Accelerating solitons in gas-filled hollow-core photonic crystal fibers

Abstract

We found the self-similar solitary solutions of a recently proposed model for propagation of pulses in gas filled hollow-core photonic crystal fibers that includes a plasma induced nonlinearity. As anticipated for a simpler model and using a perturbation analysis, there are indeed stationary solitary waves that accelerate and self-shift to higher frequencies. However, if the plasma nonlinearity strength is large or the pulse amplitudes are small, the solutions have distinguished long tails and decay as they propagate.

Dynamics of blueshifted floating pulses in gas-filled hollow-core photonic crystal fibers

“…The analysis up to this stage may seem very similar to the analysis applied to the more general equation (1) in [6]. Also, the results obtained there could possibly predict the profile characteristics of pulse solutions of (2), however, the shooting calculations with the ODE obtained in [6] and small values of peak amplitudes and plasma strengths would involve Airy function values for large arguments that are not easily evaluated.…”

“…where η = σφ T . Applying the same accelerating variable as in [6], namely, T = τ + a 4 ξ 2 + bξ and q(ξ, τ ) = F (T ) exp(iθ(ξ, T )), with F and θ real, we obtain the ODE for…”

“…On the other hand, for finite |q| th , the use of (5) ξ, expressions that clearly show that the actual dependence of the blueshift process on the peak amplitude is more complex, with both the pulse peak amplitude and the threshold intensity playing an important role in it [6].…”

“…Also, the results obtained there could possibly predict the profile characteristics of pulse solutions of (2), however, the shooting calculations with the ODE obtained in [6] and small values of peak amplitudes and plasma strengths would involve Airy function values for large arguments that are not easily evaluated. Moreover, the present ODE is, for each P th , a one parameter ODE, thus, we may obtain all the amplitudes and accelerations with one run that spans a considerable range of β.…”

“…The model was used by them to predict the extent of frequency blueshifting by means of a perturbation approach. Following these preliminary perturbation results, a thorough study on the existence of accelerating solitons to such a model, including the plasma but also the stimulated Raman scattering term, was performed [6]. There, it was shown that indeed there are self-similar pulse solutions of such model that accelerate while its central frequency blueshifts.…”