Ders Planı
1. Işığın dalga özelliği. 2. Dielektrik dalga klavuzları ve optik lifler. 3. Yarıiletkenler fiziği ve ışık yayan diyotlar. 4. Lazerler. Ara Sınav 5. Fotoalgıçlar. 6. Fotovoltaik aygıtlar. 7. Kutuplanma ve ışığın modülasyonu.
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Önerilen Ders Kitapları:
• Optoelectronics And Photonics: Principles And Practices, S.O. Kasap, Prentice Hall (2001).
• Optical Fiber Communications, J.M.Senior, | Prentice Hall | • Optical Properties of Solids, M.Fox, Oxford University Press (2001). • Semiconductor Devices: Physics and Technology, S.M.Sze, Wiley
(1985). • Introduction to Optics, Frank. L. Pedrotti, | Addison Wesley|
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1. WAVE NATURE OF LIGHT
1.1 Light Waves in a Homogeneous Medium A. Plane Electromagnetic Wave B. Maxwell's Wave Equation and Diverging Waves
1.2 Refractive Index 1.3 Group Velocity and Group Index 1.4 Magnetic Field, Irradiance and Poynting Vector 1.5 Snell's Law and Total Internal Reflection (TIR) 1.6 Fresnel's Equations
A. Amplitude Reflection and Transmission Coefficients B. Intensity, Reflectance and Transmittance
1.7 Multiple Interference and Optical Resonators 1.8 Goos-Hänchen Shift and Optical Tunneling 1.9 Temporal and Spatial Coherence 1.10 Diffraction Principles
A. Fraunhofer Diffraction B. Diffraction grating
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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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z
Ex = Eosin(!t–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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y
z
kDirection of propagation
r
O
!
E(r,t)r"
A travelling plane EM wave along a direction k.© 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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y
x
Wave fronts
z Beam axis
r
Intensity
(a)
(b)
(c)
2wo
!
O
Gaussian
2w
(a) Wavefronts of a Gaussian light beam. (b) Light intensity across beam crosssection. (c) Light irradiance (intensity) vs. radial distance r from beam axis (z).© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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!"
"
" + !"
" – !"
!kEmax Emax
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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Refractive index n and the group index Ng of pureSiO2 (silica) glass as a function of wavelength.
Ng
n
500 700 900 1100 1300 1500 1700 19001.44
1.45
1.46
1.47
1.48
1.49
Wavelength (nm)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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z
Propagation direction
E
B
k
Area A
v!t
A plane EM wave travelling along k crosses an area A at right angles to thedirection of propagation. In time !t, the energy in the cylindrical volume Av!t(shown dashed) flows through A .
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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n2z
y
O
!i
n1
Ai
" "
!r!i
Incident Light BiAr
Br
!t !t
"t
Refracted Light
Reflected Light
kt
At
Bt
B#A
B
A#
A##!r
ki
kr
A light wave travelling in a medium with a greater refractive index (n1 > n2) suffersreflection and refraction at the boundary.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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n 2
!i
n 1 > n2!i
Incidentlight
!t
Transmitted(refracted) light
Reflectedlight
k t
!i>!c!c
TIR!c
Evanescent wave
k i k r
(a) (b) (c)
Light wave travelling in a more dense medium strikes a less dense medium. Depending onthe incidence angle with respect to !c, which is determined by the ratio of the refractiveindices, the wave may be transmitted (refracted) or reflected. (a) !i < !c (b) ! i = !c (c) !i> !c and total internal reflection (TIR).
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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k i
n2
n1 > n2
!t=90°Evanescent wave
Reflectedwave
Incidentwave
!i !r
Er,//
Er,"Ei,"
Ei,//
Et,"
(b) !i > !c then the incident wavesuffers total internal reflection.However, there is an evanescentwave at the surface of the medium.
z
y
x into paper!i !r
Incidentwave
!t
Transmitted wave
Ei,//
Ei," Er,//
Et,//
Et,"
Er,"
Reflectedwave
k t
k r
Light wave travelling in a more dense medium strikes a less dense medium. The plane ofincidence is the plane of the paper and is perpendicular to the flat interface between thetwo media. The electric field is normal to the direction of propagation . It can be resolvedinto perpendicular (") and parallel (//) components
(a) !i < !c then some of the waveis transmitted into the less densemedium. Some of the wave isreflected.
Ei,"
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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Internal reflection: (a) Magnitude of the reflection coefficients r// and r!vs. angle of incidence "i for n1 = 1.44 and n2 = 1.00. The critical angle is44°. (b) The corresponding phase changes #// and #! vs. incidence angle.
#//
#!
(b)
60
120
180
Incidence angle, "i
00.10.20.30.40.50.60.70.80.9
1
0 10 20 30 40 50 60 70 80 90
| r// |
| r! |
"c
"p
Incidence angle, "i
(a)
Magnitude of reflection coefficients Phase changes in degrees
0 10 20 30 40 50 60 70 80 90
"c
"p
TIR
0
$60
$120
$180
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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The reflection coefficients r// and r! vs. angleof incidence "i for n1 = 1.00 and n2 = 1.44.
-1-0.8-0.6-0.4-0.2
00.20.40.60.8
1
0 10 20 30 40 50 60 70 80 90
"p r//
r!
Incidence angle, "i
External reflection
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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d
Semiconductor ofphotovoltaic device
Antireflectioncoating
Surface
Illustration of how an antireflection coating reduces thereflected light intensity
n1 n2 n3
AB
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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n1 n2
AB
n1 n2
C
Schematic illustration of the principle of the dielectric mirror with many low and highrefractive index layers and its reflectance.
Reflectance
! (nm)0
1
330 550 770
1 2 21
!o
!1/4 !2/4
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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A
BL
M1 M2 m = 1
m = 2
m = 8
Relative intensity
!
"!m
!m !m + 1!m - 1
(a) (b) (c)
R ~ 0.4R ~ 0.81 !f
Schematic illustration of the Fabry-Perot optical cavity and its properties. (a) Reflectedwaves interfere. (b) Only standing EM waves, modes, of certain wavelengths are allowedin the cavity. (c) Intensity vs. frequency for various modes. R is mirror reflectance andlower R means higher loss from the cavity.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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L !!m!m - 1
Fabry-Perot etalon
Partially reflecting plates
Output lightInput light
Transmitted light
Transmitted light through a Fabry-Perot optical cavity.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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!i
n 2
n 1 > n2
Incidentlight
Reflectedlight
!r
"z
Virtual reflecting plane
Penetration depth, #z
y
The reflected light beam in total internal reflection appears to have been laterally shifted byan amount "z at the interface.
A
B
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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!i
n2
n1 > n2
Incidentlight
Reflectedlight
!r
When medium B is thin (thickness d is small), the field penetrates tothe BC interface and gives rise to an attenuated wave in medium C.The effect is the tunnelling of the incident beam in A through B to C.
z
y
d
n1
AB
C
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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Incidentlight
Reflectedlight
!i > !c
TIR
(a)Glass prism
!i > !c
FTIR
(b)
n1n1n2 n1
B = Low refractive indextransparent film ( n2)
ACA
Reflected
Transmitted
(a) A light incident at the long face of a glass prism suffers TIR; the prism deflects thelight.(b) Two prisms separated by a thin low refractive index film forming a beam-splitter cube.The incident beam is split into two beams by FTIR.
Incidentlight
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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TimePQ
Field
!
Amplitude
!"
#$#
Time
(a)
!
Amplitude
!"
%! = 1/%tTime
(b)
P Q
l = c%t
Space
%t
(c)
!
Amplitude
(a) A sine wave is perfectly coherent and contains a well-defined frequency !o. (b) A finitewave train lasts for a duration %t and has a length l. Its frequency spectrum extends over%! = 1/%t. It has a coherence time %t and a coherence length l. (c) White light exhibitspractically no coherence.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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c
(a)
Time
(b)
A
B
!tInterference No interferenceNo interference
Space
c
P
Q
Source
Spatially coherent source
An incoherent beam(c)
(a) Two waves can only interfere over the time interval !t. (b) Spatial coherence involvescomparing the coherence of waves emitted from different locations on the source. (c) Anincoherent beam.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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Light intensity pattern
Incident light wave
Diffracted beam
Circular aperture
A light beam incident on a small circular aperture becomes diffracted and its lightintensity pattern after passing through the aperture is a diffraction pattern with circularbright rings (called Airy rings). If the screen is far away from the aperture, this would be aFraunhofer diffraction pattern.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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Incident plane wave
Newwavefront
A secondarywave source
(a) (b)
Another newwavefront (diffracted)
z!
(a) Huygens-Fresnel principles states that each point in the aperture becomes a source ofsecondary waves (spherical waves). The spherical wavefronts are separated by ". The newwavefront is the envelope of the all these spherical wavefronts. (b) Another possiblewavefront occurs at an angle ! to the z-direction which is a diffracted wave.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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!
A
ysin!
y
Y
!
! = 0
"y
z"y
ScreenIncidentlight wave
!
R = Large
!
cb
Light intensity
a
y
y
z
(a) (b)
(a) The aperture is divided into N number of point sources each occupying "y withamplitude # "y. (b) The intensity distribution in the received light at the screen far awayfrom the aperture: the diffraction pattern
Incidentlight wave
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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The rectangular aperture of dimensions a ! b on the leftgives the diffraction pattern on the right.
ab
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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!"
S1
S2
S1
S2
A1
A2
I
y
Screen
!"s
L
Resolution of imaging systems is limited by diffraction effects. As points S1 and S2get closer, eventually the Airy disks overlap so much that the resolution is lost.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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dz
y
Incidentlight wave
Diffraction grating
One possiblediffracted beam
!
a
Intensity
y
m = 0m = 1
m = -1
m = 2
m = -2
Zero-orderFirst-order
First-order
Second-order
Second-order
Single slitdiffractionenvelope
dsin!
(a) (b)
(a) A diffraction grating with N slits in an opaque scree. (b) The diffracted lightpattern. There are distinct beams in certain directions (schematic)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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Incidentlight wave
m = 0
m = -1
m = 1Zero-order
First-order
First-order
(a) Transmission grating (b) Reflection grating
Incidentlight wave
Zero-orderFirst-order
First-order
(a) Ruled periodic parallel scratches on a glass serve as a transmission grating. (b) Areflection grating. An incident light beam results in various "diffracted" beams. Thezero-order diffracted beam is the normal reflected beam with an angle of reflection equalto the angle of incidence.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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First order
!
Normal tograting planeNormal to
face
d
!
Blazed (echelette) grating.© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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Two confocal spherical mirrors reflect waves to and fromeach other. F is the focal point and R is the radius. Theoptical cavity contains a Gaussian beam
Wave front
Spherical mirrorOptical cavity
Spherical mirror
A B
L
R
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
2!
R
F
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n1
n2
n3
B1
A1 A2 A3A0
C1
B2
B3
B4
B5
C2 C3
B6
Thin film coating of refractive index n2on a semiconductor device© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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L
Fabry-Perot etalon
Output lightInput light
!
!
!
!
LensBroadmonochromaticsource Screen
Screen
k
FP etalon
Fabry-Perot optical resonator and the Fabry-Perot interferometer (schematic)
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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n 1n 3
n 2Air
Glass substrate
Thin layer
(a)
Glass substrate
Thin layer
PrismLaser lightd = Adjustable coupling gap
(b)
(a) Light propagation along an optical guide. (b) Coupling of laser light into a thin layer -optical guide - using a prism. The light propagates along the thin layer.
© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
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