Negative Frequencies Get Real
Date: Monday, June 18, 2012 @ 22:47:16 GMT
Topic: Science

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...

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