Families of stationary modes in complex potentials.

We show that a general class of complex asymmetric potentials of the form w2(x)-iw(x)(x), where w(x) is a real function, allows for the existence of one-parametric continuous families of the stationary nonlinear modes bifurcating from the linear spectrum and propagating in Kerr media. As an example, we introduce an asymmetric double-hump complex potential and show that it supports continuous families of stable nonlinear modes.