Dissipative solitons with a Lagrangian approach

Ankiewicz, Adrian; Akhmediev, Nail; Devine, Natasha

doi:10.1016/j.yofte.2006.12.001

Cited by 50 publications

(30 citation statements)

References 21 publications

(31 reference statements)

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“…The phase factor is accounted for in the θ term and, as shown below, can predict the observed behavior of the solutions to a reasonable extent. The standard variational approach for systems with dissipative terms can be modified as [43,45] d dz…”

Section: Variational Approachmentioning

confidence: 99%

Nonlocal gap solitons inPT-symmetric periodic potentials with defocusing nonlinearity

Jisha

Alberucci²,

Brazhnyi

et al. 2014

Phys. Rev. A

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Existence and stability of PT -symmetric gap solitons in a periodic structure with defocussing nonlocal nonlinearity are studied both theoretically and numerically. We find that, for any degree of nonlocality, gap solitons are always unstable in the presence of an imaginary potential. The instability manifests itself as a lateral drift of solitons due to an unbalanced particle flux. We also demonstrate that the perturbation growth rate is proportional to the amount of gain (loss), thus predicting the observability of stable gap solitons for small imaginary potentials.

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Section: Variational Approachmentioning

confidence: 99%

Nonlocal gap solitons inPT-symmetric periodic potentials with defocusing nonlinearity

Jisha

Alberucci²,

Brazhnyi

et al. 2014

Phys. Rev. A

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“…The effect of dissipative factors can be taken into account using the Ritz-Kantorovich method [51][52][53][54] when the reduced Euler-Lagrange equations are driven by a dissipative "source" [52]:…”

Section: Perfectly Saturable Absorbermentioning

confidence: 99%

“…The most famous and studied one is based on the complex nonlinear Ginzburg-Landau equation which can be treated as a dissipative extension of the nonlinear Schrödinger equation [45]. 2 A very productive approach to the study of this class of equations is based on the so-called variational approximation (VA) [49][50][51]. The non-dissipative effects can be described by the Lagrangian density:…”

Section: Introductionmentioning

confidence: 99%

Theory of Laser Energy Harvesting at Femtosecond Scale

Калашников¹

2018

High Power Laser Systems

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Energy scaling of femtosecond laser pulses has a lot of applications in nanoscale micromachining, precision time-resolution spectroscopy, high-harmonic generation, surgery, etc. Besides applied sciences and technology, there are fundamental applications of energy harvesting at femtosecond scale. In particular, it is possible to study and control intra-atom and molecular dynamics at attosecond level as well as to map the quantum processes directly with unprecedented spatial and temporal resolution. This "mesoscopic" union of classical and quantum phenomena provides with new insights into fundamental issues of quantum mechanics of open systems including possible application in the field of quantum computing. In this work, we consider a theory of femtosecond pulse energy harvesting using the dissipative soliton generation in both solid-state and fiber mode-locked lasers and the femtosecond pulse enhancement in an external resonator. The femtosecond pulse energy, width, and spectrum scaling laws are presented in the explicit and physically meaningful form.The second approach is based on the energy storing in an external high-Q resonator (so-called enhancement resonator, ER) coupled synchronously with a femtosecond pulse oscillator [26][27][28]. This simple idea faces difficulties when it is realized on a femtosecond scale because nonlinear effects and group-delay dispersion (GDD) tend to destroy a synchronization between a laser and ER. These issues will be outlined, and some modifications of ER technique will be proposed. DS energy scalingThe DS energy and width scaling are connected closely with a duality between amplification of the maximum number of laser modes and simultaneous spectral condensation, i.e., the concentration High Power Laser Systems

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“…Most powerful approaches to the theory of DSs have been developed in the framework of approximated techniques (for review see [44]): AM [165,167,[217][218][219][220][221], VA [77,177,[222][223][224]225] and MM [175,210,222,226]. The most impressive results obtained are: (i) physically relevant representation of DS parametric space was revealed (it is a so-called master diagram, see [44] for review and Figure 10); (ii) such a representation allows understanding the structural properties of DS and its energy-scaling laws (i.e.…”

Section: Fiber Lasermentioning

confidence: 99%

Dissipative Solitons in Fibre Lasers

Калашников¹,

Sergeyev²

2016

Fiber Laser

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Iσωeχdiψcipliσaχy cτσcepω τf diψψipaωive ψτliωτσ iψ uσfτlded iσ cτσσecωiτσ wiων ulωχafaψω fibχe laψeχψ. Tνe diffeχeσω mτde-lτckiσμ ωecνσiqueψ aψ well aψ expeχimeσωal χealizaωiτσψ τf diψψipaωive ψτliωτσ fibχe laψeχψ aχe ψuχveyed bχiefly wiων aσ empνaψiψ τσ ωνeiχ eσeχμy ψcal-abiliωy. "aψic ωτpicψ τf ωνe diψψipaωive ψτliωτσ ωνeτχy aχe elucidaωed iσ cτσσecωiτσ wiων cτσcepωψ τf eσeχμy ψcalabiliωy aσd ψωabiliωy. Iω iψ ψντwσ ωνaω ωνe paχameωχic ψpace τf diψψi-paωive ψτliωτσ νaψ χeduced dimeσψiτσ aσd cτmpaχaωively ψimple ψωχucωuχe ωνaω ψimplifieψ ωνe aσalyψiψ aσd τpωimizaωiτσ τf ulωχafaψω fibχe laψeχψ. Tνe maiσ deψωabilizaωiτσ ψceσaχiτψ aχe deψcχibed aσd ωνe limiωψ τf eσeχμy ψcalabiliωy aχe cτσσecωed wiων impacω τf τpωical ωuχ-buleσce aσd ψωimulaωed Ramaσ ψcaωωeχiσμ. Tνe faψω aσd ψlτw dyσamicψ τf vecωτχ diψψipa-ωive ψτliωτσψ aχe expτψed.Keywords: Ulωχafaψω fibχe laψeχ, mτde-lτckiσμ, diψψipaωive ψτliωτσ, στσ-liσeaχ dyσamicψ, vecωτχ ψτliωτσψ, τpωical ωuχbuleσce, ψωimulaωed Ramaσ ψcaωωeχiσμ . IntroductionOveχ ωνe laψω decadeψ, ulωχafaψω fibχe laψeχ ωecνστlτμieψ νave demτσψωχaωed a χemaχkable pχτμχeψψ. "y defiσiωiτσ [ -], ωνeψe ωecνστlτμieψ cτσceχσ μeσeχaωiτσ, maσipulaωiτσ aσd applicaωiτσ τf τpωical pulψeψ fχτm a fibχe laψeχ τχ a laψeχ-amplifieχ ψyψωem wiων i peak pτweχ P 0 exceediσμ ψubψωaσωially aσ aveχaμe laψeχ pτweχ P ave aσd ii pulψe widωνψ wνicν aχe mucν leψψeχ ωνaσ a laψeχ χτuσd-ωχip peχiτd T. Sucν a defiσiωiτσ caσ be χe-iσωeχpχeωed iσ ωeχmψ τf a laψeχ mτde-ρτcπiσμ, wνicν meaσψ a pνaψe-lτcked iσωeχfeχeσce τf ωνe M laψeχ eiμeσmτdeψ pχτduciσμ aσ equidiψωaσω ωχaiσ τf ulωχaψντχω pulψeψ. Tνeσ, ∝ /M M iψ a σumbeχ τf lτcked eiμeσmτdeψ aσd iψ aσ iσωeχ-mτde fχequeσcy iσωeχval defiσed by T ∝ / aσd P 0 ∝ MP ave [ , ]. Iω meaσψ ωνaω a mτde-lτcked laψeχ μeσeχaωeψ a cτmb τf equidiψωaσω τpωical fχequeσcieψ cτmpχiψiσμ ωνe bχτad ψpecωχal χaσμe ∆ ∝ M . Iω iψ cleaχ ωνaω ωνe ψubψωaσωial eσνaσcemeσω τf P 0 by ωνe facωτχ τf M ∝ / ~ ÷ , i.e. upωτ τveχ-MW level [ , ] aσd -χeducωiτσ ~T/M, © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. [ , ]. Tνe exωχaτχdiσaχy peak pτweχψ iσ cτmbiσaωiτσ wiων ωνe dχaψωic pulψe widων decχeaψe bχiσμ ωνe νiμν-field pνyψicψ τσ ωableωτpψ τf a mid-level uσiveχψiωy lab [ -]. Mτχeτveχ, ωνe τveχ-MHz pulψe χepeωiωiτσ χaωeψ pχτvide ωνe ψiμσal χaωe impχτvemeσω facωτχ τf ÷ iσ cτmpaχiψτσ wiων ωνaω τf claψψical cνiχped-pulψe amplifieχψ [ ]. "ψ a χeψulω, ωνe ψiμσal-ωτ-στiψe χaωiτ eσνaσceψ ψubψωaσωially, aψ well."στωνeχ aψpecω τf ωνe ulωχafaψω laψeχ applicaωiτσψ iψ cτσσecωed wiων ψωudyiσμ στσ-liσeaχ pνeστmeσa [ ]. Ulωχafaψω laψeχψ became aσ effecωive plaωfτχm fτχ iσveψωiμaωiτσ τf μeσeχal στσ-liσeaχ pχτceψψeψ ψucν aψ iσψωabiliωieψ aσd χτμue waveψ [ , ], ψelf-ψimilaχiωy [ ] aσd ωuχbu-leσce [ ]. " cτνeχeσω ψelf-τχμaσizaωiτσ iσ ψucν στσ-liσeaχ ψyψωemψ [ , ] iψ ωνe keyψωτσe τ...

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Dissipative solitons with a Lagrangian approach

Cited by 50 publications

References 21 publications

Nonlocal gap solitons inPT-symmetric periodic potentials with defocusing nonlinearity

Nonlocal gap solitons inPT-symmetric periodic potentials with defocusing nonlinearity

Theory of Laser Energy Harvesting at Femtosecond Scale

Dissipative Solitons in Fibre Lasers

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