  We analyse the optical (or microwave) tunnelling properties of
electromagnetic waves passing through thin films presenting a specific index
profile providing a cut-off frequency, when they are used below this frequency.
We show that contrary to the usual case of a square index profile, where
tunnelling is accompanied with a strong attenuation of the wave due to
reflection, such films present the possibility of a reflectionless tunnelling,
where the incoming intensity is totally transmitted.
