1 / 37

A.D. Wilson-Gordon, H. Shpaisman and H. Friedmann, Department of Chemistry, Bar-Ilan University,

EFFICIENT PARAMETRIC AMPLIFICATION IN DOUBLE  SYSTEMS IN THE ABSENCE OF TWO-PHOTON MAXIMAL COHERENCE. A.D. Wilson-Gordon, H. Shpaisman and H. Friedmann, Department of Chemistry, Bar-Ilan University, Ramat Gan 52900, Israel. 2.  1.  2. 1. Two-level system: pump and probe.

melanie-ashley
Download Presentation

A.D. Wilson-Gordon, H. Shpaisman and H. Friedmann, Department of Chemistry, Bar-Ilan University,

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. EFFICIENT PARAMETRIC AMPLIFICATION IN DOUBLE  SYSTEMS IN THE ABSENCE OF TWO-PHOTON MAXIMAL COHERENCE A.D. Wilson-Gordon, H. Shpaisman and H. Friedmann, Department of Chemistry, Bar-Ilan University, Ramat Gan 52900, Israel

  2. 2 1 2 1 Two-level system: pump and probe • If self-focusing and diffraction balanced, Gaussian pump propagates as a spatial soliton • If pump-induced cross focusing of probe balanced by diffraction, the weak probe propagates as if it is a spatial soliton • If pump is sufficiently intense, radiation generated at FWM frequency • Parametric amplification between probe and FWM via the pump • Process occurs over many diffraction lengths: EIPM important

  3. Self-focusing Nonlinear refractive index Thus Focusing obtained when Self-focusing obtained when laser is detuned to the blue!

  4. Coherent Population Trapping(CPT) 3 2 1 • Fields are equally intense • Population trapped in lower levels • Two-photon coherence is maximal: • Zero absorption

  5. 3 2 1 Electromagnetically Induced Transparency(EIT) • Pump and probe fields • Population optically pumped into state |2> • Two-photon coherence is small

  6. Double  System 4 3 • Several possible configurations • Highly efficient FWM when CPT occurs (Harris) 2 1

  7. Model • Three or four beams with Gaussian transverse intensity profile (GTIP) • Beams copropagate • Assume steady-state • Compare results with plane-wave beams • Cases studied: • CPT with maximal coherence , either initially or on propagation • Four identical beams with 0 and  phase • Three strong fields • Two strong fields • Incoherent pumping from state 2 to 4 (not shown here) • Raman detuning (not shown here)

  8. Maxwell-Bloch Equations Rabi frequency for transition Density matrix element Diffraction length Interaction length Direction of propagation Transverse radial coordinate

  9. Bloch Equations

  10. Notation

  11. Multiphoton Resonance Condition

  12. Analytical Solution Real part – refraction Imag part – absorption FWM Effect of phase: when =0, a=1; when =, a=-1

  13. CPT and Maximal Two-Photon Coherence • When CPT exists, no absorption or focusing or defocusing occurs since (1)=0 • Phase-matching unimportant • Maximum FWM occurs within a propagation distance less than diffraction length • This is completely different from a two-level system

  14. CPT and Maximal Two-Photon Coherence

  15. Transverse Intensity Profile

  16. Comparison: GTIP’s and PW’s

  17. CPT and Maximal Two-Photon Coherence

  18. Transverse Intensity Profile

  19. Comparison: GTIP’s and PW’s

  20. Onset of CPT vs. Maximum Conversion • For detuning , CPT exists at the outset. Maximum conversion of 87% occurs at 0.047. • For detuning , CPT occurs at 0.1, whereas maximum conversion of 73% occurs at 0.009. • Thus, it is possible to get efficient conversion before CPT, without focusing, defocusing or ring formation

  21. CPT and Maximal Two-Photon Coherence

  22. Focusing • Focusing can occur before CPT established • Beams blue-detuned • Nonlinear length sufficiently long • Maximum FWM can still occur within a short propagation distance • Phase-matching still unimportant

  23. Three strong lasers

  24. Initial gain at FWM frequency gain

  25. Focusing Focusing Focusing

  26. Focusing Focusing Focusing Focusing Maximum focusing and conversion

  27. Max Max Comparison: GTIP’s and PW’s

  28. Two strong lasers: strong-weak-strong –weak configuration

  29. Two strong lasers: strong-weak-strong –weak configuration

  30. Two strong lasers: strong-weak-strong –weak configuration

  31. Focusing on propagation

  32. Phase dependence • When field at FWM frequency absent or small at outset, phase is unimportant • When field at FWM frequency present at outset, dramatic phase effects can be obtained

  33. Four Strong Fields: phase 0 vs. 

  34. Zero PhaseNo Change on Propagation: CPT

  35. Four strong fields: phase 

  36. Phase Focusing on propagation: no CPT

  37. Conclusions • Efficient FWM in double lambda systems can be obtained even before CPT occurs • It is obtained at short propagation distances • Focusing can be obtained by blue one-photon detuning • Often accompanied by ring formation

More Related