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• Anything from your side?

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Where do we stand?

• Optical imaging:

• Focusing by a lens

• Angular spectrum

• Paraxial approximation

• Gaussian beams

• Method of stationary phase

• The diffraction limit: How well can we focus light?

• Optical microscopy

• Optical imaging systems

• Real-world (dipolar) sources: Fluorophores and scatterers

• Example: Fluorescence microscopy (diffraction limited)

• Superresolution techniques:

• Example: STED microscopy

• Example: Localization microscopy

• Example: Scanning probe microscopy


Population of excited state in absence of STED beam

• 4-level system created by two electronic states (of a fluorophore) and vibrational excitation

• Vibrational relaxation infinitely fast

• Start in ground state, turn on pump

• Population of excited state as a function of time follows “charging” curve of a capacitor


Population of excited state in absence of STED beam

• Start in excited state (with certain probability), turn on depletion laser (to generate stimulated emission)

• Exponential decrease of population as function of time

• Depletion field “helps” spontaneous emission


Stimulatedemission

STED – how it works

• Apply a weak/short pump pulse (linear regime of charging curve)

• Apply a strong depletion pulse

• Register fluorescence photons arriving after depletion pulse



• FWHM of area of remaining pumped fluorophores after STED pulse


Characteristic saturation intensity:

Standard diffraction limit

HW2!


• FWHM of area of remaining pumped fluorophores after STED pulse


Characteristic saturation intensity:

So what is the secret here?The pump beam is focused to the diffraction limit.The STED beam is focused to the diffraction limit. Why is the resolution beyond the diffraction limit?

STED – how it really works


Excitation beam profile

Depletion beam profile

Willig et al., Nat. Meth. 4, 915(2007)

STED microscopy - example

• Imaging color centers in diamond


Rittweger et al., Nat. Photonics 3, 144 - 147 (2009)

• Why do I need laser pulses?

• Could I also do this with CW lasers?

• If yes, how?

Where do we stand?





• Gaussian beams






• Example: Fluorescence microscopy





STORM/PALM – localization microscopy

Different names for (in principle) the same technique:

• Photoactivated localization microscopy (PALM)

• Stochastic optical reconstruction microcopy (STORM)


STORM – localization microscopy

• Abbe tells me how closely spaced two sources can be for them to be discernible

• But how well can I localize a single emitter? (given that I know it is a single one)


PALM, STORM – localization microscopy

• Emitter 1 on, emitter 2 off localize emitter 1 better than diffraction limit

• Emitter 2 on, emitter 1 off localize emitter 2 better than diffraction limit

For this technique we need fluorophores which can be switched on and off(“photoactivated” or “stochastic”)


detector

Source plane

Imaging system

STORM

• https://www.microscopyu.com/tutorials/stochastic-optical-reconstruction-microscopy-storm-imaging


Nobel prize in chemistry 2014


Eric Betzig, Stefan W. Hell and William E. Moerner

"for the development of super-resolved fluorescence microscopy".

Fluorescence microscopy – scanning vs. wide-field


Photodiode(no spatial resolution)

x,y-scanner

laserDichroic beamsplitter

Stage position

Photo-current

Position on CCD chip

CCDcounts

CCD camera


Scanning technique.Resolution set by size of pump spot on sample

Wide-field imaging.Resolution set by PSF of imaging system

Both limited by diffraction.

Fluorescence microscopy – scanning vs. wide-field



x,y-scanner


Stage position

Photo-current


CCDcounts

CCD camera


Wide-field imaging.Resolution set by PSF of imaging system

STED vs. STORM microscopy



x,y-scanner


Stage position

Photo-current

CCD camera



CCDcounts

Scanning technique. Wide-field imaging.

Where do we stand?





• Gaussian beams






• Example: Fluorescence microscopy





Near-field microscopy


Confocal:

Near-field:

• So far we played some tricks to enhance the resolution of an image in the far-field (what were these tricks?)

• But how can we exploit evanescent (near-)fields?

Fields behind an aperture


Fields behind an aperture


z

Fields behind a (Gaussian) aperture


The principle of NSOM


NSOM – how it’s really done

• Metal coated fiber tip


Hecht et al., J Chem. Phys. 112, 7761

300 nm

NSOM – operation modes

Localized excitation

• Create subdiffraction-sized illumination spot with aperture probe

• Collect scattered field/fluorescence with conventional far-field optics

Localized detection

• Excite with conventional far-field optics

• Collect scattered field/fluorescence with aperture probe

Localized excitation and detection

• …


NSOM – localized detection

• Field distribution in photonic crystal waveguide

• Interferometric technique allows phase sensitive mapping of field


Gersen et al., Phys. Rev. Lett. 94, 123901Rothenberg and Kuipers, Nat. Phot. 8, 919

The idea of NSOM is not new…


If a small colloidal particle, e.g. of gold, be deposited upon a quartz slide placed above a Zeiss cardioid

condenser of NA 1.05, then, all rays of light from the condenser which reach the surface of the slide will be

totally reflected by the surface, except those which strike the surface at the base of the particle. These will be

scattered in all directions and if the objective of a microscope is suitably arranged above the slide, a proportion

of the rays so scattered will come to a focus in the eye of an observer, or upon a photographic plate, or a photo-

electrical cell suitably placed.[Synge then proposes to place a very thin stained biological section onto a quartz cover glass and to raster scan it in close distance over the irradiated particle. He argues that the amount of light received from the particle and collected by the objective will depend upon the relative opacity of the different parts of the section.]

Sketch sent by Synge to Einstein in 1928



If a small colloidal particle, e.g. of gold, be deposited upon a quartz slide placed above a Zeiss cardioid

condenser of NA 1.05, then, all rays of light from the condenser which reach the surface of the slide will be

totally reflected by the surface, except those which strike the surface at the base of the particle. These will be

scattered in all directions and if the objective of a microscope is suitably arranged above the slide, a proportion

of the rays so scattered will come to a focus in the eye of an observer, or upon a photographic plate, or a photo-

electrical cell suitably placed.[Synge then proposes to place a very thin stained biological section onto a quartz cover glass and to raster scan it in close distance over the irradiated particle. He argues that the amount of light received from the particle and collected by the objective will depend upon the relative opacity of the different parts of the section.]


Einstein’s reply: “prinzipiell unbrauchbar”




Synge: “It was my original idea to have a very small hole in an opaque plate, as

you suggest, and it was in this form that I had mentioned it to several people… A better way could be, if one could construct a little cone or pyramid of quartz glass having its point P brought to a sharpness of order 10−6 cm. One could then coat the sides and point with some suitable metal (e.g. in a vacuum tube) and then remove the metal from the point, until P was just exposed. I do not think such a thing would be beyond the capacities of a clever experimentalist.

Scattering NSOM


Schnell et al., Nature Photonics 3, 287 - 291 (2009)

• L<<l

• Illuminate with far field

• insert tip to scatter out near-field components into far-field detector

Scattering NSOM

• L<<l



• Implementation of Synge’s idea: metal nano-particle at end of glass tip



Metal nanoparticle (~100 nm)

Glass tip

Scattering NSOM

• L<<l



• Implementation of Synge’s idea: metal nano-particle at end of glass tip



Metal nanoparticle (~100 nm)

Glass tip

Particle acts as an optical antenna!

A metal nanoparticle as an optical antenna

• Particle gets polarized by pump field and generates large local (dipolar) field

• Scan tip over sample with single fluorescing molecules


Anger et al., PRL 96, 113002 (2006)

A metal nanoparticle as an optical antenna


without Au particle : with Au particle antenna:

Anger et al., PRL 96, 113002 (2006)

So far…

• So far, light emitters just reported their position

• But there is more: light emitters probe their local environment


Summary

• What is the angular spectrum?

• How well can I focus a beam of light with a lens?

• Which functional form does the focal field distribution of a lens have?

• What is the focal depth of a focused beam?

• What is the magnification of an imaging system?

• What is the point-spread function?

• How well can I localize a single emitter?

• What is the resolution limit of STED/PALM/NSOM?


Overview


• Optical antennas

• Spontaneous emission control

• Optical forces


An antenna is a device that focuses electromagnetic energy into a sub-wavelength volume.


Where does radiation come from?

• From the source terms in the inhomogeneous wave equation

• In the monochromatic case (remember )

For which source current distribution j(r) should we solve this equation?

www.photonics.ethz.ch

HW1

46

Where does radiation come from?

The Green function

Green function solves operator L for d-source

In matrix form:

Field distribution (desired)Source term (given)Differential operator (given)


B is given, A is sought

Knowing G, we can calculate the field A for any source B!

d-function is mother of all source terms!d-source is the impulse, Green function the impulse response (in space)

So we need d-current distribution here!

Back to the wave equation:


What is that?

What is so awesome about G?

The Green function of the wave equation

With G we can calculate the field distribution E of any current distribution j!


For dipole:


The Green function of the wave equation

The Green function of free space

In cartesian coordinates and in a linear, homogeneous and isotropic medium (see EM notes for derivation):

with



Wikipedia.org

52

Dipole fields

• Polarization• Radiation pattern• Near-field vs. far-field


Wikipedia.org

53

Dipole fields

What is wrong with this animation/plot:• No axis labels• No colorbar• Not units

Dipole fields for z-oriented dipole

54

Er

E

FF

NF IF

IF

FFNF IF

Hf

NB:• There is no magnetic near-field• Far-fields are transverse• Intermediate field is 90° out of

phase with near- and far-field

Distance dependence of dipole fieldsNF IF

FFNF IF

Time averaged energy density:

Caution: only far-field shown here!

Dipole radiation pattern

56

We calculated the power radiated by a dipole in free space by integrating the Poynting vector flux through a large sphere


Power radiated by a dipole in free space

?

We could• Make a huge sphere enclosing everything and integrate Poynting

vector• Make a very small sphere enclosing only the dipole and calculate

the net Poynting flux Both approaches are costly since we• Need to perform integrations• Might not be able to enclose the entire system


Power radiated in an inhomogeneous environment

Inhomogeneity

Primary field (G0)scattered field (Gs)

source

?

We could• Make a huge sphere enclosing everything and integrate Poynting

vector• Make a very small sphere enclosing only the dipole and calculate

the net Poynting flux Both approaches are costly since we• Need to perform integrations• Might not be able to enclose the entire system



Inhomogeneity


source

Is there an easier way?

The energy radiated by a dipole equals the work done by the dipole’s own field on the dipole itself!



Thought experiment:Displace positive and negative charge with respect to each other and let go.

+ -

The energy radiated by a dipole equals the work done by the dipole’s own field on the dipole itself!


Power radiated by a dipolePower dissipated in volume V (c.f. Poynting’s theorem):

Cycle averaged (monochromatic case):

Inhomogeneity


source


Power radiated by a dipolePower dissipated in volume V (c.f. Poynting’s theorem):

Cycle averaged (monochromatic case):

Radiated power is proportional to the local density of states (LDOS)

Inhomogeneity


source

We can now calculate the power dissipated by the oscillating dipole by knowing the field only at one point, namely the dipole’s location!

Split Green function of a complex photonic system into the “free-space part” and a “scattered part”.


Inhomogeneity


source

63


Primary field generated by the source at its own location

Secondary field generated by the source, scattered by the environment

Radiated power is proportional to the local density of states (LDOS)

In homogeneous medium (HW):

Same result as by integration of Poynting vector:


HW3

64

Power radiated in free space

Free-space LDOS:

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