I have a pulse signal that is very short (around a pico second)
How do I extend it to like a 10n sec?
using either digital or analog circuit components

 

There is a circuit called monostable multivibrator that is designed to do this.
However, you do need to tell us what is generating 1ps pulse, the voltage amplitude and impedance of the driver.
I think you want to look at a pulse stretcher circuit based on ECL (emitter coupled logic) design.

 

Picoseconds? A micro-micro second? Are you sure about that? For a rise time in that range you would be looking at 100 GHz. Maybe this belongs in a physics discussion rather than an electronics discussion.