a 3-D investigation of 2-D organic micro-billiard lasers Light from the edge: a 3-D investigation of 2-D organic micro-billiard lasers Clément Lafargue1, S. Lozenko1 , S. Bittner1, C. Ulysse2, C. Cluzel3, J. Zyss1, M. Lebental1 1 – Laboratoire de Photonique Quantique et Moléculaire, ENS de Cachan. 2 – Laboratoire de Photonique et de Nanostructures , CNRS, Marcoussis. 3 – Laboratoire de mécanique et technologie, ENS de Cachan. 25’’ Joke billiard Molecular quantum photonics lab

Dye-doped polymer micro-cavity Organic microlasers Conventional laser Dye-doped polymer micro-cavity Amplifying medium + Resonating Cavity Usual configuration weak confinement n ≈ 1.5 40’’ Low index = weak confinement, desirable effect Deep reasons : selection of few orbits, WGM: Microsphères et microtores de Silice, Cavity quantum electrodynamics group

LPQM – microlaser group topics Chaotic cavities POSTER, I. Gozhyk : Towards the control of polarization properties of solid state organic lasers I. Gozhyk, PRA 86, 043817 (2012) Lebental, APL 88, 031108 (2006) Unidirectional lasing N.Djellali, APL 95, 101108 (2009) Emission Diffraction Measurement and model POSTER, S. Bittner : Localization of modes in a dielectric square resonator Semi-classical modeling S.Lozenko “Microfluid” EU Project Analyte solution flow Numerical modeling 90’’ Interessé/ intrigué par les directions d’émission , on a s’est retrouvé confronté au problème du coin diélectrique. Mécanisme de sortie -> joue aussi sur la compétition en tre modes vu que pertes=gain De plus on s’est dit qu’on pouvait peut-être apporter qqchose grâce à nos machins sur le prb même du coin diélectrique

Motivation: diffraction at dielectric corners and edges no solution Metallic corner Sommerfeld 1896 30’’ Steady-state Fil rouge diffraction : expliquer les similitudes et différences des différents cas (diff du FP, dif du carré , diff du triangle-diffractiv orbit) A standing wave in a resonator to explore the corner

Outline Background on organic microlasers Fabrication Experiment Emission/diffraction properties Fabry-Pérot like cavities Square cavities Triangular microlasers 20’’ 4

Outline Background on organic microlasers Fabrication Experiment Emission /diffraction properties Fabry-Pérot like cavities Square cavities Triangular microlasers 5’’ 5 5

Organic microlaser: Fabrication Cavity n≈1.5 PMMA + Dye SiO2 n=1.45 n2=1 0.6-0.7 μm Fabrication: Electron-beam lithography 50-200 µm Microscope photograph SEM photograph 1μm 0.6 µm 50-200 µm Arbitrary cavity shapes Different laser dyes 40’’ 6 6

Organic microlasers: characterization Excitation geometry Lasing thresholds pumping 532 nm Emission diagrams ~610 nm emission collecting lens Spectrometer Spectrum L 40’’ Pulsed pumping Typical spectrum Images Wavelength [nm] 7

Organic microlasers: characterization Experimental Measurements Lasing thresholds Emission diagrams Spectrum L 20’’ Images

Organic microlasers: characterization Experimental Measurements Lasing thresholds FAR FIELD DETECTION Emission diagrams Spectrum L 20’’ Dire ‘square’, ‘stadium’ ‘sharp lobes’ Images Physical Review A 75, 033806 (2007)

Semi-classical approach Organic microlasers: characterization Experimental Measurements Lasing thresholds F.S.R. Emission diagrams Semi-classical approach Spectrum L 20’’ FSR linked to the length of PO Expliquer differentes PO Images Periodic Orbits PRA 76, 023830 (2007)

Organic microlasers: characterization Experimental Measurements Lasing thresholds Emission diagrams Spectrum L 20’’ Images

Outline Background on organic microlasers Fabrication Experiment Emission/diffraction properties Fabry-Pérot like cavities Square cavities Triangular microlasers 10’’ 12 12

3D emission- latitude diagrams FP Measurement: 50’’ Emission UPLIFTED 13

3D emission- latitude diagrams FP Sergey Lozenko J.A.P. 111, 103116 (2012) z Measurement: x 50’’ Thin Angular lobes Free-standing 14

3D emission - latitude diagrams FP Model: Slit diffraction   Interference (wafer) 50’’ Remind that it is a FP Enlight the differences C. Lafargue, to be submitted 15

Outline Background on organic microlasers Fabrication Experiment Emission/diffraction properties Fabry-Pérot like cavities Square cavities Triangular microlasers 20’’ 16 16

Square microlaser : diffractive outcoupling Diamond orbit confined by total internal reflection … nL = n x 2√2 a 50’’

Square microlaser : diffractive outcoupling Diamond orbit confined by total internal reflection … … but losses occur via diffraction 30’’ 18

Square microlaser : diffractive outcoupling Pump : 30’’ + example pola effect Camera Pump polarization effects I. Gozhyk, PRA 86, 043817 (2012),

Square microlaser : diffractive outcoupling The diffraction at the corners here is not at all understood, but it would be important to do so the latitude diagrams depend strongly on the kind of mode inside the resonator -> maybe there is some kind of connection between the diffraction in the two different directions.

Outline Background on organic microlasers Fabrication Experiment Emission/diffraction properties Fabry-Pérot like cavities Square cavities Triangular microlasers 20’’ 21 21

Periodic Orbits in triangles A not so simple shape (not regular contour) No totally confined periodic orbits An open mathematical question:  «  Does a periodic orbit in a triangle exist ? » Alain Grigis, University Paris XIII ?

FP winning 100° 40°

FP not always winning Camera view 110° 35° 35° 110° Despite the fact FP is in family, the other isolated orbit is winning

Diffractive orbit 98.04° 40° 41.96° « DO not exist in classical mechanics »

Summary Diffraction effects from the edges on different contours : 3D Fabry-Pérot emission well understood Square : emission at the corners 3D emission depends on the cavity shape Triangles Identification of orbits Switching between different types of orbits Observation of a diffractive orbit

Perspectives 5’’ clement.lafargue@ens-cachan.fr

110° 110° 700

phi= 60° phi= -22° Incidence 0° Incidence 40°

Does a periodic orbit in a triangle exist ? Alain Grigis, University Paris XIII Acute triangles feet of the altitudes Less than 100° triangles: Journal of Experimental Mathematics, 18, p. 137 (2008) Rational triangles : angles = pp/m , unfolding theory Others … 31

Information in the laser spectrum : Length L of the periodic orbit Semi-Classical point of view Information in the laser spectrum : Length L of the periodic orbit Lasing L n1 n2 32 32

Periodic orbits & trace formula Density of states Wave physics Semi-classical limit Classical physics PRE 83, 036208 (2011) Sum on periodic orbits Length of the orbits Fresnel reflexion coefficients Coeff depending only on classical quantities

Effective index approximation Electromagnetism z Passive cavity (no laser) : resonances w ? Boundary conditions Outside Inside (Dxy + neff ² k²) z Effective index approximation 34

From electromagnetism to wave chaos 2D problem Boundary conditions diffraction 35

Resonance computation Square: not integrable Diamond -1.2 100 Charles Schmit, Eugène Bogomolny Phys. Rev. E 83, 036208 (2011) 36

How to fabricate ? What are the emission directions ?

3D – Polarization selection q q Pump polarization Camera 38

3D – Polarization selection Pump polarization : (Camera) 39