Coupling between disordered photonic structure and DBT molecules

Coupling between disordered photonic structure and DBT molecules: possible chain of hybrid modes F. Sgrignuoli; G. Mazzamuto; C. Toninelli Summer School- Ecole thématique du CNRS Waves and disorder

What are the Necklace or Hybrid states ? Light transport in disordered media: Ø In Diffusive Regime quasi-modes are spatially and spectrally overlapped Ø In AL Regime the modes are spatially and spectrally isolated Is there something else? Necklace/Hybrid states [1] J. B. Pendry, J. Phys C, 20, 733 (1987) & A. V. Tartakovskii et al, Sov. Phys Semicond, 21, 370 (1987) [2] Bertolotti, et all, Phys Rev E, 74, 035602 (2006) [3] Bertolotti et all, PRL, 94, 113903 (2005) [4] M. Ghulinyan, PRL, 99, 063905 (2007) [5] M. Ghulinyan, PRA, 76, 013822 (2007)

A B B A … A B Ø Time resolved experiment Ø Necklace arise when more than one resonance exist in the sample Ø The localized modes are spectrally narrow and have a Lorentzian line shape Ø The necklace Transmission peaks are non Lorentzian A symmetric pulse shape is observed that exhibits a fast decay time and a relative large delay, tipical of multiple resonance Bertolotti, et all, Phys Rev E, 74, 035602 (2006) ; [2] Bertolotti et all, PRL, 94, 113903 (2005)

Ø White light interferometer: cross-correlation using a fixed Mach-Zender and interferometer coupled with a scannig Fourier-trasform spectrometer. Ø Direct observation of multiple resonance behaviour of these states via transmission measurement of the phase. Bertolotti et all, PRL, 94, 113903 (2005)

Necklace or Hybrid states: Ø Multipeaked states: the em filed can be peaked in more than one separated area of the sample Ø Coupling of several distinct localized modes: spatial and spectral overlap Ø Short lived modes Ø Dominate the transmission: chain of hybridized localized modes, extended from one end of the sample to the other Coupling [1] J. B. Pendry, J. Phys C, 20, 733 (1987) & A. V. Tartakovskii et al, Sov. Phys Semicond, 21, 370 (1987) [2] L. Lanonté, et al, Optics Letters, 37, 11, (2012) [3] Vaneste et all, PR A, 79, 041802 (2009) [4] Bertolotti, et all, Phys Rev E, 74, 035602 (2006) [5] Bertolotti et all, PRL, 94, 113903 (2005) [6] M. Ghulinyan, PRL, 99, 063905 (2007) [7] M. Ghulinyan, PRA, 76, 013822 (2007)

Network A Network is made of: Ø Platform composed by: Ø Nodes: The information is processed and stored Ø Channels: Transmit information between nodes Building blocks: a reliable interface ensuring information gets transferred Node: Cavity mode + DBT molecule q Single emitter access q Efficiently couple to photonic structures q No dephasing/ Coherence See the talk of C. Toninelli for more information J. I. Cirac, et al. , Physical Review Letters, 78, 3221 (1997)

A Random Quantum Network Platform: 2 D Ph. C + small disorder (σ≈5%) Ø Promotes Anderson Localization (AL) [Sajeev John] Ø AL: interplay between order and disorder Ø Coupling in the range of DBT emission: FF, d, n “ad hoc”. Average Q factors Si 3 N 4 Modes appears at the band edge Frequency (u/l) See the talk of Scheffold, Florescu

SUMMARY What we have learned about these hybrid states: Ø They can appear in 1 D and 2 D localized systems (experimental proof) Ø WEAK COUPLED MODES: ü Crossing between the modes: same spatial profile at the same wavelength (crossing point) ü Spatial and Spectral overlapping ü Multiple Resonances: phase jump of Ø STRONG COUPLING ü Anti-crossing between the modes: same spatial profile at different wavelengths (ac point) OPEN QUESTIONS: ① How to measure their statistical probability? ② How to find evidences? ③ Does our residual periodicity helps?

SIMULATION TOOL Verify the existence and count the # of WEAKLY and STRONGLY COUPLED STATES… 70 different disorder realizations STEP 2 STEP 1 GOAL 2 D Simulations (FDTD): DBT Random Located Electric Dipole EM Field Distribution Post processing Analysis: FFT Amplitude and Phase Map Mode Intensity; Spreading Factor; Complexity Factor …

Coupling between Localized States Mode B @790. 3 nm Mode A @790. 3 nm

Anti. Crossing Point “Characterization”: S. C. Modes

Evolution of the Mode A as a function of ns Mode A ns=1 @787. 2 nm Mode A ns=1. 05 @787. 3 nm Mode A ns=1. 1 @787. 4 nm Mode A ns=1. 5 @787. 5 nm Mode A ns=1. 2 @787. 6 nm Mode A ns=1. 25 @788 nm Mode A ns=1. 3 @788. 02 nm Mode A ns=1. 35 @788. 8 nm Mode A ns=1. 4 @788. 6 nm ØAnticrossing point: same spatial mode profile at two different frequencies ØExchange between the modes after the AC ØSingle peak in phase Strongly EvolutionØof. Modes the Mode B as coupled a function of ns Mode A ns=1. 65 @800 nm Mode A ns=1. 7 @803 nm Mode A ns=1. 75 @806 nm Mode A ns=1. 8 @809 nm Mode A ns=1. 45 @791 nm Mode A ns=1. 5 @793 nm Mode A ns=1. 55 @795 nm Mode A ns=1. 6 @798 nm Mode B ns=1 @783. 9 nm Mode B ns=1. 05 @783. 9 nm Mode B ns=1. 1 @783. 9 nm Mode B ns=1 @783. 9 nm Mode B ns=1. 2 @783. 9 nm Mode B ns=1. 25 @783. 9 nm Mode B ns=1. 3 @783. 9 nm Mode B ns=1. 35 @783. 9 nm Mode B ns=1. 45 @783. 9 nm Mode B ns=1. 5 @784 nm Mode B ns=1. 55 @784 nm Mode B ns=1. 6 @784. 2 nm Mode B ns=1. 65 @784. 4 nm Mode B ns=1. 7 @784. 6 nm Mode B ns=1. 75 @784. 7 nm Mode B ns=1. 8 @784. 8 nm Mode B ns=1. 85 @784. 9 nm We can count one Mode A ns=1. 85 @812 nm

Coupling between Localized States Mode A @790. 3 nm Mod B@ 788. 8 nm Mode C @ 786. 8 nm

Coupling between Localized States

Crossing Point “Characterization”: W. C. Modes 2 peaks Mode B 2 peaks Mode C 1 peaks 2 peaks exchanged

Crossing Point “Characterization”: W. C. Modes Mode B @ 788. 8 nm Mode B @ 788. 9 nm ns=1. 3 ns=1. 4 Mode B @ 788. 7 nm Mode B@ 788. 8 nm Mode B @ 788. 9 nm ns=1. 45 ns=1. 5 ØCrossing point: same spatial mode profile at the same frequency Ø One peak in the mode intensity at the crossing point ØModes Weakly coupled CROSSING POINT We can count one Mode C @ 786 nm Mode C @ 788. 7 nm Mode C @789. 2 nm Mode C @ 790 nm

Coupling between Localized States @ 783 nm

Bi-modal Mode: Analysis Mode e 1 @ 783 nm Mode e 2 @ 783 nm

ü Conclusion & FUTURE WORKs Numerical Simulation tool implemented Ø STRONG COUPLING REGIME: ü Anti-crossing between the modes: same spatial profile at different wavelengths ü Exchange of the modes after the anticrossing point ü Single peaked in the phase: standing wave due to the coupling constant Ø WEAK COUPLING REGIME: ü Crossing between the modes: same spatial profile at the same frequency ü At the crossing point: one peak in the mode intensity ² More understanding about the phase behaviour in the weak coupled regime is needed: test the double peak in the phase on a test bed of coupled Photonic Crystal cavity ² Distribution of the mode volume ² Evaluation of the Q-factors: SC: crossing of the Q-factor WC: anticrossing of the Q-factor ² Compare the PROBABILITY in partially disordered and fully random PC ² EXPERIMENTS

LAB 66 Costanza DBT Andrea Giacomo Sofia Fabrizio Sharish