Chapter 2a

Chapter 2:

Dielectric waveguide and optical fibre

Optical Fiber Network Map

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Communication Systems

• Each form of communication systems have the basic motivations as:– To improve the transmission fidelity/accuracy– To increase the data rate– To increase the transmission distance between relay

stations

Communication Systems

• Data are usually transferred over the channel by superimposing the information onto a sinusoidally varying electromagnetic wave (carrier).

• The amount of information that can be transmitted is directly related to the frequency range over which the carrier operates, increasing the carrier frequency theoretically increases the available transmission bandwidth

Fig. 1

Charles K. Kao

The introduction of optical fiber systems will revolutionize the communications networks. The low-transmission loss and the large bandwidth capability of the fiber systems allow signals to be transmitted for establishing communications contacts over large distances with few or no provisions of intermediate amplification.”

Historical Perspective of Optical Fiber Communication

• 1880 Graham Bell’s Photo-phone• 1960 Invention of laser for unguided transmission.• 1966 Kao demonstrated transmission of light through

optical fiber, but the attenuation was then 1000 dB/km compared to coaxial cable with attenuation of 5 dB/km

• 1976 Attenuation of fiber reduced to 5 dB/km• At present, the minimum attenuation of glass fiber is

reported to be 0.2 dB/km.

Fiber Optic as a Communication Medium

• Wide bandwidth (up to 10 terahertz), higher bit rate (up to 40 Gbps)

• Low attenuation (as low as 0.2 dB/km, attenuation is almost constant at any signaling frequency within the specified bandwidth of fiber)

• Electromagnetic immunity (signals are not distorted by the EMI)

• Light weight• Small sizes• Safety (does not carry electricity)• Security (cannot be tapped to eavesdrop)

Three common types of fibre materials

1. All glass fibre– The refractive index range of glass is limited, hence the refractive index

difference n1-n2 to be small. The small value then reduces the light coupling efficiency of the fibre.

– The attenuation loss is the lowest.– Suitable for long distance transmission and high capacity.

2. Plastic Cladded Silica (PCS)– Higher loss, suitable for shorter links.– Tunable refractive index, the refractive index difference can be large.

Therefore, the light coupling efficiency is better. 3. All Plastic Fibre

– Highest loss for very short links.– The core size are large (1mm), light coupling efficiency is high.

Rectangular Dielectric-Slab (Planar) Waveguide

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Rectangular Dielectric-Slab (Planar) Waveguide Within an integrated optic network, light is

transferred through rectangular dielectric-slab waveguide

The rectangular structure is much easier to analyse than the circular fibre geometry.

It will help us to visualize the light propagation in fibres.

Mode of Propagation in Dielectric-Slab (Planar) Waveguide

• To analyse the mode of the electric field pattern for a light propagating in a slab dielectric wave guide, the following considerations are taken into account:

1. A light ray travelling in the guide must interfere constructively with itself to propagate successfully.

2. Two arbitrary wave 1 and 2 that are initially in phase must remain in phase after reflections.

3. Interferences of waves such as 1 and 2 leads to a standing wave pattern along the y direction, which propagates along z.

1. Constructive interference with itself for a light ray travelling in the guide

• Consider a slab of dielectric of thickness 2a – Refractive index of core is n1

– Refractive index of cladding is n2 (< n1)

• Let a plane wave type of light ray propagating in the waveguide as shown in Fig. 2

– This ray is reflected at B and at C– Just after the reflection at C, the wavefront at C

interferes with the wavefront at A (its own origin).– Unless these wavefronts at A & C are in phase, the

two will interfere destructively & destroy each other.

n2

n2

d = 2a

k1

Light

A

B

C

E

n1

A light ray travelling in the guide must interfere constructively with itself topropagate successfully. Otherwise destructive interference will destroy thewave.

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

z

y

x

Fig. 2

Waveguide condition

• For constructive interference,D f (AC) =k1 (AB+BC) – 2f = m (2p)

m = 0, 1, 2,… and k1 = k n1 = 2pn1/l k & l are free space wavevector & wavelengthf is a phase change due to total internal reflection at B or C• Thus, waveguide condition is

[2 p n1 (2a)/l] cosqm – fm = m p [1]

fm indicates that f is a function of the incidence angle qm.• So for each m, there will be one allowed angle qm and one

corresponding fm.

2. Constructive interference for two arbitrary parallel rays travelling in the guide

• The same waveguide condition as the first consideration can be derived if we consider two arbitrary parallel rays entering the guide as in Fig.3.

• The rays 1 & 2 are initially in phase– Ray 1 suffers two reflections at A & B and then again

travel parallel to ray 2– Unless the wavefront on ray 1 just after reflection at B

is in-phase with the wavefront at B’ on ray 2, the two would destroy each other.

n2

n2

z2a

y

A

1

2 1

B

A

B

C

k1

Ex

n1

Two arbitrary waves 1 and 2 that are initially in phase must remain in phaseafter reflections. Otherwise the two will interfere destructively and cancel eachother.


Fig. 3

3. Constructive interference of waves such as 1 & 2 leads to a standing wave

pattern

• If we were to consider the interference of many rays as shown in Fig. 3, – we would find that the resultant wave has a stationary

electric field pattern along y-direction,– and this field pattern travels along the guide, z-axis.

• Consider ray 1 after reflection at A is travelling downward, whereas ray 2 is still travelling upward as shown in Fig.4– The two meet at C, distance y above the guide centre– These two wave interfere to give

E (y, z, t) = 2Eo cos (my + ½m) cos ( t– mz+ ½m)

n2

z

ay

A

1

2

A

C

kE

x

y

a y

Guide center

Interference of waves such as 1 and 2 leads to a standing wave pattern along the y-direction which propagates along z.


Fig. 4

• E1(y,z,t) = Eo cos (t – mz + my + m)

E1= Eo cos [(t – mz +½m)+ (my + ½m)]

• E2(y,z,t) = Eo cos (t – mz – my)

E2= Eo cos [(t – mz +½m) – (my + ½m)]

• E (y, z, t) = E1(y,z,t) + E2(y,z,t)

E = 2Eo cos (my + ½m) cos (t – mz +½m)

E = 2 Em (y) cos (t – mz +½m)

• where Em (y) = Eocos (my + ½m)

Field distribution along y

• A light wave propagating along the guide is E (y, z, t) = 2Em(y) cos ( t– mz) []– in which Em(y)=Eocos(my + ½m) is the field along y

for a given m. (no time dependence & corresponds to a standing wave pattern along y)

– Em(y) is travelling down the guide along z

m =k1sinm =(2 n1/) sinm

m =k1cosm =(2 n1/) cosm

m = m (y) = m – y/a(m +m)

The electric field pattern in a slab dielectric waveguide

• Fig. 5 shows the field pattern for the lowest mode, m=0, with maximum intensity at the centre– The whole field distribution is moving along z with

a propagation vector b0.

• Fig. 6 illustrates the field pattern for the first three modes, m=0, 1 & 2.

n2

Light

n2

n1

y

E(y)

E(y,z,t ) = E(y)cos(t – 0z)

m = 0

Field of evanescent wave(exponential decay)

Field of guided wave

The electric field pattern of the lowest mode traveling wave along theguide. This mode has m = 0 and the lowest . It is often referred to as theglazing incidence ray. It has the highest phase velocity along the guide.


Fig. 5

y

E(y)m = 0 m = 1 m = 2

Cladding

Cladding

Core 2an1

n2

n2

The electric field patterns of the first three modes ( m = 0, 1, 2)travelling wave along the guide. Notice different extents of field

penetration into the cladding.

Fig. 6

Mode of propagation

• Each m leads to an allowed qm value that corresponds to a particular travelling wave in the z-direction as described in eqn.[2]– Each of these travelling waves with a distinct field pattern,

Em(y), constitutes a mode of propagation.– m identifies these modes and is called the mode number.

• The light energy can be transported only along the guide via one or more of these possible modes of propagation– Since qm is smaller for larger m, higher mode exhibit more

reflections & penetrate more into the cladding

Broadening of input light pulse

• Light that is launched into the core of the waveguide can travel down the guide at different group velocities.– When they reach the end of the guide they constitute the

emerging light beam• If a short duration light pulse is launched into the

dielectric waveguide, the light emerging from the other end will be a broadened light pulse – Light energy would have been propagated at different group

velocities along the guide as shown in Fig. 7– The light pulse therefore spreads as it travels along the guide

Low order modeHigh order mode

Cladding

Core

Light pulse

t0 t

Spread,

Broadenedlight pulse

IntensityIntensity

Axial

Schematic illustration of light propagation in a slab dielectric waveguide. Light pulseentering the waveguide breaks up into various modes which then propagate at differentgroup velocities down the guide. At the end of the guide, the modes combine toconstitute the output light pulse which is broader than the input light pulse.


Fig. 7

2 2 1/21 2

2( )

aV n n

V –number also known as V-parameter, normalized thickness, and normalized frequency.

For a given free space wavelength λ, the V-number depends on the waveguide geometry (2a) and waveguide properties, n1 and n2.

Science

Chapter 2a