  This paper is concerned with uniqueness results in inverse acoustic and
electromagnetic scattering problems with phaseless total-field data at a fixed
frequency. Motivated by our previous work ({\em SIAM J. Appl. Math. \bf78}
(2018), 1737-1753), where uniqueness results were proved for inverse acoustic
scattering with phaseless far-field data generated by superpositions of two
plane waves as the incident waves at a fixed frequency, in this paper, we use
superpositions of two point sources as the incident fields at a fixed frequency
and measure the modulus of the acoustic total-field (called phaseless acoustic
near-field data) on two spheres enclosing the scatterers generated by such
incident fields on the two spheres. Based on this idea, we prove that the
impenetrable bounded obstacle or the index of refraction of an inhomogeneous
medium can be uniquely determined from the phaseless acoustic near-field data
at a fixed frequency. Moreover, the idea is also extended to the
electromagnetic case, and it is proved that the impenetrable bounded obstacle
or the index of refraction of an inhomogeneous medium can be uniquely
determined by the phaseless electric near-field data at a fixed frequency, that
is, the modulus of the tangential component with the orientations $\mathbf
e_\phi$ and $\mathbf e_\theta$, respectively, of the electric total-field
measured on a sphere enclosing the scatters and generated by superpositions of
two electric dipoles at a fixed frequency located on the measurement sphere and
another bigger sphere with the polarization vectors $\mathbf e_\phi$ and
$\mathbf e_\theta$, respectively. As far as we know, this is the first
uniqueness result for three-dimensional inverse electromagnetic scattering with
phaseless near-field data.
