1. Nonlinear Near-Field Tomography George Y. Panasyuk University of Pennsylvania Philadelphia, PA

2. SPM (AFM, STM, NSOM, …) NSOM (Near-Field Scanning Optical Microscopy) Near-Field Optical Tomography NSOM measurements 3D sample structure

3. Near-Field Scanning Optical Microscopy (NSOM) E. Betzig and J. Trautman. Science 1992 - Illumination mode - Collection mode

4. 3D Effects in NSOM collection mode z measured in units of wavelength

5. Topographic images Topographic image Near-Field images Local Spectra of Clusters of Silver Particles V.Markel, V.Shalaev, M Moskovits at al, PRB 1999

7. Reconstruct the medium from measurements of the scattered field Incident wave Scattered wave Scattering medium Inverse Scattering

8. Collection Mode Near-Field Tomography Vary direction of incidence and scan probe measure amplitude and phase......

9. Near-Field Optical Tomography z measured in units of wavelength S.Carney, J.Schotland, App. Phys. Lett. 2000

10. Photon Scanning tunneling microscopy (PSTM) Experiment Tip height 200 nm FOV = 300 nm x 500 nm = 633 nm Sample: gold nanoparticle DATA

11. PSTM Reconstructions Reconstructed ImageAFM Image S.Carney, S.Bozhevolnyi, J.Schotland, Phys. Rev. Lett. 2004 Re(  (gold)) = -0.9

12. Collection Mode Near-Field Tomography Vary direction of incidence and scan probe measure amplitude and phase......

13. Basic Equations Maxwell Equation for Electric Field Equivalent integral equation Linearization :

14. Forward series = + + + … = = η ; = = =

15. Inverse Series η=η (1) + η (2) + η (3) + η (4) … η (1) == K + E s, η (2) = η (3) = + + η (4) = 7 diagrams, … = K +

16. Linear = η (1) η (1) +η (2) +η (3) +η (4) η (1) + η (2) η (1) +η (2) +η (3)

17. Equatorial crossection x/λ

18. 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.