Second harmonic generation (SHG) based on a quadrupole effect in photonic-crystal slabs (PCSs) consisting of centrosymmetric materials is presented. The results show that SHG occurs when the pump mode with an asymmetric electromagnetic field distribution is coupled with the eigenmode of the PCS. Theoretical and experimental studies also show that the phase match condition can be achieved without resorting to birefringence or a quasi-phase-match condition when two conditions coincide: the fundamental mode and the second harmonic mode are the eigenmodes of the PCS, and they can be excited simultaneously by tuning the dispersion curves so that they cross by changing the thickness of the waveguide layer. The concept of the asymmetry of the electromagnetic field spatial mode can be used in a microcavity to obtain harmonic generation.
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