A perturbative theory of soliton propagation in the presence of third order dispersion

Elgin, J.N.; Brabec, Thomas; Kelly, Stephen M.

doi:10.1016/0030-4018(94)00602-q

Cited by 81 publications

(50 citation statements)

References 17 publications

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“…(a) −iu ttt and/or u 4t : these higher-order derivatives are necessary to describe sub-picosecond pulses [1][2][3][4][5][6][7][8][9][10][11][12]; in particular, conditions for including u 4t and discarding −iu ttt are discussed in [7,9], (b) |u| 4 u: this higher-order nonlinearity is used when we want to describe the propagation of pulses when the light intensity approaches the values which produce the "saturation" of the refractive index [13][14][15][16][17][18][19][20], (c) i(|u| 2 u) t : this term is necessary to describe the self-steepening of the optical pulses [21][22][23], (d) u(|u| 2 ) t : this term is associated with the effect of Raman scattering [24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Pulse Propagation Models with Bands of Forbidden Frequencies or Forbidden Wavenumbers: A Consequence of Abandoning the Slowly Varying Envelope Approximation and Taking into Account Higher-Order Dispersion

2017

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Abstract:We study linear and nonlinear pulse propagation models whose linear dispersion relations present bands of forbidden frequencies or forbidden wavenumbers. These bands are due to the interplay between higher-order dispersion and one of the terms (a second-order derivative with respect to the propagation direction) which appears when we abandon the slowly varying envelope approximation. We show that as a consequence of these forbidden bands, narrow pulses radiate in a novel and peculiar way. We also show that the nonlinear equations studied in this paper have exact soliton-like solutions of different forms, some of them being embedded solitons. The solutions obtained (of the linear as well as the nonlinear equations) are interesting since several arguments suggest that the Cauchy problems for these equations are ill-posed, and therefore the specification of the initial conditions is a delicate issue. It is also shown that some of these equations are related to elliptic curves, thus suggesting that these equations might be related to other fields where these curves appear, such as the theory of modular forms and Weierstrass ℘ functions, or the design of cryptographic protocols.

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Section: Introductionmentioning

confidence: 99%

Pulse Propagation Models with Bands of Forbidden Frequencies or Forbidden Wavenumbers: A Consequence of Abandoning the Slowly Varying Envelope Approximation and Taking into Account Higher-Order Dispersion

2017

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“…However, it has been originally presented at the background of the propagation of higher-order soliton. In that situation, higher-order soliton was propagated in the anomalous GVD regime which is generally perturbed by the third-and higher-order dispersion [10][11][12][13]. In our previous work, the roles of the self-steepening (SS) effect in the generation and controlling of DW in metamaterials are disclosed [14], and in photonic crystal fiber, the manipulation of DW by the frequency chirped is unfolded [15,16].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Dispersive Wave Generation in Gas-Filled Photonic Crystal Fiber with the Normal Dispersion

Deng

Zhang

2017

Advances in Condensed Matter Physics

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The absence of Raman and unique pressure-tunable dispersion is the characteristic feature of gas-filled photonic crystal fiber (PCF), and its zero dispersion points can be extended to the near-infrared by increasing gas pressure. The generation of dispersive wave (DW) in the normal group velocity dispersion (GVD) region of PCF is investigated. It is demonstrated that considering the selfsteepening (SS) and introducing the chirp of the initial input pulse are two suitable means to control the DW generation. The SS enhances the relative average intensity of blue-shift DW while weakening that of red-shift DW. The required propagation distance of DW emission is markedly varied by introducing the frequency chirp. Manipulating DW generation in gas-filled PCF by the combined effects of either SS or chirp and three-order dispersion (TOD) provides a method for a concentrated transfer of energy into the targeted wavelengths.

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“…Fiber-optic Cherenkov radiation (FOCR), also known as dispersive wave generation or nonsolitonic radiation, describes the radiation from a fiber-optic soliton when perturbed by higher-order fiber dispersion [1][2][3][4][5]. First theoretically studied in 1986, FOCR has attracted renewed research interest in company with the advent of photonic crystal fibers (PCFs) whose properties can be flexibly engineered [6].…”

Section: Introductionmentioning

confidence: 99%

Fiber-optic Cherenkov radiation in the few-cycle regime

Chang¹,

Chen²,

Kärtner³

2011

Opt. Express

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Fiber-optic Cherenkov radiation has emerged as a wavelength conversion technique to achieve isolated spectrum in the visible wavelength range. Most published results have reinforced the impression that CR forms a narrowband spectrum with poor efficiency. We both theoretically and experimentally investigate fiber-optic Cherenkov radiation excited by fewcycle pulses. We introduce the coherence length to quantify the Cherenkovradiation bandwidth and its dependence on propagation distance. Detailed numerical simulations verified by experimental results reveal three unique features that are absent when pumped with often-used, long pulses; that is, continuum generation (may span one octave in connection with the pump spectrum), high conversion efficiency (up to 40%), and broad bandwidth (70 nm experimentally obtained) for the isolated Cherenkov radiation spectrum. These merits allow achieving broadband visible-wavelength spectra from low-energy ultrafast sources which opens up new applications (e.g. precision calibration of astronomical spectrographs). ©2011 Optical Society of America

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A perturbative theory of soliton propagation in the presence of third order dispersion

Cited by 81 publications

References 17 publications

Pulse Propagation Models with Bands of Forbidden Frequencies or Forbidden Wavenumbers: A Consequence of Abandoning the Slowly Varying Envelope Approximation and Taking into Account Higher-Order Dispersion

Pulse Propagation Models with Bands of Forbidden Frequencies or Forbidden Wavenumbers: A Consequence of Abandoning the Slowly Varying Envelope Approximation and Taking into Account Higher-Order Dispersion

Dynamics of Dispersive Wave Generation in Gas-Filled Photonic Crystal Fiber with the Normal Dispersion

Fiber-optic Cherenkov radiation in the few-cycle regime

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