Non-envelope formulation for femtosecond optical pulses in semiconductors

Mel’nikov, Igor V.; Mihalache, Dumitru; Moldoveanu, Florin; Panoiu, Nicolae C.

doi:10.1134/1.567339

Cited by 15 publications

(8 citation statements)

References 6 publications

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“…Both nonlinear evolution equations are completely integrable by the IST method and have been extensively studied as a lowest-order approximation to the complete set of Maxwell-Bloch equations beyond the SVEA; see, e.g., Refs. [70,71,[73][74][75].…”

Section: Next It Is Convenient To Rewrite the Bloch Equations In Terms Ofmentioning

confidence: 99%

“…The continuing experimental progress in the study of the wave dynamics of FCPs in nonlinear optical media has paved the way for the development of new theoretical approaches to model their propagation in physical systems. Three classes of main dynamical models for FCPs have been put forward: (i) the quantum approach [48][49][50][51][52], (ii) the refinements within the framework of SVEA of the nonlinear Schrödinger-type envelope equations [53][54][55][56][57][58][59][60][61][62][63], and the non-SVEA models [64][65][66][67][68][69][70][70][71][72][73][74][75][76][77][78][79][80][81][82]. Extremely short pulses can be described by solving directly the Maxwell-Bloch equations for a two-level system.…”

Section: Introductionmentioning

confidence: 99%

“…Sech-type solutions have been derived [83]. The propagation of FCPs in Kerr media can be described beyond the SVEA by using the modified Korteweg-de Vries (mKdV) [70][71][72], sine-Gordon (sG) [73][74][75], or mKdV-sG equations [76][77][78][79][80]. Note also a reduced Maxwell-Duffing model, very close to the mKdV equation, for the description of extremely short pulses in nonresonant media [84].…”

Section: Introductionmentioning

confidence: 99%

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Models of few optical cycle solitons beyond the slowly varying envelope approximation

2013

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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues.Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited.In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit:

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Section: Next It Is Convenient To Rewrite the Bloch Equations In Terms Ofmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Models of few optical cycle solitons beyond the slowly varying envelope approximation

2013

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“…[13]). The so-called short-pulse equations can be expressed in a rather simple form in the case of unidirectional propagation [14][15][16][17][18][19][20][21][22][23], and the models taking into account the beam diffraction can describe complex spatiotemporal dynamics [24][25][26][27][28][29][30][31][32]. The field equations have been used, in particular, to study self-focusing and spatiotemporal collapse dynamics of * kozlov@mail.ifmo.ru optical pulses [27][28][29][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Self-phase modulation and frequency generation with few-cycle optical pulses in nonlinear dispersive media

et al. 2012

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We analyze nonlinear effects associated with the spatiotemporal propagation of few-cycle optical pulses in nonlinear dispersive media, including nonlinearity-induced self-phase modulation, generation of higher harmonics, and the effects of diffraction. First, we discuss the nonlinear equations governing the spatiotemporal propagation of short pulses in dispersive and diffractive nonlinear media and demonstrate a link between the field equation and the cubic nonlinear Schrödinger equation employed for describing the evolution of the pulse envelope. Then, for several different regimes of competitive scales, we study the self-action effects of few-cycle pulses and describe, both analytically and numerically, the pulse self-modulation and self-focusing, including the transformation of the spectral density and harmonic generation in the cases of weak and strong dispersion. Finally, we analyze the effect of the beam diffraction on self-action of the Gaussian few-cycle pulses.

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“…The continuing experimental progress in the study of wave dynamics of few-cycle pulses (FCPs) in nonlinear optical media has paved the way for the development of new theoretical approaches to model their propagation in a lot of physical settings. Three classes of main dynamical models for FCPs have been put forward in the past years: (i) the quantum approach [10][11][12][13][14], (ii) the refinements within the framework of slowly varying envelope approximation (SVEA) of the nonlinear Schrödinger-type envelope equations [15][16][17][18][19][20][21][22][23][24], and (iii) the non-SVEA models [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. The propagation of FCPs in Kerr media can be described beyond the SVEA by using the modified Korteweg-de Vries (mKdV) [31][32][33], sine-Gordon (sG) [34][35][36], or mKdV-sG equations [37][38][39][40]…”

Section: Introductionmentioning

confidence: 99%

Derivation of a modified Korteweg–de Vries model for few-optical-cycles soliton propagation from a general Hamiltonian

Triki

Leblond

Mihalache

2012

Optics Communications

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Propagation of few-cycles optical pulses in a centrosymmetric nonlinear optical Kerr (cubic) type material described by a general Hamiltonian of multilevel atoms is considered. Assuming that all transition frequencies of the nonlinear medium are well above the typical wave frequency, we use a long-wave approximation to derive an approximate evolution model of modified Korteweg-de Vries type. The model derived by rigorous application of the reductive perturbation formalism allows one the adequate description of propagation of ultrashort (few-cycles long) solitons.

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Non-envelope formulation for femtosecond optical pulses in semiconductors

Cited by 15 publications

References 6 publications

Models of few optical cycle solitons beyond the slowly varying envelope approximation

Models of few optical cycle solitons beyond the slowly varying envelope approximation

Self-phase modulation and frequency generation with few-cycle optical pulses in nonlinear dispersive media

Derivation of a modified Korteweg–de Vries model for few-optical-cycles soliton propagation from a general Hamiltonian

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