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)