Infinite hierarchy of solitons: Interaction of Kerr nonlinearity with even orders of dispersion

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Infinite hierarchy of solitons: Interaction of Kerr nonlinearity with even orders of dispersion

Antoine F. J. Runge, Y. Long Qiang, Tristram J. Alexander, M. Z. Rafat, Darren D. Hudson, Andrea Blanco-Redondo, and C. Martijn de Sterke

Phys. Rev. Research 3, 013166 – Published 22 February 2021

Abstract

Temporal solitons are optical pulses that arise from the balance of negative group-velocity dispersion and self-phase modulation. For decades, only quadratic dispersion was considered with higher order dispersion often thought of as a nuisance. Following the recent observation of pure-quartic solitons, we here provide experimental and numerical evidence for an infinite hierarchy of solitons that balance self-phase modulation and arbitrary negative pure, even-order dispersion. Specifically, we experimentally demonstrate the existence of solitons with pure-sextic ( $β_{6}$ ), -octic ( $β_{8}$ ), and -decic ( $β_{10}$ ) dispersion, limited only by the performance of our components, and we numerically show the existence of solitons involving pure 16th-order dispersion. These results broaden the fundamental understanding of solitons and present avenues to engineer ultrafast pulses in nonlinear optics and its applications.

Received 11 December 2020
Accepted 5 February 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.013166

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Nonlinear optics Ultrafast optics

Atomic, Molecular & Optical

Authors & Affiliations

Antoine F. J. Runge ^1,*, Y. Long Qiang ¹, Tristram J. Alexander¹, M. Z. Rafat ¹, Darren D. Hudson², Andrea Blanco-Redondo³, and C. Martijn de Sterke^1,4

¹Institute of Photonics and Optical Science (IPOS), School of Physics, University of Sydney, NSW 2006, Australia
²CACI-Photonics Solutions, 15 Vreeland Road, Florham Park, New Jersey 07932, USA
³Nokia Bell Labs, 791 Holmdel Road, Holmdel, New Jersey 07733, USA
⁴University of Sydney Nano Institute (Sydney Nano), University of Sydney, NSW 2006, Australia

^*Corresponding author: antoine.runge@sydney.edu.au

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Vol. 3, Iss. 1 — February - April 2021

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Images

Figure 1
Numerically calculated temporal stationary solution for $k = 6$ (blue), 8 (red), 10 (green), and 16 (black) with a same pulse width (FWHM) of $τ = 1 ps$ . Temporal profiles in linear (a) and logarithmic (b) scales. Corresponding linear (c) and logarithmic (d) spectra. The different solutions have been shifted vertically for clarity.
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Figure 2
Schematic of the erbium-doped laser cavity with the following components: Er, erbium; WDM, wavelength division multiplexer; LD, laser diode; OC, output coupler; PC, polarization controller; FP, fiber polarizer.
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Figure 3
Spectral and temporal measurements of pure high-order dispersion solitons: sextic (top row), octic (middle row), and decic (bottom row) dispersion. The applied dispersion is $β_{6} = - 500 {ps}^{6} / km$ , $β_{8} = - 15 \times 10^{3} {ps}^{8} / km$ , and $β_{10} = - 1 \times 10^{6} {ps}^{10} / km$ , respectively. (a)–(c) Measured (blue) and calculated (red-dashed) spectra. (d)–(f) Measured spectrograms. (g)–(i) Retrieved temporal intensity (blue), phase (orange), and corresponding calculated temporal shapes (red-dashed).
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Figure 4
Numerical (red circles) and experimental (blue diamonds) values of the flatness $F$ of the PHEOD soliton spectrum versus dispersion order.
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Figure 5
Measured PHEOD soliton output spectra for different dispersion orders. (a) Sextic PHEOD soliton spectra for $β_{6} = - 50$ (yellow), $β_{6} = - 100$ (orange), and $β_{6} = - 500 {ps}^{6} / km$ (blue). (b) Octic PHEOD soliton spectra for $β_{8} = - 100$ (cyan), $β_{8} = - 200$ (green), and $β_{8} = - 1000 {ps}^{8} / km$ (purple). (c) Decic PHEOD soliton spectra for $β_{10} = - 5000$ (green), $β_{10} = - 10 \times 10^{3}$ (cyan), and $β_{10} = - 50 \times 10^{3} {ps}^{10} / km$ (red). Colored circles show the $k th$ power of the measured sidebands positions versus sideband order for the (d) sextic, (e) octic, and (f) decic PHEOD soliton spectra. The solid lines correspond to linear fits.
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Figure 6
Measurement of energy-width scaling properties of the pure high-order dispersion Kerr solitons. The circles mark the measured pulse energy $E$ versus pulse duration. (a) Pure-sextic soliton energy for $β_{6} = - 500$ (red), $β_{6} = - 1000$ (blue), and $β_{6} = - 2000 {ps}^{6} / km$ (green). (b) Pure-octic soliton energy for $β_{8} = - 15 \times 10^{3}$ (red), $β_{8} = - 30 \times 10^{3}$ (blue), and $β_{8} = - 60 \times 10^{3} {ps}^{8} / km$ (green). (c) Pure-decic soliton energy for $β_{10} = - 2 \times 10^{5}$ (red), $β_{10} = - 5 \times 10^{5}$ (blue), and $β_{10} = - 1 \times 10^{6} {ps}^{10} / km$ (green). The solid curves are fits for (a) pure-sextic, (b) -octic, and (c) -decic solitons from Eq. (7).
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