Current issues in coherence for small laser sources

Transcription

1 Current issues in coherence for small laser sources G.L. Lippi Institut Non Linéaire de Nice Université de Nice-Sophia Antipolis and UMR 7335 CNRS with the support of : P.1

2 Coworkers At the INLN Experiments Tao Wang (Ph.D. Student) B. Benzimoun (Intern, Univ. Clermont-Ferrand) At CNR (Italy) Numerics G.P. Puccioni Firenze (Italy) P.2

3 Outline of talk 0. General Introduction and Overview of the Problem I. Coherence in Macroscopic Lasers II. Coherence in Micro- and Nanolasers III. Statistical Mixture of Thermal and Coherent light IV. Oscillations in Coherence Function V. Additional Remarks P.3

4 Light-matter interaction Brief reminder Absorption A Stimulated Emission Einstein cofficients B Spontaneous Emission P.4

5 What is a laser? Brief reminder Active medium Feedback Feedback Coherent Emission Spontaneous Emission Photon # (+ spontaneous emission) Threshold: gain = losses Pump P.5

6 What is a laser? Cavity modes Lasing mode Resonance enhancement P.6

7 What is a laser? Cavity modes Leaky modes Numerous! Spontaneous emission High losses Macroscopic laser > 105 modes < 10-5 P.7

8 What is a laser? Nanolaser Suppression of Spontaneous emission Coherent Emission + Spontaneous Emission Limit: 1 mode =1 P.8

9 I. Coherence in Macroscopic Lasers Experiments (and theory) He-Ne = 6328 Å Cavity volume ~ 1 cm3 < 10-8 I.1

10 Statistics of Light 1967 Thermal light photocount statistics: Laser light photocount statistics: Superposition of thermal and laser light: G L S I.2

11 Statistics of Light 1967 Evolution of the statistical photon mixture I.3

12 Moment distributions 1967 I.4

13 Moment distributions 1967 I.5

14 II. Coherence in Micro- and Nanolasers Experiments and theory 0.8 m < < 1.5 m Cavity volume < 10 m3 > 10-4 II.1

15 Power curves for small lasers Threshold representation Coherence? Threshold II.2

16 Power curves for small lasers Size Q small d = 1.5 m 1850 medium d = 5 m 9000 large d = 8 m II.3

17 Correlations in small lasers Size Q small d = 1.5 m 1850 medium d = 5 m 9000 large d = 8 m II.4

18 Correlations in small lasers For the larger laser the g(3)(0) function does not match the theoretically expected values Coherence? Wiersig et al., Nature 460, 245 (2009) II.5

19 Correlations in small lasers Blue Green Courtesy of X. Hachair II.6

20 Correlations in small lasers II.7

21 Correlations in small lasers Summary g(1)(t) shows very short coherence time g(2)(0) remains above 1 drops below 1 shows strong photon bunching (g(2) > 1) g(3)(0) for larger, high Q, laser inconsistent with theoretical values for thermal light 1.5 m nanolaser: unsatisfactory convergence g(4)(0) constant value (1.5-2) II.8

22 III. Statistical mixture of thermal and coherent light Does it hold for nano- and microlasers? III.1

23 Statistical mixture III.2

24 Statistical mixture III.3

25 Statistical mixture Statistical mixture III.4

26 Interferometric measurements Measure average correlation in a scanning Michelson interferometer + h.c. Compute normalized correlation: Technique borrowed from Photon-correlation Fourier Spectroscopy X. Brockmann et al., Opt. Expr. 14, 6333 (2006) III.5

27 Interferometric measurements Chaotic field Stable coherent field III.6

28 Interferometric measurements Fluctuating coherent field Statistical mixture III.7

29 Interferometric measurements Photon-correlation Fourier spectroscopy III.8

30 III.9

31 Statistical superposition? Summary Contradicting information coming from two different experiments 1. In the intermediate threshold region a statistical superposition of chaotic light (spontaneous emission) and coherent light (laser) is emitted by the device 2. The light emitted by the device is coherent, but exhibits (strong) amplitude fluctuations Comparison between the two experiments difficult: Pulsed regime Entirely different devices Reproducibility of samples III.10

32 IV. Oscillations in coherence function Experiments and theory in Microcavities and nanocavities IV.1

33 Coherent oscillations Nanolaser Low Q cavity High Q cavity IV.2

34 Microlaser coherence IV.3

35 Coherent oscillations Microlaser Oscillations in coherence IV.4

36 Coherent oscillations Violation of Siegert relation (through population oscillations) Numerical: Rate Equations (discrete variables) IV.5

37 Coherent oscillations Experimental data from Phys. Rev. A 85, (2012) Rate equations simulations (discrete variables) IV.6

38 Coherent oscillations Summary Oscillations in coherence g(2)( ) appear both in (some) nanolasers in microlasers Result from coherent oscillations between population and e.m. field Can give rise to misinterpretation of g(2)( ) as imperfect coherence IV.7

39 V. Additional remarks V.1

40 Physical origin of coherent oscillations Origin of oscillations Photon number Continuous approximation Average values >> 1 Atom/carrier number V.2

41 Physical origin of coherent oscillations Origin of oscillations Photon number Discrete states Average values >> 1 Atom/carrier number V.3

42 Physical origin of coherent oscillations Origin of oscillations Photon number Discrete states Average values > 1 Atom/carrier number V.4

43 Physical origin of coherent oscillations Origin of oscillations Photon number Discrete states Average values ~ 1 Atom/carrier number V.5

44 Physical origin of coherent oscillations Origin of oscillations Photon number Discrete states Average values ~ 1 Photon loss Atom/carrier number V.5

45 Physical origin of coherent oscillations Origin of oscillations Photon number Discrete states Average values ~ 1 Photon loss Next step Atom/carrier number V.5

46 Physical origin of coherent oscillations Origin of oscillations Photon number Discrete states Average values ~ 1 Photon loss Next step Discrete process responsible for remnant of oscillation in a coherent interaction Atom/carrier number V.5

47 Modeling small lasers, Master equation approach Neqs = n s V.6

48 Modeling small lasers Phys. Rev. Lett. 102, (2009) Uniform random walk on the grid defined by the Master Equation Pulsing regime V.7

49 Physical modeling of small lasers Preliminary results G.P. Puccioni and G.L. Lippi V.8

50 Autocorrelations Preliminary results G.P. Puccioni and G.L. Lippi V.9

51 Spiking output Preliminary results G.P. Puccioni and G.L. Lippi V.10

52 Autocorrelations Preliminary results G.P. Puccioni and G.L. Lippi V.11

53 Autocorrelations Preliminary results G.P. Puccioni and G.L. Lippi V.11

54 Autocorrelations Summary From First Principles, Granular Modeling: Strong spiking regime g(2)(0) grows and then decreases Strong fluctuations in g(2)(0) before reaching coherent value g(3)(0) and g(4)(0) converge later Increased sensitivity to fluctuations in higher order correlations (especially g(4)(0)) V.12

55 Reproducing coherent oscillations Preliminary results Power spectrum G.P. Puccioni and G.L. Lippi V.13

56 Reproducing coherent oscillations Preliminary results Power spectrum G.P. Puccioni and G.L. Lippi V.14

57 Reproducing coherent oscillations Preliminary results Power spectrum G.P. Puccioni and G.L. Lippi V.15

58 Reproducing coherent oscillations Summary From First Principles, Granular Modeling: Oscillations present in signal mimicking the physical process Power spectrum shows peak features Autocorrelation > 1 (coherent oscillations) Oscillations in correlation Higher order correlations more sensitive (in amplitude and shape) V.16

59 Conclusions Correlations widely used (and necessary) for characterizing coherence in micro- and nanolasers Results strongly dependent on experimental system (reproducibility of samples, intrinsic features...) Most small lasers are pulsed: influence on correlations? Problems with higher correlations Coherent oscillations, statistical mixture of light... Many open questions C

60 Thank you for your attention!

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62 Nature 460 Wiersig et al.

63 Nature 460 Wiersig et al.

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