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

1 Organic micro-lasers Melanie �������� 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 Resonances in Mathematical Physics, January 2009

2 To put Cachan on the map… Charles-de-Gaulle Airport RER B (urban train) ENS of Cachan Coll: E. Bogomolny, R. Dubertrand, C. Schmit Orsay University (LPTMS)

3 Outline Organic micro- lasers as test-beds for wave chaos of open systems I Micro-lasers and wave chaos II Existing tools (what we can do) III Open questions

4 I Wave chaos for closed systems Conjectures Spectra: random Wavefunctions: random matrix theory superposition Bohigas et al. , PRL 52 1 (1984) Berry, J. Phys. A 10 2083 (1977) 135 mm Experiments with metallic stadium-shaped microwave cavities Alt et al., PRE 60 , 2851-2857 (1999) Stein et al., PRL 75 , 53-56 (1995)

5 I Lasing: basic ingredients Pumping No direct connexion between pumping and emission 4000 Intensity (counts) 3000 Amplifying Cavity medium 2000 • Directions of emission ? 1000 • Spectrum ? 0 605 610 615 620 625 Wavelength (nm)

6 I Organic micro-lasers Plastic micro-lasers 50-100 µm Photography A cavity n=1.5 Matrix host: polymer (PMMA) Guest: laser dye (DCM) λ ~ 0.6 µm

7 Plastic micro-lasers 50-100 µm • Cheap • Easy • Low refractive index • Modular (mask) Photography A cavity χ c = 42 ° n=1.5 Matrix host: polymer (PMMA) χ c χ Guest: laser dye (DCM) n = 1.5 λ ~ 0.6 µm n = 1 Lebental et al., APL 88 031108 (2006)

8 I Microlasers: cavity shapes Photographies from an optical microscope

9 I Practical applications Chang Optical telecommunications Campillo 1996 Chemical/biological sensors Vahala 2004 Practical applications of micro-resonators in optics and photonics, Matsko, 2009.

10 I From electromagnetism to wave chaos TE E polarization Boundary conditions Inside Outside TE Effective index approximation Effective index approximation Passive cavity (no laser)

11 I From electromagnetism to wave chaos TM B polarization Boundary conditions Inside Outside TE Effective index approximation Effective index approximation TM Passive cavity (no laser)

12 Outline I Micro-lasers and wave chaos Cavity shape Billiard (open) Laser effect To fill the resonances with photons II Existing tools (what we can do) III Open questions

13 Outline I Micro-lasers and wave chaos II Existing tools (what we can do) • Wavefunctions Numerics • Directions of emission & Theory Experiments • Spectra III Open questions

14 II Experimental set-up Information about : • Lasing • Spectrum Pico-second • Directions of emission 532 nm laser Cavity Detector ~ 620 nm wafer (eg. Spectrometer) Rotating mount

15 II Lasing ? Laser threshold 3 60x10 • Ease for detection Intensity (counts) 40 • Coherence 20 kR exp ~ 200 – 1000 0 30 60 90 120 -2 ) Pump energy (pJ.µm

16 II Stadium: directions of emission R L 90 90 135 45 135 45 L/R=0.5 L/R=1 180 0 180 0 225 315 225 315 270 270

17 II Stadium: directional emission Emission in the far-field pattern 60 90 50 Experiments Ray simulations 135 45 40 L/R=0.5 θ (degrees) 30 L/R=1 20 180 0 10 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 225 315 L/R 270

18 II Chaotic cavity: lens model 60 Experiments 50 Ray simulations Lens model 40 θ (degrees) ANALYTIC 30 20 10 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 L/R

19 II Wave numerical simulations Helmholtz equations inside and outside + dielectric boundary conditions Boundary element method

20 II Wave simulations Open cavity Closed cavity Stein et al., PRL 75 , 53-56 (1995)

21 II Wave simulations Far-field pattern L/R=0.3 L/R=1 L/R=2 Individual well confined wavefunctions

22 II Refractive escape: Rays or waves ? 60 60 Ray simulations Ray simulations 50 50 Wave simulations Wave simulations Experiments 40 40 θ (degrees) θ (degrees) 30 30 20 20 10 10 PRA 75 0 0 033806 0.5 0.5 1.0 1.0 1.5 1.5 2.0 2.0 2.5 2.5 3.0 3.0 3.5 3.5 (2007) L/R L/R

23 II Consequences of the lens model 90 135 45 180 0 225 315 270

24 II Polygons

25 II Polygons

26 Outline I Micro-lasers and wave chaos II Existing tools (what we can do) • Wavefunctions • Directions of emission • Spectra III Open questions

27 II Spectra 1200 1000 Intensity (counts) 800 Experiments 600 400 200 0 595 600 605 610 615 620 625 Wavelength (nm)

28 II Spectra Open cavity Closed cavity 1200 1000 Intensity (counts) 800 600 400 200 0 595 600 605 610 615 620 625 Wavelength (nm) Alt et al., PRE 60 , 2851-2857 (1999)

29 II Spectra: periodic orbit Length L of the periodic orbit ? 1.0 Normalized intensity 0.8 0.6 0.4 0.2 0.0 600 602 604 606 608 610 Wavelength (nm)

30 II Spectra: periodic orbit Fourier transform 1.0 1200 Intensity (counts) Fourier transform 800 0.5 400 0.0 0 0 500 1000 1500 2000 2500 600 610 620 Optical length (µm) Wavelength (nm)

31 II Test: Fabry-Perot resonator 4000 Intensity (counts) 3000 2000 1000 0 605 610 615 620 625 Wavelength (nm)

32 II Spectra: periodic orbit Experiments Experiments Fit experiments Fit experiments 800 800 Theory : 2a*n Theory : 2a*n Theory : 2a*n mod Theory : 2a*n mod Optical length (µm) Optical length (µm) 700 700 n (with group 600 600 velocity correction) a 500 500 = 1.64 400 400 Inferred 300 300 independently 100 100 150 150 200 200 250 250 Width a (µm) Width a (µm) Without any adjusted parameter

33 II Spectra: periodic orbit Direct measure of the geometrical length Experiments 800 Fit experiments Theory Optical length (µm) 700 600 a n = 1.64 500 400 300 100 150 200 250 Width a (µm) PRA 76 023830 Without any adjusted parameter (2007)

34 II Spectra: square 3000 Intensity (counts) 2000 Diamond 1000 0 595 600 605 610 615 Wavelength (nm)

35 II Spectra: square Experiments 700 Fit experiments Theory : Optical length (µm) 600 500 400 a 300 60 80 100 120 140 a (µm) Without any adjusted parameter

36 II Spectra: periodic orbits Cardioid 1200 1000 Intensity (counts) 800 600 400 200 0 595 600 605 610 615 Wavelength (nm)

37 Outline I Micro-lasers and wave chaos II Existing tools (what we can do) III Open questions • Prediction of the dominant periodic orbit • Resonances & lasing modes • Diffraction on a dielectric corner

38 III Spectra: trace formula Density of states Wave physics Integrable ??? Semi-classical limit Chaotic Classical physics Proved for Fabry-Perot and disk

39 III Spectra and trace formula (a) Periodic orbit: isolated or in family ? Odd number of sides Isolated Photography In family

40 III Spectra and trace formula (a) In family Isolated Single Double pentagon pentagon

41 III Spectra and trace formula (a) 1060 µm 300 1.0 Fourier transform (a.u.) Intensity (counts) 200 0.5 530 µm 100 0 0.0 595 600 605 610 615 0 1000 2000 3000 Wavelength (nm) Optical length (nm) Single pentagon Double pentagon

42 III [ Superscars ] Superscar model no light in the center PRL 92 244102 (2004) PRA 76 023830 (2007)

43 Numerical simulations Superscar model

44 III Spectra and trace formula (b) Change of dominant periodic orbit with a parameter

45 III Spectra (b): experiments

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 ?

47 Outline I Micro-lasers and wave chaos II Existing tools (what we can do) III Open questions • Prediction of the dominant periodic orbit • Resonances & lasing modes • Diffraction on a dielectric corner

48 III Lasing and losses Rectangle l Im(kl) Re(kl)

49 III Lasing and losses Question • Diamond disappears when Fabry-Perot appears. or • Diamond and FP coexist, but the out-coupling of FP is too big to see diamond.

50 III Lasing and losses

51 III Lasing and losses For a periodic orbit Experimental Laser threshold Losses evidences Questions • Which connexion with trace formula (c p ) ? • Which meaning for resonances ?

52 III Models for micro-lasers Laser effect To fill the resonances with photons (second quantization) Resonances are not orthogonal

53 III Models for micro-lasers • Helmholtz equations with n complex Nosich et al. JOSAA 25 2884 (2008) • Maxwell-Bloch equations Türeci, Stone et al. Nonlinearity 22 C1 (2009) Harayama et al. PRL 8 2 3803 (1999)

54 Outline I Micro-lasers and wave chaos II Existing tools (what we can do) III Open questions • Prediction of the dominant periodic orbit • Resonances & lasing modes • Diffraction on a dielectric corner