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We employ the formal analogy between quadratic and nonlocal solitons to investigate analytically the properties of solitons and soliton bound states in second-harmonic generation in the regime of negative diffraction or dispersion of the second harmonic. We show that in the nonlocal description this regime corresponds to a periodic nonlocal response function. We then use the strongly nonlocal approximation to find analytical solutions of the families of single bright solitons and their bound states in terms of Mathieu functions.
Original languageEnglish
JournalPhysical Review A (Atomic, Molecular and Optical Physics)
Publication date2012
Volume86
Journal number2
Pages023849
Number of pages10
ISSN1050-2947
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 3

Keywords

  • Diffraction, Solitons
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