#### Transcript Leakage-radiation microscopy (LRM)

Leakage Radiation Microscopy C.E. Garcia-Ortiz October, 2012 Outline Introduction to LRM ◦ ◦ ◦ ◦ ◦ Surface plasmon polaritons Imaging techniques Leakage radiation Numerical aperture and effective index Local excitation The LRM setup LRM imaging examples Direct, and Fourier space imaging Filtering in LRM Surface plasmon polaritons (SPPs) k SP P 2 d m d m Surface plasmon resonance Kretschmann configuration Plasmonics Imaging techniques SNOM LRM TPL Scanning Near-field optical microscopy Leakage radiation microscopy Two-photon luminescence Leakage radiation (LR) R e k S P P n k 0 sin q L R SPP nglass k SP P qLR LR 2 d m d m LR Due to boundary conditions and conservation of the in-plane wave-vector along the different interfaces, SPPs leak through the thin gold film into the glass substrate. Leakage-radiation microscopy (LRM) consists in detecting these leaky waves. Wave-vector in-plane conservation E 0 exp i β x t E 0 exp i k L R x t One boundary condition that must be satisﬁed is that the phases of the waves must match at the interface (z = 0) at all times. z Metal β kspp Dielectric (n) qLR kLR = nk0 kLR x x t z0 k LR x t z0 And since the frequency do not change β x z0 x sin q L R q L R sin 1 k LR x z0 k LR x Re k LR Re nk 0 Re nk 0 Leakage radiation cone SPP nglass qLR LR LR H. J Simon, J. K. Guha, Opt. Comm. 18, 391 (1976). Example: Lets put some numbers to these equations… d 1 700 nm k0 2 2 d m d m m 16 1.5 i n 1.5 9.2 10 q L R 43.4 6 i 2.6 10 4 B. Hecht, D. Pohl, H. Heinzelmann, and L. Novotny, Ultramicroscopy 61, 99 (1995). Problem with common substrates Total internal reflection SPP q c sin LR qLR nglass 1 n air n glass 41.8 q L R 43.4 Leakage radiation can not get out! Solution SPP Refractive index matching liquid Refractive index matching liquid (Oil) LR qLR nglass Objective lens Oil Immersion Microscope Objective The SPP effective index neff and the numerical aperture (NA) The numerical aperture (NA) of an objective is related to the work distance and size of the lens aperture. The NA is given by N A n sin q If we have an objective with a NA = 1.25, it can accept light at a maximum angle q = 56°. The SPP effective index n eff Re k0 n eff n sin q L R The LR that can be detected with an objective of numerical aperture NA1 is directly dependant on the neff of the SPP. The limiting case occurs when q = qLR and this yields n eff N A1 For our previous example we can calculate the neff n eff 1.03 1.25 N A Local excitation of surface plasmons Incident beam SPP Refractive index matching liquid (Oil) LR qLR nglass Objective lens Oil Immersion Microscope Objective Local excitation of surface plasmons The leakage radiation experimental setup Laser LRM imaging examples C. Garcia et al, Appl Phys B Laser Optic, Vol.107, No 2 (2012) A B Direct and Fourier space The Fourier plane ky kSPP LR TL kx Filtering in LRM: Fourier transform and filters Without filtering Transmitted light is filtered Desired image (well filtered)