A taxonomy of optical dissipative structures in whispering-gallery mode resonators with Kerr nonlinearity

Balakireva, Irina; Chembo, Yanne K.

doi:10.1098/rsta.2017.0381

Cited by 9 publications

(5 citation statements)

References 41 publications

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“…Such condensation manifests in soliton fluids, molecules and crystals, as observed in diverse physical systems 2,9,10 . The underlying forces are responsible for various emergent phenomena, such as self-organization of Bose-Einstein condensates, soliton crystallization in micro-cavities, soliton fission in supercontinua or rogue waves in optical fiber [10][11][12][13][14][15] . It is wellknown that ultrashort solitons can form highly-stable bound-states, and these optical soliton molecules arise from balanced forces during propagation in passive fibers and in dissipative laser resonators [2][3][4][5]8,[16][17][18][19][20][21] .…”

mentioning

confidence: 99%

Resonant excitation and all-optical switching of femtosecond soliton molecules

2019

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The emergence of confined structures and pattern formation are exceptional manifestations of concurring nonlinear interactions found in a variety of physical, chemical and biological systems 1 . Optical solitons are a hallmark of extreme spatial or temporal confinement enabled by a variety of nonlinearities. Such particle-like structures can assemble in complex stable arrangements, forming "soliton molecules" 2,3 . Recent works revealed oscillatory internal motions of these bound states, akin to molecular vibrations 4-8 . These observations beg the question as to how far the "molecular" analogy reaches, whether further concepts from molecular spectroscopy apply in this scenario, and if such intra-molecular dynamics can be externally driven or manipulated. Here, we probe and control such ultrashort bound-states in an optical oscillator, utilizing real-time spectroscopy and time-dependent external perturbations. We introduce two-dimensional spectroscopy of the linear and nonlinear bound-state response and resolve anharmonicities in the soliton interaction leading to overtone and sub-harmonic generation. Employing a non-perturbative interaction, we demonstrate all-optical switching between distinct states with different binding separation, opening up novel schemes of ultrafast spectroscopy, optical logic operations and all-optical memory.Mirroring the hierarchy of the atomic and molecular composition of matter, fundamental solitons constitute stable entities which can aggregate to form structures of increased complexity. Such condensation manifests in soliton fluids, molecules and crystals, as observed in diverse physical systems 2,9,10 . The underlying forces are responsible for various emergent phenomena, such as self-organization of Bose-Einstein condensates, soliton crystallization in micro-cavities, soliton fission in supercontinua or rogue waves in optical fiber [10][11][12][13][14][15] . It is wellknown that ultrashort solitons can form highly-stable bound-states, and these optical soliton molecules arise from balanced forces during propagation in passive fibers and in dissipative laser resonators [2][3][4][5]8,[16][17][18][19][20][21] . Recent real-time studies have revealed rapid transients, internal vibrations and even chaotic dynamics 6,7,[22][23][24] .In this study, we transfer the concepts of optical spectroscopy to the case of ultrafast soliton molecules by driving them with an external perturbation and monitoring their response in real time. We discover a resonance in the response of soliton molecules to external perturbation and probe the associated anharmonic binding potential (Fig. 1a, approach I). Applying stronger, non-perturbative stimuli, we also demonstrate reliable and reversible all-optical switching between two different bound states (Fig. 1a, approach II)suggesting applications in fast optical sampling and pulse control.

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confidence: 99%

Resonant excitation and all-optical switching of femtosecond soliton molecules

2019

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“…Hence, we proved the following theorem Theorem 3. Let A(τ, ξ) be the solution of Equation (1) such that A ∈ C 2 [0, T 1 ], C k b (R) for integer k ≥ 0 and X be the leading approximation function (3). Let u(t, x) be a solution of Equation (2).…”

Section: Resultsmentioning

confidence: 99%

“…with real valued parameters, which is nothing else but a damped driven nonlinear Schrödinger equation. It models spatiotemporal pattern formation in dissipative, diffractive and nonlinear optical cavities submitted to a continuous laser pump [2][3][4][5][6]. The same model was shown rather immediately to also appear in dispersive optical ring cavities [7].…”

Section: Introductionmentioning

confidence: 88%

Justification of the Lugiato-Lefever Model from a Damped Driven ϕ4 Equation

Akbar¹,

Gunara²,

Susanto³

2020

Mathematics

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The Lugiato-Lefever equation is a damped and driven version of the well-known nonlinear Schrödinger equation. It is a mathematical model describing complex phenomena in dissipative and nonlinear optical cavities. Within the last two decades, the equation has gained much attention as it has become the basic model describing microresonator (Kerr) frequency combs. Recent works derive the Lugiato-Lefever equation from a class of damped driven ϕ 4 equations closed to resonance. In this paper, we provide a justification of the envelope approximation. From the analysis point of view, the result is novel and non-trivial as the drive yields a perturbation term that is not square integrable. The main approach proposed in this work is to decompose the solutions into a combination of the background and the integrable component. This paper is the first part of a two-manuscript series.

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“…Whispering gallery mode (WGM) resonators 1 – 3 with high quality (Q) factors are widely used in numerous research fields and engineering technologies, 4 such as nonlinear optics, 5 , 6 cavity quantum electrodynamics, 7 sensors, 8 , 9 and lasers 10 – 12 WGM resonators are made of various materials and use different methods.…”

Section: Introductionmentioning

confidence: 99%

Pressure-based fast tuning of high-Q crystalline whispering gallery mode resonator

Rong

Xing

et al. 2023

Opt. Eng.

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The whispering gallery mode resonator based on a fluoride crystalline material offers the advantage of an ultrahigh quality factor, however, its fast tuning remains a challenge. We propose a tuning method for a CaF 2 crystalline resonator using external pressure loading. Through our theoretical calculations and simulations, we discovered that the frequency shift induced by deformation during the pressure tuning of the crystalline resonator is greater than that induced by changes in refractive index. Both shifts were of the same order of magnitude, indicating that both factors must be considered. The experimental results show tuning rates of 1114.6 and 888.2 MHz/MPa in the transverse electric and transverse magnetic modes, respectively. The tuning system can respond to a signal frequency of up to 1.2 MHz.

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A taxonomy of optical dissipative structures in whispering-gallery mode resonators with Kerr nonlinearity

Cited by 9 publications

References 41 publications

Resonant excitation and all-optical switching of femtosecond soliton molecules

Resonant excitation and all-optical switching of femtosecond soliton molecules

Justification of the Lugiato-Lefever Model from a Damped Driven ϕ4 Equation

Pressure-based fast tuning of high-Q crystalline whispering gallery mode resonator

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