CREOL, College of Optics & Photonics, University of Central Florida

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Optical Properties of Nanostructured Materials Fall 2013 – Class 3 slide 1

OSE6650 - Optical Properties of Nanostructured Materials

Challenge: excite and detect the ‘near field’

Thus far: Nanostructured materials can act as optically ~homogeneous media

- Knowing the field distribution within medium allowed us to find effective index - Nanostructuring allowed for the structural design of new optical properties - Applications: structured Fresnel lens, engineered modes and dispersion,

single-material anti-reflection coatings

Today:

- Go beyond effective medium approach: local fields inside structured media - Discuss technique to visualize these local fields: near-field microscopy!

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Local fields near polarizable objects

Remember: particle placed in external field  polarization and surface charge External potential for static applied field:

Example: Ez(x,z) for 10nm diameter Si particle (n=3.5) in air

z

E

r

a

out in out in out 3 0 3

1

2 

_





















Small structure can take long wavelength light, and generate local response field Fields close to polarized objects: ‘near fields’. Next: define this more precisely

Spatial field variations - limits

Time varying fields (e.g. oscillatory) lead to spatially varying fields Single frequency in free space  sinusoidal variations of E(x,t)

Field variation described by wavevector k (spatial frequency) given by |k|=2/

Questions: limits on spatial frequency in free space? (i.e. without nanostructures)

Consider plane wave incident on flat substrate:

2

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Wavevector magnitude

Given the magnitudes of kxand kz:

we have a well-known ‘wavevector conservation law’ :

In free space: total length of k-vector components adds up to n/c

In three dimensions:

 ‘if fields are rapidly varying along x, they are not varying rapidly along y and z’

cos

sin

cos



with



with

Limitations of free space optics

Example: illumination of flat surface from free space: sin Smallest feature size ~ /2 / 2 sin with n=1

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Evanescent field decay

Illumination from within high index material: maximum kx= n k0

For high angle kx> k0 (above critical angle)  no radiation into free space

Check: above sample 

We find an imaginary k_z  exponential field decay into air: evanescent wave

kx> k0

High spatial frequency components may exist, but do not radiate into free space Used in immersion microscopy, immersion lithography

Interpretation of evanescent decay

Microscopic interpretation of evanescent field:

Incident wave generates oscillating dipole moment along surface We all know that oscillating dipoles radiate …. But apparently not here?

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The near-field

Far-field illumination

- Spatial frequency of EM fields inside homogeneous media has upper limit of nk0

The near-field

- small objects (=inhomogeneous medium!) can be polarized by incident fields Einwhich have large wavelength

- resulting localized surface charges generate E(x,t) contributions with spatial variations that can occur over distances x << 

- These field distributions cannot be detected in the far field

Mathematical method for finding radiative and non-radiative field contributions: Take spatial Fourier transform, look for k > k₀

+ + + ++ + + -

-E

Fourier description of spatial field distribution

For any arbitrary field distribution in the x-y plane E(x,y,z) at a given frequency Can find the Fourier transform

Tells us “How much of each spatial frequency is present”

Some of these wavevector contributions have  radiation

But: wavevectors may exist with  invisible in the far field

Example:

nanoparticle with d  

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Spatial Fourier transform: check

Example: normal field distribution in x,y plane along a surface. Corresponding F.T. ?

kx

ky

Assume that 0= 500nm

Does this field contain near-field components along z? How can you tell? kz= ?

Draw all possible (kx, ky) values for plane =500nm wave in arbitrary (x,y,z) direction

500 nm

Spatial Fourier transform: check

Example: Exfield distribution in x,y plane. What is the corresponding F.T. ?

k_x k_y

Assuming oscillation at =2c/500nm. Draw kmaxin vacuum.

Does this field distribution contain near-field components? kz= ?

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Near fields vs. frequency

Low frequency: kmaxsmall

High frequency: kmaxlarge

Only E(k_x,k_y,) components that lie within light cone can be detected in far field along z

nonrad rad

Near-field exist and contain important information, but: near-fields are ‘invisible’

Challenge: excite and detect the ‘near field’

To visualize the near-field: bring field to detector, or bring detector to field

- use conversion element that can ‘scatter the near field’ (couples NF to far field) - general idea: small (<< ) polarizable structure(probe) will polarize



E_local

and generate scattered/reradiated dipole radiation



E_local

Detect scattered field vs. position of probe  relative map of local field! - need: movable nanoprobe

+ + + ++ + + -

-E

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Challenge: excite and detect the ‘near field’

Idea not new: E. H. Synge: A suggested model for extending microscopic resolution into the ultra-microscopic region, Phil. Mag. 6, 356 (1928).

Obtain image by 2D scanning: Near-field Scanning Optical Microscopy (NSOM) Experimental realization took several technological advances:

- reproducible nanoprobes

- accurate probe or sample movement - accurate probe position detection - low noise optical detectors

Challenge: transmission efficiency through nano-aperture

Classically: transmitted power proportional to area  a2

BUT: Far-field Poynting vector S_Tthrough nanoscale circular aperture with radius

a in thin perfectly conducting plate is ∝ ∝

Transmitted power integrated over 2 independent of r, with P_T (a/)4 _P i

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Near field detection : Types of tips

Aperture style probe

- Metal coated (typically Al – high plasma frequency: good ‘blocking ability’) - Can be fabricated on optical fiber, or on hollow/transparent AFM-type cantilever - Acts as nano-radiator or nano-collector, aperture ( <<)

- Low transmission efficiency (~10-6 _{- 10}-3_{for vis. light, 50-100nm aperture)}

Transparent uncoated: tip apex couples near-fields to guided modes Apertureless uncoated: tip apex scatters near-fields to far-field

Aperture style probe Transparent uncoated Non-transparent

Types of probes

Tapered metal-coated fiber probe ‘hand made’, fragile, thermally sensitive

Collection / illumination path enclosed

Tapered bent metal coated fiber probe  ‘hand made’, fragile, thermally sensitive

 Collection / illumination path ‘shielded’

AFM style microfabricated probe Robust, not very temperature sensitive Collection path open: risk of background

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Typical illumination mode NSOM measurement setup

nanostructures

x-y scan for image formation z-scan for tip-sample distance

control _Collection

objective  to detector

Transparent sample on scanning stage Laser source Fiber

Near-field microscopy modes – illumination mode

Light incident through fiber, generates localized ‘point dipole radiator’ near surface

Scan sample or tip,

Collect transmitted light vs. position  High resolution transmission map Requires transparent sample Places conductive ‘big’ object near surface: tip may affect near-fields!

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Near-field microscopy modes – collection mode

Light incident from below, generates near-fields on patterned/rough sample surface

Scan sample or tip,

Near-fields + incident wave excite electron oscillation on tip aperture  weak coupling to fiber modes Collect transmitted light vs. position  High resolution transmission map Requires transparent sample Entire surface always illuminated: Not ideal with ‘bleaching’ samples

Near-field microscopy modes – reflection mode

Light incident through fiber, small reflection back into tip, and away along sample

Scan sample or tip,

Collect transmitted light vs. position  High res. reflection/scattering map Works with opaque samples

Signal collection tricky:

- Outside fiber: large part of 4 angle blocked by tip and sample

- Collection lens with high NA needed - Back-reflection into fiber: weak,

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Near-field microscopy modes – Photon scanning tunneling mode

In PSTM, a ‘potential barrier’ separates two media that support propagating modes

Total internal reflection No light emitted

Small air gap: Light tunneling possible

Small air gap + fiber Light tunneling into guided mode toward detector

picture from http://www.chem.vu.nl/~sneppen/literaturereport.pdf

PSTM

Near-field microscopy modes – photon scanning tunneling mode

Light incident under total-internal reflection condition. Small field overlap with tip of fiber, weak coupling into guided mode

Scan sample or tip,

Collect near-field (+ scattered radiating components) vs. position

 High resolution map of near-fields Transparent ‘high’ index samples only

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Near-field microscopy modes – scattering mode / apertureless NSOM

Light illuminates sharp tip (metal, high index e.g. Si), generates field concentrated near tip apex. Interaction with surface region affects total tip scattering

Scan sample or tip,

Collect distance dependent part of scattered light vs. position

 High res. reflection/scattering map Works with opaque and transparent ‘Tip throughput’ not as much a concern  Can work at higher resolution But: requires oscillating tip

Nano-aperture formation, example 1 – pulled fiber

1. Starting point: glass fiber

2. Heat and pull: tapering occurs

3. Pull till break: sharp glass tip (also possible via etching) 4. Evaporate metal at an angle

+ rotate fiber

Result: metal coated fiber with tiny aperture at end (diameter ~50nm possible) Advantage: ‘easy’ to make Disadvantage: not reproducible, slow

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Alternative method for taper fabrication : etching

Starting point: glass fiber

Insert fiber in etchant, start retreating at constant speed Top part: etched the least

Bottom: etched the most

Pulled and etched fiber probes

from: www.chem.ucsb.edu/~buratto_group/nsom.htm

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Nano-aperture formation, example 2 – microfabricated tip

expose <111> planes anisotropic etch oxidize surface

etch back substrate deposit metal Starting point : Si wafer

open up tip (e.g. FIB)

This is followed by release from the handler wafer (possible due to lateral patterning – not shown)

SEM of near-field probes designed for use with Witec AlphaSNOM

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Optical Properties of Nanostructured Materials Fall 2013 – Class 3 slide 31 Vx=100

Sample movement and distance control

Sample can be moved using piezo stage – placement accuracy ~1 nm

Feedback loop required: tip needs to be close, but cannot withstand much force Accurate measurement of tip angle using beam deflection method:

Vx=0

A-B = 0 A-B = -1

Look at laser beam deflection angle (A-B signal): if A-B becomes negative, move sample stage back (or tip up, depending on system)

 Vz,piezo(x,y) represents height map of the sample

Scanning Near-field Optical Microscopy (NSOM)

intensity

tip position

1. Illuminate tip aperture (through fiber, or free space as in this example) 2. Scan sample OR tip and collect transmitted photons in far field

e.g. using collection objective under sample

 optical maps with sub-diffraction limit resolution possible, BUT rather slow (typically several minutes per scan)

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Distance control using fiber probes

For straightpulled fibers, beam deflection method is impractical Alternate common method: tuning fork feedback

Fiber is mounted on mechanical resonator

small (few nm) lateral amplitude can be driven by piezo block At close (few nm) proximity, tip-sample interaction affects

resonance frequency  amplitude changes

Use piezo driving circuit response as feedback parameter

Images from http://www.olympusmicro.com/primer/techniques/nearfield/nearfieldintro.html For bentpulled fibers, beam deflection can be used

No reflected spot, but reflected line Production of bent fiber probes not trivial

Some additional losses in bent fiber part (number?)

Example system at CREOL: the AlphaSNOM

Control electronics

Piezo stage

Sample position

Collection optics + detector (remove lid to see..)

Tip mounted on objective

See http://kik.creol.ucf.edu/laboratory.html

- Microfabricated tips - Beam deflection feedback - Sample scanning, tip fixed

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Resolution comparison: diffraction limited vs. near-field in transmission

far-field image: through optical

microscope: diffraction limited features observed at 532nm

Diffraction limit at this  ~ 300 nm 1 micron

NSOM image: Sub-wavelength

details of the sample are visible (dark dots are Al islands)

1 micron

Test sample: containing aluminum islands with ~60nm diameter, much

smaller than the diffraction limit. Measured with Witec AlphaSNOM

Example: phase detection of waveguide modes

Tip as ‘pickup element’ – PSTM mode

See Balistreri et al. -http://ieeexplore.ieee.org/iel5/50/20337/00939798.pdf

Mapped mode in straight waveguide

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Near-field microscopy

Summary:

- Nanostructures support non-radiative local field components with k > k₀ - A nanostructured probe in the near-field region ( ) can convert

part of these components into far-field radiation (scattered light)

- Scanning a nanoscale probe near sample surface allows mapping of near-field. This forms the basis of Near-field microscopy

- Different configurations:

> Transmission mode (illumination and collection mode) > Reflection mode

> Photon Scanning Tunneling Microscopy (PSTM) mode

Note:

- Transmission of aperture probes  d4

_and

_{d < 50nm diameter is difficult}

- Good/excellent resolution at visible frequencies: ~15-50nm - Exact tip shape affects which components of the field are scattered