Tunneling Analog

frustrated total internal reflection (FTIR) - tunneling - barrier penetration

What it shows:
In quantum mechanics, it is possible for a particle to tunnel through a potential barrier because its wave function has a small but finite value in the classically forbidden region. Here we use FTIR as an optical analog of this quantum mechanical phenomenon.

How it works:
A 45°-90° prism will deflect a beam of light by total internal reflection. When two such prisms are sandwiched back-to-back and pressed together, the air-glass interface can be made to vanish and the beam then propagates onward undisturbed. This transition, from total to no reflection, occurs gradually as the air film is made to thin out by progressively squeezing the prisms together harder until they make intimate contact. Optically speaking, if the evanescent wave extends with appreciable amplitude across the rare medium (air) into a nearby medium of higher refractive index (the 2nd prism), energy may flow across the gap (FTIR). 1


This is an entirely qualitative demonstration of barrier penetration. As the air gap between the prisms in the FTIR case is only several wavelengths thick, no attempt is made to measure it. The glass prisms measure 1.5" on the side and are 1" thick. A small vice or clamp is used to squeeze the prisms together, the variable air gap being simply adjusted by the pressure. The light source is a HeNe laser and two mutually perpendicular screens serve as detectors.

Setting it up:
This can be set up on the lecture bench or a separate cart, whichever is more convenient. Obviously the demonstration should be oriented so that the audience can see the laser beam(s) hitting the screen(s). The vise or clamp pushes on the corner edges of the prisms and so care should be taken to protect the glass with some hard rubber or wood - otherwise you will very likely chip or crack a corner off the prism(s)! Also, be sure to clean the contact surfaces of the prisms before sandwiching them together.

Comments:
The hypotenuse faces of the two prisms can be positioned so as to transmit and reflect any desired fraction of the incident light. Commercial devices which perform this function are known as cube beam splitters. A good (and simple) accompaniment to this demonstration is an aquarium full of water. It's not possible to look diagonally through the aquarium (TIR), but pressing ones finger against the glass spoils the total reflection where it makes intimate contact with the glass. On the other hand (no pun intended), TIR is not spoiled in the whorls of the fingerprint which show up silvery (because the glass acts like a mirror there). This demonstrates the rapid (exponential) decrease of the fields in the light waves with distance from the glass. Repeating the demonstration with a wet finger further makes the point. Rather than try to video project all of this, it's better to invite the students to come down after class and experience this firsthand (there goes that pun again). Rating **

References:
H. Georgi, The Physics of Waves, (Prentice Hall, NJ, 1993) pp 276-280
D.D. Coon, Am J Phys 34, 240 (1966). Coon performed the above experiment quantitatively using single photons of light - something more akin to particle barrier penetration!

1 The "appreciable amplitude" must be enough to drive electrons in the "frustrating" medium so that they in turn will radiate waves, permitting energy to flow.