1. About Omics Group OMICS GroupOMICS Group International through its Open Access Initiative is committed to make genuine and reliable contributions to the scientific community. OMICS Group hosts over 400 leading-edge peer reviewed Open Access Journals and organize over 300 International Conferences annually all over the world. OMICS Publishing Group journals have over 3 million readers and the fame and success of the same can be attributed to the strong editorial board which contains over 30000 eminent personalities that ensure a rapid, quality and quick review process. OMICS Group

2. About Omics Group conferences OMICS Group signed an agreement with more than 1000 International Societies to make healthcare information Open Access. OMICS Group Conferences make the perfect platform for global networking as it brings together renowned speakers and scientists across the globe to a most exciting and memorable scientific event filled with much enlightening interactive sessions, world class exhibitions and poster presentations OMICS GroupOMICS Group Omics group has organised 500 conferences, workshops and national symposium across the major cities including SanFrancisco,Omaha,Orlado,Rayleigh,SantaClara,Chicago,P hiladelphia,Unitedkingdom,Baltimore,SanAntanio,Dubai,H yderabad,Bangaluru and Mumbai.

3. Laser Dynamics: Weak versus Strong Harmonic-Expansion Modelling Belkacem Meziane Université d’Artois, Faculté des Sciences Jean Perrin, Rue Jean Souvraz, SP18, 62307, Lens Cedex, France e-mail: belkacem.meziane@univ-artois.fr UNITE DE CATALYSE ET DE CHIMIE DU SOLIDE *- UMR CNRS 8181

4. 4

5. I-The Lorenz-Haken model Lamb self-consistent analysis P(t) (source)Maxwell’s equations Field E(t) Schrödinger equation Excitation parameter 2C quantifies the pumping mechanism with respect to its level at lasing threshold, and Normalized quantities 5

6. Objectives 6 Analytical prospects outside the chaotic regime strange attractor Chaos Computer solutions only! Blurry physics! Self-pulsingAnalytical handling! Blur dissipation!

7. Typical solution Figure 1 7

8. Standard linear stability analysis For a Perturbed steady-state, E(t), P(t) and D(t) write Assuming With (Hopf bifurcation) Instability Threshold Ocsillation frequency 8

9. 9 Weak-harmonic analysis: Generic expression for the transient frequency Figure 2

10. 10 Steady state ( )

11. ( ) 11

12. Added in proof At the instability threshold Yielding Same formula as the one extracted from linear stability analysis ! 12

13. Figure 3  = 3,  = 0.1

14. Typical pulsing solution 14 Figure 4

15. Properties of the permanent solution The permanent solution evolves to satisty An adapted strong harmonic-expansion takes the form ip, op in-phase, out-of-phase components 15

16. How to handle the analytical aspects: Elements of an iterative method Start with 16

17. Equation (1c) yields 17

18. 18

19. Main results First-order field-amplitude Permanent pulsing-frequency (Figure 3) ? Third-order field-amplitude where 19

20. Fifth-order term 20

21. 21

22. Parameters appearing in E 5 Numerical example 22

23. 23

24. Commentaries LSA yields analytical information -at the instability threshold ( ) only! () -for the transient time-trace only ! ( ) Weak-harmonic analysisformulaes with precise information at any excitation level, be it below, at, or above 2C 2th ! Strong-harmonic expansions handles most of the unstable permanent regime pulsing frequency field-amplitudes of the first few orders Main drawback tedious algebra ? Ref «Pulse structuring in laser-light dynamics: from weak to strong sideband analyses»; II The Lorenz-Haken model Belkacem Meziane, Chap. II, in «Atomic, Molecular and Optical Physics: New Research», pp61-107 Editors: L. T. Chen, Nova Science Publishers, New York (2009) (ISBN: 978-1-60456-907-0)

25. II-The integro-differential « Maxwell-Bloch » system Basic equations (1a) (1b) (1c) Where Gaussian spectral distribution w: spectral doppler shift State equation 25

26. Saturated gain profile at stable steady-state 26

27. Unstable solution 27

28. Transient regime weak-harmonic analysis Start with Eq. (1a) where 28

29. Transient frequency Ratio (3b)/(3a)(3c) 29

30. Gain profiling Field oscillations Dip oscillations Pprofile remains centered at w=0 ! 30

31. Pulsing regimeStrong-harmonic analysis Satisfies Eq. 1a pulsing frequency 31

32. Pulsing frequency Transient frequency 32

33. Dynamic gain-profiling Pulsing field Lateral hole-burning effect Competition between lateral and centered atomic packets 33

34. Eigenfrequency notion: Simple physics versus complicated algebra Masse-spring system k m Excitationreaction Third-order components yield 34

35. Added in proof If we set w=0, we are left with Also derived directly from the Lorenz-equations! Closed form eigenfrequency of the Lorenz-Haken model Ref.2 «Pulse structuring in laser-light dynamics: from weak to strong sideband analyses»; I The Integro- differential « Maxwell-Bloch» system Belkacem Meziane, Chap. I, in « Atomic, Molecular and Optical Physics: New Research », pp1-59 Editors: L. T. Chen, Nova Science Publishers, New York (2009) (ISBN: 978-1-60456-907-0) 35

36. Conclusion 36

37. Let Us Meet Again We welcome all to our future group conferences of Omics group international Please visit: www.omicsgroup.com www.Conferenceseries.com http://optics.conferenceseries.com/