Welcome again! - ETH Z · 2019. 8. 13. · Welcome again! 1 Martin Frimmer ([email protected])...

Welcome again!

www.photonics.ethz.ch 1

Martin Frimmer ([email protected])Photonics LaboratoryHPP M24

Nano-optics studies light-matter interactions on the sub-wavelength scale. The goal of this course is to quantitatively understand the fundamental concepts of nano-optics, including

• Superresolution microscopy

• Quantum light sources

• Optical antennas

• Optical forces

• …

Administrative details: Lab/Research Projects

• First name/ last name?

• Check website for group assignments

• Find your team-mates

• Determine a spokesperson to contact your supervisor


Why nano-optics?

• The energy scale of our interest corresponds to about 1 µm wavelength

• The length scales of scientific and technological interest are approaching the atomic scale Read Feynman’s talk “There is plenty of room at the bottom.”

We need to control electromagnetic fields and their interaction with matter at sub-λ scales.


10 eV1 eV100 meV

kT Ry

ionizing

Thermal noise

LIFE

1 nm 1 m

Size mismatch

On the menu today

• Motivation: Why nano-optics?

• Repetition: electromagnetism

• Optical imaging:

• Focusing by a lens

• Angular spectrum

• Paraxial approximation

• Gaussian beams

• Method of stationary phase

• The diffraction limit

• Fluorophores

• Example: Fluorescence microscopy

• Example: STED microscopy

• Example: Localization microscopy

• Example: Scanning probe microscopy


How does focusing by a lens work?


Boundless.com

What does the field distribution here look like?



Boundless.com



x

q1 = ± 80°

k k

Intensity



x

q1 = 0°, ±15°, ±30°, ±45°,

±60°, ±75°+apodization

Intensity

Angular spectrum


MATH :

Physics :

Together:

Angular spectrum


Physics :

Together:

Paraxial approximation


mit

Fields propagate predominantly in z-direction !

Gaussian beams


Gaussian Beams


Waist Radius

Wavefront Radius

Phase Correction

Rayleigh Range

Note that we started with ONLY the field distribution in the plane z=0!

Gaussian Beams


A better description of focused fields


Boundless.com

Can we measure this field distribution?

Mapping the field distribution in the focus


fluorescence rate ~ excitation ratex

y

contrast ~ | m .E(x,y;zo)| 2

Detector has no spatial resolution

Fluorescent molecules – Jablonski diagram





y


Map of focal intensity distribution





y


Map of focal field distribution


Can we calculate this field distribution?

Far-field


Example


2 Lx

2 Ly

Angular spectrum in terms of far-field


For kz ~ k: Fourier Optics !

From method of stationary phase:

Boundless.com

Back to the lens

• We can calculate the field near a focus if we just know the far-field


So what does a lens do?


Ray Continuity

(energy conservation)



Ray Continuity


Sine Condition

(aplanatic system)



Ray Continuity


Sine Condition

(aplanatic system)

What about this term?

Project plane on sphere




Ray Continuity


Sine Condition

(aplanatic system)

Field after lens


Angular spectrum representation


Change coordinates

Coordinates on reference sphereCoordinates in focal region NA

Simplest case: Focusing of (0,0)-Gaussian beam


:

Gaussian Beam sent into lens

Let’s skip some lengthy coordinate transformations and integrations…

Integrate over


The solution… is a bit lengthy


Apodization function:

Strongly focused Gaussian beam


Weakly focused beam

• Assume strongly overfilled back-aperture

• Assume small NA


Focal plane (z=0):

Not Gaussian !

:

Why is this a jinc?




y


Map of focal intensity distribution


Single molecule detection


What does the image of a point-source look like


Source Plane Image Plane

Point-spread function


On the menu today







• Gaussian beams



• Fluorophores






Angular spectrum


Farfield of dipole :

Paraxial approximation


On the menu today







• Gaussian beams



• Fluorophores






Classical resolution limit

www.photonics.ethz.ch 48E. Abbe, Arch. Mikrosk. Anat. 9, 413 (1873).

Source Plane Image Plane

4 4

Abbe’s Resolution Limit

www.photonics.ethz.ch 49E. Abbe, Arch. Mikrosk. Anat. 9, 413 (1873).

Welcome again! - ETH Z · 2019. 8. 13. · Welcome again! 1 Martin Frimmer ([email protected])...

Documents

Transcript of Welcome again! - ETH Z · 2019. 8. 13. · Welcome again! 1 Martin Frimmer ([email protected])...