We propose a convex optimization approach for an array synthesis pattern to enhance\nthe electromagnetic field in the gap region of a dielectric bow-tie antenna. This method allows the\ninduction of the desired antenna modes by exploiting the concurrent excitation of the structure with\nplane waves with different propagation directions and complex amplitudes. By engineering the\nexcitation coefficients of the array, different modes are excited in the bow-tie antenna and the radiation\npattern of the generated second harmonic (SH) field is modified accordingly. Using our approach,\nwe demonstrate both the feasibility of performing synthesis of the SH radiation pattern in dielectric\nantennas and the possibility of developing innovative sensing applications in photonics.
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