Nano Science (Lec 12 Plasmonic)

Nano Science (Lec 12 Plasmonic) - MAE 287/EE 257 1 From the...

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MAE 287/EE 257 1
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Where c is the speed of light in vacuum, n is the refraction index of the media. The solution of the Maxwell’s equation can be a set of electromagnetic waves, where w =2 p f with f as the frequency of the optical wave, and k=2 p n/ l with as the wavelength of the optical wave. )] r - t ( Exp[ t) , r ( )] r - t ( Exp[ t) , r ( 0 0 k i H H k i E E y x From the Maxwell’s equation, we arrive at, 2 2 2 2 22 nn E= - E H= - H cc   2
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James Clerk Maxwell (1831 - 1879) Maxwell's equations for source-free media (no charge, no current) 0 0 - 0 0 H E t H E t E H 3
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In a media with refractive index of n (n>1), the wavelength will be reduced. x y H x E y 0 0 λ Wavelength in a media λ = n λ : wavelength in vacuum x y H x E y 4
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The scientific and industrial communities are becoming more interested in the optical wavelength at nanoscale, but the x-ray and EUV light can hardly be manipulated, so alternative techniques must be utilized. 5
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Simply imagine a metal sphere comprised of many discrete, evenly- distributed positive ions. Now imagine a free electron cloud hovering just around the positive ions. The electrons can also be approximated as a negative charge distribution. 6
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Plasmons are electronic oscillations in metal under the influence of external electric field, or you could think of them as electronic charge density waves. When the electrons move around under the influence of external electric field of an optical wave, they are pulled back toward the positive charge distribution, thus they end up oscillating over/about the positive charge distribution. 7
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Plasmon can be generated by optical wave. An electron in a metal in an electric field follows, 2 2 - e E eff x m t where is the efftive mass of the electron. e is the charge of the electron. x is the displacement of the electron. E is the electric field of the external field generated by optical wave. eff m Eq. 18.8 in the text book, with the electronic absorption term omitted. 8
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The electric field of the optical wave can be represented by, 0 E E e iωt The electronic displacement, 0 x x e iωt Then, 2 0 eff 0 x m E ωe And the dipole moment per unit volume, 2 e e 2 eff e p - e x - E m  Where e is the electronic concentration in metal 9
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The dielectric constant at frequency w is, 2 2 e 22 0 0 eff e p ( ) 1 1- 1 - m p E  Where w p is called plasma frequency, 2 e p 0 eff e m 10
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2 33 e 22 15 1 pe 0e 11 3 ep 1 5.86 10 2 The plasma frequency, e 9 10 (cm ) (/s) m For silver, cm /s The frequences of visible lights are ranged between 4 - 8 Hz. For visible l .17 10 10 10 igh      ts, , ( ) <0, the dielectric constant of metals for visible lights is negative.
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This note was uploaded on 04/17/2011 for the course MAE 287 taught by Professor Yongchen during the Winter '11 term at UCLA.

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Nano Science (Lec 12 Plasmonic) - MAE 287/EE 257 1 From the...

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