Zazen is not simply emptying the mind, or not thinking. It is existing now, in the present, without applying the dualities of good and bad, self and other, to what we experience. The famous zen master Dogen said that to sit meditation is to be enlightened; it is not a process or an experience, it is simply 'being'. This probably all sounds very esoteric and obscure, but it is something that is beyond the scope of words and concepts, and I have to resort to re-hashed cliches found in the hundreds of books on zen.
There
are strong links between zen and the samurai. They adopted it because of its non-attached, non-materialistic approach that allowed them to face death with indiference, and because it developed
joriki, or single pointed concentration, vital for success in martial arts and on the battlefield. This concentrated state of mind also fostered the other zen arts practised by the samurai such as calligraphy, painting and the tea ceremony.
So, in response to PeterR, zazen actually is about developing mental focus, and this is done not by emptying the mind, but by reducing the mental 'static' of thousands of thoughts, emotions and experiences stored up during life. I'm not sure where you got the idea that zen and budo are unconnected, because the opposite is true. Hope this clears things up, or at least encourages discussion.