Recurrent nonlinear modulational instability via down-conversion in quadratic media
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917057789952000 |
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| author | Armaroli, Andrea Ferraresi, Simone Bellanca, Gaetano Malaguti, Stefania Baronio, Fabio Trillo, Stefano |
| author_facet | Armaroli, Andrea Ferraresi, Simone Bellanca, Gaetano Malaguti, Stefania Baronio, Fabio Trillo, Stefano |
| contents | We investigate the induced modulation instability in second-harmonic generation beyond the early stage of the linearized growth of the modulation. We find a regime of recurrence (quasi-periodic conversion and back-conversion between the pump and the modulation) which is genuine of the parametric conversion process in quadratic media. Such recurrence is mainly driven by a process of non-degenerate downconversion, showing no analogy to the cascading regime which mimics the cubic (Kerr) nonlinearities. We consider two different steady states, i.e., a pure second-harmonic and a mixed fundamental/second-harmonic state. Both exhibit this dynamics, which we show to be amenable to a description in terms of reduced frequency-truncated models. The comparison with full numerical simulations of the starting model prove the validity and robustness of the reduced models in characterizing in a simple and elegant way a wide range of modulationally-unstable steady states. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_01983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Recurrent nonlinear modulational instability via down-conversion in quadratic media Armaroli, Andrea Ferraresi, Simone Bellanca, Gaetano Malaguti, Stefania Baronio, Fabio Trillo, Stefano Optics Pattern Formation and Solitons We investigate the induced modulation instability in second-harmonic generation beyond the early stage of the linearized growth of the modulation. We find a regime of recurrence (quasi-periodic conversion and back-conversion between the pump and the modulation) which is genuine of the parametric conversion process in quadratic media. Such recurrence is mainly driven by a process of non-degenerate downconversion, showing no analogy to the cascading regime which mimics the cubic (Kerr) nonlinearities. We consider two different steady states, i.e., a pure second-harmonic and a mixed fundamental/second-harmonic state. Both exhibit this dynamics, which we show to be amenable to a description in terms of reduced frequency-truncated models. The comparison with full numerical simulations of the starting model prove the validity and robustness of the reduced models in characterizing in a simple and elegant way a wide range of modulationally-unstable steady states. |
| title | Recurrent nonlinear modulational instability via down-conversion in quadratic media |
| topic | Optics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2511.01983 |