Quantum switching in negative-index metamaterials

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Quantum switching in negative-index metamaterials

• Alexander K. Popov, S. A. Myslivets, T. F.
  George, and V. M. Shalaev
• University of Wisconsin-Stevens Point, Stevens
  Point, WI 54481 (apopov_at_uwsp.edu)
• Institute of Physics of Russian Academy of
  Sciences, 660036 Krasnoyarsk
• University of Missouri-St. Louis, St. Louis, MO
  63121
• School of Electrical Computer Engineering,
  Purdue University,
• West Lafayette, IN 47907

• Outline
• Embedded tailored strong resonant nonlinearities
  ?(3)
• and quantum interference
• Extraordinary features of FWM and OPA in NIMs vs
  PIM
• backward waves, distributed feedback,
  cavity-free OPO
• OPA assisted by Raman gain and quantum
  interference
• compensating losses in NIMs

CEWQO07
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Left-handedness of NIMs
H
RHM
E
Energy flow
k
H
LHM
Backward wave
k
Energy flow
E
In vacuum (and most materials) the right-hand
rule relates E, H, and k Note normally e gt 0
and µ gt 0 Consequence phase velocity (along k)
and group velocity (along the Poynting ExH
vector) are in the same direction
Mandelstam 1944 Veselago -1967
In NIMS, S and k are counter-directed (backwa
rd waves)
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Physics would be dull and life most unfulfilling
if all physical phenomena around us were linear.
Fortunately, we are living in nonlinear world.
While linearization beautifies physics,
nonlinearity provides excitement in Physics.
Y.R. Shen. Principles of Nonlinear Optics.
NONLINEAR OPTICS WITH BACKWARD WAVES
Early proposals for natural crystals, ? (2), only
optical-FIR phase-matching possible
Harris, APL, (1966) Volyak, Gorshkov, Radiot.
Elektr. (1973) Yariv, Quantum Electronics, 2d
ed., NY Wiley, (1975). NLO with backward waves
in NIMs Lapine, Gorkunov, Ringhofer, PRE
(2003). Shadrivov, Zharov, Kivshar, PRL (2003)
APL (2005) JOSA (2006). Agranovich, Shen,
Baughman, Zakhidov, PRB (2004). Scalora,
D'Aguanno, Bloemer, Centini, Mattiucci, de
Ceglia, Kivshar, OE (2006). Popov, Shalaev, OL
(2006), Appl. Ph. B (2006), LPL
(2006). Maimistov, Gabitov, EPJ, (2007)
http//arxiv.org/abs/nlin/0702023.
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Fantasies need details.   M. Svetlov
The dreams to custom-design nonlinear optical
materials with nonlinear coefficients largely
outperforming those of natural crystals seem to
become true ?(2)NIM/?(2)KDP2 105 ?NIM,THG
10-7, ?KDP,SHG 10-11 M. W. Klein, M.
Wegener, N. Feth, and S. Linden, "Experiments on
second- and third-harmonic generation from
magnetic metamaterials," Opt. Express 15,
5238-5247 (2007) Many challenging theoretical,
experimental and fabrication problems, however,
are still to be addressed.
We explore an alternative approach associated
with the tailored auxiliary strong resonant
nonlinearities embedded in NIM. Manipulating
transparency, refraction index and nonlinear
response of the NIM sample with the control
laser(s) becomes possible.
t
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The Basic Idea
One cannot find a thing so little that couldnt
embrace even more little one. Kozma Prutkov
Four-level centers embedded in NIM
OPA assisted by the Raman Gain
?4 probe ?1, ?3 control fields, ?2 ?1?3-
?4 - idler. Idler can be Raman-enhanced and
then contributes back to OPA at ?4 .

• OPA compensation of losses, transparency and
  amplification at ?4 in negative-index
  frequency-domain cavity-less generation of the
  counter- propagating entangled right- and
  left-handed photons.
• Control local optical parameters through
  quantum interference

.
Linear ?'and ? may remain unchanged.
(n lt 0, K-K relationship, causality principle)
Depine, Lahtakia (2004), Stockman (2007)
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I think all this is very simple. E. Rutherford
Quantum control of resonant NLO coupling
Constructive and Destructive Interference
Classic physics, e.g., optics
y? a sin ( kz - ?t), y2 a sin (kz?t), y
y1y2 (2a sin kz ) cos(?t)
Quantum optics
Density-matrix approach Popov, Myslivets,
George, OL (2000) OE (2000) PRA (2005).
Constructive interference - enhanced
susceptibility Destructive interference -
decoupling electron from light.
Quantum switching changing oscillations
relative phase, e.g., through resonance
detuning.
Resonance detunings O1 ?1-?gl, etc. Here,
Oi/ Gml 1. Rabi coupling frequencies G1,2
E1,2dij/2?.
Optical resonance HWHM Gij 1012 s-1, Raman
1010 s-1, lifetimes 10-8 s. G 1012 s-1 ? I
(10100) kW/(0.1mm)2
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It's strange. Sure is strange. -from "Season of
the Witch" by Donovan
Manipulating local optical parameters with
control laser(s)
Density-matrix approach Popov, Myslivets,
George, OL (2000) OE (2000) PRA (2005).
y4O4/G4.
G1G3 50 GHz, O1 O3 2.5 G1.
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OPA in PIMs
Very diverse and contradictious gossips have been
circulating about those territories cut from the
world and administrative influence. Arkady and
Boris Strugatsky
OPA of Backward Waves in Double-Domain NIM-PIM
?4- signal, ?2 - idler
a4,2, ?k ? 0 gL?(j1)p/2 z 0, ?4?8
?
a4,2, ?k?0, ?4 ? e2gz
?
n(?4)lt0
S2 ?
? S4
Asymmetry in the equations (opposite signs)
caused by the waves backwardness
FWM Frequency conversion
OPA, SHG in ?(2) NIM Popov, Shalaev, OL
(2006), APB (2006)
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"I have not failed. I have successfully
identified twelve hundred materials that won't
work." Thomas Edison
Compensating losses in NIMs
NARROW-BAND FREQUENCY-TUNABLE TRANSPARENCY
WINDOW IN THE NEGATIVE INDEX FREQUENCY
DOMAIN QUANTUM SWITCHING
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It depends on what the meaning of 'is' is."
Bill Clinton (M.L. Testimony)
G1G3 50 GHz, (P 10 kW, Ø 0.1 mm), O1 O3
2.5 G1, y4O4/G1, y4 (max)1.3 ? gLra
0.21. Max amplification (generation threshold)
at L/Lra 11.5. sra 10-16 cm2, N 1019 cm-3
, Lra-1 ara 103 cm-1 ? L (10100) µm.
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If you obtain -i while solving a real problem,
dont be frustrated. Just multiply it by i.
Students folklore

• Summary
• Nonlinear optics in NIMs with tailored embedded
  nonlinearities.
• Strong resonant nonlinearities, quantum control
  with the control lasers.
• Compensating losses in NIMs frequency-tunable
  transparency windows.

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An economist is an expert who will know tomorrow
why the things he predicted yesterday didn't
happen today. Laurence J. Peter

• Further studies
• Account for the specific spectroscopic properties
  of the embedded resonant centers and of the
  NIMs structural elements.
• Different coupling schemes.
• Malti-parameteric optimization, phase-matching,
  negative index survival.
• Specific applications.

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THANK YOU