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

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

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

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

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

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

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

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

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

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

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

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

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

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

15 Quantum description of atomic polarization x/a 0 electron density depends upon relative phase of superposition components

16 Faraday optical isolator optical ‘diode’ passes incident light but rejects reflection polarizer magneto-optical glass B 45º rotation in permanent magnetic field