Nano-photonic antennas are one of the key compo- nents in integrated photonic transmitter and receiver systems. Conventionally, grating couplers, designed to couple into an op- tical fiber, suffering from limitations such as large footprint and small field-of-view (FOV) have been used as on-chip antennas. The challenge of the antenna design is more pronounced for the receiver systems, where both the collected power by the antenna and its FOV often need to be maximized. While some novel solutions have been demonstrated recently, identifying fundamental limits and trade-offs in nano-photonic antenna design is essential for devising compact antenna structures with improved performance. In this paper, the fundamental electromagnetic limits, as well as fabrication imposed constraints on improving antenna effective aperture and FOV are studied, and approximated performance upper limits are derived and quantified. By deviating from the conventional assumptions leading to these limits, high-performance multi-mode antenna structures with performance characteristics beyond the conventional perceived limits are demonstrated. Finally, the application of a pillar multi-mode antenna in a dense array is discussed, an antenna array with more than 95% collection efficiency and 170◦ FOV is demonstrated, and a coherent receiving system utilizing such an aperture is presented.