Organic micro-lasers Melanie 100 m N. Djellali, S. Lozenko, I. - - PowerPoint PPT Presentation

▶
organic micro lasers
SMART_READER_LITE
LIVE PREVIEW

Organic micro-lasers Melanie 100 m N. Djellali, S. Lozenko, I. - - PowerPoint PPT Presentation

Sep 05, 2022 321 likes •927 views

1 Organic micro-lasers Melanie 100 m N. Djellali, S. Lozenko, I. Gozhyk, J. Lautru, I. Ledoux, and J. Zyss Laboratory for Quantum and Molecular Photonics (LPQM) ENS of Cachan Resonances in Mathematical Physics,

slide-1
SLIDE 1

1

Organic micro-lasers

Melanie

Resonances in Mathematical Physics, January 2009

100 µm

  • N. Djellali, S. Lozenko, I. Gozhyk, J. Lautru, I. Ledoux, and J. Zyss

Laboratory for Quantum and Molecular Photonics (LPQM) ENS of Cachan

slide-2
SLIDE 2

2

To put Cachan on the map…

Coll: E. Bogomolny, R. Dubertrand, C. Schmit (LPTMS) Orsay University ENS of Cachan Charles-de-Gaulle Airport RER B (urban train)

slide-3
SLIDE 3

3

Outline I Micro-lasers and wave chaos II Existing tools (what we can do) III Open questions

Organic micro-lasers as test-beds for wave chaos of open systems

slide-4
SLIDE 4

4

I Wave chaos for closed systems

Wavefunctions: random superposition

Conjectures

Spectra: random matrix theory

Berry, J. Phys. A 10 2083 (1977) Bohigas et al. , PRL 52 1 (1984) Stein et al., PRL 75, 53-56 (1995) 135 mm Alt et al., PRE 60, 2851-2857 (1999)

Experiments with metallic stadium-shaped microwave cavities

slide-5
SLIDE 5

5

I Lasing: basic ingredients

Cavity Amplifying medium

4000 3000 2000 1000

Intensity (counts)

625 620 615 610 605

Wavelength (nm)

Pumping

No direct connexion between pumping and emission

  • Directions of emission ?
  • Spectrum ?
slide-6
SLIDE 6

6

I Organic micro-lasers

Matrix host: polymer (PMMA) Guest: laser dye (DCM)

50-100 µm

Photography

λ ~ 0.6 µm

A cavity n=1.5

Plastic micro-lasers

slide-7
SLIDE 7

7

Lebental et al., APL 88 031108 (2006)

  • Cheap
  • Easy
  • Low refractive index
  • Modular (mask)

Matrix host: polymer (PMMA) Guest: laser dye (DCM)

50-100 µm

Photography

λ ~ 0.6 µm

A cavity n=1.5

χc χ

χc = 42 °

n = 1.5 n = 1

Plastic micro-lasers

slide-8
SLIDE 8

8

I Microlasers: cavity shapes

Photographies from an optical microscope

slide-9
SLIDE 9

9

Chemical/biological sensors Optical telecommunications

I Practical applications

Chang Campillo 1996 Vahala 2004 Practical applications of micro-resonators in optics and photonics, Matsko, 2009.

slide-10
SLIDE 10

10

I From electromagnetism to wave chaos

Inside Outside

Boundary conditions

Effective index approximation Effective index approximation

E

TE polarization

TE

Passive cavity (no laser)

slide-11
SLIDE 11

11

I From electromagnetism to wave chaos

Inside Outside

Boundary conditions

Effective index approximation Effective index approximation

TM TE B

TM polarization

Passive cavity (no laser)

slide-12
SLIDE 12

12

I Micro-lasers and wave chaos II Existing tools (what we can do) III Open questions Outline

Cavity shape Billiard (open) Laser effect To fill the resonances with photons

slide-13
SLIDE 13

13

Outline I Micro-lasers and wave chaos II Existing tools (what we can do) III Open questions

  • Wavefunctions
  • Directions of emission
  • Spectra

Numerics & Theory Experiments

slide-14
SLIDE 14

14

II Experimental set-up

Detector (eg. Spectrometer) Pico-second laser Rotating mount wafer Cavity 532 nm ~ 620 nm

Information about :

  • Lasing
  • Spectrum
  • Directions of emission
slide-15
SLIDE 15

15

II Lasing ?

60x10

3

40 20

Intensity (counts)

120 90 60 30

Pump energy (pJ.µm

  • 2)

Laser threshold

  • Ease for detection
  • Coherence

kRexp ~ 200 – 1000

slide-16
SLIDE 16

16

II Stadium: directions of emission

45 90 135 180 225 270 315

R L

45 90 135 180 225 270 315

L/R=0.5 L/R=1

slide-17
SLIDE 17

17

45 90 135 180 225 270 315

Emission in the far-field pattern

II Stadium: directional emission

L/R=0.5 L/R=1

60 50 40 30 20 10

θ (degrees)

3.5 3.0 2.5 2.0 1.5 1.0 0.5

L/R

Experiments Ray simulations

slide-18
SLIDE 18

18

60 50 40 30 20 10

θ (degrees)

3.5 3.0 2.5 2.0 1.5 1.0 0.5

L/R

Experiments Ray simulations Lens model

ANALYTIC II Chaotic cavity: lens model

slide-19
SLIDE 19

19

II Wave numerical simulations

Helmholtz equations inside and outside + dielectric boundary conditions Boundary element method

slide-20
SLIDE 20

20

II Wave simulations

Open cavity Closed cavity

Stein et al., PRL 75, 53-56 (1995)

slide-21
SLIDE 21

21

II Wave simulations

Individual well confined wavefunctions

L/R=0.3 L/R=1 L/R=2

Far-field pattern

slide-22
SLIDE 22

22

II Refractive escape: Rays or waves ?

60 50 40 30 20 10

θ (degrees)

3.5 3.0 2.5 2.0 1.5 1.0 0.5

L/R

Ray simulations Wave simulations

60 50 40 30 20 10

θ (degrees)

3.5 3.0 2.5 2.0 1.5 1.0 0.5

L/R

Ray simulations Wave simulations Experiments

PRA 75 033806 (2007)

slide-23
SLIDE 23

23

45 90 135 180 225 270 315

II Consequences of the lens model

slide-24
SLIDE 24

24

II Polygons

slide-25
SLIDE 25

25

II Polygons

slide-26
SLIDE 26

26

Outline I Micro-lasers and wave chaos II Existing tools (what we can do) III Open questions

  • Wavefunctions
  • Directions of emission
  • Spectra
slide-27
SLIDE 27

27

II Spectra

1200 1000 800 600 400 200

Intensity (counts)

625 620 615 610 605 600 595

Wavelength (nm)

Experiments

slide-28
SLIDE 28

28

II Spectra

Open cavity Closed cavity

1200 1000 800 600 400 200

Intensity (counts)

625 620 615 610 605 600 595

Wavelength (nm)

Alt et al., PRE 60, 2851-2857 (1999)

slide-29
SLIDE 29

29

1.0 0.8 0.6 0.4 0.2 0.0

Normalized intensity

610 608 606 604 602 600

Wavelength (nm)

II Spectra: periodic orbit

Length L of the periodic orbit ?

slide-30
SLIDE 30

30

II Spectra: periodic orbit

Fourier transform

1.0 0.5 0.0

Fourier transform

2500 2000 1500 1000 500

Optical length (µm)

1200 800 400

Intensity (counts)

620 610 600

Wavelength (nm)

slide-31
SLIDE 31

31

4000 3000 2000 1000

Intensity (counts)

625 620 615 610 605

Wavelength (nm)

II Test: Fabry-Perot resonator

slide-32
SLIDE 32

32

800 700 600 500 400 300

Optical length (µm)

250 200 150 100

Width a (µm) Experiments Fit experiments Theory : 2a*n Theory : 2a*nmod

a

II Spectra: periodic orbit

800 700 600 500 400 300

Optical length (µm)

250 200 150 100

Width a (µm) Experiments Fit experiments Theory : 2a*n Theory : 2a*nmod

n (with group velocity correction) = 1.64 Without any adjusted parameter Inferred independently

slide-33
SLIDE 33

33

a

800 700 600 500 400 300

Optical length (µm)

250 200 150 100

Width a (µm) Experiments Fit experiments Theory

II Spectra: periodic orbit

n = 1.64

Without any adjusted parameter

Direct measure of the geometrical length

PRA 76 023830 (2007)

slide-34
SLIDE 34

34

II Spectra: square

Diamond

3000 2000 1000

Intensity (counts)

615 610 605 600 595

Wavelength (nm)

slide-35
SLIDE 35

35

II Spectra: square

Without any adjusted parameter

a

700 600 500 400 300

Optical length (µm)

140 120 100 80 60

a (µm)

Experiments Fit experiments Theory :

slide-36
SLIDE 36

36

1200 1000 800 600 400 200

Intensity (counts)

615 610 605 600 595

Wavelength (nm)

Cardioid

II Spectra: periodic orbits

slide-37
SLIDE 37

37

Outline I Micro-lasers and wave chaos II Existing tools (what we can do) III Open questions

  • Prediction of the dominant periodic orbit
  • Diffraction on a dielectric corner
  • Resonances & lasing modes
slide-38
SLIDE 38

38

Classical physics Density of states Wave physics

??? III Spectra: trace formula

Integrable Chaotic Semi-classical limit

Proved for Fabry-Perot and disk

slide-39
SLIDE 39

39

III Spectra and trace formula (a)

Photography

Odd number of sides

Isolated In family

Periodic orbit: isolated or in family ?

slide-40
SLIDE 40

40

III Spectra and trace formula (a)

Single pentagon Double pentagon

Isolated In family

slide-41
SLIDE 41

41

III Spectra and trace formula (a)

300 200 100

Intensity (counts)

615 610 605 600 595

Wavelength (nm)

Single pentagon Double pentagon

1.0 0.5 0.0

Fourier transform (a.u.)

3000 2000 1000

Optical length (nm)

530 µm 1060 µm

slide-42
SLIDE 42

42

III [ Superscars ]

Superscar model no light in the center

PRA 76 023830 (2007) PRL 92 244102 (2004)

slide-43
SLIDE 43

43

Superscar model Numerical simulations

slide-44
SLIDE 44

44

III Spectra and trace formula (b)

Change of dominant periodic orbit with a parameter

slide-45
SLIDE 45

45

III Spectra (b): experiments

slide-46
SLIDE 46

46

III Trace formula: summary

Semi-classical limit

Proved for Fabry-Perot and disk Evidenced by experiments and numerical simulations How to see the sub-dominant periodic orbits ?

slide-47
SLIDE 47

47

Outline I Micro-lasers and wave chaos II Existing tools (what we can do) III Open questions

  • Prediction of the dominant periodic orbit
  • Diffraction on a dielectric corner
  • Resonances & lasing modes
slide-48
SLIDE 48

48

Re(kl) Im(kl)

Rectangle

III Lasing and losses

l

slide-49
SLIDE 49

49

III Lasing and losses Question

  • Diamond disappears when

Fabry-Perot appears.

  • Diamond and FP coexist,

but the out-coupling of FP is too big to see diamond.

  • r
slide-50
SLIDE 50

50

III Lasing and losses

slide-51
SLIDE 51

51

III Lasing and losses

Laser threshold Losses

For a periodic orbit

Experimental evidences

Questions

  • Which meaning for resonances ?
  • Which connexion with trace formula (cp) ?
slide-52
SLIDE 52

52

III Models for micro-lasers Resonances are not orthogonal

Laser effect To fill the resonances with photons (second quantization)

slide-53
SLIDE 53

53

III Models for micro-lasers

  • Helmholtz equations with n complex

Nosich et al. JOSAA 25 2884 (2008)

  • Maxwell-Bloch equations

Harayama et al. PRL 82 3803 (1999) Türeci, Stone et al. Nonlinearity 22 C1 (2009)

slide-54
SLIDE 54

54

Outline I Micro-lasers and wave chaos II Existing tools (what we can do) III Open questions

  • Prediction of the dominant periodic orbit
  • Diffraction on a dielectric corner
  • Resonances & lasing modes
slide-55
SLIDE 55

55

III Diffraction

Metallic

Sommerfeld (1896) D

Dielectric n

D

???

slide-56
SLIDE 56

56

Square: not (yet) integrable

III Diffraction

Rémy Dubertrand, Thesis.

slide-57
SLIDE 57

57

III Diffraction

Collaboration with C. Ulysse (LPN)

slide-58
SLIDE 58

58

Summary & Perspectives

Organic micro-lasers

  • Well-behaved microlasers

Practical applications (sensors) Open billiards

  • Existing tools for wave chaos

Far-field patterns Periodic orbits Losses

Open questions

  • Trace formula for dielectric billiards
  • Diffraction on a dielectric corner
  • Resonances & lasing modes
slide-59
SLIDE 59

59

  • C. Schmit &
  • R. Dubertrand