Light waves interfering at a beam splitter
The applet below gives a pictorial representation of how light behaves at a beam splitter. We have included extra phase changes to the light entering and emerging from the beam splitter to simplify matters. These phase changes can be incorporated into fine adjustment of the optical path lengths of the light before and after the beam splitter. The end result is that light coming down from the top can be thought of as being transmitted and reflected in phase, whereas the light coming from the left is transmitted in phase but reflected with a 180o phase shift.
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Light (red wave) is travelling from the left to the beam splitter. 50% of this light is reflected down the page with a 180o phase shift and the rest is transmitted through the beam splitter in phase. Light (red wave) is also travelling down from the top. Again, 50% is reflected to the right and the rest is transmitted through the beam splitter, both in phase. The reflected and transmitted waves interfere and the result is shown as the blue waves.
Move the slider to set the phase of the vertical red wave. Look at what happens when the phase is set to 0o. The waves travelling downwards interfere destructively and so no light emerges in that direction. In contrast, the waves travelling to the right interfere constructively and so all the light emerges in that direction.
Now look at what happens when the phase is set to 180o. All the light emerges downwards.
Phase changes and the resulting constructive and destructive interferences are used to perform quantum calculations in the quantum search algorithm.