Wave-Wave Interactions: Wave interference- coherence

Waves created in a laboratory typically do not form an infinitely long sine function. The length over which a wave forms a coherent sine function with a well-defined phase is called the coherence length. One can think of a wave produced in a laboratory, for example the electro-magnetic wave produced by a laser, as a series of coherent pulses with lengths given by the coherence length, where the phase within one pulse is constant, but can jump randomly when going from one pulse to the next. If one moves an integer number of wavelengths within a coherent pulse one is sure to find oneself at the same part of the waveform. On the other hand, if one moves more than one coherence length within the wave, one cannot be sure of where one will be on the wave even if the move is an integer number of wavelenegths.

  The coherence length is critical in determining whether interference will take place. In the applet below, a single wave composed of a series of coherent pulses is split into two. One of the beams is delayed by a delay generator ( a material with high index of refraction placed in the beam path, or an extra path length produced by mirrors). The beams recombine at the right side of the screen. The delay generator produces an effective path difference between the top and bottom waves, which shifts them with respect to each other. Notice that when the path difference is less than one coherence length, the waves from the same pulses interfere and one can get perfect interference (e.g., always constructive or always destructive). One the other hand when the path difference is greater than the coherence length, one is interfering pulses that have random phase differences and therefore the interference can vary from constructive to destructive as the waves move to the right. In this case, the light can be treated as incoherent and the the intensities, rather than the electric fields add.

  In the applet below, try varying the path difference for the two waves when the coherence length is long. Adjust the path length so that you get destructive interference and not that each pulse pair interferes destructively despite the fact that the phase jumps randomy between adjacent pulses. Now try shortening the coherence length and increasing the path difference. Notice that uncorrelated pulse pairs aare now interfereing with each other and that it is impossible to get interference that is always destructive. For some pairs the interference is destructive, for others it is cinstructive, so over time there is no coherent interference.

Use the above simulation to answer the questions in the pop-up window quiz.