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Abstract We address propagation and entanglement of Gaussian states in optical media characterised by nontrivial spectral densities. In particular, we consider environments with a finite bandwidth $$J(\omega ) = J_0 \left[ \theta (\omega -\Omega ) - \theta (\omega - \Omega - \delta )\right] $$ J ( ω ) = J 0 θ ( ω - Ω ) - θ ( ω - Ω - δ ) , and show that in the low temperature regime $$T\ll \Omega ^{-1}$$ T ≪ Ω - 1 : (i) secular terms in the master equation may be neglected; (ii) attenuation (damping) is strongly suppressed; (iii) the overall diffusion process may be described as a Gaussian noise channel with variance depending only on the bandwidth. We find several regimes where propagation is not much detrimental and entanglement may be protected form decoherence.