I am looking into full multigrid, FMG, and several sources, including these slides, that a lot of people are referring to, state that the prolongation operator used in FMG the first time you visit a finer grid should be of higher order than the prolongation operator used otherwise. What is a concrete example of such a higher order operator? For the prolongation in the other steps of multigrid, I use the operator suggested in the slides page 56. 
Full Multigrid Prolongation Operator
interpolation;multigrid