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Sharlene Dorsey
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1 Administrative details: Anything from your side? 1

2 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 2

3 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 3

4 Population of excited state in absence of STED beam Start in excited state (with certain probability), turn on depletion laser Exponential decrease of population as function of time Depletion field helps spontaneous emission 4

5 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 5

6 STED how it works FWHM of area of remaining pumped fluorophores after STED pulse Standard diffraction limit Characteristic saturation intensity: 6

7 STED how it works 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? 7

8 STED how it really works Willig et al., Nat. Meth. 4, 915(2007) Excitation beam profile Depletion beam profile 8

9 STED microscopy - example Imaging color centers in diamond Rittweger et al., Nat. Photonics 3, (2009) Why do I need laser pulses? Could I also do this with CW lasers? If yes, how? 9

10 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 Example: STED microscopy Example: Localization microscopy Example: Scanning probe microscopy 10

11 STORM/PALM localization microscopy Different names for (in principle) the same technique: Photoactivated localization microscopy (PALM) Stochastic optical reconstruction microcopy (STORM) 11

12 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) 12

13 STORM localization microscopy detector Let s assume we image 2 emitters spaced at a distance smaller than the diffraction limit Imaging system Source plane 13

14 STORM localization microscopy detector Emitter 1 on, emitter 2 off localize emitter 1 better than diffraction limit Imaging system Source plane 14

15 STORM localization microscopy detector Imaging system Let s assume we image 2 emitters spaced at a distance smaller than the diffraction limit Emitter 2 on, emitter 1 off localize emitter 2 better than diffraction limit Source plane 15

16 STORM localization microscopy detector Imaging system 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 Source plane 16

17 Remember this slide? Jablonski diagram Long-lived states (fluorescence is off ) Molecules blink 17

18 Remember this slide? Jablonski diagram Long-lived states (fluorescence is off ) Molecules blink When continuously exciting a molecule, the fluorescence intensity switches on and off Some fluorophores are also photoswitchable, such that light of a specific wavelength turns the emitter on or off www3.nd.edu Most molecules stochastically switch between a bright and a dark state. Furthermore, there are photoswitchable emitters. 18

19 STORM

20 Nobel prize in chemistry 2014 Eric Betzig, Stefan W. Hell and William E. Moerner "for the development of super-resolved fluorescence microscopy". 20

21 Fluorescence microscopy scanning vs. wide-field x,y-scanner Scanning Dichroic laser technique. Wide-field laser imaging. beamsplitter Resolution set Both by size limited of by Resolution diffraction. set by PSF of pump spot on sample imaging system Photodiode (no spatial resolution) CCD camera Dichroic beamsplitter Photocurrent CCD counts Stage position Position on CCD chip 21

22 Fluorescence microscopy scanning vs. wide-field x,y-scanner laser Photodiode (no spatial resolution) Photocurrent Dichroic beamsplitter Wide-field laser imaging. Resolution set by PSF of imaging system CCD camera CCD counts Dichroic beamsplitter Stage position Position on CCD chip 22

23 STED vs. STORM microscopy Scanning x,y-scanner technique. Wide-field imaging. laser Dichroic beamsplitter laser Dichroic beamsplitter Photodiode (no spatial resolution) CCD camera Photocurrent CCD counts Stage position Position on CCD chip 23

24 What are we actually doing here? 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 Example: STED microscopy Example: Localization microscopy Example: Scanning probe microscopy 24

25 Wait a minute Did the microscopy techniques discussed so far make use of any evanescent fields? 25

26 Near-field microscopy 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? Confocal: Near-field: 26

27 Near-field scanning optical microscopy (NSOM) Hecht et al., J Chem. Phys. 112,

$NSOM operation modes Localized excitation Create subdiffraction-sized illumination spot$ optics Localized detection Excite with conventional far-field optics Collect scattered

optics Localized detection Excite with conventional far-field optics Collect scattered

28 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 28

29 NSOM localized detection Gersen et al., Phys. Rev. Lett. 94, Rothenberg and Kuipers, Nat. Phot. 8, 919 Field distribution in photonic crystal waveguide Interferometric technique allows phase sensitive mapping of field 29

30 Scattering NSOM Schnell et al., Nature Photonics 3, (2009) L<<l Illuminate with far field insert tip to scatter out near-field components into far-field detector 30

L<<l Illuminate with far field insert tip

31 Scattering NSOM Schnell et al., Nature Photonics 3, (2009) Glass tip Metal nanoparticle (~100 nm) Particle acts as an optical antenna! L<<l Illuminate with far field insert tip to scatter out near-field components into far-field detector extreme implementation: metal nano-particle at end of glass tip 31

32 A metal nanoparticle as an optical antenna Anger et al., PRL 96, (2006) Particle gets polarized by pump field and generates large local (dipolar) field Scan tip over sample with single fluorescing molecules 32

33 A metal nanoparticle as an optical antenna Anger et al., PRL 96, (2006) without Au particle : with Au particle antenna: 33

34 The idea of NSOM is not new Sketch sent by Synge to Einstein in

35 So far So far, light emitters just reported their position But there is more: light emitters probe their local environment 35

36 Summary What is the angular spectrum? How well can I focus a beam of light with a lens? Which functional form does the focus of a lens have? What is the focal depth of a focused beam? What is the point-spread function? How well can I localize a single emitter? What is the resolution limit of STED/PALM/NSOM? 36

37 Where does radiation come from? 37

38 Where does radiation come from? From the source terms in the inhomogeneous wave equation In the monochromatic case (remember HW1 ) For which source current distribution j(r) should we solve this equation? 38

39 The Green function 39

40 The Green function Differential operator (given) Field distribution (desired) Source term (given) 40

41 The Green function Differential operator (given) Field distribution (desired) Source term (given) Green function solves operator L for d-source 41

42 The Green function Differential operator (given) Field distribution (desired) Source term (given) Green function solves operator L for d-source In matrix form: 42

43 What is so awesome about G? B is given, A is sought Knowing G, we can calculate the field A for any source B! 43

44 What is so awesome about G? 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) 44

45 What is so awesome about G? 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) Back to the wave equation: So we need d-current distribution here! 45

46 What is so awesome about G? 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) Back to the wave equation: What is that? So we need d-current distribution here! 46

47 The oscillating dipole Harmonic time dependence: An oscillating dipole is a point-like time-harmonic current source. 47

48 The Green function of the wave equation With G we can calculate the field distribution E of any current distribution j! 48

49 The Green function of the wave equation For dipole: 49

50 The Green function of the wave equation For dipole: 50

51 The Green function of free space In cartesian coordinates and in a linear, homogeneous and isotropic medium (see EM notes for derivation): with 51

52 Dipole fields Wikipedia.org Polarization Radiation pattern Near-field vs. far-field 52

53 Dipole fields Wikipedia.org What is wrong with this animation/plot: No axis labels No colorbar Not units 53

54 Dipole fields for z-oriented dipole NF IF NF IF FF HW1 IF FF H f E r E 54

55 Dipole fields for z-oriented dipole NF IF NF IF FF IF FF H f E r E NB: There is no magnetic near-field Far-fields are transverse Intermediate field is 90 out of phase with near- and far-field 55

56 Distance dependence of dipole fields NF IF NF IF FF Caution: only far-field shown here! Time averaged energy density:

57 Dipole radiation pattern 57

58 Power radiated by a dipole in free space We calculated the power radiated by a dipole in free space by integrating the Poynting vector flux through a large sphere 58

59 Power radiated in an inhomogeneous environment source Inhomogeneity Primary field (G 0 ) scattered field (G s )? 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 59

60 Power radiated in an inhomogeneous environment source Inhomogeneity Primary field (G 0 ) scattered field (G s )? We could Make a huge sphere enclosing everything and integrate Poynting vector Make a Is very there small sphere an enclosing easier only the way? 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 60

61 Power radiated in an inhomogeneous environment Thought experiment: Displace positive and negative charge with respect to each other and let go. + - The The energy energy radiated radiated by by a a dipole dipole equals equals the the work work done done by by the the dipole s dipole s own own field field on on the the dipole dipole itself! itself! 61

62 Power radiated by a dipole source Power dissipated in volume V (c.f. Poynting s theorem): Inhomogeneity Cycle averaged (monochromatic case): Primary field (G 0 ) scattered field (G s ) 62

63 Power radiated by a dipole source Power dissipated in volume V (c.f. Poynting s theorem): Primary field (G 0 ) Radiated power is proportional to the local density of states (LDOS) Inhomogeneity scattered field (G s ) Cycle averaged (monochromatic case): We can now calculate the power dissipated by the oscillating dipole by knowing the field only at one point, namely the dipole s location! 63

64 Power radiated in an inhomogeneous environment source Inhomogeneity Split Green function of a complex photonic system into the freespace part and a scattered part. Primary field (G 0 ) scattered field (G s ) Primary field generated by the source at its own location Secondary field generated by the source, scattered by the environment 64

65 Power radiated in free space In homogeneous medium (HW): HW3 Free-space LDOS: Same result as by integration of Poynting vector: Radiated power is proportional to the local density of states (LDOS) 65

Radiation-matter interaction.

Radiation-matter interaction. Radiation-matter interaction Radiation-matter interaction Classical dipoles Dipole radiation Power radiated by a classical dipole in an inhomogeneous environment The local density of optical states (LDOS)