Second harmonic generation

• Driving field at frequency w producing a nonlinear polarisation at frequency 2w

• Polarisation at frequency 2w is given by

• Polarisation at frequency w is given by

deff is an effective nonlinear coefficient that depends on the direction of propagation and polarisation of the fields etc.

• We now assume a steady state (d/dt=0) and a losslesss medium (a=0) to obtain expression for the growth of the field at frequency w and 2w given by

where

• COUPLED WAVE EQUATIONS

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