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Introduction to Nonlinear Quantum Optics - What, Why, and Where

This course provides an overview of nonlinear optics with a focus on quantum phenomena. Explore the classification of processes, phase matching, and quantum nonlinear optics. Understand how the output is a nonlinear function of the input, typically involving frequency changes. Delve into the equations for nonlinear optics media, including Maxwell equations and assumptions. Learn about second harmonic generation and different types of polarization. Discover energy and momentum conservation principles and explore phase matching in experiments. Dive into quasi-phase matching techniques and their applications in entangled photon sources. This course will enhance your understanding of non-linear optics through comprehensive content and valuable insights.

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Introduction to Nonlinear Quantum Optics - What, Why, and Where

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  1. Non-Linear Optics Quantum optics course 2/27/19 Lior Cohen

  2. Nonlinear optics - what? why? where? Classification of processes Phase matching QUANTUM nonlinear optics Outline

  3. output is nonlinear function of the input usually frequency changes Nonlinear physics

  4. Equations for nonlinear optics media Maxwell equations assumptions

  5. Second harmonic generation w1=w c w2=2w (2) w

  6. Second harmonic generation w c 2w (2) w

  7. Second harmonic generation w c 2w (2) w

  8. Type I – one polarization • Type II – two polarizations Classification of processes w 2w w w 2w w

  9. Collinear (all k-vectors aligned) • Non-collinear Classification of processes w 2w w w 2w w

  10. Energy conservation Phase matching momentum conservation KSignal KIdler KPump

  11. Energy and momentum conservation • Where • The index refraction monotonically increases with frequency. Phase matching - problem

  12. Angular tuning with Birefringence crystal Phase matching - solution no ne

  13. Angular tuning with Birefringence crystal Phase matching - solution w 2w w `

  14. Angular tuning with Birefringence crystal Phase matching - solution no ne

  15. Phase Matching - results Bosenberg, W. R., Pelouch, W. S., & Tang, C. L. App. Phys. Lett. , 55(19), 1952-1954. (1989). ‏

  16. Down conversion c 2w (2) w ? t→-t

  17. QUANTUM!! c 2w (2) w

  18. Equation • Idler (o-pol) • Signal (e-pol) Phase matching – non collinear Type ii

  19. Equation • Idler and pump (o-pol) • Signal (e-pol) Phase matching – non collinear Type ii

  20. Phase matching – experiment (Type ii) No polarizer H polarizer V polarizer ` `

  21. Phase matching – experiment (Type ii)

  22. Part B – quasi phase matching

  23. Second harmonic generation • 1D longitude vs. transverse QPM • 2D QPM • Angular orbital momentum (AOM) • Down conversion • (Quasi) Phase matching • Entangled photon source Outline – quasi phase matching

  24. Phase matching (semantics)

  25. Quasi phase matching Regular crystal Phase matching Modified crystal Quasi phase matching

  26. Quasi phase matching

  27. phase matching A. Arie and N. Voloch, Laser Photon. Rev. 4, 355 (2010).

  28. 1D longitude QPM N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Phys. Rev. Lett. 108, 233902 (2012).

  29. 1D longitude vs. transverse QPM N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Phys. Rev. Lett. 108, 233902 (2012).

  30. Bragg diffraction transverse QPM

  31. Non-linear Bragg diffraction Phase matching: transverse QPM k2w Gn k2w Gn kw kw

  32. Nonlinear Raman-Nath diffraction NL Raman-Nath= NL Bragg with phase mismatch transverse QPM

  33. Nonlinear Raman-Nath diffraction transverse QPM S. M. Saltiel, D. N. Neshev, W. Krolikowski1, A. Arie, O.Bang, and Y. S. Kivshar, Opt. Lett. 34, 848 (2009).

  34. Nonlinear Raman-Nath diffraction transverse QPM S. M. Saltiel, D. N. Neshev, R. Fischer,W. Krolikowski, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).

  35. Nonlinear Raman-Nath diffraction transverse QPM

  36. LiNbO3 Up 82% SFG 2d quasi phase Matching Spot diameter = 150 mm ⇒ I~1012 W/m2 N. G. R. Broderick, G.W. Ross, H. L. Offerhaus,D. J. Richardson, and D. C. Hanna, crystal, Phys. Rev. Lett. 84(19), 4345–4348 (2000).

  37. Angular orbital momentum

  38. 2D QPM – down conversion Real space Reciprocal lattice E. Megidish, A. Halevy, H. S. Eisenberg, A. Ganany-Padowicz, N. Habshoosh, and A. Arie Opt. Express 21, 6689 (2013)

  39. Crystal design Real space Material – LiTaO3 (SLT) Circular motif: A. Arie, N. Habshoosh, and A. Bahabad, “Quasi phase matching in two-dimensional nonlinear photonic crystals,” Opt. Quant. Electron. 39, 361–375 (2007).

  40. 2D QPM – down conversion E. Megidish, A. Halevy, H. S. Eisenberg, A. Ganany-Padowicz, N. Habshoosh, and A. Arie Opt. Express 21, 6689 (2013)

  41. Phase matching– entanglement source b-BaB2O4 BBO crystal pump beam h 1 2 v

  42. 2D QPM path entanglement source Reciprocal lattice E. Megidish, A. Halevy, H. S. Eisenberg, A. Ganany-Padowicz, N. Habshoosh, and A. Arie Opt. Express 21, 6689 (2013)

  43. 2D QPM path entanglement source E. Megidish, A. Halevy, H. S. Eisenberg, A. Ganany-Padowicz, N. Habshoosh, and A. Arie Opt. Express 21, 6689 (2013)

  44. R.W Boyd, Nonlinear optics, 3rd edition , Elsevier (2007) More bibliography

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