  Let $\Omega \subset \mathbb R^3$ be a waveguide which is obtained by
translating a cross-section in a constant direction along an unbounded spatial
curve. Consider $-\Delta_{\Omega}^D$ the Dirichlet Laplacian operator in
$\Omega$. Under the condition that the tangent vector of the reference curve
admits a finite limit at infinity, we find the essential spectrum of
$-\Delta_{\Omega}^D$. Then, we state sufficient conditions that give rise to a
non-empty discrete spectrum for $-\Delta_{\Omega}^D$; in particular, we show
that the number of discrete eigenvalues can be arbitrarily large since the
waveguide is thin enough.
