Optoelectronics Lecture Topic 2 Wave Nature of Light r2ccf.ee.ntu.edu.tw/~ypchiou/Intro_EO/Ch01 Wave Nature … · · 2010-02-23?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

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Chapter 1Wave Nature of Light

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WAVE NATURE OF LIGHT

1.1 Light Waves in a Homogeneous Medium

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

1.7 Multiple Interference and Optical Resonators

1.8 Goos-Hnchen Shift and Optical Tunneling

1.9 Temporal and Spatial Coherence

1.10 Diffraction Principles

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1.1 Light Waves in a Homogeneous Medium

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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)

A. Plane Electromagnetic Wave

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propagation constant (wave number):

phase:

cos( )x o oE E t kz = +

( , ) Re[ exp( )exp ( )]

( , ) Re[ exp ( )]

x o o

x c

E z t E j j t kzorE z t E j t kz

=

=

ck /=

Monochromatic plane wave

0 += kzt

WavefrontA surface over which the phase of a wave is constant

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The optical field refersthe electric field

z

Ex = Eosin(t z )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.


-k

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y

z

k

Direction of propagation

r

O

E(r,t)r

A travelling plane EM wave along a direction k?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

k

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constantot kz = + =

v dz vdt k

= = =

Wave vector

Phase velocity

)cos(),( 00 += rktEtrE

zkykxkrk zyx ++=

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B. Maxwells Wave Equation and Diverging Waves

No divergenceAmplitude is independent of x and y

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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2 2 2 2

2 2 2 2rE E E E

x y z t + + =

co s( )AE t krr

=

(5)

(6)

Maxwells EM wave equation

Spherical wave (Wavefronts are spheres.)

Optical divergence: the angular separation of wavevectorson a given wavefront (spherical wave: 360 deg.)

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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).


w0 : waist radius2w0: spot size

422 ow

=

( ) (7)

Gaussian wave beam divergence

22

r

e

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1.2 Refractive Index

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1v r o o

=

v rcn = =

(1)

(2)

1r N

+

Isotropic: material structure is the same in all directions, n independent of directione.g. cubic and non-crystalline

Anisotropic: Structure => physical properties depend on direction

Refractive index

Phase velocity

http://cst-www.nrl.navy.mil/lattice/

The stronger the interaction between the field and the dipoles, the slower the propagation of the wave. (relative permittivity)

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Example 1.2.1 Relative permittivity and refractive index

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Example 1.2.1 Relative permittivity and refractive index

Molecular (polarized) + atomic + electronic

Atomic (ionic or covalent) + electronic

Electronic

Permittivity due to different polarizations

Vacuum

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1.3 Group Velocity and Group Index

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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.


-

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v ( ) phase velocitygdvacuum cdk

= = = (2)

2v [ ][ ]( )ck

n

= = (3)

Material dispersion: waverform changes

1)( == kv kg

(1)vgddk

=d

dk

1=

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Dispersive medium

v ( )gd cmedium dndk n

d

= =

v ( )gg

cmediumN

=

gd nN nd

=

(4)

(5)Group index

(approximation)

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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 1900

1.44

1.45

1.46

1.47

1.48

1.49

Wavelength (nm)


Around 1300nm

minimal Ng

zero dispersion

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Example 1.3.1 Group velocityConsider two sinusoidal waves that are close in frequency:

frequencies = - and + Their wave vectors are: k - k and k + k1. Resultant wave: Ex(z,t) = ?2. What is the group velocity?

(the speed of propagation of the maximum electric field along z)

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Example 1.3.2 Group and phase velocity

Consider a light wave traveling in a pure SiO2 (silica) glass medium. If the wavelength of light is 1 m and the refractive index at this wavelength is 1.450, what is the phase velocity, group index and group velocity?

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1.4 Magnetic Field, Irradiance and Poynting Vector

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z

Propagation direction

E

B

k

Area A

vt

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 Avt(shown dashed) flows through A .


vx y ycE B Bn

= =

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vx y ycE B Bn

= =

2 21 12 2o r x yo

E B

=

22 2( v )( ) v vo r x o r x o r x y

A t ES E E BA t

= = =

(1)

(2)

(3)

S = Energy flow per unit time per unit area

(instantaneous irradiance)

electrical energy density = magnetic energy density(i.e. energy per unit volume)

Total Energy: 20 xr E

BEv r = 02S

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2 3 21 (1.33 10 )2average o o o

I S c nE nE = = =

21 v2average o r o

I S E = =

(4)

(5)

(6)

Average irradiance (intensity)

Poynting vector

BEv r = 02S

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Example 1.4.1 Electric and magnetic fields in light

The intensity (irradiance) of the red laser beam from a He-Ne laser at a certain location has been measured to be about 1mW/cm2. What are the magnitudes of the electric and magnetic fields? What are the magnitudes if this beam is in a glass medium with a refractive index n = 1.45?

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1.5 Snells Law and Total Internal Reflection (TIR)

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n2z

y

O

i

n1

Ai

ri

Incident Light Bi Ar

Br

t t

t

Refracted Light

Reflected Light

kt

At

Bt

BA

B

A

Ar

ki

kr

A light wave travelling in a medium with a greater refractive index (n1 > n2) suffersreflection and refraction at the boundary.

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i rt

1 1v v'sin sini r

t tAB

= =

Reflection

i = r

1 2

i 1 2

t 2 1

v v 's in s in

s in v s in v

i t

t tA B

no rn

= =

= =

(1)

Snells Law

Refraction

2

1

sin cnn

= (2)

Critical angle (if n1 > n2)

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n2

in

1 > n2i

Incidentlight

t

Transmitted(refracted) light

Reflectedlight

k t

i>ccTIR

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).


TIR and evanescent wave

TIR: i > c sint > 1 t : imaginary angle

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1.6 Fresnels Equations

A. Amplitude reflection and Transmission coefficients (r and t)

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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,


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exp ( )exp ( )exp ( )

i io i

r ro r

t to t

E E j t k rE E j t k rE E j t k r

= = =

tangential tangential(1) (2)E E=

tangential tangential(1) (2)B B=

Transverse electrical field (TE)Ei, , Er, , Et, : electrical field components

perpendicular to z-direction

Transverse magnetic field (TM)Ei,// , Er,// , Et,// : magnetic field components

perpendicular to z-direction

Boundary conditions

r = in1sin1 = n2sin2

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2 2 1/ 20,

2 2 1/ 20,

cos [ sin ]cos [ sin ]

r i i

i i i

E nrE n

= =

+

0,2 2 1/ 2

0,

2 coscos [ sin ]

t i

i i i

Et

E n

= =+

(1a)

(1b)

Define: n = n2 / n1

2 2 1/ 2 20,//

// 2 2 1/ 2 20,//

[ sin ] cos[ sin ] cos

r i i

i i i

E n nrE n n

= =

+

0,//// 2 2 2 1/ 2

0,//

2 coscos [ sin ]

t i

i i i

E ntE n n

= =+

(2a)

(2b)

// // 1 and 1r nt r t + = + = (3)

3/19/2009

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1 2//

1 2

n nr rn n

= =

+

2

1

tan pnn

=

(4)

(5)

=> linearly polarized wave

Normal incidence

2 2 1/ 20,

2 2 1/ 20,


r i i

i i i

E nrE n

= =

+ (1a)

2 2 1/ 2 20,//

// 2 2 1/ 2 20,//


r i i

i i i

E n nrE n n

= =

+(2a)

Brewsters angle or polarization angle

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General formula

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Internal reflection: (a) Magnitude of the reflection coefficients r// and rvs. 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

0

0.1

0.2

0.30.4

0.5

0.60.7

0.80.9

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)42

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Applications Camera polarization filters (PL) Sunglasses Laser tubes (Brewster angle)

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http://health.howstuffworks.com/sunglass.htm/printable

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2 2 1/ 2 20,//

// 2 2 1/ 2 20,//


r i i

i i i

E n nrE n n

= =

+(2a)

2 2 1/ 20,

2 2 1/ 20,


r i i

i i i

E nrE n

= =

+ (1a)

// //

1.0 exp( )1.0 exp( )

r jr j

= =

(amplitude of the ref. is equal to that of inc. with phase change)

2

1

sin inn

> > n

Total internal reflection: i > c

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Internal reflection: (a) Magnitude of the reflection coefficients r// and rvs. 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

0

0.1

0.2

0.30.4

0.5

0.60.7

0.80.9

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


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2 2 1/ 2

// 2

[sin ]1 1tan( )2 2 cos

i

i

nn

+ = (7)

2 2 1/ 2[sin ]1tan( )2 cos

i

i

n

= (6)

Phase change in TIR

, ( , , ) exp ( )y

t izE y z t e j t k z 2 =

2 2 1/ 22 1

2

2 [( ) sin 1]in n

n 2

=

(8)

(9)

Evanescent wave

Attenuation coef.

Penetration depth 2/1 =

ci >

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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

0

0.2

0.4

0.6

0.81

0 10 20 30 40 50 60 70 80 90

p r//

r

Incidence angle, i

External reflection

Internal reflectionn1 > n2 no phase change at normal incidence

External reflectionn1 < n2 phase shift of 180 at normal incidence

No phase change fortransmitted light

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Example 1.6.1 Evanescent wave

Total internal reflection (TIR) of light from a boundary between a more dense medium n1 and a less dense medium n2 is accompanied by an evanescent wave propagating in medium 2 near the boundary. Find the functional form of this wave and discuss how its magnitude varies with the distance into medium 2.

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21 v2 r o o

I E =

2 2, ,//2 2

// //2 2, ,//

| | | || | and R | |

| | | |ro ro

io io

E ER r r

E E

= = = =

2 *,// ,// ,//| | ( )( )ro ro roE E E=

(10)

(11)

B. Intensity, Reflectance and TransmittanceLight intensity or irradiance

Reflectance R

r: complexR: real

(12)

Transmittance T

2

1

22

,1

2,2

coscos

cos

cos

== t

nn

En

EnT

i

t

ioi

tot

2//

1

22

//,1

2//,2

// coscos

cos

cost

nn

En

EnT

i

t

ioi

tot

==

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1 2// 2

1 2

4( )

n nT T Tn n

= = =+

(14)

(15)

Transmittance

R + T =1

Power conservation (valid for arbitrary incident angle)

Normal incidence

21 2//

1 2

( )n nR R Rn n

= = =

+(13)

e.g. air-glass: R = (1.5-1)2/(1.5+1)2 = 4%

Reflectance

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Example 1.6.2 Reflection of light from a less dense medium (internal reflection)

A ray of light is traveling in a glass medium of n1 = 1.45 becomes incident on a less dense glass medium of n2 = 1.43. Suppose the free space wave length of the light ray is 1m.

(a) What should the minimum incidence angle for TIR be?(b) What is the phase change in the reflected wave when i = 85 and

i = 90(c) What is the penetration depth of the evanescent wave into medium

2 when i = 85 and i = 90

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Example 1.6.3 Reflection at normal incidence. Internal and external reflection

Consider the reflection of light at normal incidence on a boundary between a glass medium of refractive index 1.5 and air of refractive index 1.

(a) If light is traveling from air to glass, what is the reflection coefficient and the intensity of the reflected light w.r.t. that of the incident light?(b) If light is traveling from glass to air, what is the reflection coefficient and the intensity of the reflected light w.r.t. that of the incident light?(c) What is the polarization angle in the external reflection in (a) above? How would you make a polariod device that polarizes light based on the polarization angle?

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d

Semiconductor ofphotovoltaic device

Antireflectioncoating

Surface

Illustration of how an antireflection coating reduces thereflected light intensity

n1 n2 n3

AB

Example 1.6.4 Antireflection (AR) coatings on solar cells

Consider wavelength around 700-800 nm

No AR coating: n1 (air) = 1 and n2 (Si) = 3.5

With AR coating: n1 (air) = 1, n2 (Si3N4) = 1.9, n3 (Si) = 3.5

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Twolayers:Air|1.587|2.520|Ge1.00|0.250|0.250|4.00

Threelayers:Air|1.587|2.00|2.520|Ge1.00|0.250|0.250|0.250|4.00

Onelayer:Air|2.00|Ge1.00|0.250|4.00

Onelayer

Twolayers

Threelayers

Antireflection coating

g=0/;0 isquarterwavelengthwithrefractiveindexconsidered

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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

Example 1.6.5 Dielectric mirrors

Definition: a stack of dielectric layers of alternating refractive indices1. n1 < n22. t1 = 1 / 4 and t2 = 2 / 4 (quarter wavelength of the light in the layer)

where 1 = 0/n1 and 2 = 0/n2

At 0: reflected waves from the interfaces interfere constructively mirror

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e.g. fiber Bragg gratings, photonic crystals (1D to 3D), structures in nature70

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1.7 Multiple Interference and Optical Resonators

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LC optical resonators (narrow band around f0) Store energy Filtering light at certain frequencies

(wavelengths) Used in laser, interference filter, and

spectroscopic applications

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A

B

L

M1 M2 m = 1

m = 2

m = 8

Relative intensity

m

m m + 1m - 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.

Stationary or standing EM waves

( ) 1,2,3...m L m = =2

(1)

Cavity mode:

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( ) ; / 22m f fcv m mv v c LL

= = =

2 exp( 2 )A B A Ar j kL+ = +

(2)

2 4 6

...

exp( 2 ) exp( 4 ) exp( 6 ) ...cavityE A B

A Ar j kL Ar j kL Ar j kL

= + +

= + + + +

21 exp( 2 )cavityAE

r j kL=

Lowest frequency = ?

Free spectral range = ?

Fabry-Perot optical resonator

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2 2(1 ) 4 sin ( )o

cavityII

R R kL=

+

max 2 ; (1 )o

mII k L mR

= =

1/ 2

; 1

fm

v Rv FF R

= =

(3)

(4)

(5)

21 exp( 2 )cavityAE

r j kL=

Spectral width (FWHM) Finesse

Finesse: the ratio of mode separation to spectral width f m

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L mm - 1

Fabry-Perot etalon

Partially reflecting plates

Output lightInput light

Transmitted light

Transmitted light through a Fabry-Perot optical cavity.

2

transmitted incident 2 2

(1 )(1 ) 4 sin ( )

RI IR R kL

=

+(6)

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Example 1.7.1 Resonator modes and spectral width

Consider a Fabry-Perot optical cavity of air of length 100 micros with mirrors that have a reflectance of 0.9. (a) Calculate the cavity mode nearest to 900 nm. (b) Calculate the separation of the modes and the spectral width of each mode.

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1.8 Goos-Hanchen Shift andOptical Tunneling

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i

n2

n1 > 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


iz tan2=

Lateral shift of the reflected beam due to TIR

Goos-Haenchen shift

In Ex. 1.6.2 n1=1.45, n2=1.43, inc. at 85 deg. =0.78m, => z ~ 18 m

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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


Frustrated total internal reflection (FTIR)

Optical tunneling

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Incidentlight

Reflectedlight

i > cTIR

(a)Glass prism

i > c

FTIR

(b)

n1

n1n

2 n1

B = Low refractive indextransparent film ( n

2)

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


Frustrated total internal reflection

Beam splitter Gap thickness and Refractive index

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1.9 Temporal and Spatial Coherence

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Perfect coherence: any two points such as P and Q separated by any time interval are always correlated.

TimePQ

Field

Amplitude

Time

(a)

Amplitude

= 1/t

Time

(b)

P Q

l = ct

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.

spectralwidth

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Perfect coherence: all points on the wave are predictable Temporal coherence

Measures the extent to which two points separated in time at a given location in space can be correlated

e.g. 589 nm of sodium lamp, v ~ 5 x 1011 Hz, t ~ 2 x 10-12 s = 2 ps He-Ne laser, v=1.5 x 109 Hz, l ~ 200 mm Laser devices have substantial coherence length, and therefore

widely used in wave-interference studies and applications

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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.

Mutual temporal coherenceover the time interval

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1.10 Diffraction Principles

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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.


Fraunhofer diffraction Incident light beam: a plane waveObservation (detection): far away from the aperture

Fresnel diffraction

A. Fraunhofer Diffraction

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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.

Huygens-Fresnel principle

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A

ysin

y

Y

= 0

y

zy

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

sinky =

( ) exp( sin )E y jky (1)

0( ) exp( sin )

y a

yE C y jky

=

== (2)

89

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0( ) exp( sin )

y a

yE C y jky

=

== (2)

1 sin2 1sin( sin )

2( ) 1 sin2

j kaCe a ka

Eka

=

'

2 2

1sin( sin )2( ) [ ] (0) sinc ( ); sin1 sin

2

C a kaI I ka

ka

1= = =

2(3)

sin ; m 1, 2, ...ma = = (4)Zero intensity at

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

a

b


'

2 2

1sin( sin )2( ) [ ] (0) sinc ( ); sin1 sin

2

C a kaI I ka

ka

1= = =

2

Rectangular aperture

sin 1.22D = (5)Divergence angle of Airy disk

Airy rings (circular aperture)

91

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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.


Rayleigh criterion: two spots are resolvable when the principal max.of one diffraction pattern coincides with the min. of the other.

sin 1.22D =

92

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Example 1.10.1 Resolving power of imaging systems- two neighboring coherent sources are examined through an imaging

system with an aperture of diameter D- angular separation of the two sources at the aperture: - diffraction pattern of the sources: S1 and S2Q: The human eye has a pupil diameter of about 2 mm. What would be the

minimum angular separation of two points under a green light of 550 nm and their minimum separation if the two objects are 30 cm from the eye?

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.


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dz

y

Incidentlight wave

Diffraction grating

One possiblediffracted beam

a

Intensity

y

m = 0

m = 1

m = -1

m = 2

m = -2

Zero-order

First-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)

sin m 0, 1, 2, ...d m = ; = (7)

B. Diffraction grating Periodic series of slits in an opaque screenGrating equation

Bragg diffraction condition

(Normal to the grating)

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Incidentlight wave

m = 0

m = -1

m = 1

Zero-order

First-orde

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.


(sin sin ) m 0, 1, 2,...m id m = ; = (8)

(not normal to the grating)

i : angle of incidence w.r.t. grating normal

95

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First order

Normal tograting planeNormal to

face

d

Blazed (echelette) grating.


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Blazed diffraction grating

=

=

=

=+=+

=+=

am

ma

if

mama

b

b

ib

ibi

mi

ibm

bmbi

2arcsin

sin2

)]2sin([sin)sin(sin

2)(

Number of grooves/mm and blazed angle determine the wavelength range of the grating.

N grating normalN groove face normal

m

+_

97

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Monochromator Fancy stickers Nature structures (birds, fish, bugs)

98

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Other application Enhancement of light extraction in LED, OLED

structures Reduce total internal reflection Inhibit undesired direction

Nature, 2009

Documents

Optoelectronics Lecture Topic 2 Wave Nature of Light r2ccf.ee.ntu.edu.tw/~ypchiou/Intro_EO/Ch01 Wave Nature … · · 2010-02-23?1999 S.O. Kasap, Optoelectronics (Prentice Hall)