  We theoretically investigate second harmonic generation that originates from
the nonlinear, magnetic Lorentz force term from single and multiple apertures
carved on thick, opaque metal substrates. The linear transmission properties of
apertures on metal substrates have been previously studied in the context of
the extraordinary transmission of light. The transmission process is driven by
a number of physical mechanisms, whose characteristics and relative importance
depend on the thickness of the metallic substrate, slit size, and slit
separation. In this work we show that a combination of cavity effects and
surface plasmon generation gives rise to enhanced second harmonic generation in
the regime of extraordinary transmittance of the pump field. We have studied
both forward and backward second harmonic generation conversion efficiencies as
functions of the geometrical parameters, and how they relate to pump
transmission efficiency. The resonance phenomenon is evident in the generated
second harmonic signal, as conversion efficiency depends on the duration of
incident pump pulse, and hence its bandwidth. Our results show that the
excitation of tightly confined modes as well as the combination of enhanced
transmission and nonlinear processes can lead to several potential new
applications such as photo-lithography, scanning microscopy, and high-density
optical data storage devices.
