Ders Planı - Hacettepe Üniversitesiyunus.hacettepe.edu.tr/~bacioglu/FIZ454/notes/Chapter1(Color).pptx.pdfÖnerilen Ders Kitapları: • Optoelectronics And Photonics: Principles

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.

1

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|

2

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

3

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)

4

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)

5

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)

6

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


7

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)

8

!"

"

" + !"

" – !"

!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)

9

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)


10

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 .


11

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.


12

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).


13

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,"


14

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


15

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


16

d

Semiconductor ofphotovoltaic device

Antireflectioncoating

Surface

Illustration of how an antireflection coating reduces thereflected light intensity

n1 n2 n3

AB


17

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


18

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.


19

L !!m!m - 1

Fabry-Perot etalon

Partially reflecting plates

Output lightInput light

Transmitted light

Transmitted light through a Fabry-Perot optical cavity.


20

!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


21

!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


22

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


23

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.


24

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.


25

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)

26

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.


27

!

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


28

The rectangular aperture of dimensions a ! b on the leftgives the diffraction pattern on the right.

ab


29

!"

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.


30

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)


31

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.


32

First order

!

Normal tograting planeNormal to

face

d

!

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

33

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


2!

R

F

34

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)

35

L

Fabry-Perot etalon

Output lightInput light

!

!

!

!

LensBroadmonochromaticsource Screen

Screen

k

FP etalon

Fabry-Perot optical resonator and the Fabry-Perot interferometer (schematic)


36

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.


37

Documents

Ders Planı - Hacettepe Üniversitesiyunus.hacettepe.edu.tr/~bacioglu/FIZ454/notes/Chapter1(Color).pptx.pdfÖnerilen Ders Kitapları: • Optoelectronics And Photonics: Principles