nonlinear near-field tomography george y. panasyuk university of pennsylvania philadelphia, pa
Post on 22-Dec-2015
215 views
TRANSCRIPT
SPM (AFM, STM, NSOM, …)
NSOM (Near-Field Scanning Optical Microscopy)
Near-Field Optical Tomography
NSOM measurements 3D sample structure
Near-Field Scanning Optical Microscopy(NSOM)
E. Betzig and J. Trautman. Science 1992
- Illumination mode
- Collection mode
Topographic images
Topographic image
Near-Field images
Near-Field images
Local Spectra of Clusters of Silver Particles
V.Markel, V.Shalaev, M Moskovits at al, PRB 1999
Reconstruct the medium from measurements of
the scattered field
Incident wave
Scattered wave
Scattering medium
Inverse Scattering
Collection Mode Near-Field Tomography
Vary direction of incidence and scan probe
measure amplitude and phase
.
.
.
Near-Field Optical Tomography
z measured in units of wavelength
S.Carney, J.Schotland, App. Phys. Lett. 2000
Photon Scanning tunneling microscopy (PSTM) Experiment
Tip height 200 nm
FOV = 300 nm x 500 nm
= 633 nm
Sample: gold nanoparticle
DATA
PSTM Reconstructions
Reconstructed Image AFM Image
S.Carney, S.Bozhevolnyi, J.Schotland, Phys. Rev. Lett. 2004
Re((gold)) = -0.9
Collection Mode Near-Field Tomography
Vary direction of incidence and scan probe
measure amplitude and phase
.
.
.
Basic EquationsMaxwell Equation for Electric Field
2 2 20 0( ) ( ) ( ) 4 ( ) ( )E r n z k E r k r E r
Equivalent integral equation
20( ) ( , ')[ ( ') ( ')] ( ')scat inc scatE r k drG r r E r E r r
�
Linearization: 20( ) ( , ') ( ') ( ')scat incE r k drG r r E r r
�
r
'r'( , )G r r
�
Forward series
;G�
incE
1 2 2 2 2 1 1 1
0 0
( ; , ) ( ; ) ( ; , ) ( ; ) ( , )L L
incddz dz dpG q Q z z p q Q z G p z z q p z E q z
����
= + + + …
= = η; =
=
=
0
( , ) ( , ) ( , )L
incdzG q Q z Q z E q z K ���
scatE
Inverse Series
η = η(1) + η(2) + η(3) + η(4) …
η(1) = = K+Es,
η(2) =
η(3) = + +
η(4) = 7 diagrams, …
= K+
Conclusions:
- The main result is an approach developed for solving the non-linear inverse problem;
- Non-linear corrections improve significantly the accuracy and quality of a reconstructed image.
Future work :
- Developing of a non-linear approach for solving the inverse problem for the apertureless modality.