Quadratic solitons for negative effective second-harmonic diffraction as nonlocal solitons with periodic nonlocal response function

Esbensen, B. K.; Bache, Morten; Królikowski, Wiesław; Bang, Ole

doi:10.1103/physreva.86.023849

Cited by 33 publications

(8 citation statements)

References 45 publications

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“…The first observation of a temporal cascaded self-defocusing soliton [16] was actually carried out in the resonant regime (see [9]), but this was prior to the discovery of a nonlocal resonance regime for such an interaction [9] and the SH spectrum was not recorded to document the connection between soliton formation and the SH spectral resonance. The spatial equivalent of a resonant nonlocal nonlinearity occurs when the SH experiences negative diffraction or when the phase mismatch is negative [59], but the analytical soliton solutions are very elusive [68,69] due to an oscillatory nature of the nonlocal response in time/space domain that comes as a consequence of the spectral resonance. To our knowledge, a soliton-induced nonlocal resonance, spatially or temporally, has yet to be experimentally observed.…”

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confidence: 99%

Soliton-induced nonlocal resonances observed through high-intensity tunable spectrally compressed second-harmonic peaks

2014

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Experimental data of femtosecond thick-crystal second-harmonic generation shows that when tuning away from phase matching, a dominating narrow spectral peak appears in the second harmonic that can be tuned over 100's of nm by changing the phase-mismatch parameter. Traditional theory explains this as phase matching between a sideband in the broadband pump to its second-harmonic. However, our experiment is conducted under high input intensities and instead shows excellent quantitative agreement with a nonlocal theory describing cascaded quadratic nonlinearities. This theory explains the detuned peak as a nonlocal resonance that arises due to phase-matching between the pump and a detuned second-harmonic frequency, but where in contrast to the traditional theory the pump is assumed dispersion-free. As a soliton is inherently dispersion-free, the agreement between our experiment and the nonlocal theory indirectly proves that we have observed a soliton-induced nonlocal resonance. The soliton exists in the self-defocusing regime of the cascaded nonlinear interaction and in the normal dispersion regime of the crystal, and needs high input intensities to become excited. A common observation in second-harmonic generation (SHG) of broadband laser pulses in thick crystals, is that when a phase mismatch ∆k is imposed, the second harmonic (SH) spectrum is dominated by a spectrally compressed peak that is wavelength-tunable through ∆k [1][2][3][4][5][6][7][8]. Figure 1(a) shows data from an experiment we performed using a thick β-barium borate (BBO) crystal. The input fundamental wave (FW, center frequency ω 1 ) was an intense femtosecond pulse loosely focused and collimated at the crystal entrance to avoid diffraction. The tuning around ∆k = 0 was achieved by rotating the external angle of the crystal. A striking wavelength tunability over 100's of nanometers is possible, and the peak is also strongly compressed compared to the ideal thin-crystal bandwidth (in this case about 40 nm FWHM). The compressed SH peak pertains for large negative tuning angles, while it disappears for large positive tuning angles (here +5• ). The spectral compression is traditionally explained by a phase-matched sidebands theory, which uses the classical result that the SH efficiency ∝ sinc 2 [∆kL/2]: this explains the decreasing bandwidth in a thick crystal, and the frequency dependence of ∆k(ω) = k 2 (ω) − 2k 1 (ω/2) explains how a SH sideband frequency strongly detuned from the degenerate SH frequency ω 2 = 2ω 1 can become phase matched when ∆k(ω 2 ) = 0. Figure 1(c) shows the predicted phasematching wavelengths by the phase-matched sidebands theory, and remarkably it cannot explain the experimental data for large positive tuning angles.Instead an alternative nonlocal theory, shown in Fig. 1(b), predicts "resonance" wavelengths in the nonlocal response function that up to +4• are in excellent agreement with the experimental peak positions. At +5• the phase-matching condition behind this resonance is no longer fulfilled, yielding a broadband, non-...

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confidence: 99%

Soliton-induced nonlocal resonances observed through high-intensity tunable spectrally compressed second-harmonic peaks

2014

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“…Finally, we show in Fig. 4 the computation of the 2-peak soliton with the sine-oscillation response R S (x) = − sin(|x|/w m )/(2w m ) [41,42], which could hardly be obtained by other known methods as far as we have tried. The best accuracy of 3.2 × 10 −11 is achieved when M m = 25 and M k = 179.…”

Section: Examplesmentioning

confidence: 94%

Perturbation-iteration method for multi-peak solitons in nonlocal nonlinear media

Hong

Tian

et al. 2018

J. Opt. Soc. Am. B

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An perturbation-iteration method is developed for the computation of the Hermite-Gaussian-like solitons with arbitrary peak numbers in nonlocal nonlinear media. This method is based on the perturbed model of the Schrödinger equation for the harmonic oscillator, in which the minimum perturbation is obtained by the iteration. This method takes a few tens of iteration loops to achieve enough high accuracy, and the initial condition is fixed to the Hermite-Gaussian function.The method we developed might also be extended to the numerical integration of the Schrödinger equations in any type of potentials.

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“…Typically nonlocal kernels decay to zero at large distances and we will take σ as the parameter that controls the spatial extension (width) of the coupling. In some instances, such as in optical systems with quadratic nonlinearities, one encounters spatially periodic nonlocal kernels [43]. The analysis that follows can also be applied to periodic kernels and in that case σ can be taken as a characteristic parameter of the kernel.…”

Section: Systemmentioning

confidence: 99%

Formation of localized structures in bistable systems through nonlocal spatial coupling. I. General framework

et al. 2014

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The present work studies the influence of nonlocal spatial coupling on the existence of localized structures in one-dimensional extended systems. We consider systems described by a real field with a nonlocal coupling that has a linear dependence on the field. Leveraging spatial dynamics we provide a general framework to understand the effect of the nonlocality on the shape of the fronts connecting two stable states. In particular we show that nonlocal terms can induce spatial oscillations in the front tails, allowing for the creation of localized structures, that emerge from pinning between two fronts. In parameter space the region where fronts are oscillatory is limited by three transitions: the modulational instability of the homogeneous state, the Belyakov-Devaney transition in which monotonic fronts acquire spatial oscillations with infinite wavelength, and a crossover in which monotonically decaying fronts develop spatial oscillations with a finite wavelength. We show how these transitions are organized by codimension 2 and 3 points and illustrate how by changing the parameters of the nonlocal coupling it is possible to bring the system into the region where localized structures can be formed.

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Quadratic solitons for negative effective second-harmonic diffraction as nonlocal solitons with periodic nonlocal response function

Cited by 33 publications

References 45 publications

Soliton-induced nonlocal resonances observed through high-intensity tunable spectrally compressed second-harmonic peaks

Soliton-induced nonlocal resonances observed through high-intensity tunable spectrally compressed second-harmonic peaks

Perturbation-iteration method for multi-peak solitons in nonlocal nonlinear media

Formation of localized structures in bistable systems through nonlocal spatial coupling. I. General framework

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