I have an application where I need as large a physical aperture as possible. By physical, I mean actual aperture in mm, not as an f-number. I also need this lens to focus to about 0.5m. I have the 85mm Nikkor f/1.4, which has a diameter of about 60mm, but doesn't focus close enough for me. Sigma have a 180mm f/2.8 macro which should be about 64mm diameter. Is there anything commercially available that is larger?
Astronomy is where large aperture "lenses" are commonly used. Look for "refracting telescope". There are two types: achromatic (not very good for photography) and "APO" or apochromatic (preferred choice but more expensive). The catch is: no AF, not designed for close focusing so the performance may suffer, much darker (f/6, f/7, f/8)