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# Snell law 1 - PowerPoint PPT Presentation

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:

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## PowerPoint Slideshow about 'Snell law 1' - pelham

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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:

n2

n1

n2

n1

k

z

x

y

Snell law 2

n2 = n

TM = linear polarization in the plane Oxz

• The transmitted polarization is along z

n1 = 1

• The wave vector along z is immaginary: exponential decay

• The wave vector along x is higher than w/c

• Notice that high k means small l: higher spatial resolution

Angular spectrum

• Decomposition of the field in plane waves at z constant

• The field should satisfy the Helmholtz equation

• Fourier component can be written as:

• The evolution along z can be deduced by the field at z=0

Angular spectrum 2

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

Angular spectrum 3

Example 1: 1D periodic grating

y

We measure the field intensity far away form O along the z axis

x

z

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

x

z

ê

Angular spectrum 4

Example 2:

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

Sample surface

• Aperture SNOM

• The light is collected near the sample by a tapered optical fiber with a subwavelenght aperture

• Low light throughput

• Resolution limited to l/10

Physical mechanism SPATIAL FILTERING

• True spectroscopic information (including PL, EL, etc)

• Dependence only on the tip geometrical properties

• No dependance on the tip physical properties

• No wavelenght dependence

• The near field decays exponentially with distance

• The tip should be kept at a controllede distance from the sample surface

• Feed back mechanism: shear force (similar to AFM tapping mode)

• Feedback detection: quartz oscillator (STM current is not suitable for biological samples; optical methods are disturbing the optical response).

Electrodes

Piezo actuator

Impedance

detector

Feedback

xyz piezo

collection

Transmission

illumination

Illumination

collection

Reflection

collection

Illumination

Collection

• Aperture SNOM

• Operational modes

fiber

Laser

Pol. control

feedback

control

Topographic

image

xyz

Scanner

nf optical

image

Inverted

optical microscope

Detector

• Aperture SNOM

• Typical set up

Monochromator

method

Al coating

Hydrofluoric acid

Chemical etching

Glass

heating

Heating and pulling

method

Aluminum vapor

pulling

breaking

• Aperture SNOM

• SNOM tips

Optical fiber

• SNOM tips

• Calculation of the distribution of electric field as a function of the tip geometry

Source: InAs Qdot

Point like source l/40 below the surface

• Aperture SNOM

• SNOM tips - pulling

Metal coating

Core

• SNOM tips - etching

Metal coating

Core

Light propagation

Holes are dug by various methods:

The best results are obtained by FIB

• Photopolimerization

• 90% wt Pentaerythritol triacrylate (monomer)

• 8% wt methyldiethanolamine (cosynergist)

• 2% wt eosin (dye)

• High sensitivity to the argon laser light (514 nm)

• SNOM tips - polymerization

Metal coating

Core

Light propagation

• SNOM “japanese” etching

Three different etching steps

Solution NH4F:HF:H2O

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

• Application1: blood cell with malaria disease

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

• Application1: blood cell with malaria disease

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

• Colocalization of host membrane and PF proteins

• Control experiment:

• PfHRP1 is bound with antibodies marked either with green or red. The perfect overlap excludes any instrumental effect

• Colocalization of host protein (green) and MESA protein (red)

• good colocalization Mesa and host proteins interact oin the cell surface

• Colocalization of host protein (green) and PfHRP1 protein (red)

• No interaction at the cell membrane

• NB the three ijmages refers to different blood cells groups

• Application1: blood cell with malaria disease

• Application2: single molecule detection and FRET mechanism

• Application2: single molecule detection and FRET mechanism

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

The experiment:

Testing the subwavelkenght modulation induced on the local density of states of the optical modes by the fabrication of nanometric opticla corrals

Substrate ITO

Modulators 100nm100nm50nm gold particles deposited by e-beam lithography

• Application3: optical quantum corral

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!

• Application3: optical quantum corral

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

• Application3: optical quantum corral

Teorical optical LDOS in x, y and z direction

Near field results in trasmission.

Best results obtained with a gold coated tip without apertures

(the tip

At the tip the polarization is tilted along z

The Snom data are fitted with a 1:4 mixing of the zx,y) polarization

• Application3: optical quantum corral

• Application4: excitonic wave function of a quantum dot

Low temperature operation

Illumination collection mode

• Application4: excitonic wave function of a quantum dot

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

• Application4: excitonic wave function of a quantum dot

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

Apertureless SNOM

• Scattering SNOM

Unlimited resolution

Chemical sensitive

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

• Typical experimental set-up

• The main problem is that the light scattered by the tip that carries the information on tip-sample interaction is overwhelmed by background light by several orders of magnitude

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

• It works!

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.

l=633nm

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.

BUT

Topographic effects are not excluded:

It is true chemical contrast?

(This is a big issue in SNOM and the major source of SNOM artifacts)

l=633nm

800nm

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

Apertureless SNOM

• Tip-enhanced SNOM

Unlimited resolution

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

• Field enhancement on a tip apex

• Antenna effect

• Set-up for tip-enhanced SNOM

• Raman scattering from a single CNT

Here the excitation is localized, while the light scattered by the nanotube is then collected in far field through the optical microscope.

• Confocal microscope

• SNOM raman image taken at the G’ band wavelenght

With metal tip

without

• Raman scattering from a single CNT

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!!!!!!!!

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