Numerical modeling of cylindrically symmetric nonlinear self-focusing using an adaptive fast Hankel split-step method

Banerjee, Partha P.; Nehmetallah, George; Chatterjee, Monish Ranjan

doi:10.1016/j.optcom.2004.12.048

Cited by 22 publications

(12 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equations (1,2) and (13) were simulated assuming the cylindrical symmetry of the problem, thus the fast Hankel transform for the space-domain was utilized 31 . For the integration, we used the Euler numerical scheme.…”

Section: Resultsmentioning

confidence: 99%

Influence of tunnel ionization to third-harmonic generation of infrared femtosecond laser pulses in air

Tamulienė

Juškevičiūtė

Buožius

et al. 2020

Sci Rep

View full text Add to dashboard Cite

Here we present an experimental as well as theoretical study of third-harmonic generation in tightly focused femtosecond filaments in air at the wavelength of $$1.5 \,\upmu \hbox {m}$$ 1.5 μ m . At low intensities, longitudinal phase matching is dominating in the formation of 3rd harmonics, whereas at higher intensities locked X-waves are formed. We provide the arguments that the X-wave formation is governed mainly by the tunnel-like ionization dynamics rather than by the multiphoton one. Despite of this fact, the impact of the ionization-induced nonlinearity is lower than the one from bound–bound transitions at all intensities.

show abstract

Section: Resultsmentioning

confidence: 99%

Influence of tunnel ionization to third-harmonic generation of infrared femtosecond laser pulses in air

Tamulienė

Juškevičiūtė

Buožius

et al. 2020

Sci Rep

View full text Add to dashboard Cite

show abstract

“…Specifically, we consider the case of nonlinear propagation of one and two-transverse dimensional beams and three dimensional bullets through NIMs. As in the case of NLS type equations 8,9 , we show that by using an adaptive Fourier Bessel split-step (AFBSS) method and variational techniques 10,11 , nonlinearity management achieved through a periodic variation of the nonlinearity coefficient 11 can stabilize spatial and spatio-temporal solitons.…”

Section: On the Basis Of A Dispersion Relation For A Drude Mediummentioning

confidence: 89%

“…(21) has the same form of a 1 and 2 transverse dimensional solutions which tend to self-focus as they propagate, if the initial power exceeds a critical power c P . This phenomenon has been extensively studied by us10 where we have used an AFBSS (Hankel) transform method to track the signal near the collapse.We can analytically find a solitary wave solution to Eq. (21) by setting assumptionProc.…”

mentioning

confidence: 99%

An adaptive Fourier Bessel split-step method and variational techniques applied to nonlinear propagation in negative index materials

Banerjee

Nehmetallah

2006

SPIE Proceedings

Self Cite

View full text Add to dashboard Cite

Starting from a simple dispersion relation that models negative index materials, we derive and develop the underlying partial differential equation for wave propagation in such a medium. In the first part we study the linear characteristics of wave and beam propagation in NIMs. In the second part we heuristically perform a nonlinear extension of the linear partial differential equation by adding cubic nonlinear terms as in the nonlinear Klein Gordon equation, and (d+1+1)-dimensional envelope solitary wave solutions are derived. Also, using variational techniques and an adaptive Fourier Bessel split-step numerical method, we show that nonlinearity management through a periodic variation of the nonlinearity coefficient helps in stabilization of spatial solitons.

show abstract

“…As in the case of NLS type equations [7], we show that by using an adaptive Fourier Bessel split-step (AFBSS) method [8] and variational techniques [9,10], nonlinearity or diffraction/dispersion management achieved through a periodic variation of the nonlinearity or diffraction/dispersion coefficient [9,10] can stabilize spatial and spatio-temporal solitary waves.…”

Section: Introductionmentioning

confidence: 94%

“…This phenomenon has been extensively studied in Ref. [8] where we used an Adaptive Fast Hankel Split Step transform method to track the signal near the collapse.…”

Section: (1 2+0+1)-dimensional Envelope Solitary Wavesmentioning

confidence: 99%

The effects of dispersion, diffraction, and nonlinearity management in negative index materials

Banerjee

Nehmetallah

2007

Photonic Metamaterials

Self Cite

View full text Add to dashboard Cite

We analyze linear and nonlinear propagation in negative index materials by starting from a dispersion relation and by deriving the underlying partial differential equations (PDEs). Transfer function for propagation is also derived in spatial frequency domain. Using existing numerical methods, based on fast Fourier-Bessel transforms, we study the stability of the solitary wave solutions. Nonlinearity and dispersion management are then incorporated to find stable solutions of the underlying PDEs.

show abstract

Numerical modeling of cylindrically symmetric nonlinear self-focusing using an adaptive fast Hankel split-step method

Cited by 22 publications

References 17 publications

Influence of tunnel ionization to third-harmonic generation of infrared femtosecond laser pulses in air

Influence of tunnel ionization to third-harmonic generation of infrared femtosecond laser pulses in air

An adaptive Fourier Bessel split-step method and variational techniques applied to nonlinear propagation in negative index materials

The effects of dispersion, diffraction, and nonlinearity management in negative index materials

Contact Info

Product

Resources

About