Course title: Optoelectronics

Course no.: EEE 809

Contact hours: 03
Credit: 3.0

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Modulation of light
• Modulator: A device which changes the irradiance (or direction) of the light passing
through it.

• Types of modulators: Depending on the construction of modulators-

1. Mechanical choppers and shutters
2. Passive (or dye) modulators
3. Electro-optic
4. Magneto-optic
5. Elasto-optic (acousto-optic)

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Modulation of light

Application:
1. Wideband analog optical communication systems
2. Switching for digital information recording
3. Information storage and processing
4. Pulse shaping
5. Beam detection and scanning
6. Frequency stabilization
7. Q-switching of lasers

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Circular and Elliptical Polarization
• A beam of light consists of two plane polarized wave trains with their planes of
polarization at right angles to each other and which may also be out of phase.
• As a special case: amplitude of the two wave trains are equal and the phase difference is
𝜋
2
and propagating in the z direction. So, the components of electric fields are-
𝐸𝑥 = 𝑖𝐸0cos(𝑘𝑧 − 𝜔𝑡)
𝐸𝑦 = 𝑗𝐸0𝑠𝑖𝑛(𝑘𝑧 − 𝜔𝑡)
Total electric field is the vector sum of the two components
𝐸 = 𝐸𝑥 + 𝐸𝑦 = 𝐸0(𝑖𝐸0cos(𝑘𝑧 − 𝜔𝑡) + 𝑗𝐸0𝑠𝑖𝑛(𝑘𝑧 − 𝜔𝑡))
The resultant expression can be interpreted as a single wave in which the electric vector is
constant at a given point in space is constant in amplitude but rotates with angular
frequency 𝜔. Waves such as this are said to be circularly polarized.

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Circular and Elliptical Polarization

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Circular and Elliptical Polarization

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Circular and Elliptical Polarization

• When the amplitude of the electric vectors of the two waves are not the same but the
phase difference remains at 𝜋2 then the resultant vector at any point in space rotates at
frequency 𝜔 but changes in magnitude.
𝐸𝑥 = 𝑖𝐸0cos(𝑘𝑧 − 𝜔𝑡)
𝐸𝑦 = 𝑗𝐸0′𝑠𝑖𝑛(𝑘𝑧 − 𝜔𝑡)
• Where 𝐸0≠ 𝐸0′ and the major and minor axes of the ellipse are parallel to the x and y
axes.
• The resultant wave is said to be elliptical polarized and in fact, plane and circular
polarization is a special case of elliptical polarization.

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Circular and Elliptical Polarization

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Circular and Elliptical Polarization

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Circular and Elliptical Polarization

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Birefringence
• Birefringence is the optical property of a material having a refractive index that
depends on the polarization and propagation direction of light.
• The refractive index of the crystals varies with direction of propagation and the
polarization of the light. These crystals are known as Birefringent materials.
• Birefringence is responsible for the phenomenon of double refraction whereby a ray of
light, when incident upon a birefringent material, is split by polarization into two rays
taking slightly different paths and travel with different velocities.
• Known as demultiplexer.
• Example: calcite, Quartz, Topaz, Tourmaline, etc.

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Birefringence
• Ordinary ray that passes through the crystal
obeying Snell’s law
• Extraordinary ray that diverges as it passes
through the crystal and then emerges parallel
to the its ordinary direction
• This is found to be the case unless the
direction of the incidence of the original beam
is parallel or perpendicular to the optic axis.

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Optic Axis

• An optic axis of a crystal is a direction in which a ray of transmitted light suffers

no birefringence (double refraction). An optical axis is a direction rather than a single line:
all rays that are parallel to that direction exhibit the same lack of birefringence.

• For light propagating along an optic axis, though, the speed does not depend on the
polarization, so there is no birefringence although there can be optical activity (a rotation
of the plane of polarization) that direction exhibit the same lack of birefringence.

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Optic Axis

Characteristics:
1. It is direction not a line.
2. If three edges of crystal are of equal length then line joining blunt corners will give
direction of optic axis otherwise not.
3. An unpolarized light travelling along optic axis does not split into o-ray and e-ray.
4. The two refracted beams have same velocity along optic axes.
5. Uniaxial crystals have only one optic axis.
6. Crystal is symmetric about an optic axis.

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Principle Section

It is plane containing the direction of propagation and the optic axis.

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Optical Activity
• Crystals and liquids that have the ability to rotate the plane of polarization of light passing
through them are called optically active.
• When a beam of plane polarized light is incident normally on a crystal plate of quartz cut
perpendicular to the optic axis, it is found that the emergent beam is also plane polarized
but that its electric vector vibrates in a different plane from that of the incident light.
• The plane of vibration may be rotated in a clockwise sense looking against the oncoming
light by right handed or dextrorotatory crystals. Or in a counterclockwise sense by left-
handed or levorotatory crystals.
• Rotation depends on the thickness of the crystal plate and the wavelength.

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Optical Activity

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Quarter wave plate
𝜋
• When a crystal plate cut in such a that introduces a phase difference of 2
between O-ray
and E-ray is called a quarter plate wave.
• A phase difference of 𝜋2 is equivalent to an optical path difference
λ
n0d − ncd =
4
where d is the plate thickness.
• When a plane polarized light is incident on a quarter-wave plate the emergent light is in
general elliptical polarized.
• If the plane of polarization of the incident beam is inclined at 45̊ to the privileged
direction then the emergent light is circularly polarized.
• Phase difference= 2𝜋 ∗ 𝑜𝑝𝑡𝑖𝑐𝑎𝑙 𝑝𝑎𝑡ℎ 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 2𝜋 ∗ λ =𝜋
λ λ 4 2

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Electro-optic effect
• When a electric field is applied across an optical medium the distribution of electrons
within it is distorted so that the polarizability and hence the refractive index of the
medium changes anisotropically.
• The result of this electro-optic effect may be to introduce new optic axes into naturally
doubly refracting crystals.
• Example: KDP, GaAs
• The change in refractive index as a function of the applied field can be obtained from

Where r is the linear electro-optic coefficient and P is the quadratic electro-optic coefficient.

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Pockel and Kerr Effect
Pockel’s effect:
• In solid, the linear variation in the refractive index
associated with rε is known as Pockel’s effect.
• The precise effect of the applied electric field depends on
the crystal structure and symmetry of the material
under consideration.
• With KDP, if the electric field is applied in the z-direction
then the x and y principal axes are rotated through 45
into new principal axes x’ and y’ and the refractive indices
in these new direction become

• And if the variation comes from the quadratic term is

known as Kerr effect.

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Pockel’s effect:

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Pockel’s effect:

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Pockel’s effect:

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Pockel’s effect:

• We have taken Ez to equal V/L where V is the applied voltage.

• So the net phase shift or total retardation between the two waves resulting from
the
application of the voltage V is seen to be

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Half Wave Voltage

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Half Wave Voltage
• A beam of plane polarized light incident on the modulator would have it’s plane of
polarization rotated by 90 degree when a voltage 𝑉𝜋 is applied to the modulator.

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Half Wave Voltage

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Half Wave Voltage

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Half Wave Voltage

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Kerr Modulator

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Scanning & Switching

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Magneto Optic devices

• When a magnetic field is applied across an optical medium the distribution of electrons
within it is distorted so that the optical properties of some substances.

• However, electric field generation is easier than to generate magnetic fields thus, Electro-
optic devices are usually preferred than magneto-optic devices.

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Magneto Optic devices: Faraday Effect
(Optical Isolator)
• Faradey found that when a beam of plane polarized light passes through a substance
subjected to a magnetic field its plane of polarization is observed to rotate by an amount
proportional to the magnetic field component parallel to the direction of polarization
• In Faradey’s effect the sense of rotation of the plane of polarization is independent of the
direction of propagation
• In optical activity the sense of rotation is related to the direction.
• The amount of rotation will be dependent on the applied magnetic field,

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Magneto Optic devices: Faraday Effect
(Optical Isolator)

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Magneto Optic devices: Faraday Effect

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Acousto-optic devices
• The acousto optic effect is the change in the refractive index of a medium caused by the
mechanical strains accompanying the passage of an acoustic wave through the medium.

• The strain and hence the refractive index varies periodically with a wave length equal to
that of the acoustic wave.

• The refractive index changes are by the photo elastic effect which occurs in all
materials on the application of a mechanical stress. It can be shown that the change in
refractive index is proportional to the square root of the acoustic power

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Acousto-optic devices

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