Martin Frimmer ([email protected]) Photonics Laboratory HPP … · 2021. 1. 13. · Administrative...
Transcript of Martin Frimmer ([email protected]) Photonics Laboratory HPP … · 2021. 1. 13. · Administrative...
Welcome again!
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Martin Frimmer ([email protected])Photonics LaboratoryHPP M24
• Check out the “Orientation sheet” on Moodle
Administrative details• 3 homework problems: find on Moodle, hand in on Moodle
• Dates for paper presentations fixed (please be available)
• Exams will take place in last week of semester (precise schedule to be published)
• You should have all necessary information to decide whether you want to follow this course. If you don’t want to get credit/take the exam, please sign out of the course by Tuesday, 29 Sep. (You are welcome to keep following the lectures and I can add you as a guest in case you want to access the Moodle.)
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Administrative details: Paper Presentations• I will assign the students I haven’t had feedback from
• I’ll share the schedule as soon as possible
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Today’s question
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Why do I not see the atoms that make up your skin when I look at you?
Maxwell’s equations for complex fields
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Spectral representation: For monochromatic fields:
Note that I dropped the underscore for complex fields!
The Helmholtz equation, plane and evanescent waves
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2. Dispersion relation:
1. Plane waves: 3. Speed of light:
4. Refractive index:
for
How do you generate evanescent waves?
Simple imaging systems
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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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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
k
θ1 = 0°
I(x) = E(x) E*(x) = ?
Intensity
How does focusing by a lens work?
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xI(x) = E(x) E*(x) = ?
θ1 = 20°
k
Intensity
How does focusing by a lens work?
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x
θ1 = ± 20°
k k
I(x) = E(x) E*(x) = ?
Intensity
How does focusing by a lens work?
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x
θ1 = ± 80°
k k
Intensity
How does focusing by a lens work?
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x
θ1 = 0°, ±45°
kkk
k
Intensity
How does focusing by a lens work?
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x
θ1 = 0°, ±15°, ±30°, ±45°, ±60°, ±75°
Intensity
How does focusing by a lens work?
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x
θ1 = 0°, ±15°, ±30°, ±45°, ±60°, ±75°
+apodization
Intensity
Angular spectrum
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MATH :
Angular spectrum
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MATH :
PHYS :
Angular spectrum
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MATH :
PHYS :
Together:
Angular spectrum
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PHYS :
Together:
Paraxial approximation
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mit
Fields propagate predominantly in z-direction !
Gaussian beams
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The Gaussian Beam
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Beam waist
Wavefront radius
Phase correction (Gouy phase)
Rayleigh length
Field in focal plane z=0:
The Gaussian Beam
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The Gaussian Beam has one free parameter. Which one?
The Gaussian Beam
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The Gaussian Beam has one free parameter. Which one?
The Gaussian Beam is an approximation!When is it a good approximation?
Does the Gaussian Beam contain evanescent field components?
Far-field
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s=
Example
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2 Lx
2 Ly
Example: Party-Party Goggles
Party-Party Goggles
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Party !
Party!Laser
Magic foil
500 µm
Party-Party
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Party !
Party!Laser
Magic foil
500 µm
FFT
SLM technology uses Fourier optics
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Party !
Party!Laser
Magic foil
Adaptive Version: Spatial light modulator (SLM)
A better description of focused fields
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Better than Gaussian beams, but not much to do analytically.