optics and some method

8/12/2019 optics and some method

http://slidepdf.com/reader/full/optics-and-some-method 1/13

Prof. K. C . Kim

Spring 2014

1

Applied Optics and Optical Measurement Techniques

LN#2. Index of Refraction (Sections 3-4, 3-5)

Scattering and Transmission (Sections 4.1 and 4.2)

Electric Dipole Model of E-M wave interaction with atom:

*Ground state electron: at the lowest energy level.

*Excited state electron: at any higher levels.

Resonant Excitation: When the incident E-M energy level (h ) matches with the energyrequired for a specific QUANTUM energy level jump of an electron, the electron absorbs

the incident energy, and then very likely and very rapidly the energy is transferred tocollisions, random diffusion, thermal dissipation and so on before photons can be emitted.

>>> This is called Dissipative non-radiative absorption. (e.g. Microwave oven,

Coloration as a result of transmission/reflection at the remaining (non-resonant)

frequencies. Transparency: visible resonant )

>>>For extremely high power, well-collimated, narrow-banded, often short-

pulsed incident E-M can result in significant (almost always accompanies a ‘population

inversion’ of electrons) radiative emission out of the resonant excitation and study of thisradiative spectrum related with material properties is called “Spectroscopy.” (e.g. Lasing,

Laser Induced Fluorescence, Raman Spectroscopy; scatteringincident )

Non-Resonant Excitation: When the incident E-M energy frequency is lower than theresonant ones, the electron at the ground state starts to vibrate conforming to an

oscillating dipole and begin to re-radiate at the same frequency.

>>> This is called Elastic Scattering ( scatteringincident ) including

Reflection/Refraction. This is also called a spontaneous emission. The emission lifetime

is ~10-8

s and the number of photons emitted is an order of 108/s.

resonant h E

resonant h E



Prof. K. C . Kim

Spring 2014

2

E-M Radiation by Electric Dipole Oscillation:

[Each participating atom to behave as a tiny source of spherical wavelets]

Non-oscillating steady dipole

2

2

2

14

1

r

q

r

q r E

o but 0 B since

t

E B o o

Oscillating dipole

t r

q

t r

q t r E

o

2

2

2

14

1,

and 0 B since

t

E B o o

Def’n of Index of Refraction: E

o

ooo K c

cT n

/1

/1, (3.1)

( o E / K : dielectric constant)

( o for most transparent materials.)

*Dispersion: frequency-dependency of refractive index.



Prof. K. C . Kim

Spring 2014

3

Forced Oscillator or Electric Dipole Model for Index of Refraction:

*Dipole moment is defined as the amount of charge (q) of each pole multiplied by the separationdistance ( d ), i.e., p = qd . The dipole moment per unit volume of the medium is called

electric polarization P pN where N is the atom number density.

*For most materials P and E are related as P E o … A better conducting material

carries higher polarization under a given electric field (3.2)

t E t E o cos

(Resonance frequency at e o m k / )

x m kx F

t cos Eq t Eq F

oeSpring

oee M E

2

2

22cos

dt

x d m x m t Eq F e oe oe (3.3)

The solution for x( t) of the second-order, inhomogeneous ODE, Eq. (3.3), is given

as,

t E mq

t x o

o

ee

cos/

22 (3.4)

With, the dipole moment of N atoms per unit volume, xN q P e (3.5),

nucleus



Prof. K. C . Kim

Spring 2014

4

Combining Eqs. (3.1) to (3.5) gives,

2/1

22

2

22

2

2 11

11

oeo

e

oeo

e

m

Nqnor

m

Nqn

Note: The dimension ofe o

e

m

Nq

2

is frequency (s-1

)

For a low density material ( n ~ 1), such as gas, which also has a single resonant

frequency, the second term is usually small, and we have

22

21

2

11

oe o

e

m

Nq n

[cf . x f x

xf f x x f 2

11...0''

!20'01

22/1 for x ~ 0]

For multiple ( j) oscillation modes,

j oj

j

e o

e f

m

Nq n

22

2

2 1

with 0.1 j f (3.6)

With damping, i.e., for the case of partially dissipative absorption, the equation of motion, Eq.(3.3) will be modified to

2

22

dt

x d m

dt

dx m x m t cos Eq F ee oe oe

where denotes the damping constant. Now the modified solution is given as,



Prof. K. C . Kim

Spring 2014

5

j j oj

j

e o

e

i ri

f

m

Nqin n n

22

222 1 (3.7)

Real part of n: the refractive index

Imaginary part of n: the absorption index

[Example]

Just for convenience, let’s assume a single mode oscillation.

For non-absorbing ( j oj

22 ) material, such as glass or air and for the resonance

frequency o in UV,

As long as the range of 22 oj or o (for example, for the visible light spectra)

22

22 1

1

oe o

e

m

Nq n

For o , n is larger than unity and gradually increases with increasing .

For o , n is less than unity and gradually increases to unity with increasing .

For o~ , ( ~ o 100 nm for typical glass material), j term becomes dominant,

and the absorption is significant.



Prof. K. C . Kim

Spring 2014

6

Example: Some semiconductors have the resonant wavelength in the visible range, and thus,

they are opaque in the visible range but transparent in infrared range (see theinserted photo on p. 73).

Example: Since leadglass o a fusedsilic o (both in UV range), leadglass a fusedsilic n n for

the visible range of o .

(Ref. To Table 3.3, Figs. 3-40 to 43)



Prof. K. C . Kim

Spring 2014

7

REVIEW PAGE

Maxwell’s E-M wave equation: 2

2

2

2

2

2

2

2

2

t

E

z

E

y

E

x

E E o o

(Since the equation is independent of wavelength and so have no fundamental differences

between -rays, x-rays, UV, visible light, IR, microwaves, broadcast waves and so on.)

*E-M waves travel the free space (vacuum) without being dissipated or altered. [Immortal!]

*E-M waves may be dissipated WHEN they interact with atoms in a medium, primarily as in

thermal absorptive dissipation.

*Reminder: EM-radiation does not tire or diminish and photons are timeless and

existing only at the speed of light c. Zero mass, but non-zero energy, h E carried by

a single photon.

The energy density is given as 2 E

c

S pu o

Where S is the resulting power per unit area, and t r k E t E o cos .

Since E oscillates at frequency range beyond any detection or recognition limit, time-

average power per unit area is of interest, which is called Irradiance I , i.e.,

2

2 o

o

T E

c tS I

Submicroscopic scattering: absorption and re-emission of EM-radiation by oscillating electrons

of atoms or molecules. The former is called a resonant absorption [ resonantincident ]. The latter

is called a ground-state vibration [ resonantincident ].

Nitrogen and oxygen are invisible as they are resonant at UV. Abundant nitrogen oxygenatoms/molecules at high altitude absorb most of UV coming from the outer space including the

sun. This will make the survival of living cells on the earth ever possible. … What a God’s trick!

The atom or molecules are called submicroscopic scatterers. No scattering exists in free space, because of no scatterers, and light rays or laser beams are invisible except at the normal incident

plane.



Prof. K. C . Kim

Spring 2014

8

Rayleigh scattering: Light scattering by submicroscopic scatterers, i.e., for the case of

1.0 p d [e.g., ~ 500 nm for visible light onto nanoparticles, atoms or molecules of 1-nm

range].

rV KE rV E E scatterer oi scatterer oi os //

A simple dimensional analysis shows that rV K / must be dimensionless, and so K has units of2 L ~ 2 . Thus,

242

222

r r

V K

E

E

I

I

oi

os

i

s

Ex. Rayleigh scattering ratio between a blue Ar-ion laser ( = 488 nm: blue) and a

helium-neon laser ( = 630 nm: red): The former scatters 2.8 times more than the latter.

82

488

6304

.

Ex. This frequency dependency of scattering diminishes as the scatterer size increases,

i.e., p d : white - clouds, fog, cigarette smoke - nanoparticles before (blue) and after

inhalation – microparticles (white).

Eoi

Eos



Prof. K. C . Kim

Spring 2014

9

Example of Rayleigh scattering:

Blue sky

White (the sun light) R-Y

B

Red-yellow sky at the dawn or dusk?



Prof. K. C . Kim

Spring 2014

10

Observation-Angle Dependency of Rayleigh Scattering

[Tips: Only the lateral E-field component of the scattering is viewed as E-M field emission.]

224

2

cos r E

E

I

I

oi

os

i

s

*The angle dependence of Rayleigh scattering is not apparent in the practical situation

where multiple atoms (scatterers) are randomly polarized in general.

E oi: Incident amplitude

E os =cos E oi

E os = 0

E os = E oi



Prof. K. C . Kim

Spring 2014

11

[From this point on, our primary consideration is for non-resonant excitation and re-radiation by the ground-state vibration, i.e., the elastic scattering.]

Transmission, reflection, and refraction are macroscopic manifestations of the

submicroscopic scattering

CASE I: Transmission of Light Thru Scarce Media ( (~500 nm) l (intermolecular

distance): for mostly above 100 miles altitude)

Keynote: Side scattering is not interferes because of the scarceness of the waves, i.e., lowerchance of fashioned interference and randomly different phase lags, i.e., incoherent side

scattering (e.g. blue sky). In other words, the side scattering is visible as all of the side scattered

rays are added to enhance the visibility.

P’

P

More Descriptions: For random, widely spaced scatterers bombarded by an incident wave,the scattered (or re-radiated) wavelets are essentially independent of one another in all directions

except forward. The scattered wavelets have little interference because of their wide variation of

optical path lengths, polarities and phases from the widely spaced scatterers. Accordingly, the net

irradiance at a P is the algebraic sum of the scattered irradiance from each molecule.

However, the forward scattering does not change the light paths (optical path lengths) very much,and waves all arrive at P’ pretty much in phase and interfere constructively.

Example: A laser beam is visible through a vacuum chamber.



Prof. K. C . Kim

Spring 2014

12

CASE II: Transmission of Light Thru Dense Media (wave length >> l)

*Most ordinary air environment below 100 miles altitude, liquid, glass, crystals etc., for

example, ~ 500 nm and l ~ 3 nm for STP air.

Keynote: Little or no side or back scattering (destructive interference), but nearly

undiminished forward scattering retaining its phase (constructive interference).

*Both molecules, a distance of 2/ apart, re-radiate at the same time as they are bombarded by

the incident radiation simultaneously. Then the both wavelets cancel in the transverse direction

and negate the lateral irradiance each other. Similarly, the back-scattering re-radiation waveletswill destructively interfere with a part of the incident radiation waves.

Thus, the back and side scattering will be small compared with the (nearly) constructive forwardscattering, and more so for denser medium.

Example: A laser beam is invisible through a vacuum chamber from its side view.

Cigarette smoke – visible in a dusty environment at STP (?)

/2

optics and some method

Documents