Reflectionless Tunnelling of Light in Gradient Optics

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.