Ultrashort Optical Pulse Propagation in terms of Analytic Signal

Amiranashvili, Shalva; Demircan, Ayhan

doi:10.1155/2011/989515

Cited by 30 publications

(8 citation statements)

References 45 publications

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“…We now introduce some important definitions that will be crucial for the following discussion, mainly following [28][29][30][31].…”

Section: Derivation Of the Envelope Equation For The Analytic Signal mentioning

confidence: 99%

“…It can be proved that the fields E and E * are the classical analogues of the annihilation and creation operators a and a † used after quantization of the electromagnetic field, see e.g. [28,29]. This fact is quite understandable since a and a † are related to the positive and negative energy parts of the electric field, which in quantum optics correspond to absorption and emission of a photon [22].…”

Section: Derivation Of the Envelope Equation For The Analytic Signal mentioning

confidence: 99%

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Interaction between optical fields and their conjugates in nonlinear media

Conforti¹,

Marini²,

Tran³

et al. 2013

Opt. Express

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Motivated by recent experimental results, we demonstrate that the ubiquitous pulse propagation equation based on a single generalized nonlinear Schrödinger equation is incomplete and inadequate to explain the formation of the so called negative-frequency resonant radiation emitted by optical solitons. The origin of this deficiency is due to the absence of a peculiar nonlinear coupling between the positive and negative frequency components of the pulse spectrum during propagation, a feature that the slowly-varying envelope approximation is unable to capture. We therefore introduce a conceptually new model, based on the envelope of the analytic signal, that takes into account the full spectral dynamics of all frequency components, is prone to analytical treatment and retains the simulation efficiency of the nonlinear Schrödinger equation. We use our new equation to derive from first principles the phase-matching condition of the negative-frequency resonant radiation observed in previously reported experiments.

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“…We now introduce some important definitions that will be crucial for the following discussion, mainly following [28][29][30][31].…”

Section: Derivation Of the Envelope Equation For The Analytic Signal mentioning

confidence: 99%

Section: Derivation Of the Envelope Equation For The Analytic Signal mentioning

confidence: 99%

Interaction between optical fields and their conjugates in nonlinear media

Conforti¹,

Marini²,

Tran³

et al. 2013

Opt. Express

View full text Add to dashboard Cite

show abstract

“…36 This formulation allows one to take into account waveguide geometries with arbitrary dispersion profiles, eliminating nonresonant four-wave mixing contributions and treating pulses with arbitrary durations. 36 In addition, well-established pseudospectral methods for solving the GNLSE, such as split-step Fourier method and RK4IP method, can be adequately modified and implemented for the analytic signal formulation. Consider the pulse optical field in the frequency domain Eðz; ωÞ, the complex-valued analytical signal is defined as 37 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1 1 6 ; 9 7 Eðz; tÞ ¼…”

Section: Modeling Of Few-cycle Pulses Propagationmentioning

confidence: 99%

“…Moreover, using the Taylor expansion coefficients approximation makes the GNLSE invalid when investigating the propagation of multiple optical pulses with distinctive central frequencies 33 – 35 A nonenvelope formulation based on the description of the pulse dynamics in terms of the analytic signal for the electric field has been proposed to overcome the shortcomings of the GNLSE 36 . This formulation allows one to take into account waveguide geometries with arbitrary dispersion profiles, eliminating nonresonant four-wave mixing contributions and treating pulses with arbitrary durations 36 .…”

Section: Modeling Of Few-cycle Pulses Propagationmentioning

confidence: 99%

Numerical investigation of coherent supercontinuum generation via soliton implosion in ZBLAN photonic crystal fiber

Medjouri¹,

Abed

2022

Opt. Eng.

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We numerically investigate coherent supercontinuum (SC) generation extending from the deep ultraviolet to the mid-infrared spectral region using few-cycle optical pulses, pumped into a ZBLAN photonic crystal fiber. The finite difference method is used to optimize the fiber structure and achieve two zero dispersion wavelengths, with a broad anomalous dispersion region. The propagation of ultrashort pulses and their nonlinear dynamics is accurately modeled by employing the forward unidirectional propagation equation for the analytic signal of the pulse electric field. We show that by pumping in the anomalous regime of dispersion, the high-order solitons undergo an implosion process and spectral broadening is achieved via the contribution of self-phase modulation, self-steepening, and shock formation, along with a strong transfer of energy into a nonsolitonic resonant Cherenkov-like radiation in the normal dispersion region. Furthermore, numerical results indicate that broadband supercontinua spanning the region from 0.22 to 4.6 μm is successfully achieved with a pulse having a soliton order and duration of 12 and 6 fs, respectively. In addition, the deterministic feature of the implosion mechanism exhibits very low sensitivity to the input quantum noise and achieves excellent coherence properties. The proposed multioctave SC source is found promising for various potential applications, such as two-photon excited autofluorescence, bioimaging, spectroscopy, optical signal processing, and medicine.

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“…The underlying propagation models are derived in terms of the analytical signal (AS) for the real optical field. 1,2 They are exempt from the commonly adopted slowly varying envelope approximation but feature as prominent limiting case the envelope-based generalized nonlinear Schrödinger equation (GNLSE) with all usual effects. 3 In addition, it is easy to amend the discussed propagation model to also feature a delayed Raman response.…”

Section: Introductionmentioning

confidence: 99%

Accurate propagation of ultrashort pulses in nonlinear waveguides using propagation models for the analytic signal

Melchert¹,

Morgner

Roth³

et al. 2018

Computational Optics II

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Accurate propagation of ultrashort pulses in nonlinear waveguides using propagation models for the analytic signal," ABSTRACT We present a numerical approach for the accurate simulation of the complex propagation dynamics of ultrashort optical pulses in nonlinear waveguides, especially valid for few-cycle pulses. The propagation models are derived for the analytical signal, which includes the real optical field, exempt from the commonly adopted slowly varying envelope approximation. As technical basis for the representation of the medium dispersion we use rational Padé approximants instead of commonly employed high-order polynomial expansions. The implementation of the propagation equation is based on the Runge-Kutta in the interaction picture method. In addition, our modular approach easily allows to incorporate a Raman response and dispersion in the nonlinear term. As exemplary use-cases we illustrate our numerical approach for the simulation of a few-cycle pulse at various center frequencies for an exemplary photonic crystal fiber and demonstrate the collision of a soliton and two different dispersive waves mediated by their group-velocity event horizon.Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 10/10/2018 Terms of Use: https://www.spiedigitallibrary.org/terms-of-use ω>0 c 0 0 (2ω) −1 n(ω)|E ω (z)| 2 = const. 1 In effect, the soliton reacts to the scattering event by adjusting its center frequency and temporal width to conform to a global energy and momentum conservation constraint. This above process is repeated upon the mutual encounter of S and DW2. In summary, the center frequency of S increases from its initial value ω S = 1.5 rad/fs to ω S = 1.55 rad/fs above the propagation distance z = 2 m. This corresponds to an increase of its group velocity from v 0 = 0.20427 µm/fs to v fin = 0.20430 µm/fs. Also, its width decreases from τ S = 20 fs to τ S = 14.2 fs. Finally, note the appearance of small oscillations in the soliton

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Ultrashort Optical Pulse Propagation in terms of Analytic Signal

Cited by 30 publications

References 45 publications

Interaction between optical fields and their conjugates in nonlinear media

Interaction between optical fields and their conjugates in nonlinear media

Numerical investigation of coherent supercontinuum generation via soliton implosion in ZBLAN photonic crystal fiber

Accurate propagation of ultrashort pulses in nonlinear waveguides using propagation models for the analytic signal

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