1. School of Physics & Astronomy University of Southampton Light and Matter Controlling light with light Tim Freegarde

2. is a tensor of rank • potential is anharmonic for large displacements Optical nonlinearity • restoring force is nonlinear function of displacement • polarization consequently varies nonlinearly with field

3. consider with • exploit the nonlinear susceptibility Electro-optic effect • nonlinearity mixes static and oscillatory fields • Pockels (linear) and Kerr (quadratic) effects

4. in non-centrosymmetric materials, dominates • nonlinearity mixes static and oscillatory fields Pockels (linear electro-optic) effect • applying intrinsic permutation symmetry,

5. in centrosymmetric materials, • nonlinearity mixes static and oscillatory fields Kerr (quadratic electro-optic) effect • applying intrinsic permutation symmetry,

6. where • consider strong field • again exploit the nonlinear susceptibility Second harmonic generation • distortion introduces overtones (harmonics)

7. incident field: fundamental • new frequency: second harmonic Second harmonic generation • constant component: optical rectification • generated intensities depend upon square of fundamental intensity • focussed and pulsed beams give higher conversion efficiencies • non-centrosymmetric materials required

8. the harmonic polarization need not be parallel to , • if the fundamentalfield contains differently polarized components Second harmonic generation then the harmonic field contains their products

9. where • if the fundamentalfield contains different frequency components Sum and difference frequency generation then the harmonic field contains their products

10. voltage applied to crystal controls birefringence and hence retardance Pockels cell • mounted between crossed linear polarizers • longitudinal and transverse geometries for modulation field polarizer • allows fast intensity modulation and beam switching polarizer modulation voltage

11. bias Pockels cell to transmission Sideband generation Pockels cell • add r.f. field to modulate transmitted intensity • transmitted field contains sum and difference frequency sidebands

12. combines in pairs, to produce sums and differences energy e.g. • fields may be at optical, radio or quasistatic frequencies Harmonic generation • higher terms in susceptibility may combine more frequencies • frequency tripling, quadrupling • high harmonic generation • total photon energy conserved:

13. for contributions to emerge in phase, • choose opposite polarizations for and Phase matching • transit time through crystal • harmonic beam is superposition of contributions from all positions in crystal • use birefringence to offset dispersion • conservation of photon momentum

14. B • optical properties may also be influenced by magnetic fields Faraday (magneto-optic) effect • consider effect of longitudinal field upon bound electrons • induced circular birefringence, characterized by Verdet constant magneto-optical glass • non-reciprocal

15. Quantum description of atomic polarization x/a0 x/a0 • electron density depends upon relative phase of superposition components

16. B Faraday optical isolator • 45º rotation in permanent magnetic field • optical ‘diode’ passes incident light but rejects reflection polarizer magneto-optical glass polarizer • http://physics.nadn.navy.mil/physics/faculty/mungan/scholarship/FaradayIsolators.pdf