Lecture 13 - Super resolution, Near-field Scanning Optical Microscopy

Lecture 13 - Super resolution, Near-field Scanning Optical Microscopy

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E H Lecture#13 What we discussed in previous Lectures Coupling light to surface plasmon-polaritons • Kretchman geometry • Grating coupling 2 //, SiO sp m = ± kk G 2 //, sin SiO d sp c ω εθ = = Θ • Coupling from a metal dot Guiding geometries • Stripes and wires • Line defects in hexagonal arrays (2d photonic crystals) • Nanoparticle arrays
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The Diffraction Limit (a quick reminder) Diffraction limit Predicted by Ernst Abe more than a century ago Put in mathematical form by Raleigh 1.22 2s i n r n λ θ Δ≥ Where Δ r = minimum resolvable distance between two objects λ = wavelength of light n = refractive index of the medium Θ = semi-angle of the objective used for collecting the light Criterion was established assuming propagating waves Can criterion can be circumvented by going to the near-field of an object? (!) High quality microscopes Δ r ≈λ /2 250 nm for visible light
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Existence of Non-propagating Fields Intuitive picture Continuity: Spatial field distribution close to an object must reproduce charge and current density on the object + - λ Object with spatial variations < λ Near objects the EM fields necessarily vary on a length scale, L << λ Note: non-propagating fields only exist close to objects
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Origin of non-propagating fields near a small object (d < λ ) Heisenberg uncertainty relation Heisenberg’s uncertainty relation states: 1 x xk Δ ⋅Δ Consider a plane wave: ( ) (, ,,) (, ,)e x p xyz Uxyzt Axyz ikx ky kz t ω =+ + Consider a scattering event from an object of size Δ x x λ Δ << k Δ 0 k c = z x or 1/ x kx Δ ≥Δ Heisenberg: For some field components k x > 1/ Δ x >>1/ λ and thus k x >> k 0 The fields do not propagate because: 22 2 0 0 zx kk k =−< In other words k z is necessarily imaginary
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2 32 11 sin ( ) 4 ikr z r ik k Ep t e rr r θ πε ⎛⎞ =− ⎜⎟ ⎝⎠ Collection non-propagating fields in close proximity to an object Example: Oscillating dipole Electric fields in a point P are given by () 12 2 cos 4 ikr rz r ik t e z p x y z P E r
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This note was uploaded on 01/10/2011 for the course ECE 695s taught by Professor Staff during the Fall '08 term at Purdue.

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Lecture 13 - Super resolution, Near-field Scanning Optical Microscopy

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