optical properties of materials

Optcal Properties

C. Optical Properties of Materials

Contents

• light (9.1)

• refractive index, n (9.2)

• dispersion, n(l) (9.3)– vg, Ng, zero dispersion (9.4)

• principles– Snell (9.6): direction

– Fresnel (9.7): amplitudes, phases

• losses & origins– n-jK, er'-jer", k'-jk" (9.8)

– lattice absorption (9.9)

– VB CB absorption (9.10)

– scattering (9.11)

• case studies– optical fibre (9.12)

– luminescence, phosphor (9.13)

Objectives

• What happens when light shines

on a material?

• colors of materials

• Why are some materials

transparent and others not?

• Optical applications:

– optical fibers

– optical amplification

– luminescence, phosphors

– nanostructures

12102308

v.2019.AUG

Reference: S.O. Kasap (3rd,4th Ed.) Chap. 9; RJD Tilley (Understanding solids, 2nd Ed) Chap. 14.

Optcal Properties 2102308 2

• optical properties of matter describe the interaction of light with matter

• types of interactions: scattering, reflection, absorption, transmission, diffraction…

• properties of light: wave-particle duality

– for propagation & scattering, light = EM wave

– for absorption & emission, photons = particle

• visible light has energy ~1.8-3.1 eV, wavelength ~400-700 nm (visible spectrum) vs.

• a much wider electromagnetic spectrum (Fig./Table 14.1) (L1)

• wavelength l of interest: 10 nm (X-rays) – 100 mm. Selected applications:

– germicide/cosmetic: 300-400 nm (UV)

– display: 400-700 nm (VIS)

– optical communication: 1.3 and 1.55 mm (IR)

• light is an oscillating electromagnetic (EM) field where electric component E ⊥ to magnetic component B, both of which ⊥ to propagation direction k (Fig. 9.1) (L2-L3)

– simplest description: monochromatic light travelling in space in 1D (Fig. 9.2)

– more complete description must be in 3D (Fig. 9.3)

• light can be generated by electrons in atoms, molecules, solids (crystals) dropping from high to low energy levels/bands (L4-L5). Other courses explain the principle of light generation by semiconductor devices (2102385, SKJ), and lasers (2102589, SPY)

9.1 Light(L0)

Optcal Properties 32102308

(L1)

Optcal Properties 4

“Light -”yx BE

oox kztEE cos

k is propagation constant or wavenumber

monochromatic plane wave:

phase

Which (E, B) is more important?

- Electric and magnetic fields always

co-exist by virtue of Faraday’s Law:

time-varying (B field E field)

- Most materials (atoms in the periodic

table) only respond to E, thus B is

usually ignored

- Optical field refers to E field

an electromagnetic wave

in 1D:

spacetime

2102308

E

t

z

l

Ttime

space

l

/2

/2

/1

k

T

Tf

light-related vocabularies:

- monochromatic: single or very narrow

range of l (red laser yes, the sun no)

- coherent: photons constituting light

beam are in phase (laser yes, LED no)

- polarization: direction of E field,

light sources can be (*) unpolarized,

(a) plane polarized, (b) elliptically

polarized, (c) circularly polarized,

*

(L2)

Optcal Properties

“planes”

for any given plane, the phase

is a constant which moves dz at

every dt phase velocity:

l

l

/2

/2

/1

k

T

Tf

fkdt

dzv

okzt

5

- propagation

monochromatic plane wave propagates in space at velocity v

2102308

oo tEt,E rkr cos

1D (far from source)

3D (close to source)

plane wave

spherical wave

(L3)


H2

GAS SOLID

semiconductors

direct indirect

InP Si

- generation(L4)


- generation by hot bodies (incandescence)H2, He W C

• heated elements/molecules: () electrons excited to

E2 and relaxed to E1 (Fig. 14.4), releasing photons

• output spectrum depends solely on temperature T

described by Planck’s law of blackbody radiation

(L5)

Optcal Properties

- incident light is mostly Reflected, Absorbed, Transmitted (refracted, non-normal

incidence), and partly scatterd (Fig. 14.13) (I1). Other types of interactions:

diffraction, fluorescent…

- conservation of energy: (ignoring scattering and secondary effects)

- optical materials/systems often designed to maximize or minimize R, A or T (l) –

see pix (I1)

- interaction of light with

- metals (I2): reflection, mostly

- non-metals: absorption, luminescence (I3)

- results of light-matter interactions:

- colours: (I4) CdS, Hope, (I5) ruby

- opacity: internal reflection by microstructure determines opacity (I5)

- refractive index: light slowed down, bent (refracted) (I6)

RATo IIII

8

Light-Matter Interaction

2102308

RAT(I0)


(I1)

Transmission

AbsorptionReflection

Cloaking

R

A

T(smooth)

(rough)

surface condition

Light-Matter Interaction

“interaction” overview of applications

http://en.wikipedia.org/wiki/Image:Fiber_optic_bundle.jpg

Optcal Properties

Absorption

• Metals have fine succession of energy states.

• Near-surface electrons absorb visible light.

• Metals appear reflective (shiny) because

• Reflectivity = IR/Io is ~ 0.90-0.95.

(reflected light same frequency as incident)

Energy of electron

filled states

unfilled states

E

IR “conducting” electron

re-emitted photon from

material surface

AuPd

since IA + IR ~ 1 IT ~ 0; therefore, all metals are opaque (except thin foil < 100 nm, transmit visible light)

10

Light interaction with metals

Reflection

Colors

Color of metals dictated by interfacial

property (metal/insulator interface) called

“surface plasmon resonance (SPR)”Transmission (none)

2102308

RAT(I2)

Optcal Properties

Absorption (conditional): if hn > Egap

• If EG < 1.8 eV, full absorption; color is black ([email protected], [email protected] eV)

• If EG > 3.1 eV, no absorption; colorless ([email protected], glass@9 eV), transparent (!), see (I5)

• If EG in between or has impurity level, partial absorption; material has a color.

incident photon

energy hn

Energy range of visible light:

11

Light interaction with non-metals

(insulators, semiconductors)

Luminescence

(re-emitted light)

2102308

Reflection: depends on n, ex.

- R ≈ 4% for glass (insulator, n ~ 1.4)

- R ≈ 30 % for Si (semicond, n ~ 3.5)

- for details, see Fresnel (9.7)

RAT(I3)

Optcal Properties

• Colour determined by sum of frequencies of

- transmitted light, scattered light

- re-emitted light from electron transitions

• Ex. 1 (Semiconductor): Cadmium Sulfide (CdS)

- Egap = 2.4 eV,

- absorbs higher energy visible light (blue, violet),

- Red/yellow/orange is transmitted, gives color.

CdS

122102308

Origin of color:

Boron (0-8 ppm depends on position, av. 0.36 ppm)

• Ex. 2 (Insulator)

The Hope Diamond = C (+ % B)

- Egap = 5.6 eV

- luminesce after UV exposure (l<220nm)

- phosphorescence

(re-emission occurs with delay time > 1 s)

LDR

Diamond

http://nhminsci.blogspot.com/2012/05/hope-diamond-blue-by-day-red-by-night_22.html

(I4)

Light-Matter Interaction: Results

(2.48 eV)

(1.88 eV)


Ruby

(mineral)

Ruby

(laser)

• Ex. 3 (Insulator)

Ruby = Sapphire (Al2O3) + Cr2O3

- Egap > 3.1eV

- pure sapphire is colorless

- adding Cr2O3 : (0.5-2) at. %

• alters the band gap

• blue light is absorbed

• yellow is absorbed

• red is transmitted

• Result: Ruby is deep red.

Transparency of insulators

dictated by microstructure:

single-crystal

poly-crystal (dense)

poly-crystal (porous)

Intrinsically transparent dielectrics can be

made translucent/opaque by “interior”

reflection/refraction/scattering.

Opacity/Transparency

(I5)


(EG>3.1eV)

http://en.wikipedia.org/wiki/Image:Ruby.xtal.700pix.jpg

Optcal Properties

• Transmitted light distorts electron clouds.

+

no transmitted

light

• Result 1: Light is slower in a material vs vacuum.

Index of refraction (n) = speed of light in a vacuum speed of light in a material

Material

Lead glass

Silica glass

Soda-lime glass

Quartz

Plexiglas

Polypropylene

Diamond

n

~ 2

1.46

1.51

1.55

1.49

1.49

2.41

- Adding large, heavy ions (e.g. lead, Pb)

can decrease the speed of light.

• Result 2: Intensity of transmitted light decreases

with distance traveled (thick pieces less transparent)

-- see later in Losses (9.8)

• Result 3: Light can be “bent”

or “refracted”, see later Snell (9.6)

Refraction (qi ≠ 0): a change in propagation direction of a wave when it changes a medium

2102308 14

Si O Pb

Si O

Si O Na Ca

Si O

C O H

C O H

C

(I6)



• refractive index (n) measures how much light slows down in a material, with respect

to vacuum. Speed of light in i) vacuum = c, ii) material = phase velocity v (), ∴ n

• materials slow down light due to light-matter interaction: atoms/molecules/grains in

optical/dielectric materials are polarized by the electric field component of light E

(Reminder: polarization mechanisms), Fig. A (R1)

• propagation of light (E) in a material is effectively delayed (phase lag) wrt. vacuum

• (from ) material permittivity er stronger dipoles (drag ) delays

• atoms/molecules in medium are polarized at the same frequency as E, hence the

frequency of light does not change, but other wave propagation & parameters do

change, Table A (R1). Typical wavefronts in films, Fig. B (R1)

• n is not a constant, but can change with

incident direction, especially in some

crystals (birefringent) which show

optical anisotropy (9.14) (R2,R3)

• n is not a constant, but can change with

incident wavelength, thus n(l), see

example (R4), for details next section

9.3 Dispersion

r

rrroror

v

cn

ccv

e

ememmee

1

9.2 Refractive Index (n) (R0)

optical materials are

non-magnetic (mr ≅ 1)


102 104 106 108 1010 1012 1014 1016ƒ

Orientational,

Dipolar

Interfacial and

space charge

Ionic

Electronic

er'

er''

er' = 1

1102

Radio Infrared Ultraviolet light

102 104 106 108 1010 1012 1014 1016ƒ

Orientational,

Dipolar

Interfacial and

space charge

Ionic

Electronic

er'

er''

er' = 1

1102

Radio Infrared Ultraviolet light

Dielectric properties of materials

- complex relative permittivity as a function of frequency

- contribution of various polarization mechanisms

)()( fn

n

r

r

el

e

(R1)

- Estimate n in Film 1, Film 2

- Film 1 is lossy, 2 lossless

vacuum medium

f f

c = lof v = lf

lo l lo/n

ko k = nko

oo

oo

k

k

f

f

v

cn

l

l

l

l

l

l

/2

/2

Table A: Wave propagation parameters Fig. B Wave travelling into optical films

Fig. A

Optcal Properties

Fig. 9.25: A line viewed through a cubic sodium chloride (halite)crystal (optically isotropic) and a calcite crystal (opticallyanisotropic).

From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)

http://Materials.Usask.Ca

Optical anisotropy (9.14)

- most non-crystalline materials (glasses, liquids) and all cubic crystals are optically

isotropic (they “look” the same in all directions)

- crystals are different: n of crystals depend on direction of electric field in the

propagating light beam

- Optically anisotropic crystals are called bi-refringent because incident light beam

may be doubly refracted (Figs. 9.25, 9.26)

Figure 9.26 Two polaroid analyzers are placed with theirtransmission axes, along the long edges, at right angles to eachother. The ordinary ray, undeflected, goes through the leftpolarizer whereas the extraordinary wave, deflected, goes throughthe right polarizer. The two waves therefore have orthogonalpolarizations.

From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)

http://Materials.Usask.CaApplications: polarising beam splitter, phase contrast microscopy...

182102308

(R2)

Optcal Properties

Table 9.3 Principal refractive indices of some optically isotropic and anisotropic crystals

(near 589 nm, yellow Na-D line).

Optically isotropic n = no

Glass (crown) 1.510

Diamond 2.417

Fluorite (CaF2) 1.434

Uniaxial - Positive no ne

Ice 1.309 1.3105

Quartz 1.5442 1.5533

Rutile (TiO2) 2.616 2.903

Uniaxial - Negative no ne

Calcite (CaCO3) 1.658 1.486

Tourmaline 1.669 1.638

Lithium niobate (LiNBO3) 2.29 2.20

Biaxial n1 n2 n3

Mica (muscovite) 1.5601 1.5936 1.5977

non-crystalline

crystalline (cubic)

In noncrystalline materials, n is isotropic.

In crystalline materials, n is anisotropic.

19

oe nn

eo nn

wiki/Birefringence

n is frequency dependent

n maybe direction dependent

o

r

r

N

n

e

e

e

1

2102308

ISO

TR

OP

ICA

NIS

OT

RO

PIC

(R3)

http://upload.wikimedia.org/wikipedia/commons/0/0e/Positively_birefringent_material.svg


Material er(LF) er(LF)] n (optical)

Diamond 5.7 2.39 2.41 (at 590 nm)

Si 11.9 3.44 3.45 (at 2.15 mm)

SiO2 3.84 2.00 1.46 (at 600 nm)

How are these measured in practice?

LF: kHz; e.g. by C-V measurement

HF: (Optical) 1015 Hz; Snell’s

e r

Dielectric resonance

electronic

dipolar

Physical origin of dispersion relation:

• Examples

case 1 (=): same polarization mechanism ( )

case 2 (): additional polarization mechanism ( ) at low frequency

(R4)

)()( fn

n

r

r

el

e

?

=

Optcal Properties

9.3 Dispersion n(l)

21

- dispersion relations: interrelations of wave properties (l, f, v, n), most importantly n(l) ()

- dispersion occurs when pure plane waves of different wavelengths have different propagation

velocities, so that a wave packet of mixed wavelengths tends to spread out in space ()

- brief physics of dispersion (D1)

- the cause: imperfect light sources, they all have finite width l, or FWHM (D2)

- the effect: group velocity and group index (9.4) (D3)

- the results: pulse spread (), poor system performance (bit-error rate, BER )

- the remedy: zero dispersion (D4)

2102308

(D0)

dispersion in prism causes different

colors to refract at different angles, splitting

white light into a rainbow of colors

dispersion in optical fiber communication

≠


22

22 1

o

nll

ll

Brief Physics of dispersion relation

22

0

2

induced

induced

2

/

1

e

e

e

e

e

o

er

r

m

ZexZep

p

N

n

(D1)

- in real crystals, atoms interact very complicated. In general, a material can have polarization

mechanisms each with a different resonance frequency. This leads to a semi-empirical dispersion

relation:

- Example n(l) for GaAs (0.89-4.1 mm) at 300K

(obtained empirically):

27670

783107

2

22

.

..n

l

l

[l in mm]

3

2

2

3

2

2

2

2

1

2

2

12 )(C

B

C

B

C

BAn

l

l

l

l

l

ll

B1,2,3, C1,2,3 : Sellmeier coefficients

Sources: Batop.com, Wiki

dispersion relation in a material with a single polarization

mechanism with a single resonant wavelength lo


The cause of dispersion: engineering & physics

Dispersion occurs when pure plane waves of different wavelengths have different propagation velocities, so that

a wave packet of mixed wavelengths tends to spread out in space. (Wiki)

Light sources:

- broadband: Sun, incandescent – for general lighting

- narrowband: light-emitting diodes (LEDs), (LDs) – for communication

Color depends on material (EG)

Color purity (full-width at half-maximum:

FWHM) depends on device (structure /

mechanism):

-LEDs (homojunction [p-n], spontaneous

emission): FWHM ~ 30 nm

-LDs (heterojunction [p+-n+], stimulated

emission): FWHM ~ few nm

FWHM = 0 (perfect monochrome) cannot

be achieved.

no perfect monochromatic waves

not single value

Heisenberg: tE

Typical spectra of RGB LEDs. Source: Wiki

FWHM

(D2)

EG

E


The effect of dispersion: 9.4 Group velocity and group index

Information:

phase travels @ phase velocity (v)

Emax travels @ group velocity (vg)

Note that eyes/detectors measure intensity (E2)

v = c/n and = vk

vg =d /dk

v = c and = ck

vg = d /dk = c = phase velocity for all l’s

in a medium: n > 1 (l dependent)

g

g

g

N

cv

d

dnn

c

kv

n

cv

lld

d

l

Ng group index

Dispersion occurs when pure plane waves of different wavelengths have different propagation velocities, so that

a wave packet of mixed wavelengths tends to spread out in space. (Wiki)

x

x

E

E2

in vacuum: n = 1 (l independent)

(D3)


The remedy: eliminate / minimise?

ll

d

dnn

group index

Ex. 9.6: find the phase velocity, group index, and group velocity of light (1300 nm) travelling in a

pure silica glass.

n = 1.447 v = 2.07 108 m/s

Ng = 1.462 vg = 2.052 108 m/s

Zero-dispersion

ll

ll

d

dN

cLd

dt

d

dt

L

c

d

dN

L

ct

v

cN

gg

gg

g

g

g

1

(D4)

Optcal Properties

9.6 Snell’s law and TIR

Trigonometry:

i & t

1

2

1

2

sin

sin

sin

sin

n

n

tvBABB

tvBAAA

t

i

i

t

q

q

q

q

n1 > n2

Requirement for wave propagation =

Constructive interference: wavefronts for

reflected and refracted (transmitted) waves

must be in phase with incidence wave =

i & r

ri

r tvBAAA

qq

q

1sin

ALL other angles interfere destructively

=

Snell’s law

262102308

/

=

(1621)

http://upload.wikimedia.org/wikipedia/commons/7/7f/Willebrord_Snell.jpg

Optcal Properties

90when tci qqq

TIR leads to wave propagation in a dielectric medium

21

2

2

2

12

0

12

/

i

y

,t

sinn

nn

kztjexpet,z,yE

ql

penetration depth = 1/

from Snell’s law:

1

21sinn

ncq

Fiber axis

n2

n1

n2

q q

Cladding

TIR

Lightray

Core

Emitter

Input Output

Optical Fiber

Photodetector

Digital signal

Information Informationt

An optical fiber link for transmitting digital information in communications.

The fiber core has a higher refractive index so that the light travels along the

fiber inside the fiber core by total internal reflection at the core-cladding

interface.

272102308

Optcal Properties

9.7 Fresnel’s equations

- a set of four equations (Fresnel, 1818) used to determine the

magnitudes and phases of reflected and transmitted waves

at the interface of two transparent materials with different

refractive indices, see (F1)

- the results (mainly reflection coefficients) are plotted in two example cases:

- internal reflection, when n1 > n2, see (F2)

- external reflection, when n1 < n2, see (F3)

- human eyes (and optical detectors) sense intensity (E2), not the magnitude of the

optical field (E), hence appropriate to plot reflectance and transmittance (F4)

- the equations provide mathematical guideline to the designs of some important

normal-incidence (qi = 0°) applications:

- low-reflection coating: aims to absorb all incident radiation, useful in solar cells

and photodetectors, see anti-reflection coating (ARC) (F6)

- high-reflection coating: aims to reflect all incident radiation, useful as mirrors,

see quarter wave stack (F7)

- various optical filters: low-pass, high-pass, bandpass (similar in principle to

electronic filters)

282102308

(F0)

1788--------1827

http://www.google.com/imgres?imgurl=http://www-scf.usc.edu/~kallos/images/fresnel.jpg&imgrefurl=http://www-scf.usc.edu/~kallos/light1.htm&usg=__zncZIXg6fyPQ-OzA3yHVHcARFvA=&h=480&w=391&sz=44&hl=en&start=2&um=1&itbs=1&tbnid=DHF2tBTqAfhu1M:&tbnh=129&tbnw=105&prev=/images?q=fresnel&um=1&hl=en&safe=off&rls=com.microsoft:th:IE-SearchBox&tbs=isch:1


n2

z

y

x into paperq

i

n1

> n2

qr

Incident

wave

qtqt = 90

o

Transmitted wave

Et,

Evanescent

wave

Reflected

wave

Reflected

wave

Incident

wave

qi

qr

Ei,

(a) qi < qc then some of the wave is

transmitted into the less dense medium.

Some of the wave is reflected.

(b) qi > qc then the incident wave suffers

total internal reflection. There is a decaying

evanescent wave into medium 2

Ei,

y

ki

kt

kr

Et,

Ei,Ei,

Er,

Er,

kr

Et,

Er,

Er,

Governing principles:

A. Snell’s law:

B. electromagnetism:

C. Boundary conditions:

Etangential (1) = Etangential (2)

Btangential (1) = Btangential (2); for non magnetic media

2211 sinsin qq nn

E

c

nBE

c

nB //// and

→ qi = qr and1

2

n

nn

ii

i

i

t

ii

ii

i

r

nE

Et

n

n

E

Er

qq

q

qq

qq

22,

,

22

22

,

,

sincos

cos2

sincos

sincos

ii

i

i

t

ii

ii

i

r

nn

n

E

Et

nn

nn

E

Er

qq

q

qq

qq

cossin

cos2

cossin

cossin

222//,

//,

//

222

222

//,

//,

//

1;1 //// ntrtr

/

/

/

/

(F1)

Optcal Properties

Example:

n1 = 1.44 and n2 = 1

normal incidence :

21

21//

nn

nnrr

(n1 > n2)Internal Reflection

set r// = 0

8.34tan

1

21

n

npq

44sin,

44.1

1

1

21

n

nn cq

(r, r// complex)

(+, real)

(+, real)

(–, real)

polarization angle

Brewster’s angle

30

= 0 @ qi = 0

2102308

set qi = 0

(F2)

Optcal Properties

Transmitted light in both internal and external reflection does not experience

phase shift (t is always +ve, qi < qc)

(main concern is reflected light for propagation)

External Reflection

Example:

n1 = 1 and n2 = 1.44 no critical angle

c

nn

n

n

q

q

qq

no

)1(sin)(

sinsin

221

21

2

1

31

2.5544.1tan 1

pq

= @ qi = 0

2102308

(n1 < n2)

0sin,1

44.1 22 inn q

(F3)

Optcal Properties

Reflectance (R) and Transmittance (T)

R + T = 1

2

//

1

2

2

//,1

2

//,2

//

2

1

2

2

,1

2

,2

2

//2

//,

2

//,

//

2

2

,

2

,

and

and

tn

n

En

EnTt

n

n

En

EnT

rE

ERr

E

ER

i

t

i

t

i

r

i

r

At normal incidence (qi = 0):

2

21

21//

2

21

21//

4

nn

nnTTT

nn

nnRRR

(practical angle in laser diodes, or cavity structures)

32

Ex:

Ref

lect

ance

(%

)

2102308

(F4)

http://upload.wikimedia.org/wikipedia/commons/a/a0/Fresnel2.png

Optcal Properties

Ex. 9.8

Ex. 9.9

n = 1.44

n = 1.46

l = 1300 nm

i) Find minimum angle for TIR

ii) Find penetration depth of evanescent wave in the upper medium when qi = 87 and 90

air glass

1 n 1.5

Find reflection coefficients and reflectance in

each case

Internal Reflection

Internal and External Reflection

ii) use:2/1

2

2

2

12 1sin2

i

n

nnq

l

qi () 1/ (mm)

87 0.906

90 0.859

332102308

thicker than 5 * penetration depth

(F5)

Optcal Properties

Ex. 9.10: n1 = 1, n3 = 3.5, calculate R without ARC layer.

Insert ARC layer to minimise reflection. A and B must be:

of similar amplitude n2 = (n1n3)1/2 *** Proof

out of phase d = ?

700 nmRequirement: maximum light transmitted to

PV for electricity generation

n1 < n2 < n3

Max Absorption (PV)

34

air/ARC = ARC/semic.

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(F6)

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Optcal Properties

Ex. 9.11: Dielectric MirrorsQ) Why do we need dielectric mirrors?

A) Bend light without absorption (cf metallic mirrors)

Design criterion: A,B,C interfere constructively.

n1 < n2

Show that waves A, B and C interfere constructively.

note: l1 = l0/n1, l2 = l0/n2

Max Reflection (LD,VCSEL)

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(F7)

Optcal Properties

9.8 Loss and complex refractive index

- for transparent insulators (EG > 3.1 eV), the light-matter interaction

can be described simply by the (real) refractive index n

- for metals (no EG) and semiconductors (EG few eV), large number

of free electrons cause absorption (loss) of light and the light-matter

interaction must be described by a complex refractive index N = n − jK

- loss quantified by absorption coeficient , related to absorption index K, the

imaginary part of complex refractive index N (L1)

- example (n,K) spectra of amorphous Si (a solar cell material) (L2), using a simple

optical test setup (L3). Note relationship between optical and dielectric properties

in (L2), with calculation example in (L4)

- loss of photons (between source and detector) is caused by absorption and scattering

- two intrinsic absorption mechanisms (anything “intrinsic” can’t be removed):

- lattice absorption (9.9): photons to phonons (heat), IR active

- band-to-band absorption (9.10): photons to carriers (EHPs), UV active

- one intrinsic scattering mechanism, Rayleigh (9.11), UV-VIS-IR active

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(L0)

Optcal Properties

(linear) Absorption Coefficient

zktjexpzkexpE

zkjktjexpEE

kztjexpEE

o

o

o

Plane waveLossless:

Lossy:

Intensity:

Kkk

zII

zkEI

o

o

22 where

expor

2exp2

EXP. determine K(l)

from absorption /transmission measurements

at normal incidence as a function of freq.

Since er is complex n is also complex written as NIn fact, propagation constant k is complex: k k' – jk''

k' describes propagation:

phase velocity v = /k'

k" describes absorption:

attenuation along z

k0 is propagation constant in a vacuum (no loss, real #)

oo k

kjk

k

kn – jKN

n refractive index

K absorption indexokk

okk

note:

37

oo

oo

k

k

f

f

v

cn

l

l

l

l

l

l

/2

/2

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(extinction coefficient)

Beer’s law*

* Bouguer, Beer, Lambert

R A T

R,T A

(L1)

Optcal Properties

a-Si

EG

photon

energy

lossless:

lossy:

'''22

'''

2 and

,0

rr

rr

r

nKKn

jjKn

nk

ee

ee

e

EXP. determine R(l)

from reflectance measurement at

normal incidence as a function of freq.

22

222

1

1

1

1

K n

Kn –

N

NR

Hence, complex refractive index:(n,K) collectively called optical constants but they vary with wavelength, hence not

constants as name suggest

& get n – jK (l)

38

from 9.7 (Fresnel)

Optical constants (n and K) can also be found from ellipsometry (a kind of reflection measurement, see

JA Woollam.com), the principle is based on polarization and angle of incidence (Fresnel’s equations)

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Knrr ,, ''' ee

dielectric / optical

Kramers-Konig relation

(L2)


Io

It

Ir

broadband lightsource

monochromator

material under test

photodetector

l , photon energy

l

l , photon energy

l , photon energy

l , photon energy

It / IoIr / Io , R

(k", K)n

beamsplitter (50:50)

R (n,K)

z

(L3)Setup for (n,K) measurements

R

K

n

Optcal Properties

Ex. 9.12 Spectroscopic ellipsometry measurements on a Si crystal at 826.6 nm show that

the real and imaginary parts of complex relative permittivity are 13.488 and 0.038. Find

complex refractive index, absorption coefficient at this wavelength, and phase velocity.

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(L4)

Optcal Properties

z

Propagation

directionk

Ions at equilibrium positions in the crystal

Forced oscillations by the EM wave

Ex

9.9 Lattice absorption

vibrate at frequency of E

- the electric component of the lightwave (E) interacts

with ions in the lattice

- the interaction is strongest when the frequency of the

lightwave (color, energy) match the natural lattice

vibration frequency (1012 Hz, in the IR region)

Lattice absorption through a crystal. The field in the EM wave oscillates the ions, which

consequently generate "mechanical" waves in the crystal; energy is thereby transferred from

the wave to lattice vibrations.

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Optcal Properties

9.10 Band-to-band absorption

Indirect materials:

hEhv G

phonon energy

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- at sufficiently high energy, light interacts with

valence electrons in the bonds, freeing them ( EHPs)

- electrons are transferred from (valence) band-to-

(conduction) band, requiring minimum photon energy:

- for direct materials, Fig. (a), the interaction only involve photons & electrons, but

for (b) indirect materials, Fig. (b), phonons are involved too (conservations of energy & momentum)

- (band-to-band) absorption spectra, l, show sudden change around l () of materials (B1)

- optical detection systems performance limited mainly by choice of material and device (B2)

Direct materials:

GEhv

)(

24.1)(

eVEm

hcE

G

offcutG mll

(B0)

Optcal Properties

Most photon (63% or 1-1/e) absorbed

over penetration depth d 1

)exp()( xIxI o

Semiconductor Eg (eV) lg (mm) Type

InP 1.35 0.91 D

GaAs0.88Sb0.12 1.15 1.08 D

Si 1.12 1.11 I

In0.7Ga0.3As0.64P0.36 0.89 1.4 D

In0.53Ga0.47As 0.75 1.65 D

Ge 0.66 1.87 I

InAs 0.35 3.5 D

InSb 0.18 7 D

Table 9.2 Band gap energy Eg at 300 K, cut-off

wavelength lg and type of bandgap (D = Direct

and I = Indirect) for some photodetector materials.

Si photodiodes cannot be used for optical

communication @ 1.3, 1.55 mm. Ge OK.

Ex 9.17: A GaAs LED emits at 860nm. Si

photodetector is to be used. What should be the thickness of Si that absorbs most of the radiation?

Given (Si) @ 860nm is 6104 m-1.

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(= 2k = 2koK)

NIR

MIR

(B1)


surface recombination

(device limit)

bandgap limit

(material limit)

Photodetectors

- materials: energy gap (EG) dictates detection range

- devices: structure (p-n, p-i-n, APD, ...) dictates speed (RC), sensitivity

- systems: available as 0D (point), 1D (line), 2D (area) detection

- commercial products: embedded in tablet, smartphone, robots, cars...

Silicon (UV-VIS-NIR) III-V, II-VI (NIR, MIR)

(B2)

Optcal Properties

- scattering is due to small particles embedded (solid) or suspended (liquid, gas) in transparent media

- scattering reduces light intensity in the main direction by radiating part of the incident energy in all

directions; the radiation pattern (angle dependent intensity: I(q )) depends on the relative size

between the incident wavelength l and the particle size:

- particle size < l10 Rayleigh scattering (see )

- particle size l Mie scattering

- colour of sky: blue (daytime, ), pink/red (sunrise/sunset, ) due to

i) eye sensitivity (peaks around green, 555 nm)

ii) the visible spectrum (bell shape, range 400-700 nm), and

iii) 1/l4 — shorter l (blue) scattered more, longer l (red) forwarded more, by atmospheric dusts

- attenuation in optical fiber (9.12) is fundamentally limited by iii)

9.11 Light scattering in materials

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https://bilimfili.com/hiperfizik/hbase/atmos/blusky.html#c1

GMT

GMT + 7

iiiiii

Optcal Properties

9.12 Attenuation in optical fibers

- optical fiber materials are mainly glass (A0) and polymer (A1), optical transmission through

fibers always suffer from loss, quantified by attenuation (dB/km), see

- intrinsic loss mechanisms in GOF: lattice absorption (9.9) and Rayleigh scattering (9.11), the

latter due to non-crystalline state of glass (small density fluctuation)

- extrinsic loss mechanisms: hydroxyl (OH−), metallic (Fe2+) impurity, negligible by 1979

- comparison between electrical (Cu) vs optical (GOF, POF) signal transmission, Table 1 (A2)

- when nature gives you a loss, it also gives you a gain (EDFA) (A3)

water byproducts

Resonance @ 2.7 mm

(first harmonic @ 1.4 mm)

(second @ ~1 mm, negligible in

high-quality fibre)

Stretching of Si-O bond

(resonance @ 9 mm)

(for Ge-O: 11 mm, graded index)

- Not shown, below 500 nm, sharply since photons excite electrons from VB CB (9.10)

- loss @ 1.5 mm (dB/km): 0.2 in 1979, now = 0.16, intrinsic limit. (Source: Tilley 2011)

(9.9)(9.11)

(9.10)

46

Glass optical fiber (GOF)

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4/1 lI

(A0)

wavelength (mm)

)0(

)(log

10

P

xP

x


Plastic optical fiber (POF)

Material

PMMA: Poly (methyl methacrylate)

(C5O2H8)n

Other names:

Acrylic glass, Plexiglas

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(A1)


Benefits of optical fibers in

communications systems:

1. transmission distance

2. transmission speed

3. information density

4. no electromagnetic

interference (EMI)

Speed:

- light in space: c=3x108 m/s

- light in glass: 0.67c

- electrons in Cu: 0.01c

- electrons in Si: 0.001c

(vsat = 107 cm/s at 300 K)

(A2)


Erbium doped fiber amplifier (EDFA) (A3)

- active region of EDFA system consists of 30-m section of fiber doped with Er3+ (Fig. 14.35a)

- how it works: weak optical signal enters (1), and after being pumped by laser diodes (LD) (2),

leaves as output (3) with increased intensity: input (1) + pump (2) output (3)

- material: Erbium (III) ion (Er3+), not atom. The electronic structure of Er3+ is [Xe] 4f11, the 4f-

shell is well shielded (by the outer 5s, 5p shells) from the environment (SiO2), thus energy levels

(not bands): ground state 4I15/2 (GS), and next 2 excited states 4I13/2, 4I11/2 (Fig. 14.35b)

- physics: LD 980nm shone (4) Er3+ excited from 4I15/2 to 4I11/2, but (5) quickly relaxes by non-

radiative radiation to 4I13/2 and stays there for a long time, when an input photon (1) l1480 nm

arrives, it entices the excited Er3+ (at 4I13/2) to return to GS by stimulated emission (6), think laser.

Thus, 1 photon in, 2 photons out. Gain!

- effectively, power transfers from LD (2)

to output (3), which is an amplified version

of input (1)

(a) (b)

(1) (3)

(2)

(4)

(5)

(6)(7)

Optcal Properties

9.13. Luminescence

• Incandescence: emission of radiation from thermal source (L5)

• Luminescence: emission of radiation by a material due to absorption and conversion of energy

(non-thermal source) (Fig. 15.9). Note the emission is always lower in energy than excitation.

• Luminescence classified by excitation source (M1)

(a) Photoluminescence (PL): luminescence from materials excited by photons. Ex. PL fibers in banknotes

(b) Cathodoluminescence (CL): luminescence from materials excited by energetic electrons. Ex. CRT

• Luminescence classified by time (emission after excitation)

– < 10 ns: fluorescence

– > 10 ns: phosphorescence

• Luminescent materials (phosphors):

– fluorescent lamps, TV screens (M1,2)

– white LEDs (M2)

– quantum dots (QDs) (M3-M5)

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(M0)


Al2O3 : Cr3+

TV Screen phosphor

Host matrix (e.g. Al2O3)

Activators or

luminescent centers

(e.g. Cr3+)

(c) A typical phosphor = host + activators

Incident

light

Phosphor

Phosphor

Heat

Emitted light

Incident

electrons

(b) Cathodoluminescence

Phosphor

Heat

Emitted light

Incident

light

(a) Photoluminescence

Photoluminescence, cathodoluminescence and a typical phosphor

halophosphate

Ca10F2P6O24 : (Cl−,Sb3+,Mn2+)

(M1)

Optcal Properties

Yellow

phosphor

emission

Blue

chip

emission

Total white emission

350 450 550 650 750

0.5

0

1.0

Wavelength (nm)

(b)

InGaN chip: blue

emission

Phosphor (YAG):

yellow emission

Yellow

Blue

White LED

(a)

Application: White LEDs

(a) A typical “white” LED structure. (b)

The spectral distribution of light emitted

by a white LED. Blue luminescence is

emitted by the GaInN chip and “yellow”

phosphorescence or luminescence is

produced by a phosphor. The combined

spectrum looks “white”.

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Mercury (Hg) emission spectrum (for fluorescent lamp)

- white light from fluorescent lamp comes from the phosphor

(RGB mixture) excited by sharp lines of Hg ions

(Hg atoms previously excited by energetic electrons)

- the spectrum of Hg (left) and energy level diagram (right)

(M2)


(M3)Quantum Dots (QDs)

- bulk materials, carriers free to move in three dimensions (3D)

- nanomaterials, carriers motion limited in 1 or more dimensions. The three types of quantum

nanostructures: quantum wells (2D), quantum wires (1D), quantum dots (0D) (Fig. 3.4) (M4)

- electron energy levels: see equations [1D], [3D] (M4). Optical properties (absorption, emission)

of nanostructures depend on material (atoms), bonding (lattice constant), and size:

- for quantum wells, size means thickness, emission at energy E > EG (Fig. 14.38) (M5)

- for QDs, size depends on shape, but generally a×b×c (length×width×height). See energy

diagram (Fig. 14.41) and size-dependent emission spectra (Fig. 14.40) (M5)

- quantum dots maybe synthesized by various techniques: wet chemistry, chemical vapor

deposition (CVD), molecular beam epitaxy (MBE)


(M4)

2

2

2

2

2

2

*

2

2

2*

2

8),,(:[3D]

8:[1D]

c

n

b

n

a

n

m

hnnnE

nam

hE

zyxzyx

n

(Quantum) Nanostructures

- structures with one or more dimensions in the same scale as de Broglie wavelength of

electrons (nm in metals, 10s nm in semiconductors)

- electrons confined in such structures can have only certain energies with certain wavelength

dictated by size. For confinement in:

- 1 dimension (Fig. 2.17), i.e. a well of width a, the discrete energy levels is [1D]

- 3 dimensions, in a a×b×c dot, the discrete energy levels is [3D]

- Size matters: electron energy is inversely proportional to size (E ∝ 1/a2)

[1D]

[2D] [3D]


(M5)

optical properties of materials

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