Modulational instability in nonlocal nonlinear Kerr media

We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespectively of the particular profile of the nonlocal response function. For a defocusing nonlinearity the stability properties depend sensitively on the response function profile: for a smooth profile (e.g., a Gaussian) plane waves are always stable, but MI may occur for a rectangular response. We also find that the reduced model for a weak nonlocality predicts MI in defocusing media for arbitrary response profiles, as long as the intensity exceeds a certain critical value. However, it appears that this regime of MI is beyond the validity of the reduced model, if it is to represent the weakly nonlocal limit of a general nonlocal nonlinearity, as in optics and the theory of Bose-Einstein condensates.Comment: 8 pages, submitted to Phys. Rev.

Variational Approach to the Modulational Instability

We study the modulational stability of the nonlinear Schr\"odinger equation (NLS) using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODEs) for the time evolution of the amplitude and phase of modulational perturbations. Analyzing the ensuing ODEs, we re-derive the classical modulational instability criterion. The case (relevant to applications in optics and Bose-Einstein condensation) where the coefficients of the equation are time-dependent, is also examined

Modulation instability induced by cross-phase modulation in a dual-wavelength dispersion-managed soliton fiber ring laser

We report on the observation of modulation instability induced by cross-phase modulation in a dual-wavelength operation dispersion-managed soliton fiber ring laser with net negative cavity dispersion. The passively mode-locked operation is achieved by using nonlinear polarization rotation technique. A new type of dual-wavelength operation, where one is femtosecond pulse and the other is picosecond pulse operation, is obtained by properly rotating the polarization controllers. When the dual-wavelength pulses are simultaneously circulating in the laser ring cavity, a series of stable modulation sidebands appears in the picosecond pulse spectrum at longer wavelength with lower peak power due to modulation instability induced by cross-phase modulation between the two lasing wavelengths. Moreover, the intensities and wavelength shifts of the modulation sidebands can be tuned by varying the power of the femtosecond pulse or the lasing central wavelengths of the dual-wavelength pulses. The theoretical analysis of the modulation instability induced by cross-phase modulation in our fiber laser is also presented.Comment: 26 pages, 10 figure