nanophotonics course material-2012 for students 110112

8/2/2019 Nanophotonics Course Material-2012 for Students 110112

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Nano-photonics Course material

Reference:

1. Nanophotonic by Paras N. Prasad, Wiley Interscience, 2004, USA2. Photonic Crystals: Molding the flow of Lightby John D. Joannopoulos,

Steven G. Johnson, Joshua N.Winn, Robert D. Meade April 17, 2007

3. Nanooptics By Sotoshi Kawata, Motichi Ohtsu, Masahiro Irie, Springer Verlag

20024. Optical Nanotechnologyby J. Tominga and DP Tsai, Springer 2003

5. Principles of Nano-Opticsby Lukas Novotny, BertHecht, Cambridge

University Press 2006.6. Electromagnetic Metametrials: Transmission Line Theory by Christoophe

Caloz, Tatsuo Itoh, Wiley IEEE Press 2005


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WHAT DIFFERENTIATES ELECTRONfrom PHOTON

1. Electron is a Charged particle

2. Photon is a Non-charged particle

3. Electron has mass associated with it.

4. Photon is a mass-less particle

5. Both behave as a Particle and as Wave.

6. Both are governed by EM theory but their behaviors are different

7. Electron Wave is a Vector propagation under field and thereforehas vector field while Photon is a Scalar Propagation therefore has

Vector field associated with it and both move in 3-D.

8. Electron is defined by 3 components viz. frequency orwavelength, amplitude (as voltage or current) and phase.

9. Photon has 4 components viz. frequency or wavelength,

amplitude (as power), phase and polarization.

10.Electron wave up to 300GHZ is bipolar and after that it becomes

unipolar. When it becomes unipolar it is called Electronic Photon.

11.Photon is always Unipolar.

12.Electrons posses SPIN, and their distributions are defined by

FERMI-DIRAC Statistics and therefore are called FERMIONS

13.Photons do not have SPIN therefore their distribution is governedby Bose Einstein statistics and are therefore called BOSONS.

14.Electrons being charged particles get guided within vacuum or any

media only under electric field, while photons being non-chargedparticle, need a dielectric medium for guidance.

15. Electron hassmallerDe-Broglie wave-length and Photon has a

longerDe-Broglie wave-length.


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5 B1

r` a

fffffffffff5 B B r

` a=

c

fffffe2

B r` a

for optical wave

O F = C F where C is an eigen value and is given by

c

fffffe2

and O is the Eigen function

THE DENSITY OF STORAGE ACHIEVABLE WITH Nanophotonicsdevices


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NANOPHOTONICS works BEYOND the DIFFRACTION LIMIT or is

DIFFRACTION FREE, where the x< and kx 1 and k is the

UNCERTAINITY in the wave number k . It is this characteristics that

enable HIGH RESOLUTION and HIGH FREQUENCY OPERATIONS.

When the incident light radiation

WAVELENGTH is greater than thePARTICLE SIZE Electric Dipoles are formed at

every diffraction point which explains the

DIFFRACTION FREE transmission as

OPTICAL NEAR FIELD Radiation.

1. The radiated NEAR FIELD isindependent of the phase of the

incoming incident light.

2. Therefore the SPATIALDISTRIBUTION and DECAY

LENGTH of the Optical Near FieldEnergy does not depend on the

WAVELENGTH of the incident light

but on the size, conformation and the


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REVIEW OF ELECTROMAGNETICS andMAXWELLs EQUATIONS

The basic set of FOUR Maxwells equations for Propagation

through Dielectric Medium when written in the CGS units are asfollows:

5 AB =0

5 AD =4

5 xE +1

c

ffffj k D

t

ffffffffff=0 ..(1)

5 xH@1

c

ffffj kD

t

ffffffffff=0

Eand Hare the Electric and Magnetic Field Vectors, D and B are the

Electric and Magnetic Flux Density Vectors and cis the velocity of light

in vacuum. is the charge density. Assuming that the ElectromagneticEnergy is propagating in the medium with fluctuating dielectric constant and there are no sources of light within the Dielectric Medium then =0 .


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The medium is linear for small field strengths and dielectric constant

also remains same. Further assuming a loss in isotropic medium, isconsidered real and a scalar quantity. It is independent of the operating

frequency. With these assumptions, the Electric Field Eand Electric Flux

Density D are related as

D r = r E r ..(2)

Thus is a function of space within the Micro-structured systems. Formost of the dielectrics the magnetic permeability is very close to unity

and hence

B =H ..(3)

The 1st Equation above can be written as

5 AH r,t =0

5 A ra

E r,t =0

5 xE r,tb c

+1

c

ffffj kH r,t

t

ffffffffffffffffffffffffffff=0 ..(4)

5 xH r,tb c

@ r

` a

c

ffffffffffffffj kE r,t

t

fffffffffffffffffffffffffflj

mk =0

In this, the field vectors E and H are assumed to be the functions oftime and space, i.e. t and r. Let the time dependency be denoted by an

exponential function such as

H r,t = H raejwt

E r,t = E r ,t e jwt .(5)

Substituting the above in the previous equation we have

5 AH r = 05 A r E r =0

5 xE r` a

+

j

cffffffffj k H r

` a=0 .(6)

5xH r` a@

j

c

ffffffffj k E r` a

=0


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The last TWO equations of (6) in the above set of four equations can bemanipulated to decouple each other to get equations entirely in H(r) or

E(r) as follows

5 x

1

r` a

ffffffffffffff

5 xH r

` a

J K =

c

fffff g2

L

J

M

KH r

` a

(7)

E r` a

=@jc

r` a

ffffffffffffffffffffJ K5 xH r` a

.(8)

Equation (7) above is a complex differential equation which gives the

harmonic mode in a mixed dielectric medium. If the operation of takingthe Curl, dividing by r and again taking the Curl is attributed to a

complex operation defined as operator ,then

H r` a

=

c

ffffV W2

H r` a

..(9)

Thus the result of operator H(r) with is leaving it as it is and

multiplying it by a constant

c

ffffV W2

as it Eigen Vector.

IN DIELECTRIC MEDIA


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nanophotonics course material-2012 for students 110112

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