Chemical and spatial resolution with a SNOM introduction to near field optics aperture SNOM SNOM tips apertureless SNOM applications in solid state phisics some examples in biology. Snell law 1. Total reflection in a prism Classically Snell law:
Chemical and spatial resolution with a SNOMintroduction to near field optics aperture SNOMSNOM tipsapertureless SNOM applications in solid state phisicssome examples in biology
Total reflection in a prism
Classically Snell law:
No light is classically trasmitted in a medium of lower refractive index
when a critical angle is reached:
ySnell law 2
n2 = n
TM = linear polarization in the plane Oxz
n1 = 1
Where from Helmholtz equation:
w is imaginary!
This expression of the electric field is general:
no approximations have been used until now
uand v arespatial frequencies
w introduces a decaying exponential in the expression of the Field vs z
Example 1: 1D periodic grating
We measure the field intensity far away form O along the z axis
In y direction there is no modulation so the only spatial frequency allowed is v=0; in x direction u assumes discrete values n/d n=1,2,…n.
The only wave vector allowed are etc.
Those values represent the nth diffraction order of the grating
If d<l w becomes imaginary and the only propagating wave vector is (0,0,0) and the grating is no longer diffracted.
The spatial information is retained only in the near field
êAngular spectrum 4
propagation through a small squared aperture
F 0 slowly at high spatial frequency: sharp edges.
F has a maximum for u,v (0,p/a) but, when a<l/2
And the part or all the light that maximizes F cannot propagate
Again, The spatial information is retained only in the near field
How to detect the near filed if it not propagating?
Theorem of reciprocity
[Time reversibility of the Maxwell equation]
If a plane wave is diffracted into an evanescent wave by a subwavelenght scatterer,
A subwavelenght scatterer should be diffracted into a propagating wave by the same object
Near field detection
Physical mechanism SPATIAL FILTERING
Heating and pulling
Source: InAs Qdot
Point like source l/40 below the surface
Holes are dug by various methods:
The best results are obtained by FIB
Three different etching steps
X : 1 : 1
X=10 angle 20o
X=2.7 angle 50o
The selectivity between core and cladding comes from different quartz doping with Ge
Study of blood cells infected by malaria’s plasmodium falciparium.(PF)
Pf expresses several proteins in particular PfHRP1 and MESA that arefixed on the cell membrane.
Proteins on cell membrane are colored with specific antibody marked with a red and a green fluorophor
Here PfHRP1 is marked red
Comparison between SNOM and confocal microscope images in the sdame blood cell:
SNOM is sensitive to cell surface
CM images a plane section at the focal plane
Cellular structure is resolved on the SNOM image but not in CF image
Green and red spot are due to not hybridized ssDNA (red can also arise from complete FRET effect)
Yellow spot arise from hybridized dsDNA with competing green and red emission
Testing the subwavelkenght modulation induced on the local density of states of the optical modes by the fabrication of nanometric opticla corrals
Modulators 100nm100nm50nm gold particles deposited by e-beam lithography
To test the real LDOS the tip should act as a perfetct dipole at a nanometric distance from the surface.
Real tips always pertirb the LDOS and what is measured is the combined LDOS of the sample and the tip!
Light Polarization control
Elliptical mirros that selects only the near field radiation
(propagating radiation is not allowed in the “forbidden light region with q>qc
The signal is 0 only closo to the sample
Teorical optical LDOS in x, y and z direction
Near field results in trasmission.
Best results obtained with a gold coated tip without apertures
At the tip the polarization is tilted along z
The Snom data are fitted with a 1:4 mixing of the zx,y) polarization
Low temperature operation
Illumination collection mode
Different emission spectra at increasing power (LEFT) and on different dots (Right)
The far field spectra average the different contribution and the structure is lost
Excitonic wave function mapping of different dots showing that bi-exciton is more confined
A weak alignment along
(1-10) crystallographic direction can be noticed
Physical mechanism: TIP-SAMPLE INTERACTION
Strong wavelenght dependence
Strong dependance on the tip physical properties
We model the tip as a metallic sphere
Assuming that l >>a and using a quasi-electrostatic theory
Tip polarization far away from the sample in an external electric field E
Dipole induced on the sample surface
Dipole induced on the sample surface
In a first order iterative process the dipole induced on the tip becomes
The total dipole (tip + sample) is that is having an effective polarizability
In the case of field parallel to the surface the induced dipole is opposite to the field and the effective polarizability is
In a metal b 1 and aeff is nearly 0
It is evident that aeff is increased by the interaction only for z<<a,
In other words when the tip very close to the surface
The measurable quantities are the scattered and the absorbed light that is proportional to the cross section.
Applying Mie theory of light scattering
Scatteing and absorption cross section for a gold sphere on gold and silicon substrates for normal and parallel polarization
If I’m able to scan a gold sphere close to the sample surface I can observe a contrast in scattered intensity and, therefore, a can obtain a chemical map of the surface
The dependence of a(z) is not linear.
Oscillating the tip in a non contact mode (harmonic) fashion, a non-harmonic response is obtained.
The non-harmonicity increases with the oscillation amplitude.
By collecting the nth armonic signal (n>3) the near field signal can be obtained
On the left the 1st harmonic signal is collected at fixed amplitude while changing the tip-sample distance. Even for tip-sample distance > 200nm ther is a huge signal, arising from cantilever scattering and independent of tip-sample interaction
On the right the 2nd harmonic is collected, the background is suppressed and the near field signal is restricted to a 20nm distance from the surface.
Lateral resolution and chemical contrast
Pattern of Au on silicon obtained by evaporation through a polystyrene lattice.
The chemical contrast arise from differences in the dielectric constant value at 633nm.
Topographic effects are not excluded:
It is true chemical contrast?
(This is a big issue in SNOM and the major source of SNOM artifacts)
True chemical contrast
Silicon surface with a laterally modulated p-n doping structure.
The topogarphic contrast is just 0.1nm: the surface can be told to be flat, so the contrast is purely otpical/chemical
The optical-spatial resolution is about 50 nm l is 10mm
So the resolution approaches l/200
Physical mechanism: FIELD ENHANCEMENT
Suitable only for particular light-matter interaction process
(e.g. Raman scattering, second harmonic generation, etc
Where the light detected has a different wavelenght from the excitation light.)
Strong analogy to SERS and SPR
Here the excitation is localized, while the light scattered by the nanotube is then collected in far field through the optical microscope.
With metal tip
Localization of radial breathin mode raman scattering along the nanotube
a and b arc-discharge growth
b and d CVD growth
Structural defects along the structure can be identified by raman snom experiment
Confocal vs SNOM microscopy
AND SNOM WINS!!!!!!!!