  The ultra-relativistic outflows powering gamma-ray bursts (GRBs) acquire
angular structure through their interaction with external material. They are
often characterized by a compact, nearly uniform narrow core (with half-opening
angle $\theta_{c,\{\epsilon,\Gamma\}}$) surrounded by material with energy per
unit solid angle ($\epsilon=\epsilon_c\Theta_{\epsilon}^{-a}$, where
$\Theta_{\{\epsilon,\Gamma\}}=[1+\theta^2/\theta_{c,\{\epsilon,\Gamma\}}^2]^{1/2}$)
and initial specific kinetic energy
($\Gamma_0-1=[\Gamma_c-1]\Theta_\Gamma^{-b}$) declining as power laws.
Multi-wavelength afterglow lightcurves of off-axis jets (with viewing angle
$\theta_{\rm obs} > \theta_c$) offer robust ways to constrain $a$, $b$ and the
external density radial profile ($\rho\propto R^{-k}$), even while other burst
parameters may remain highly degenerate. We extend our previous work on such
afterglows to include more realistic angular structure profiles derived from
three-dimensional hydrodynamic simulations of both long and short GRBs
(addressing also jets with shallow angular energy profiles, whose emission
exhibits unique evolution). We present afterglow lightcurves based on our
parameterized power-law jet angular profiles for different viewing angles
$\theta_{\rm obs}$ and $k=\{0,1,2\}$. We identify a unique evolutionary
power-law phase of the characteristic synchrotron frequencies ($\nu_m$ and
$\nu_c$) that manifests when the lightcurve is dominated by emission sensitive
to the angular structure of the outflow. We calculate the criterion for
obtaining single or double peaked light-curves in the general case when
$\theta_{c,\Gamma}\neq\theta_{c,\epsilon}$. We emphasize how the shape of the
lightcurve and the temporal evolution of $\nu_m$ and $\nu_c$ can be used to
constrain the outflow structure and potentially distinguish between magnetic
and hydrodynamic jets.
