Leakage-radiation microscopy (LRM)

Report
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 
z0
  k LR x   t 
z0
And since the frequency do not change
 β x  z0
  x
sin  q L R  
q L R  sin
1
  k LR x 
z0
  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)

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