Hamiltonian Framework for Short Optical Pulses

Amiranashvili, Shalva

doi:10.1007/978-3-319-20690-5_6

Cited by 10 publications

(9 citation statements)

References 59 publications

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“…5 (left) is considered, then the norm conservation yields the same relation as in Eq. (34), so that the norm of both packets grows backwards in ζ, but when viewed forwards in ζ, this fact is consistent with the conclusion previously stated that the Hawking process is self-amplifying [15].…”

Section: Norm Of the Frequency Modessupporting

confidence: 91%

“…In particular, propagation equations for ultrashort pulses based on the slowly varying envelope approximation (SVEA) present theoretical difficulties, as the field and the envelope coexist and evolve on the same scale [33]. In consequence, the electric field E(t), which is a real quantity, is replaced by a complex analytic signal E (t) [34], such that the relation between both quantities is given by…”

Section: Propagation Of Pulses In An Optical Black Hole Lasermentioning

confidence: 99%

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The theory of optical black hole lasers

Gaona-Reyes

Bermúdez

2017

Annals of Physics

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The event horizon of black holes and white holes can be achieved in the context of analogue gravity. It was proven for a sonic case that if these two horizons are close to each other their dynamics resemble a laser, a black hole laser, where the analogue of Hawking radiation is trapped and amplified. Optical analogues are also very successful and a similar system can be achieved there. In this work we develop the theory of optical black hole lasers and prove that the amplification is also possible. Then, we study the optical system by determining the forward propagation of modes, obtaining an approximation for the phase difference which governs the amplification, and performing numerical simulations of the pulse propagation of our system.

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Section: Norm Of the Frequency Modessupporting

confidence: 91%

Section: Propagation Of Pulses In An Optical Black Hole Lasermentioning

confidence: 99%

The theory of optical black hole lasers

Gaona-Reyes

Bermúdez

2017

Annals of Physics

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“…When the modulation period or the length of the wave envelope is sufficiently slow or large compared to the period or the wavelength of the carrier wave, the dynamics can be expressed by the nonlinear Schrödinger equation according to the slow envelope variation approximation [36]. In optics, the frequency of the light is much higher than the modulation frequency, δk/k c ∼ O 10 −4 , but in the typical water surface wave problem, the frequency of the propagating wave is just an order higher than the modulation frequency, δk/k c ∼ O 10 −1 .…”

Section: Spectral Broadening Due To Fast Envelope Variationmentioning

confidence: 99%

“…Since the nonlinearity of water waves is two orders of magnitude larger than the optical waves, the dynamical similarity implies that spectral bandwidth is extremely small in the optical regime. In other words, slowly varying envelope approximation is appropriate [36]. Then, why was the NLSE dynamics insufficient to reproduce the optical breathers?…”

Section: Introductionmentioning

confidence: 99%

On the Asymmetric Spectral Broadening of a Hydrodynamic Modulated Wave Train in the Optical Regime

Waseda

Fujimoto

Chabchoub

2019

Fluids

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Amplitude modulation of a propagating wave train has been observed in various media including hydrodynamics and optical fibers. The notable difference of the propagating wave trains in these media is the magnitude of the nonlinearity and the associated spectral bandwidth. The nonlinearity and dispersion parameters of optical fibers are two orders of magnitude smaller than the hydrodynamic counterparts, and therefore, considered to better assure the slowly varying envelope approximation (SVEA) of the nonlinear Schrödinger equations (NLSE). While most optics experiment demonstrate an NLSE-like symmetric solutions, experimental studies by Dudley et al. (Optics Express, 2009, 17, 21497-21508) show an asymmetric spectral evolution in the dynamics of unstable electromagnetic waves with high intensities. Motivated by this result, the hydrodynamic Euler equation is numerically solved to study the long-term evolution of a water-wave modulated wave train in the optical regime, i.e., at small steepness and spectral bandwidth. As the initial steepness is increased, retaining the initial spectral bandwidth thereby increasing the Benjamin-Feir Index, the modulation localizes, and the asymmetric and broad spectrum appears. While the deviation of the evolution from the NLSE solution is a result of broadband dynamics of free wave interaction, the resulting asymmetry of the spectrum is a consequence of the violation of the SVEA.

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“…Also, Hamiltonian formulations of reduced laser pulse propagation equations have been found a posteriori, i.e. after reduction from a parent model at the level of the equations of motion [35,36].…”

Section: Introductionmentioning

confidence: 99%