Abstract
We study modulation instability (MI) of random-phase waves in nonlinear photonic lattices. We find that an incoherent superposition of extended nonlinear eigenstates of the system, that is, an incoherent extended stationary beam, may become unstable due to nonlinearity. The instability process depends on the nonlinearity, on the structure of the diffraction curves of the lattice, as well as on the properties of the beam, whose spectrum can be comprised of Bloch modes from different bands, and from different regions of diffraction (normal/anomalous). This interplay among diffraction, incoherence, and nonlinearity leads to a variety of phenomena, including the possibility of tailoring the diffraction curve of the lattice, or the coherence properties of the beam, to enhance or suppress the instability. We present several examples of such phenomena, including a case where increasing the lattice depth flattens the diffraction curve thereby enhancing the instability, "locking" the most unstable mode to the edge of the 1st Brillouin zone for large nonlinearity, and incoherent MI in self-defocusing media.
Highlights
The nonlinear phenomenon of modulation instability (MI) occurs in diverse physical systems
We study modulation instability (MI) of random-phase waves in nonlinear photonic lattices
The instability process depends on the nonlinearity, on the structure of the diffraction curves of the lattice, as well as on the properties of the beam, whose spectrum can be comprised of Bloch modes from different bands, and from different regions of diffraction
Summary
The nonlinear phenomenon of modulation instability (MI) occurs in diverse physical systems. Our current study of incoherent lattice MI combines the phenomenon of coherent MI in (”discrete”) periodic nonlinear systems [14, 16, 17, 18, 19, 20, 21], and that of incoherent MI in homogeneous nonlinear systems [2, 3, 4, 5, 6, 7, 8, 9, 10, 11] This analysis draws upon recent studies of partially coherent wave dynamics in noninstantaneous nonlinear photonic lattices [22, 23, 24, 25, 26, 27, 28, 29], including the prediction [22] and observation [23] of random-phase lattice solitons, and the possibility of Brillouin-zone (BZ) spectroscopy [24] with incoherent light It is important to emphasize that, even though this study focuses on instability of incoherent beams, some of our conclusions (e.g., Sec. 5) hold generally for both coherent and incoherent MI in continuous nonlinear periodic structures
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