  For a transparent projection screen based on metallic nanoparticle's
localized surface plasmon resonance (LSPR), in the ideal case the metallic
nanoparticles dispersed in a transparent matrix only selectively scatter red,
green and blue light and transmit the visible light of other colours. However,
metal's optical loss and size effect at nanoscale degenerate the desired
performance by broadening the resonance peak width and increasing the
absorption ratio. In this work, it is shown that the problem can be solved by
introducing gain material. Numerical simulations are performed on
nanostructures based on silver (Ag), gold (Au) or aluminium (Al) with or
without gain material, to examine the effect of gain material and to search for
suitable structures for sharp selective scattering of red, green and blue
light. And it is found that introducing gain material greatly improves
performance of the structures based on Ag or Au except the structures based on
Al. The most suitable structures for sharp selective scattering of red, green
and blue light are respectively found to be the core-shell structures of
silica@Au, silica@Ag and Ag@silica, all with gain material.
