Generalized Miller Formulæ

Ettoumi, Wahb; Petit, Yannick; Kasparian, Jérôme; Wolf, Jean‐Pierre

doi:10.1364/oe.18.006613

Cited by 70 publications

(58 citation statements)

References 22 publications

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“…The n 2m coefficients are related to χ (2m+1) susceptibilities and have been reported in a recent article [17] at 800 nm. We then extrapolated these indexes at 1.83 µm by using generalized Miller formulas [18], providing the spectral dependence of the n 2m coefficients from the knowledge of the linear dispersion. The calculated nonlinear refractive indexes used in this article are summarized in Table I.…”

Section: Experimental and Numerical Methodsmentioning

confidence: 99%

Mechanism of hollow-core-fiber infrared-supercontinuum compression with bulk material

et al. 2010

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We numerically investigate the pulse compression mechanism in the infrared spectral range based on the successive action of nonlinear pulse propagation in a hollow-core fiber followed by linear propagation through bulk material. We found an excellent agreement of simulated pulse properties with experimental results at 1.8 µm in the two-optical-cycle regime close to the Fourier limit. In particular, the spectral phase asymmetry attributable to self-steepening combined with self-phase modulation is a necessary prerequisite for subsequent compensation by the phase introduced by glass material in the anomalous dispersion regime. The excellent agreement of the model enabled simulating pressure and wavelength tunability of sub-two cycles in the range from 1.5 to 4 µm with this cost-efficient and robust approach.

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Section: Experimental and Numerical Methodsmentioning

confidence: 99%

Mechanism of hollow-core-fiber infrared-supercontinuum compression with bulk material

et al. 2010

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“…It would overturn the picture most have of the mechanism behind long-range filamentary propagation of intense ultrashort pulses -as arising from an interplay between self-focusing due to the positive optical nonlinearity from bound electrons and defocusing due to the plasma generated by ionization. The existence of a higher-order Kerr effect would also have implications for the general nonlinear susceptibility in transparent media [7,8], including harmonic generation [9][10][11].Subsequent experimental studies of light filaments [12][13][14][15] have not supported the higher-order Kerr model, with one exception [16]. One measurement [13] found that the electron density was two orders of magnitude higher than predicted by a calculation including higher-order nonlinearities, but agreed with a simulation based on plasma defocusing alone [5].…”

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“…Loriot et al used a non-spatially resolved multishot technique limited in time resolution by the probe duration of ∼90 fs [4]. They measured the transient birefringence and inferred the higher-order Kerr coefficients from the tensorial symmetry of the nonlinear susceptibilities χ (5) , χ (7) , etc. [4,20].…”

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Optical Nonlinearity in Ar andN2near the Ionization Threshold

et al. 2011

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We directly measure the nonlinear optical response in argon and nitrogen in a thin gas target to laser intensities near the ionization threshold. No instantaneous negative nonlinear refractive index is observed, nor is saturation, in contrast with a previous measurement [Loriot et al., Opt. Express 17, 13429 (2009)] and calculations [Brée et al., Phys. Rev. Lett. 106, 183902 (2011)]. In addition, we are able to cleanly separate the instantaneous and rotational components of the nonlinear response in nitrogen. In both Ar and N2, the peak instantaneous index response scales linearly with the laser intensity until the point of ionization, whereupon the response turns abruptly negative and ∼constant, consistent with plasma generation.The optical Kerr effect, the intensity-dependent refractive index experienced by an optical pulse in a transparent medium, plays an important role in phenomena from nonlinear propagation in optical fibers [1] to modelocking in pulsed lasers [2] to filamentary propagation in condensed media and the atmosphere [3]. A recent transient birefringence measurement in the components of air reported by Loriot et al. [4] purported to show that the optical Kerr effect saturates and then becomes negative for intensities greater than 26 TW/cm 2 . A strong higher-order Kerr effect, with a crossover from positive to negative nonlinear index at intensities well below the ionization threshold, would have a huge impact on the nonlinear optics of transparent media, and has inspired theoretical works predicting plasma-free light filamentation [5] and exotic new effects in light propagation [6]. It would overturn the picture most have of the mechanism behind long-range filamentary propagation of intense ultrashort pulses -as arising from an interplay between self-focusing due to the positive optical nonlinearity from bound electrons and defocusing due to the plasma generated by ionization. The existence of a higher-order Kerr effect would also have implications for the general nonlinear susceptibility in transparent media [7,8], including harmonic generation [9][10][11].Subsequent experimental studies of light filaments [12][13][14][15] have not supported the higher-order Kerr model, with one exception [16]. One measurement [13] found that the electron density was two orders of magnitude higher than predicted by a calculation including higher-order nonlinearities, but agreed with a simulation based on plasma defocusing alone [5]. A physical mechanism for the saturation and negative response was proposed based on the nonlinear response near the threshold of ionization [17,18]. What is missing from this debate is a direct measurement of the nonlinearity that corroborates or refutes the intensity dependence observed by Loriot et al. Here, we describe such a measurement in Ar and N 2 using spectral interferometry. We find no saturation and no negative instantaneous nonlinear phase, in contrast to the original experiment [4].The technique we use, single-shot supercontinuum spectral interferometry [19], provides...

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“…1(b) the inversion intensities are plotted versus pump wavelength to summarize these trends. Without cascading, only a slight wavelength scaling [19] of the nonlinearities is seen.…”

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Higher-order Kerr effect and harmonic cascading in gases

2012

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The higher-order Kerr effect (HOKE) has been recently advocated to explain measurements of the saturation of the nonlinear refractive index in gases. Here we show that cascaded third-harmonic generation results in an effective fifth order nonlinearity that is negative and significant. Higher-order harmonic cascading will also occur from the HOKE, and the cascading contributions may significantly modify the observed nonlinear index change. At lower wavelengths cascading increases the HOKE saturation intensity, while for longer wavelengths cascading will decrease the HOKE saturation intensity.Comment: Optics Letters, in pres

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Generalized Miller Formulæ

Cited by 70 publications

References 22 publications

Mechanism of hollow-core-fiber infrared-supercontinuum compression with bulk material

Mechanism of hollow-core-fiber infrared-supercontinuum compression with bulk material

Optical Nonlinearity in Ar andN2near the Ionization Threshold

Higher-order Kerr effect and harmonic cascading in gases

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