Chapter 1a
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Transcript of Chapter 1a
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Chapter 1:
Introduction to Optics and optoelectronics
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Light has many properties that make it very attractive for information processing
1. Immunity to electromagnetic interference– Can be transmitted without distortion due to electrical
storms etc
2. Non-interference of crossing light signals– Optical signals can cross each other without distortion
3. Promise of high parallelism– 2D information can be sent and received.
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4. High speed/high bandwidth– Potential bandwidths for optical communication systems
exceed 1013 bits per second. (1250 GigaByte/second)
5. Signal (beam) steering– Free space connections allow versatile architecture for
information processing
6. Special function devices– Interference/diffraction of light can be used for special
applications
7. Ease of coupling with electronics– The best of electronics & photonics can be exploited by
optoelectronic devices
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Radiation/Light Sources
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Classification of radiation source by Flux Output
1. A point source• An LED or a small filament clear bulb with small emission
area2. An area source
• An electroluminescence panel or frosted light bulb with an emission area that is large
3. A collimated source• A searchlight with flux lines that are parallel
4. A coherent source• A laser which is either a point source or a collimated
source with one important difference: the wave in coherence source are all in phase
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Radiation spectrum1. A continuous spectrum source
• Has a wavelength of emission that ranges from ultraviolet to infrared.
2. A line spectrum source• Has a distinct narrow bands of radiation throughout the
ultraviolet to infrared range.
3. A single wavelength source• Radiates only in a narrow band of wavelength
4. A monochromatic source• Radiates at a single wavelength/a very narrow band of
wavelength.
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The nature of light
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Light wave in a homogenous medium
Ex
z
Direction of Propagation
By
z
x
y
k
An electromagnetic wave is a travelling wave which has timevarying electric and magnetic fields which are perpendicular to eachother and the direction of propagation, z.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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k
Wave fronts
rE
k
Wave fronts(constant phase surfaces)
z
Wave fronts
PO
P
A perfect spherical waveA perfect plane wave A divergent beam
(a) (b) (c)
Examples of possible EM waves
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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z
Ex = E
osin(wt–kz)
Ex
z
Propagation
E
B
k
E and B have constant phasein this xy plane; a wavefront
E
A plane EM wave travelling along z, has the same Ex (or By) at any point in agiven xy plane. All electric field vectors in a given xy plane are therefore in phase.The xy planes are of infinite extent in the x and y directions.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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Light as plane electromagnet (EM) wave
• We can treat light as an EM wave with time varying electric and magnetic fields Ex and By perpendicular to each other propagating in z
direction.
Ex (z, t) = Eo cos ( t – kz + o)Ex =electric field at position z at time t, k = 2/λ is the propagation constant, λ is the wavelengthand is the angular frequency, Eo is the amplitude of the wave and o is a phase
constant.
Ex (z, t) = Re[ Eo exp (jo) exp j(t – kz)]
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Electromagnet (EM) wave
• We indicate the direction of propagation with a vector k, called the wave vector.– whose magnitude, k = 2/λ
• When EM wave is propagating along some arbitrary direction, k, then electric field at a point r isEx (r, t) = Eo cos (t – k ∙ r + o)– Dot product (k r)∙ is along the direction of propagation
similar to kz.– In general, k has components kx , ky & kz along x, y and z
directions: (k r)∙ = kx x + ky y + kz z
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y
z
k
Direction of propagation
r
O
q
E(r,t)r¢
A travelling plane EM wave along a direction k.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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Maxwell’s Equation2 2 2 2
2 2 2 20x x x x
o o r
E E E E
x y z t
2
20xE
x
2
20xE
y
Given wave equation: Ex (z, t) = Eo cos ( t – kz + o)
22
2cos( )x
o o
Ek E t kz
z
22
2cos( )x
o o
EE t kz
t
2 2cos( ) cos( ) 0o o o o r o ok E t kz E t kz 2 2( ) cos( ) 0o o r o ok E t kz
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Phase velocity
• During a time interval t, this constant phase moves a distance z. – The phase velocity of this wave is therefore z/t.
• Phase velocity,
f is the frequency ( = 2f )
f
kdt
dzv
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Phase Velocity
2 2( ) cos( ) 0o o r o ok E t kz
2
2
1
o o rk
1/2
o o rv
f
kdt
dzv
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Group Velocity
• There are no perfect monochromatic wave in practice– All the radiation source emit a group of waves differing slightly
in wavelength, which travel along the z-direction• When two perfectly harmonic waves of frequency w–dw & w+dw and wave vectors k–dk & k+dk interfere, they generate wave packet.
• Wave packet contains an oscillating field at the mean frequency w that is amplitude modulated by a slowly varying field of frequency dw.
• The maximum amplitude moves with a wavevector dk and the group velocity is given Vg = dw/dk
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Group velocity
, cos cos
, 2 cos cos
, v
x o o
x o
g
E x t E t k k z E t k k z
E x t E t k z t kz
dz d
dt k dk
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+
–
kEmaxEmax
Wave packet
Two slightly different wavelength waves travelling in the samedirection result in a wave packet that has an amplitude variationwhich travels at the group velocity.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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What is refractive index, (n) ?
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Interaction between dielectric medium and EM wave
• When an EM wave is traveling in a dielectric medium, – the oscillating Electric Field (E-field) polarizes the molecules
of the medium at the frequency of the wave.• The field and the induced molecular dipoles become
coupled– The net effect: The polarization mechanism delays the
propagation of the EM wave.– The stronger the interaction, the slower the propagation of
the wave– r: relative permittivity (measures the ease with which the
medium becomes polarized).
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Phase velocity in dielectric medium
• For EM wave traveling in a non-magnetic dielectric medium of r , the phase velocity,
• If the frequency is in the optical frequency range, – r will be due to electronic polarization as ionic polarization
will be too slow to respond to the field.• At the infrared frequencies or below,
– r also includes a significant contribution from ionic polarization and phase velocity is slower
oor 1
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Definition of Refractive Index
• For an EM wave traveling in free space (r= 1)
velocity
(1)• The ratio of the speed of light in free space to its
speed in a medium is called refractive index n of the medium,
n= c/v = r (2)
181031 mscv
oo
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Example: phase velocity
• Considering a light wave traveling in a pure silica glass medium. If the wavelength of light is 1mm and refractive index at this wavelength is 1.450, what is the phase velocity ?
The phase velocity is given byv= c/n = 3108ms–1/1.45 =2.069108ms–1
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Refractive Index in Materials
• In free space, k is the wave vector (k=2 /) and is the wavelength
• In medium, kmedium=nk and medium = /n.– Light propagates more slowly in a denser medium
that has a higher refractive index– The frequency f remains the same– The refractive index of a medium is not necessarily
the same in all directions
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Refractive Index in non-Crystal Materials
• In non-crystalline materials (glass & liquids), the material structure is the same in all directions– Refractive index, n, is isotropic and independent
on the direction
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Refractive Index in Crystal Materials
• In crystals, the atomic arrangements and inter-atomic bonding are different along different directions
• In general, they have anisotropic properties except cubic crystals.– r is different along different crystal directions– n seen by a propagating EM wave in a crystal will
depend on the value of r along the direction of the oscillating E-field
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Cubic crystal
hexagonal crystal
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Refractive index and phase velocity
• For example: a wave traveling along the z-direction in a particular crystal with its E-field oscillating along the x-direction– Given the relative permittivity along this x-direction is rx
then , – The wave will propagate with a phase velocity that is c/nx
• The variation of n with direction of propagation and the direction of the E-field depends on the particular crystal structure
rxxn