[Paper Review] Synthetic Frequency Lattices from an Integrated Dispersive Multi-Color Soliton

Grégory Moille, Curtis R. Menyuk+3 more|arXiv (Cornell University)|Oct 17, 2022

Advanced Fiber Laser Technologies4 citations

TL;DR

This paper demonstrates a synthetic frequency lattice in the eigenfrequency space of an integrated, dispersive multi-color dissipative Kerr soliton (DKS) by exploiting nonlinear coupling via four-wave mixing Bragg scattering. By leveraging the discrepancy between group and phase velocity in a 1 THz repetition rate microresonator, the authors achieve all-optical, broadband coupling across 150 THz, enabling a hidden dimension for complex frequency lattices compatible with octave-spanning microcombs.

ABSTRACT

Dissipative Kerr solitons (DKSs) in optical microresonators have been intensely studied from the perspective of both fundamental nonlinear physics and portable and low power technological applications in communications, sensing, and metrology. In parallel, synthetic dimensions offer the promise of studying physical phenomena with a dimensionality beyond that imposed by geometry, and have been implemented in optics. The interplay of DKS physics with synthetic dimensions promises to unveil numerous new physical and technological insights, yet many fundamental challenges remain. In particular, DKSs intrinsically rely on dispersion to exist while the creation of synthetic frequency lattices typically needs a dispersion-less system. We present a change of paradigm with the creation of a synthetic frequency lattice in the eigenfrequency space of a dispersive multi-color soliton through all-optical nonlinear coupling -- compatible with octave spanning microcombs -- harnessing the interplay between the cavity dispersion and the dispersion-less nature of the DKS. We examine theoretically and experimentally the nonlinear coupling mechanism in a 1~THz repetition rate resonator and demonstrate four-wave mixing Bragg scattering between the different wavepackets forming the multi-color soliton, with the microcomb ranging over 150~THz, yielding a complex all-optical and integrated synthetic frequency lattice.

Motivation & Objective

• To overcome the incompatibility between synthetic frequency lattices—typically requiring dispersion-less systems—and dissipative Kerr solitons (DKSs), which fundamentally rely on cavity dispersion for existence.
• To establish a new paradigm for synthetic dimensions in photonics by exploiting the phase velocity discrepancy between DKS wavepacket components in a dispersive cavity.
• To demonstrate all-optical, broadband nonlinear coupling in the eigenfrequency space of a DKS, enabling the creation of complex synthetic frequency lattices without external electro-optic modulation.
• To validate that high-order dispersion, often a hindrance, can instead enable nonlinear coupling in a hidden dimension orthogonal to the repetition rate space.
• To enable new platforms for simulating quantum-like phenomena, topology, and multi-level atomic systems in classical, integrated photonic systems.

Proposed method

• Theoretical modeling reduces the multi-pump DKS system to a set of coupled Lugiato-Lefever equations (LLEs) for discrete wavepacket components, treating the DKS as a stationary envelope with internal frequency components.
• Nonlinear coupling is enabled by the difference in phase rotation velocity between wavepackets due to cavity dispersion, while group velocities remain locked via cross-phase modulation.
• Four-wave mixing Bragg scattering is used as the core nonlinear process, analogous to optical parametric amplification, to generate new idler wavepackets in the eigenfrequency space.
• The system is experimentally realized in a 1 THz repetition rate Si3N4 microresonator with dual-pump excitation, enabling broadband frequency comb spanning over 150 THz.
• Phase shifts induced by linear cavity dispersion are carefully controlled to achieve long-range, coherent coupling between wavepackets in the synthetic dimension.
• Experimental validation is performed by measuring the output spectrum in the laboratory frame, showing agreement with eigenfrequency-domain modeling and confirming the existence of the synthetic lattice.

Experimental results

Research questions

• RQ1 Can synthetic frequency lattices be realized in the eigenfrequency space of a dispersive multi-color DKS, despite the inherent conflict between DKSs requiring dispersion and synthetic lattices typically assuming dispersion-less systems?
• RQ2 How can nonlinear coupling be achieved in the DKS eigenfrequency space without relying on electro-optic modulation, which is incompatible with high-repetition-rate microcombs?
• RQ3 What role does the discrepancy between group and phase velocity play in enabling nonlinear mixing and coupling in a hidden dimension orthogonal to the repetition rate space?
• RQ4 Can high-order dispersion, often detrimental, be harnessed to enable complex, long-range coupling in synthetic frequency lattices?
• RQ5 To what extent can the resulting synthetic lattice emulate multi-level atomic systems or topological phenomena in a classical, integrated photonic platform?

Key findings

• A synthetic frequency lattice is experimentally demonstrated in the eigenfrequency space of a 1 THz repetition rate DKS, spanning over 150 THz of bandwidth.
• Nonlinear coupling occurs via four-wave mixing Bragg scattering between DKS wavepacket components, enabled by the phase velocity mismatch due to cavity dispersion, despite identical group velocities.
• The system achieves all-optical coupling without electro-optic modulation, making it compatible with high-repetition-rate, octave-spanning microcombs.
• Theoretical modeling in the eigenfrequency domain shows excellent agreement with experimental observations in the laboratory frame, confirming the existence of a hidden dimension in the DKS.
• High-order dispersion is not a limitation but a key enabler of long-range coupling in the synthetic lattice, allowing for complex, reconfigurable frequency structures.
• The synthetic lattice supports configurations analogous to lambda, vee, and ladder atomic systems, opening pathways for emulating atomic physics phenomena in classical photonic systems.