  We combine lossless, phase-only transformations with fully-transmitting
linear-optical scatterers to define the principle of linear-optical phase
amplification. This enables a physical phase shift $\phi$ to be nonlinearly
mapped to a new space $\gamma(\phi)$ using linear optics, resulting in a
completely general and enhanced phase shifter that can replace any standard
one. A particular phase amplifier is experimentally realized, allowing the
phase enhancement parameter $d\gamma/d\phi$ to be continuously tuned. Placing
this enhanced phase shifter in one arm of a Mach-Zehnder interferometer led to
an intensity-phase slope more than twenty times steeper than what can be
obtained with its unamplified counterpart.
