Real-analytic diffeomorphisms with homogeneous spectrum and disjointness of convolutions

On any torus $\mathbb{T}^d$, $d \geq 2$, we prove the existence of a real-analytic diffeomorphism $T$ with a good approximation of type $\left(h,h+1\right)$, a maximal spectral type disjoint with its convolutions and a homogeneous spectrum of multiplicity two for the Cartesian square $T\times T$. The proof is based on a real-analytic version of the Approximation by Conjugation-method.