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PHASE MATCHING

PHASE MATCHING. Janez Žabkar Advisers: dr. Marko Zgonik dr. Marko Marinček. Introduction. Motivation Basics of nonlinear optics Birefringent phase matching Quasi phase matching Conclusion. Motivation. An eye-safe laser

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PHASE MATCHING

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  1. PHASEMATCHING Janez Žabkar Advisers: dr. Marko Zgonik dr. Marko Marinček

  2. Introduction • Motivation • Basics of nonlinear optics • Birefringent phase matching • Quasi phase matching • Conclusion

  3. Motivation • An eye-safe laser • Problems with other laser sources (Er:glass – low repetition rates, diode lasers – small peak powers) • Recent progress in growing large nonlinear crystals enables efficient conversion • A basic condition for efficient nonlinear conversion is phase-matching

  4. Nonlinear conversion – second harmonic generation

  5. Nonlinear optical coefficient: d = ε0χ / 2 Nonlinear optics (1) • The wave equation for a nonlinear medium is: • EM field of a strong laser beam causes polarization of material: • Putting in: • We get: • And using:

  6. Nonlinear optics (2) • The phase difference between the wave at ω3 and the waves at ω1, ω2 is: • With the non-depleted pump approximation and condition for conservation of energy: • We obtain:

  7. =1 for ∆k=0 Nonlinear optics (3) • Hence the energy flow per unit area: ∆k=0 ∆k≠0

  8. Birefringent phase matching (1) type-I phase matching for SHG: Polar diagram showing the dependance of refractive indices on propagation direction in a uniaxial, negative birefringent crystal for type-I phase matching.

  9. Birefringent phase matching (2) type-II phase matching for SHG: Polar diagram showing the dependance of refractive indices on propagation direction in a uniaxial, negative birefringent crystal for type-II phase matching.

  10. Poynting vector walk-off

  11. Birefringent phase matching (3) Dispersion in LiNbO3. The extraordinary refractive index can have any value between the curves.

  12. Fundamental field (ω1) lc = π/∆k, coherence length ∆k=k2-2k1 SH field (ω2) radiated by SH polarization SH polarization of the medium (ω2 = 2ω1) Quasi phase matching for SHG Isotropic, dispersive crystal

  13. Nonlinear optical coefficient: d = ε0χ / 2 Periodically poled crystal A schematic representation of periodically poled nonlinear crystal.

  14. growth of the SH field Performance of quasi phase matching Recall: Nonzero elements of tensor d: d11 = - d12 = - d26 d14 = - d25 For ordinary polarization: deff = d11 cos(θ) cos(3φ) For extraordinary polarization: deff = d11 cos2(θ) sin(3φ) + d14 sin(θ) cos(θ) For perfect birefringent PM (∆k=0) and d(z)=deff: Where deff is an effective nonlinear coefficient obtained from tensor d for a certain crystal, direction of propagation and polarization: Nonzero elements of tensor d: d11 = - d12 = - d26 d14 = - d25 Example: QUARTZ

  15. growth of the SH field Since: → We get: the difference to birefringent PM Second harmonic field: Performance of quasi phase matching lc perfect periodically poled structure

  16. Performance of quasi phase matching birefingent PM ∆k=0 QPM ∆k≠0

  17. Some benefits of QPM • The possibility of using largest nonlinear coefficients which couple waves of the same polarizations, e.g. in LiNbO3: • Noncritical phase matching with no Poynting vector walk-off for any collinear interaction within the transparency range • The ability of phase matching in isotropic materials, or in materials which possess too little / too much birefringence

  18. Fabrication of a periodically poled crystal

  19. Conclusion • Phase matching is necessary for efficient nonlinear conversion • Ideal birefringent PM: intensity has quadratic dependence on interaction length • QPM: smaller efficiency than birefringent PM (4/π2 factor in intensity) • Advantages of QPM (larger nonlinear coefficients,...)

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