For complete spherical concentration of light the maximum theoreticall
y possible total energy density for a given power input can be, in pri
nciple, achieved by appropriate choice of polarization and angular amp
litude variation. Illumination of a focusing system with a plane-polar
ized wave creates at the focus equal electric and magnetic energy dens
ities. By appropriate choice of radial variation this energy density c
an be maximized. For hemispherical concentration the electric energy d
ensity can be seven sixteenths of the maximum possible for a given pow
er input, and the total energy density can be seven eighths of the max
imum possible. Focusing by optical systems satisfying the sine conditi
on amongst others is also considered. For a system satisfying the sine
condition, the total energy density can be 64/75 of the maximum possi
ble.