Leakage Radiation Microscopy
C.E. Garcia-OrtizOctober, 2012
OutlineIntroduction to LRM
◦Surface plasmon polaritons◦Imaging techniques◦Leakage radiation◦Numerical aperture and effective index◦Local excitation
The LRM setupLRM imaging examplesDirect, and Fourier space imagingFiltering in LRM
Surface plasmon polaritons (SPPs) Kretschmann configuration
Surface plasmon resonance
2 d mSPP
d m
k
Plasmonics
Imaging techniques
SNOMScanning Near-field optical microscopy
LRMLeakage radiation
microscopy
TPLTwo-photon luminescence
qLR
Leakage radiation (LR)
2 d mSPP
d m
k
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.
SPP
LRLR
0Re sinSPP LRk nk q
nglass
One boundary condition that must be satisfied is that the phases of the waves must match at the interface (z = 0) at all times.
kLR = nk0
0 0LRz z
t t
β x k x
And since the frequency do not change
0 0LRz z
LRx xk
β x k x
0
0
exp
exp LR
E i t
E i t
β x
k x
0
1
0
Re Resin
Resin
LRLR
LR
nk
nk
q
q
k
x
z
kspp
kLRqLR
Metal
Dielectric(n)
Wave-vector in-plane conservation
qLR
SPP
LRLR
nglass
Leakage radiation cone
H. J Simon, J. K. Guha, Opt. Comm. 18, 391 (1976).
Lets put some numbers to these equations…
2 d m
d m
0
6 4
17002
16 1.5
1.5
9.2 10 2.6 10
43.4
d
m
LR
nm
k
i
n
i
q
B. Hecht, D. Pohl, H. Heinzelmann, and L. Novotny, Ultramicroscopy 61, 99 (1995).
Example:
qLR
SPP
LR
nglass
Total internal reflection
1sin 41.8
43.4
airc
glass
LR
nn
q
q
Leakage radiation can not get out!
Problem with common substrates
Solution Refractive index matching liquid
qLR
SPP
LR
nglass
Refractive index matching liquid (Oil)
Objective lens
Oil ImmersionMicroscope 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
sinNA n q
If we have an objective with a NA = 1.25, it can accept light at a maximum angle q = 56°.
0
Re
sin
eff
eff LR
nk
n n
q
The SPP effective index 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
1effn NA
For our previous example we can calculate the neff
1.03 1.25effn NA
Local excitation of surface plasmons
qLR
SPP
LR
nglass
Refractive index matching liquid (Oil)
Objective lens
Oil ImmersionMicroscope Objective
Incident beam
Local excitation of surface plasmons
The leakage radiation experimental setup
Laser
LRM imaging examples A
B
C. Garcia et al, Appl Phys B Laser Optic, Vol.107, No 2 (2012)
Direct and Fourier space
kx
ky
LRTL
kSPP
The Fourier plane
Filtering in LRM: Fourier transform and filters
Without filtering
Transmitted light is filtered
Desired image(well filtered)