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

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 to
propagate successfully. Otherwise destructive interference will destroy the
wave.
© 1999 S.O. Kasap,Optoelectronics(Prentice Hall)
z
y
x
Fig. 2

Waveguide condition
• For constructive interference,
Df (AC) =k1 (AB+BC) – 2f = m (2p)
m = 0, 1, 2,… and k1 = k n1 = 2pn1/
k &  are free space wavevector & wavelength
f is a phase change due to total internal reflection at B or C
• Thus, waveguide condition is
[2p n1 (2a)/] cosm – fm = m p [1]
fm indicates that f is a function of the incidence angle m.
• So for each m, there will be one allowed angle m 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
p p
k1
E
x
n1
Two arbitrary waves 1 and 2 that are initiallyin phase must remain in phase
after reflections. Otherwise the two willinterfere destructively and cancel each
other.
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 + ½m) cos ( t– mz+ ½m)

n2
z
a
y
A
1
2

A
C
k
E
x
y
ay
Guide center
p
Interference of waves such as 1 and 2 leads to a standing wave pattern along the y-
direction which propagates along z.
© 1999 S.O. Kasap, Optoelectronics(Prentice Hall)
Fig. 4

• E1(y,z,t) = Eo cos (t – mz + my + m)
E1= Eo cos [(t – mz +½m)+ (my + ½m)]
• E2(y,z,t) = Eo cos (t – mz – my)
E2= Eo cos [(t – mz +½m) – (my + ½m)]
• E (y, z, t) = E1(y,z,t) + E2(y,z,t)
E = 2Eo cos (my + ½m) cos (t – mz +½m)
E = 2 Em (y) cos (t – mz +½m)
• where Em (y) = Eocos (my + ½m)

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 + ½m) 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 =k1sinm =(2p n1/) sinm
m =k1cosm =(2p n1/) cosm
m = m (y) = mp – y/a(mp + fm)

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 0.
• 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 travelingwave along the
guide. This mode has m = 0 and the lowest . It is oftenreferred to as the
glazing 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 2a
n1
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 m 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 m 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
t
0 t
Spread, D
Broadened
light pulse
Intensity
Intensity
Axial
Schematic illustration of light propagation in a slab dielectric waveguide. Light pulse
entering the waveguide breaks up into various modes which then propagate at different
group velocities down the guide. At the end of the guide, the modes combine to
constitute the output light pulse which is broader than the input light pulse.
© 1999 S.O. Kasap, Optoelectronics(Prentice Hall)
Fig. 7

2 2 1/2
1 2
2
( )
a
V n n
p

 
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.

Chapter 2a

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Chapter 2a