Negative frequencies in scattering of pump waves at solitons

• Applicant: Dr. Shalva Amiranashvili
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas ; Mathematics ; Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2017 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 389251150

It is common practice in classical physics to deal with positive frequencies. Surprisingly, recent experiments on wave excitation in different systems revealed a novel feature: the generation of negative-frequency radiation. This concerns in particular observations of electromagnetic waves radiated or scattered by optical solitons in fibers. More precisely, the radiated spectral lines are incompatible with the standard phase-matching conditions. They can only be explained, when the phase-matching conditions are applied to negative frequencies.Any real-valued field can be represented as the sum of two complex envelopes with only positive and only negative frequencies. Only the positive frequency is measured by detectors. It is, however, just the negative-frequency component that, under proper conditions, is emitted by solitons in fibers. This experimental observation raises a number of questions related to (a) our fundamental understanding of classical electrodynamics and (b) to the practical problem of generating new spectral lines. There is a gap in our understanding, especially because the actually observed intensity of the negative-frequency radiation appears to be much larger than expected.The following problems will be addressed within the scope of this proposal.Contrary to the common practice, the complex generalized nonlinear Schrödinger equation (GNLSE) will be replaced by an unidirectional forward Maxwell equation (FME) for the real-valued pulse field. The FME will be formulated in terms of the so-called {\em classical creation-annihilation fields} to attain an in-depth understanding of the resonance excitations with negative frequencies.Selected test problems ranging from propagation of a fundamental soliton to supercontinuum generation will be computed with both GNLSE and FME. Special attention will be given to differences in results due to contribution of negative frequencies.The key experimental finding, Cherenkov radiation at negative frequencies, will be investigated in details numerically. A theory, which quantifies the intensity of the radiation for the FME, will be developed by analogy with the existing theory for the GNLSE. Collaboration with Nail Akhmediev, who pioneered the GNLSE theory of Cherenkov radiation, is planned. In the next step, scattering of dispersive waves at solitons that yields the negative-frequency waves will be investigated both numerically and analytically.In a further step, the theoretical predictions and numerics will be tested in real experiments. Collaboration with Ulf Leonhardt, who measures interactions of dispersive waves and ultrashort solitons, is planned. Here, an ultimate goal is to support the ongoing search for optical analogue of negative-frequency Hawking radiation.

• DFG Programme: Research Grants