Nanophotonics: principle and application. Khai Q. Le Lecture 4 Light scattering by small particles
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1 Nanophotonics: principle and application Khai Q. Le Lecture 4 Light scattering by small particles
2 Previous lecture Drude model, Drude-Sommerfeld model and Drude-Lorentz model for conducting media (metal): frequency dependence of ε in real metals How do optical properties of materials change at the nanoscale? Bulk gold looks yellow 12 nanometer gold particles look red
3 Light-particle interaction processes
4 Light scattering The light-particle interaction can be described using various theories. However choosing which theory to best description of the interaction depends on the ration of the wavelength to the size of the particle λ 0 d << λ 0 Rayleigh scattering d ~ λ 0 Mie scattering d > λ 0 Ray optics
5 What facts impact on the light-particle interaction? Wavelength of incident wavelength Size of particle Refractive index (n) of particle and surrounding environment λ 0 d << λ 0 Rayleigh scattering d ~ λ 0 Mie scattering d > λ 0 Ray optics
6 Rayleigh scattering: Why is the sky blue? + The Sun@zenith, sunlight travels a short distance before it reaches the eye. Only blue light is scattered towards the eyes and the sky appears blue. + At sunset (or sunrise), sunlight travels a much bigger distance before it reaches the observer's eyes. Most of the blue light has been scattered away before it can have a chance to reach the eye. Only red-green light reaches the observer's position which explain why the sky looks red-orange when the sun is at the horizon.
7 Rayleigh scattering: Why is the sky blue? N 2, O 2
8 Rayleigh scattering: Why is the sky blue?
9 Rayleigh scattering: Why is the sky blue? Oscillating charges emit EM waves
10 Rayleigh scattering: Why is the sky blue? Radiation emitted by a Lorentz osccilator
11 Rayleigh scattering: Why is the sky blue?
12 Characterize Rayleigh scattering E ic λ 0 d << λ 0 Rayleigh scattering Light interact with ultrasmall particle The scattering cross-section (units of Area): used to characterize the scattering The quasi-static approximation theory: determine the scattering cross-section
13 Characterize Rayleigh scattering E ic λ 0 I ic d << λ 0 Rayleigh scattering E scattered A particle illuminated by a beam with irradiance I ic Total power scattered by the particle is W sca W sca =C sca I ic (C sca = σ sca is scattering cross-section: dimension of area) W abs =C abs I ic (C abs = σ abs is absorption cross-section: dimension of area) C ext (σ ext ) = C abs (σ abs ) + C sca (σ sca ): extinction cross-section
14 Characterize Rayleigh scattering E ic λ 0 I ic d << λ 0 Rayleigh scattering E scattered Q sca =C sca /G (scattering efficiency, G is particle s area) Q abs =C abs /G (absorption efficiency) Q ext = C ext /G (extinction efficiency)
15 Quasi-static approximation Assumption: E-field is constant across nanoparticle Charge in particle shifts fast enough to consider electrostatic solution for any incident E-field E λ 0 Rayleigh scattering d << λ 0 x E inc k y E inc i k r t r, t E 0e E inc k E inc i t r t E e, 0 y x
16 Characterize Rayleigh scattering E λ 0 d << λ 0 Rayleigh scattering The scattering efficiency for a subwavelength dielectric particle in vacuum Q sca = 8 3 x4 ε p ε m ε p + 2ε m x = πd λ If permittivity (dielectric constant) is complex (metallic nanoparticles) Q sca = 8 3 x4 Re ε p ε m 2 ε p + 2ε m 2 x = πd λ
17 Larger particle: Mie scattering E λ 0 d ~ λ 0 What happens when we consider larger particles? Quasi-static approximation is no longer applicable We have to use Mie scattering theory
18 Mie scattering off a sphere E λ 0 d ~ λ 0 Q sca =σ sca /G (scattering efficiency, G=πR 2 )
19 Mie scattering off a sphere SiO 2 d ~ λ 0 d ~ λ 0
20 Applications: plasmonics for improved photovoltaic devices Metal particles Solar cell structure
21 Useful Mie scattering software
22 Lab section: Light scattering by spherical particles using Mieplot
23 Light scattering off particles with arbitrary shape E λ 0 What happens when we consider particles with arbitrary shape? Mie formulism are no longer applicable Numerical techniques such as FDTD, FEM, BEM, should be used.
24 MNPBEM: Matlab toolbox
25 Lab section: light scattering by arbitrary particles using MNPBEM
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