Quadratic solitons with gain and loss

Torner, Lluís; Dorring, J.; Torres, Juan P.

doi:10.1109/3.784596

Cited by 4 publications

(1 citation statement)

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“…Among the patterns, localized pulses are especially interesting. While the theory of pulses in various 1D models of the GL type was well elaborated [40][41][42][43], much less is known about 2D localized patterns (2D pulses). In order to make the pulses stable, it is first of all necessary to stabilize its zero background (trivial solution to the GL equation), which can be done within the framework of the CQ GL equation [7][8][9][10][11][12]41], or a model linearly coupling a cubic GL equation to a linear dissipative one [10].…”

Section: Spinning Solitons In Dissipative Cubic-quintic Nonlinear Mediamentioning

confidence: 99%

Spinning solitons in cubic-quintic nonlinear media

2001

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Section: Spinning Solitons In Dissipative Cubic-quintic Nonlinear Mediamentioning

confidence: 99%

Spinning solitons in cubic-quintic nonlinear media

2001

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Robustness of quadratic solitons with periodic gain

Torner

Torres

Bang

2000

Optics Communications

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We address the robustness of quadratic solitons with periodic non-conservative perturbations. We find the evolution equations for guiding-center solitons under conditions for second-harmonic generation in the presence of periodic multi-band loss and gain. Under proper conditions, a robust guiding-center soliton formation is revealed.Multicolor optical soliton formation mediated by cascading of quadratic nonlinearities has been demonstrated experimentally during the last few years in a variety of geometries and frequency-mixing processes, in settings for spatial, temporal and spatio-temporal trapping of light. 1Soliton signals exist in particular in the process of secondharmonic generation (SHG) that is addressed here, where solitons form in waveguides and in bulk crystals by the mutual trapping between the fundamental frequency and second-harmonic waves. Multidimensional soliton families exist above a threshold light intensity for all values of the phase-mismatch between the waves, and most of such solitons have been shown to be dynamically stable under propagation with the equations that model the ideal light evolution under conditions of focused and pulsed SHG. Adiabatic soliton decay and amplification in the presence of weak loss or gain, have been also studied. 2−4In this Letter we address the robustness of quadratic solitons against strong, but periodic non-conservative perturbations. To start the program we consider soliton formation in the presence of multi-frequency losses and large, but rapidly-varying periodic gain. Our goal is to derive the corresponding guiding-center evolution equations and to expose the robustness of the existing solitons under proper conditions. We believe that the results reported bear a generic fundamental interest to the robustness of quadratic soliton formation in structures with periodic non-conservative perturbations. Moreover, they might find direct applications in reduced models of multi-color laser systems with intracavity frequency generation, including self-frequency doubling schemes, operating in the solitonic regime. 5,6Here the focus is on solitons formed in one-dimensional structures under conditions for non-critical type I SHG, but the analysis can be extended to different physical settings. The evolution of the slowly-varying envelopes of the light waves in the presence of multi-frequency band loss and periodic gain can be described by the reduced equationswhere a 1 and a 2 are the normalized amplitudes of the fundamental frequency (FF) and second-harmonic (SH) waves. In the case of spatial solitons, α 1 = −1, and α 2 = −k 1 /k 2 ≃ −0.5, where k ν , with ν = 1, 2 are the linear wave numbers at both frequencies. In the case of temporal solitons, α ν stand for the ratio between the group-velocity-dispersions existing at both frequencies. The transverse and longitudinal coordinates are normalized to the beam or pulse width and to the diffraction or dispersion length at the fundamental frequency, respectively. The parameter β is the scaled phase mismatch, and Γ ν (ξ) ...

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