From APS-Physics/by Fabio Biancalana: A new resonant emission component from solitons that had been ignored has now been identified and studied.
A soliton is a localized “lump” of light that is the product of wave
effects in a nonlinear medium and can, under certain conditions, emit
low-intensity, positive frequency resonant radiation in its wake, due to
the phase matching between its momentum and the dispersion of the
medium itself. Writing in Physical Review Letters,
Eleonora Rubino at the University of Insubria in Como, Italy, and
collaborators have discovered that there should be a negative frequency
counterpart of this resonant emission, which they have identified
experimentally in two different systems...
...
It is the usual practice when dealing with the classical Maxwell
equations, to assume that only positive frequencies have an acceptable
physical meaning. When the soliton dispersion (which is basically a
straight line with a slope proportional to its velocity) and the fiber
dispersion (which is a rather complicated curve) are phase matched at
positive frequencies, positive
resonant radiation is produced, which is the one that most people
observe in experiments. However, there is no particular reason why we
have to restrict our attention to positive frequencies only, since any
electromagnetic wave is a real field, and thus it is the sum of a field
with positive frequencies and its complex conjugate field, and therefore
possesses negative frequencies.
This simple reasoning leads to a phase matching between
the soliton and the negative frequency part of the fiber dispersion, and
the curious, but logical, consequence is that this phase matching is
asymmetric, and so leads to the generation of a new resonant radiation
peak at a frequency that is not mirror symmetric with its positive
energy counterpart.
Any physical electric field is a real function, and
therefore can be expressed as a sum of two complex functions (called
envelopes), which are conjugates of each other. If the first complex
function contains only positive frequencies, the second must contain
only negative ones. These two pieces always come together, and thus
negative frequencies have always been thought to be “redundant,” i.e.,
positive and negative frequencies should contain the same physics in
classical electromagnetism. However, the point of Rubino’s work is that
this is not true...
Source article: http://physics.aps.org/articles/v5/68
