1st tranche of nanophotonics course material-2012 for students 110112

8/13/2019 1st Tranche of Nanophotonics Course Material-2012 for Students 110112

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Nano-photonics Course material

Reference:

1. Nanophotonicby Paras N. Prasad, Wiley Interscience, 2004, USA2. Photonic Crystals: Molding the flow of Lightby John . Joanno!o"los,

Ste#en $. Johnson, Josh"a N.Winn, %obert . &eade A!ril 1', 200'

(. Nanooptics )y Sotoshi *a+ata, &otichi hts", &asahiro Irie, S!rin-er

erla- 20024. Optical Nanotechnologyby J. /oin-a and P /sai, S!rin-er 200(

. Principles of Nano-Opticsby "3as No#otny, )ertecht, 5abrid-e

Uni#ersity Press 2006.6. Electromagnetic Metametrials: ransmission Line heory by 5hristoo!he

5alo7, /ats"o Itoh, Wiley I888 Press 200


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!"# $%&&EREN%#E' 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 ave.

!. Both are governed b" E# theor" b$t their behaviors are di%%erent

&. Electron ave is a 'ector propagation $nder %ield and there%orehas vector %ield while Photon is a (calar Propagation there%ore has

'ector %ield associated with it and both move in 3-).

*. Electron is de%ined b" 3components vi+. frequency orwavelength, amplitudeas voltage or c$rrent and phase.

/. Photon has 4 components vi+. frequency or wavelength,

amplitudeas power, phaseand polarization.

10.Electron wave $p to 300 is bipolarand a%ter that it becomes

unipolar. hen it becomes $nipolar it is called Electronic

Photon.

11.Photon is alwa"s Unipolar.

12.Electrons posses (PN, and their distrib$tions are de%ined b"F!"#-$#!%C(tatistics and there%ore are called F!"#&N'

13.Photons do not have (PN there%ore their distrib$tion is governedb" (ose )insteinstatistics and are there%ore called (&'&N'.

14.Electrons being charged particles get g$ided within vac$$m oran" media onl" $nder electric %ield, while photons being non-

charged particle, need a dielectric medi$m %or g$idance.

15. Electron hassmaller$e-(rogliewave-length and Photon has a

longer$e-(rogliewave-length.


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5 B 1

r` a

fffffffffff5 B B r

` a=

c

fffffe 2

B r` a

9or o!tical +a#e

O F = C F where C is an eigen value and is given b"

c

fffffe 2

and Ois the &peratorand F is the igen function

*+ $N'#*, &F '*&!% %C+#%(/ 0#*+ Nanophotonicsdevices


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N6N7P787NC( wor9s BE:7N) the );;


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!#0 &F /C*!&"%N*#C' and"%10//2s U%*#&N'

'*%*#C and $,N%"#C /C*!&"%N*#C'


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---------------------------------------------------------------------------------

+a)ss, heorem in $%&&EREN%#L and %NE+R#L &ORM

'OE' "EOREM


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+! 0 %! $!##N U%*#&N' F&! "%10//2'

U%*#&N' F&! $#/C*!#C "$#U". /%*! 0+N 0 C&"*& 4/%'"&N#C' 0 0#// $!# '4%!%* U%*#&N' F&!

"**%/#C 'U!F%C'.

*he basic set of F&U! "a5well2s equations for 4ropagation

through $ielectric "edium when written in the C' units are asfollows6


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5 AB =0

5 AD =4

5 xE + 1c

ffffj k Dt

ffffffffff=0 AAAAAAAAAAAAA..1

5 xH@1

c

ffffj kD

t

ffffffffff=0

Ma.well E/)ations cgs and M' )nits

/he syste o9!artial di99erential e>"ationsdescribin- classical electroa-netis and

there9ore o9 central i!ortance in !hysics. In the so?called c-ssyste o9 "nits, the&a;+ell e>"ations are -i#en by

@1

@2

@(

@4

+here is the electric dis!laceent 9ield, is the char-e density, is the electric 9ield,

is the s!eed o9 li-ht, is the a-netic 9ield, is the a-neti7in- 9ield, and is the

c"rrent density. As "s"al, is the di#er-enceand is the c"rl.

In the &*Ssyste o9 "nits, the e>"ations are +ritten

@

@6

@'

@B

+here is the !eritti#ity o9 9ree s!ace and is the !ereability o9 9ree s!ace. C
http://mathworld.wolfram.com/PartialDifferentialEquation.htmlhttp://mathworld.wolfram.com/Divergence.htmlhttp://mathworld.wolfram.com/Curl.htmlhttp://mathworld.wolfram.com/Divergence.htmlhttp://mathworld.wolfram.com/Curl.htmlhttp://mathworld.wolfram.com/PartialDifferentialEquation.html


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Eand Hare the Electric and #agnetic ;ield 'ectors, Dand Bare theElectric and #agnetic ;l$ )ensit" 'ectors and cis the velocit" o% light

in vac$$m. is the charge densit". 6ss$ming that the ElectromagneticEnerg" is propagating in the medi$m with %l$ct$ating dielectric

constant and there are no so$rces o% light within the )ielectric

#edi$m then =0 .

8he medi$m is linear %or small %ield strengths and dielectric constantalso remains same. ;$rther ass$ming a loss in isotropic medi$m, is

considered real and a scalar D$antit". t is independent o% the

operating %reD$enc". ith these ass$mptions, the Electric ;ield EandElectric ;l$ )ensit" Dare related as

D r = r E r AAAAAAAAAAAAA..2

8h$s is a %$nction o% space within the #icro-str$ct$red s"stems. ;ormost o% the dielectrics the magnetic permeabilit" is ver" close to $nit"

and hence

B = H AAAAAAAAAAAAAAAAAAAA..3

8he 1stED$ation above can be written as

5AH r,t =0

5A ra

E r,t =0

5 xE r,tb c

+ 1

c

ffffj k H r,t

t

ffffffffffffffffffffffffffff=0 AAAAAAA..4

5 xH r,tb c

@ r

` a

c

ffffffffffffffj kE r,t

t

fffffffffffffffffffffffffflj

mk =0

n this, the %ield vectors E and are ass$med to be the %$nctions o%

time and space, i.e. t and r. =et the time dependenc" be denoted b"

an eponential %$nction s$ch as

H r,t = H raejwt

E r,t = E r,t ej wt AAAAAAAAAAAAA.5

($bstit$ting the above in the previo$s eD$ation we have

5AH r = 05A r E r =0

5 xE r` a

+ j

c

ffffffffj k H r` a

=0 AAAAAAAAAAAAA.!


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5xH r` a

@j

c

ffffffffj k E r` a

=0

8he last 87 eD$ations o% ! in the above set o% %o$r eD$ations canbe manip$lated to deco$ple each other to get eD$ations entirel" in

Hr or Er as %ollows

5 x 1

r` a

ffffffffffffff5 xH r

` aJ K =

c

fffff g2

LJ

MKH r

` a AAAAAAAAAAA &

E r` a

= @jc

r` a

ffffffffffffffffffffJ K5 xH r` a

AAAAAAAAAAA.A*

ED$ation & above is a comple di%%erential eD$ation which gives the

harmonic mode in a mied dielectric medi$m. % the operation o%ta9ing the C$rl, dividing b" r and again ta9ing the C$rl is attrib$ted

to a comple operation de%ined as operator ,then

H r` a

=

c

ffffV W2

H r` a

AAAAAAAAAAAAA../

8h$s the res$lt o% &peratoron igen Function+7r8is leaving it

as it is and is m$ltipl"ing it b" a constant

c

ffffV W2

as its igen alue.

#N $#/C*!#C "$#%


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1st tranche of nanophotonics course material-2012 for students 110112

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