Collapse events of two-color optical beams

Sukhinin, Alexey; Aceves, Alejandro B.; Diels, Jean‐Claude; Arissian, Ladan

doi:10.1103/physreva.95.031801

Cited by 11 publications

(9 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Third, by engineering the initial phases of the seed components, the maximum intensity can be optimized for the same efficiency. Additionally, following the recent study that found that the total critical intensity for selffocusing might be higher for multicolor beams [40], we expect to find a similar delay in the transverse filamentation instability since the same nonlinear Kerr term is responsible for both effects. Such a delay might enable longer amplification before encountering this transverse instability, making MFBRA even more favorable over SF-BRA.…”

Section: Discussionsupporting

confidence: 62%

Multifrequency Raman amplifiers

Barth

Fisch

2018

Phys. Rev. E

View full text Add to dashboard Cite

In its usual implementation, the Raman amplifier features only one pump carrier frequency. However, pulses with well-separated frequencies can also be Raman amplified while compressed in time. Amplification with frequency-separated pumps is shown to hold even in the highly nonlinear, pump-depletion regime, as derived through a fluid model, and demonstrated via particle-in-cell simulations. The resulting efficiency is similar to single-frequency amplifiers, but, due to the beat-wave waveform of both the pump lasers and the amplified seed pulses, these amplifiers feature higher seed intensities with a shorter spike duration. Advantageously, these amplifiers also suffer less noise backscattering, because the total fluence is split between the different spectral components.

show abstract

Section: Discussionsupporting

confidence: 62%

Multifrequency Raman amplifiers

Barth

Fisch

2018

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…From the linear stability analysis of the system Eqs. (40,41) we obtain that always one of the linear equilibrium solutions is asymptotically stable, and the second always unstable. This fact however, does not guarantee the nonlinear stability of the system all together.…”

Section: Radial Limiting Modementioning

confidence: 69%

“…which has the so-called Townes modes as pulses solutions, if 2σ ≤ 2, [33]. The Townes modes can become stable solitons, [40], in the case of self-focusing NLS solution collapse and if their energy is smaller than the critical energy 2π ∞ 0 rT 2 (r)dr, [33]. In our case, Eq.…”

Section: Spiral Solutions In the Quadratic Approximationmentioning

confidence: 71%

“…The radial mode system of equations in the form Eq. (40,41) is separable, and the resulting PDE for ū(r, t) has a very busy expression…”

Section: Radial Limiting Modementioning

confidence: 99%

“…(72) becomes identical to the DS (or BR) equations. In this ideal case we expect that the spiral solutions, in appropriately chosen system of coordinates become a representation of Townes modes lump-solitons, or rather lump-breathers [33,40].…”

Section: Spiral Solutions In the Quadratic Approximationmentioning

confidence: 99%

See 2 more Smart Citations

Ice Spiral Patterns on the Ocean Surface

Zong¹,

Ludu²

2019

Preprint

View full text Add to dashboard Cite

We investigate a new two-dimensional compressible Navier-Stokes hydrodynamic model design to explain and study large scale ice swirls formation at the surface of the ocean. The linearized model generates a basis of Bessel solutions from where various types of spiral patterns can be generated and their evolution and stability in time analyzed. By restricting the nonlinear system of equations to its quadratic terms we obtain swirl solutions emphasizing logarithmic spiral geometry. The resulting solutions are analyzed and validated using three mathematical approaches: one predicting the formation of patterns as Townes solitary modes, another approach mapping the nonlinear system into a sine-Gordon equation, and a third approach uses a series expansion. Pure radial, azimuthal and spiral modes are obtained from the fully nonlinear equations. Combinations of multiple-spiral solutions are also obtained, matching the experimental observations. The nonlinear stability of the spiral patterns is analyzed by Arnold's convexity method, and the Hamiltonian of the solutions is plotted versus some order parameters showing the existence of geometric phase transitions.

show abstract

Collapse dynamics for two-dimensional space-time nonlocal nonlinear Schrödinger equations

Cole,

Aurko,

Musslimani

2024

Nonlinearity

View full text Add to dashboard Cite

The question of collapse (blow-up) in finite time is investigated for the two-dimensional (non-integrable) space-time nonlocal nonlinear Schrödinger equations. Starting from the two-dimensional extension of the well known AKNS q , r system, three different cases are considered: (i) partial and full parity-time (PT) symmetric, (ii) reverse-time (RT) symmetric, and (iii) general q , r system. Through extensive numerical experiments, it is shown that collapse of Gaussian initial conditions depends on the value of its quasi-power. The collapse dynamics (or lack thereof) strongly depends on whether the nonlocality is in space or time. A so-called quasi-variance identity is derived and its relationship to blow-up is discussed. Numerical simulations reveal that this quantity reaching zero in finite time does not (in general) guarantee collapse. An alternative approach to the study of wave collapse is presented via the study of transverse instability of line soliton solutions. In particular, the linear stability problem for perturbed solitons is formulated for the nonlocal RT and PT symmetric nonlinear Schrödinger (NLS) equations. Through a combination of numerical and analytical approaches, the stability spectrum for some stationary one soliton solutions is found. Direct numerical simulations agree with the linear stability analysis which predicts filamentation and subsequent blow-up.

show abstract

Collapse events of two-color optical beams

Cited by 11 publications

References 15 publications

Multifrequency Raman amplifiers

Multifrequency Raman amplifiers

Ice Spiral Patterns on the Ocean Surface

Collapse dynamics for two-dimensional space-time nonlocal nonlinear Schrödinger equations

Contact Info

Product

Resources

About