Post on 20-Aug-2020
Welcome again!
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Martin Frimmer (mfrimmer@ethz.ch)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
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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.
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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
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How does focusing by a lens work?
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Boundless.com
What does the field distribution here look like?
How does focusing by a lens work?
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Boundless.com
How does focusing by a lens work?
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x
q1 = ± 80°
k k
Intensity
How does focusing by a lens work?
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x
q1 = 0°, ±15°, ±30°, ±45°,
±60°, ±75°+apodization
Intensity
Angular spectrum
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MATH :
Physics :
Together:
Angular spectrum
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Physics :
Together:
Paraxial approximation
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mit
Fields propagate predominantly in z-direction !
Gaussian beams
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Gaussian Beams
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Waist Radius
Wavefront Radius
Phase Correction
Rayleigh Range
Note that we started with ONLY the field distribution in the plane z=0!
Gaussian Beams
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A better description of focused fields
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Boundless.com
Can we measure this field distribution?
Mapping the field distribution in the focus
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fluorescence rate ~ excitation ratex
y
contrast ~ | m .E(x,y;zo)| 2
Detector has no spatial resolution
Fluorescent molecules – Jablonski diagram
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Mapping the field distribution in the focus
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fluorescence rate ~ excitation ratex
y
contrast ~ | m .E(x,y;zo)| 2
Map of focal intensity distribution
Detector has no spatial resolution
Mapping the field distribution in the focus
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fluorescence rate ~ excitation ratex
y
contrast ~ | m .E(x,y;zo)| 2
Map of focal field distribution
Detector has no spatial resolution
Can we calculate this field distribution?
Far-field
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Example
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2 Lx
2 Ly
Angular spectrum in terms of far-field
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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
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So what does a lens do?
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Ray Continuity
(energy conservation)
So what does a lens do?
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Ray Continuity
(energy conservation)
Sine Condition
(aplanatic system)
So what does a lens do?
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Ray Continuity
(energy conservation)
Sine Condition
(aplanatic system)
What about this term?
Project plane on sphere
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So what does a lens do?
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Ray Continuity
(energy conservation)
Sine Condition
(aplanatic system)
Field after lens
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Angular spectrum representation
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Change coordinates
Coordinates on reference sphereCoordinates in focal region NA
Simplest case: Focusing of (0,0)-Gaussian beam
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:
Gaussian Beam sent into lens
Let’s skip some lengthy coordinate transformations and integrations…
Integrate over
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The solution… is a bit lengthy
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Apodization function:
Strongly focused Gaussian beam
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Strongly focused Gaussian beam
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Weakly focused beam
• Assume strongly overfilled back-aperture
• Assume small NA
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Focal plane (z=0):
Not Gaussian !
:
Why is this a jinc?
Mapping the field distribution in the focus
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fluorescence rate ~ excitation ratex
y
contrast ~ | m .E(x,y;zo)| 2
Map of focal intensity distribution
Detector has no spatial resolution
Single molecule detection
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What does the image of a point-source look like
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Source Plane Image Plane
Point-spread function
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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
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Point-spread function
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Angular spectrum
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Farfield of dipole :
Paraxial approximation
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Point-spread function
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Point-spread function
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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
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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).