Analysis has been made of the amplitudes of the second and third harmonics when
pumping a discrete frequency to the Josephson-vortex photonic crystal within the
THz range of the electromagnetic spectrum. The results of numerical simulations
show that there are certain resonance frequencies for these harmonics where the
amplitudes are strongly enhanced. The frequencies at which these resonances occur
can be tuned by an applied magnetic field and tilting the material with respect
to the incident radiation. For the second harmonic it has been possible to describe
these resonances analytically with a resonance approximation which displays good
agreement with numerical simulations at and near the resonances.
A similar perturbative method has been used to simulate the nonlinear mixing
of two discrete THz frequencies in the JV photonic crystal, producing
resonances for harmonics at the sum and the difference of these
two input frequencies. This method can allow a high degree of control over the
harmonic frequencies produced.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.