If a diode or directional coupler is fitted at the outer ends of the elements of a dipole, would this stop current reflected from the ends and so result in no standing wave on the antenna ? It can't be otherwise someone would have already thought of this. Why wouldn't this work ?
Any change in impedance at the end of a wire, different from the rest of a transmission-line-like wire, will reflect some current.
An impedance matched resistor at the ends of a dipole won't reflect a current wave, but will be highly lossy, which for an dipole antenna, is usually considered not working well. One usually wants EM radiation, not thermal radiation.
There are a number of problems with this idea.
Firstly, diodes have two terminals. The end of a dipole is just one wire. How would you even connect a diode at the end?
Also, the current at the very end of the dipole is zero. The defining property of a diode is it rectifies current, but there's no current at the end, so exactly what would the diode do? (Assuming you could even place a diode at the end, which you can't, because at a minimum the diode has a lead which acts as a little extension of the dipole beyond the diode.)
And then, rectifying your signal will introduce terrible harmonic distortion, if somehow you manage it. This is pretty undesirable in most antennas.
Directional couplers have similar problems to diodes in that it's unclear how you'd even connect them at the end of a dipole. Worse, a directional coupler has eight terminals (four ports with two terminals each) but you still only have one thing to connect.
Finally directional couplers don't separate waves going one way from the other way, which is I think what you are hoping would happen.
If you wanted an antenna with no standing waves, there is however a way to do it: make it infinitely long. In an infinitely long dipole the wave would just keep traveling down the unending wire until it had lost all its energy to radiation, and there would be no standing wave. Usefully, it would also have infinite bandwidth.
Of course infinite length is a pretty tall order, however for some microwave antennas we can settle for "long enough". For one practical application of the idea, see the infinite balun.