= Phase-conjugate mirror
{title2=$U_{\mathrm{return}}(x,y)=\gamma U_{\mathrm{incident}}(x,y)^*$}
A <phase-conjugate mirror> is an optical device that implements <phase conjugation> at its return surface. It may generate the return using an independently supplied beam, as in <digital optical phase conjugation>; its name specifies the field transformation, rather than a particular reflecting material. Conjugating the transverse <complex amplitude> and launching the returning longitudinal carrier produces the complete reversed <wavevector>. A spatially constant $\gamma$ leaves the shape of the <wavefront> unchanged; a spatially varying $\gamma$ would add its own <wavefront error>.
An ordinary flat mirror obeys the <law of reflection>. At a surface $z=L$, its reflected <plane wave> has <wavevector> $(k_x,k_y,-k_z)$, whereas a <phase-conjugate mirror> returns $(-k_x,-k_y,-k_z)$. Ordinary <specular reflection> preserves the tangential <wavevector>. At normal incidence a single <plane wave> can therefore look identical in the two cases, apart from an overall <wave phase> and strength; oblique incidence or a curved <wavefront> reveals the distinction. In boundary-envelope notation an ideal ordinary mirror multiplies the incident <complex amplitude> by a constant reflection factor $r$, while an ideal <phase-conjugate mirror> returns its <complex conjugate> times $\gamma$.
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