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Non-Linear Optics. Quantum optics course 2/27/19. Lior Cohen. Nonlinear optics - what? why? where? Classification of processes Phase matching QUANTUM nonlinear optics. Outline. output is nonlinear function of the input usually frequency changes. Nonlinear physics.
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Non-Linear Optics Quantum optics course 2/27/19 Lior Cohen
Nonlinear optics - what? why? where? Classification of processes Phase matching QUANTUM nonlinear optics Outline
output is nonlinear function of the input usually frequency changes Nonlinear physics
Equations for nonlinear optics media Maxwell equations assumptions
Second harmonic generation w1=w c w2=2w (2) w
Second harmonic generation w c 2w (2) w
Second harmonic generation w c 2w (2) w
Type I – one polarization • Type II – two polarizations Classification of processes w 2w w w 2w w
Collinear (all k-vectors aligned) • Non-collinear Classification of processes w 2w w w 2w w
Energy conservation Phase matching momentum conservation KSignal KIdler KPump
Energy and momentum conservation • Where • The index refraction monotonically increases with frequency. Phase matching - problem
Angular tuning with Birefringence crystal Phase matching - solution no ne
Angular tuning with Birefringence crystal Phase matching - solution w 2w w `
Angular tuning with Birefringence crystal Phase matching - solution no ne
Phase Matching - results Bosenberg, W. R., Pelouch, W. S., & Tang, C. L. App. Phys. Lett. , 55(19), 1952-1954. (1989).
Down conversion c 2w (2) w ? t→-t
QUANTUM!! c 2w (2) w
Equation • Idler (o-pol) • Signal (e-pol) Phase matching – non collinear Type ii
Equation • Idler and pump (o-pol) • Signal (e-pol) Phase matching – non collinear Type ii
Phase matching – experiment (Type ii) No polarizer H polarizer V polarizer ` `
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
Quasi phase matching Regular crystal Phase matching Modified crystal Quasi phase matching
phase matching A. Arie and N. Voloch, Laser Photon. Rev. 4, 355 (2010).
1D longitude QPM N. V. Bloch, K. Shemer, A. Shapira, R. Shiloh, I. Juwiler, and A. Arie, Phys. Rev. Lett. 108, 233902 (2012).
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).
Bragg diffraction transverse QPM
Non-linear Bragg diffraction Phase matching: transverse QPM k2w Gn k2w Gn kw kw
Nonlinear Raman-Nath diffraction NL Raman-Nath= NL Bragg with phase mismatch transverse QPM
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).
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).
Nonlinear Raman-Nath diffraction transverse QPM
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).
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)
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).
2D QPM – down conversion E. Megidish, A. Halevy, H. S. Eisenberg, A. Ganany-Padowicz, N. Habshoosh, and A. Arie Opt. Express 21, 6689 (2013)
Phase matching– entanglement source b-BaB2O4 BBO crystal pump beam h 1 2 v
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)
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)
R.W Boyd, Nonlinear optics, 3rd edition , Elsevier (2007) More bibliography