorymust be used.

Ray diagram or Geometric Optics approach remains useful as a way tovisualise propagation in a fibre.

Basis of EM analysis is a solution to Maxwells equations for a fibre.

For ease of analysis a fibre is frequently replaced by a planar opticalwaveguide, that is a slab of dielectric with a refractive index n1, sandwiched between two regions of lower refractive index n2.

n2

n2

n1

Planar waveguide

Source: Master 2_1




Formation of Modes in a Fibre (I)

Propagation of an individual ray takes place in a zigzag pattern as shownIn practice there is at the fibre input an infinite number of such rays, calledmore properly plane rays.Each ray is in reality a line drawn normal to a wavefront, for example the wavefront shown by the dotted line FC above. For plane waves all points along the same wavefront must have identical phase.The wavefront intersects two of the upwardly travelling portions of the same ray at A and C.

B

FE

A

CD

θθ

d

Source: Master 2_1




Formation of Modes in a Fibre (II)

Unless the phase at point C differs from that at point A by a multiple of 2π π then destructive interference takes place and the ray does not propagate.

Moving along the ray path between A and C involves a phase change causedby the distance AB and BC and a phase change caused by reflection

Combining these two phase changes and setting the result equal to a multipleof 2ππ we get a condition for propagation of a "ray", more properly now calleda mode.

Source: Master 2_1

FE

A

CD

θθ

d




Types of Optical Fibre

Three distinct types of optical fibre have developed

The reasons behind the development of different fibres are explored later

Concern here is to examine propagation in the different fibres

The three fibre types are:

Step index fibre

Graded index fibre

Singlemode fibre (also called monomode fibre)

Multimode fibres

Source: Master 2_1




Step Index Fibre

Source: Master 2_1




Step Index Fibre

Simplest and earliest form of fibre

The larger the core diameter the more modes propagate

With a large core diameter many thousands of modes can exist

N1N2

Refractive index profile for a step index optical fibre

CoreDiameter

CladdingDiameter

Core

Cladding

0

Source: Master 2_1




Normalised Frequency for a Fibre

For an optical fibre we can define the so-called normalised frequency "V"

Convenient dimensionless parameter that combines some key fibre variables

It is defined thus:

λλV =

2ππ a.NAV is also very commonly defined using the numerical aperture NA thus:

We will use this definition

Source: Master 2_1

. n1 - n22ππa

λλV =

2 2

where a is the fibre radius and λλ is the operating wavelength




Relative Refractive Index

It is also possible to define a so called relative refractive index for a fibre

Normally the symbol ∆ ∆ is used

∆∆ is defined thus:

if ∆ ∆ is << 1 then ∆∆ is given by:

Source: Master 2_1

∆∆ = n1 - n2

2n1

2 2

2

∆∆ = n1 - n2

n1

The normalised frequency V can be written in terms of ∆∆ : λλ

V = 2ππ a.n1 2∆∆




Modes in a MM Step Index Fibre

In a multimode step index fibre, a finite number of guided modes propagate. Number of modes is dependent on:

Wavelength λ, λ, Core refractive index n1

Relative refractive index difference ∆, ∆, Core radius a

Number of propagating modes (M) is normally expressed in terms of the normalised frequency V for the fibre:

M = V2

2

Source: Master 2_1

Problem: A step index fibre with a core diameter of 80 µm has a relative refractive index difference of 1.5%, a core refractive index of 1.48 and operates at 850 nm.

Show (a) that the normalised frequency for the fibre is 75.8 and (b) that the number of modes is 2873




Influence of Core Size and Wavelength

Source: Master 2_1

As the core diameter increases and with it the normalised frequency, the number of modes increases with a square law dependency on core size

As the wavelength increases the number of modes decreases

0

5000

10000

15000

20000

25000

30000

50 100 150 200 250

Core Diameter in microns

Nu

mb

er o

f m

od

es

850 nm

1320 nm




Graded Index Fibre

Source: Master 2_1




Graded Index Fibre

N1N2

Core Diameter

CladdingDiameter

Core

Cladding

0

Parabolic variation in refractive index

Typical core diameter for this fibre type: 50 to 120 µm

Different refractive index profiles have developed

Source: Master 2_1




Propagation in a Graded Index Fibre

An expanded ray diagram for a graded index fibre, showing a discrete numberof refractive index changes n1 to n6 for the fibre axis to the cladding.

Result is a gradual change in the direction of the ray, rather than the sharpchange which occurs in a step index fibre

Source: Master 2_1




Propagation in a Graded Index Fibre

Cladding

Coreba

Fibre Axis

Light ray (a) and (b) are refracted progressively within the fibre. Notice that light ray (a) follows a longer path

within the fibre than light ray (b)

Meridional (axial) rays follow curved paths in the fibre as shown

Benefits of using graded index design are considered later

Source: Master 2_1




Graded Index Fibre Profiles

Refractive index profiles for Graded Indexfibres

The index variation n(r) in a gradedindex fibre may be expressed as

a function of the distance (r)from the fibre axis

n(r) = n1 (1-2∆ ∆ (r/a))αα

n1 (1-2∆∆) = n2n(r) =

for r < a (core)

for r > a (cladding)

Most common value of the profileparameter αα is 2, a so called

parabolic profile. An infinite profileparameter implies a step index fibre

Source: Master 2_1




Modes in a Graded Index Fibre

Calculating the number of modes in a graded index fibre is very involved

As an approximation it can be shown that the number of modes is dependent on the normalised frequency V and on the profile parameter α.α.

That is M = V2

2

where ∆∆, is again given by: ∆∆ = n1 - n2

n1

αααα + 2

if ∆ ∆ is << 1

Exercise

For the most common value of αα show that for fibres with similar relative refractive indices, core radii and operating wavelengths, the number of modes propagating in a step index fibre is twice that in a graded index fibre

Source: Master 2_1




Singlemode Fibre

Source: Master 2_1




Singlemode Optical Fibre

Cladding

Small Core

N1N2

Small Core Diameter

CladdingDiameter

Core

Cladding

0

Refractive indexprofile

Source: Master 2_1




Refractive Index Profiles for SM Fibres

Multimode step index Multimode graded index

Conventional singlemode fibre (so called matched cladding)

Depressed cladding singlemode fibre (less susceptible to bend loss)

Triangular profile singlemode fibre (used in dispersion shifted fibre)

Up-and-down profile singlemode fibre (used in dispersion flattened fibre)

also called multicladding fibre




Normalised Frequency for SM Fibres

Singlemode fibre exhibits a very large bandwidth and has thus becomethe fibre of choice in most high speed communications systems.

Singlemode operation is best considered with the aid of the fibre normalised frequency V:

Single mode operation takes place where V is less than the so-called cutoff value of Vc = 2.405.

The single mode is the lowest order mode that the waveguide will support, referred to as the HE11 mode. This mode cuts off at V=0.

As will be explained practical V values are normally between about 2 to 2.4

Singlemode operation is achieved by altering the fibre radius, NA or the wavelength in use so that V lies in the range above.

λλV = 2ππ a . NA

Source: Master 2_1




Energy Distribution in a Singlemode Fibre

The amplitude distribution of the optical energy in a singlemode fibre mode is not uniform, nor is it confined only to the core

In multimode fibres if we assume a mode model instead of ray diagram approach then some small percentage of the energy is contained within the cladding close to the core, but typically < 1% so the ray model is still a valid view

Ray diagram model does not work for singlemode fibre

Source: Master 2_1

Multimode energy distribution is

confined to the core

Singlemode energy distribution peaks in the centre of the core(Darker shading = higher energy)

CladdingCore Cladding

Core

> 50 µm 7-9 µm




Mode Field Diameter and Spot Size (I)

Mode field diameter (MFD) is an important property of SM fibres.

The amplitude distribution of the HE11 mode in the transverse plane is not uniform, but is approximately gaussian in shape, as shown below

Fibre centre

The spot size is the mode field radius w. Its value relative to core radius is

given by the expression:

w a

= 0.65 + 1.619V + 2.879V- 3/2 - 6

The MFD is defined as the width of the amplitude distribution at a level 1/e (37%) from the peak or for power

13.5%from the peak

Source: Master 2_1




Mode Field Diameter and Spot Size (II)

As the V value approaches 2.4 the spot size approaches the fibre radius.

For V < 2 the spot size is significantly larger than the core size.

For V < 2 the beam is partially contained within the cladding and loss increases

For this reason V should be between about 2 and 2.4

MFD or spot size is frequently specified as well as core radius or diameter for the fibre

1.2 1.4 1.6 1.8 2.0 2.2 2.4

V value

1

1.5

2

2.5

3

w/a

Normalised spot size as a function of the fibre V value

Source: Master 2_1




Cutoff Wavelength

a NAλλ c = 2ππVc

Singlemode operation only takes place above a theoretical cutoff wavelength λλ c where V < Vc = 2.405

In practice the theoretical cutoff wavelength is difficult to measure. An alternative is EIA (Electronics Industry Association of America) cutoff wavelength, which states that the cutoff wavelength is:

The wavelength at which the power in the HE21 mode is 0.1 dB of the power in the HE11

(fundamental mode)

The EIA cutoff wavelength can be 100 nm less than the theoretical cutoff wavelength

Source: Master 2_1




SM Fibre Summary and Problem

Core size is a useful parameter for multimode fibres, but is not so useful for SM fibres.

Telecommunications systems are normally designed to work close to the cutoff wavelength for good power confinement (small spot size), but not close enough to cutoff so that significant power is carried in higher modes.

Exercise

A singlemode fibre has a core refractive index of 1.465 and a cladding refractive index of 1.46. What is the maximum core size if the fibre is to support only one mode at 1300 nm?

Answer: core radius 4.11 microns, 8.23 microns core diameter.

If the wavelength is increased to 1550 nm what is the new fibre V value, the spot size and the MFD?

Answer: V = 2.02, Spot size 5.18 microns, MFD 10.4 microns

Source: Master 2_1


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