It's common knowledge, expressed more formally in Beer's law, that a pulse of light in a medium dies off exponentially with distance as it is absorbed. But theory predicts this is not quite true. The idea, which dates back almost a century, is quite simple and based on the fact that a sharp pulse of white light has many frequencies. These all go at somewhat different speeds in a medium, and among the various frequencies will be some that can propagate a long way with little loss. This gives rise to "precursors" - signals that get ahead of the main pulse and die away very slowly, falling only with the square root of the distance. Now, Seung-Ho Choi and Ulf Österberg of Dartmouth University, New Hampshire, have observed the first clear example of this effect in laser pulses 540 fs long propagating through 700 mm of water. The work is of interest for many fields including optical imaging of the human body and long-range underwater communications.

Further reading

S-H Choi and U Österberg 2004 Phys. Rev. Lett. 92 193903.