Electrodynamics of lefthanded materials' V'G'Veselago v'veselagorelcom'ru Moscow Institute of Physic

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Electrodynamics of left-handed materials.
V.G.Veselago (v.veselago_at_relcom.ru)Moscow
Institute of Physics and Technology
(MIPT)Institute of General Physics RAS
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Electrodynamics of materials with negative
electric and magnetic permeabilities.
V.G.Veselago (v.veselago_at_relcom.ru)Moscow
Institute of Physics and Technology
(MIPT)Institute of General Physics RAS
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• Veselago Victor Georgievich,
• doctor of science (solid state physics)
• main positions

• Professor, general and applied physics, Moscow
  Institute of Physics and Technology
• Head of laboratory Magnetic materials,
  Institute of General Physics , Russian Academy of
  Sciences (GPI RAS)

additional fields of activity

• Expert (physics, informatics), Russian foundation
  for basic Research
• Expert (informatics), Russian Humanitarian
  Foundation
• Expert (physics), Supreme Attestation Commetee
  (VAC)
• Member, editorial board of Journal of
  experimental and Theoretical Physics (JETP)
• Vice editor, electronic scientific journal
  ISSLEDOVANO V ROSSII (Investigated in
  Russian) http//zhurnal.ape.relarn.ru

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MAIN PROBLEM

• The value of refractive index n(??)1/2 does not
  change after
• reverse of signs for both ? and ?.
• Question what changes?
• Possible answers
• Nothing changes. It means, that electrodynamics
  is not sensitive to signs of both ? and ?.
• Existance materials with both negative ? and ? is
  forbidden because of first principles.
• Electrodynamics for ?lt0 and ?lt0 differs from
  electrodynamics for ?gt0 and ?gt0

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Where are ? and ? singly?

• In Maxwell equations only !

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Solution of the problem

• If ?gt0 and ?gt0, vectors k, E and H are
  right-handed.
• If ?lt0 and ?lt0, vectors k, E and H are
  left-handed.
• But - it is very important -Pointing vector S,
  and vectors E and H are right-handed always,
  independently on sign of ? and ? !

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SNELL LAW IS CORRECT ALWAYS!

• The beam path at refraction on the boundary of
  vacuum and substance with refractive index n.
• 1-incident beam
• 2-refracted beam
• 3-refracted beam on nlt0
• 4-refracted beam on ngt0
• nsin?/sin?

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Sign of Doppler shift depends on sign of
refractive index

• ???onV/c
• (a) - ngt0
• (b) - nlt0
• for both cases
• A - sourse of radiation
• B - receiver
• S - Pointing vector
• k -wave vector

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Cherenkov effect for both cases

• (a) - ngt0
• (b) - nlt0

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Lenses changes their properties

• Beam path in lenses
• made of material with nlt0

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Flat quasilense

• This device can focuse light from point sourse,
  but really it is not a lense, because it is not
  able to focuse parallel beam of ligth into point.

This device transforms 3D object into 3D image
without distorsions
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What is Left Handed Electromagnetic media
Graphic of the Technical Concept The e(w)
-m(w) Diagram
Plasma - electronic in metals - ionic in
ionosphere EM waves reflected totally n has
imaginary part because em lt0 n (em)1/2 n
in
Usual dielectrics, ferroelectrics n positive
EM waves propagate through
n(em)1/2 gt0
em gt0
No isotropic material exist with mlt0
L-H matter
Victor Veselago predicted in 1967
n -(em)1/2 lt0 Negative n
Anisotropic Ferromagnets in Magnetic field n2
e (m1/- m2) mlt0 at m1 lt m2
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Where we can find left-handed materials ?

• 1. Magnetic semiconductors, like, for example,
  CDCr2Se4.
• Problems -
• Very complicated, long-time technology -(
• High dissipation -(
• 2. Mixture of electric and magnetic charges.
• Advantage -
• Fully isotropic material -))
• Problem -
• Nobody knows, how to find magnetic charge
  (monopole) -((

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1-D L-H Structures San Diego Approach
As predicted by Pendry
m(w)lt0 in one SRR
2-D composite medium split ring resonators
(SRR) provide m(w)lt0, while metallic wires
provide e(w) lt 1, for overlapping w. Lattice
constant is 8 mm
A way to 3-D
only
m(w)lt0 in SRR array
both
m(w)lt0 and e(w) lt 1
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Experimental solution of negative refraction
problem D.R.Smith al, Science, 292,77(2001)

• First question - how isotropic are left-handed
  composite materials ?
• Second question -how to decrease their frequency
  dispersion?

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Device for direct observation of negative
refraction in composite material
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Main Results

• We are able to construct artificial materials
  with regulated values of ? and ? (very important
  - not only negative, but positive too !).
• We are able to construct materials with regulated
  values of impedance Z (?/?)1/2 . this result
  gives us a possibility for matching of materials
  with different values of impedance, and eliminate
  reflection on the boundary between different
  materials
• It is necessary to reconstruct the textbooks and
  change some pedagogical methods in lecturing of
  electrodynamics. Namely, we should introduce four
  vectors E,D,H,B for all materials, and for vacuum
  also. (This point is important for only Russian
  scools and university, may be)

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????? ????????

• .??? ?????????? ?????????? ? ????? ?????????
  ????????? ?????????, ?? ?? ?????????? ? ?????
  ???????????? ????? ?????.

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????? ????????

• .??? ?????????? ?????????? ? ????? ?????????
  ????????? ?????????, ?? ?? ?????????? ? ?????
  ???????????? ????? ?????.

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????????? ???????????? ???????? ?????

• 1. ??????? ??????????? ????
• 2. ??????? ??????? ???????????????
• --------------------------------------------------
  ----
• 1(?). ????????? ??????????? ????
• 2(?). ????????? ??????? ???????????????
• ???????? ????? 1(?) !!!!!

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????????? ???????????? ???????? ?????

• 1. ??????? ??????????? ????
• 2. ??????? ??????? ???????????????
• --------------------------------------------------
  ----
• 1(?). ????????? ??????????? ????
• 2(?). ????????? ??????? ???????????????
• ???????? ????? 1(?) !!!!!

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How Fermats principle should be formulated for
media with nlt0?
Really, it is an extremum of eiconal, which can
be positive , negative or zero depending of sign
of n.
Real paths A-01-B for n1/n2gt0. A-O3-B for n1/n2
lt0
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??????? ?????, ????? ????????, ? ???????? ?
????????????? ????????????. ?.?.????????
(v.veselago_at_relcom.ru)??????????
??????-??????????? ???????????????? ????? ??????
???