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Multipolar analysis of the second harmonic generated by dielectric particles.

We studied the second harmonic generation (SHG) by two-dimensional dielectric particles made of a centrosymmetric high-index material. The calculated scattered fields at the fundamental and harmonic frequencies are decomposed on a multipolar basis, allowing the evaluation of the relative strengths of the multipolar resonances excited at the particle. With these tools, we studied the strength of the multipoles that produce the second harmonic field and the role played by those excited at the fundamental frequency.