Non-chromatic scattered soliton comb in the optical Kerr cavity

Optical frequency comb is a special light source whose spectrum contains a series of equally spaced frequency components, which has broad application prospects in optical communication, lidar, optical computing, spectral measurement, optical clock and other fields. Optical frequency comb technology based on Kerr cavity (Kerr comb) has the advantages of high repetition frequency, low power consumption, and chip-level integration, and has received widespread attention in recent years.

When the Kerr comb reaches a low-noise mode-locked state, stable optical solitos form in the resonator. A photosoliton is a localized packet of electromagnetic waves that behaves like a particle, and the physical mechanism of its production depends on a balance between linear and nonlinear effects.

In recent years, the research team of Xiaoxiao Xue and Zheng Xiaoping of Tsinghua University, in cooperation with Purdue University and other units, has carried out a series of explorations and studies around soliton dynamics and optical frequency combing technology in the Kerr cavity, and has successively proposed a new mechanism of dark soliton combing in the normal dispersion region (Nature Photonics 9, 594-600, 2015), a new method for dual-chamber mode regulation and light comb generation (Laser & Photonics Reviews 9, L23-L28, 2015), a new phase matching mechanism for second harmonic assistance (Light: Science & Applications 6, e16253, 2017), a new scheme for high-efficiency soliton light combing (Nature Photonics 13, 616-622, 2019; Laser & Photonics Reviews 11, 1600276, 2017), which solved the problems of high-reliability excitation and high-efficiency energy conversion of Kerr combs, and promoted the application of Kerr combs in the field of microwave photonics (Journal of Lightwave Technology 36, 2312-2321, 2018; Frontiers of Optoelectronics 2, 238-248, 2016)。

Under the existing theoretical framework, group velocity dispersion of light fields is often considered a necessary condition for the formation of solitons. However, dispersion-dominated soliton combs have specific pulse and spectral shapes, and have limited regulatory capabilities, which is not conducive to practical applications. For example, the ideal comb for optical communication should have a rectangular spectrum with equal power of each comb tooth, but the shape of the bright soliton comb in the abnormal dispersion region is generally hyperbolic secant, while the dark soliton comb in the normal dispersion region has a large power fluctuation, both of which are far from the ideal shape.

In this paper, the researchers discovered a new type of soliton state that is inherently dispersion-independent, called “non-dispersed solitons.” Unlike conventional solitons, non-dispersion solitons can be stable in the absence of dispersion at all. They further revealed that the physical nature of non-dispersive solitos is an intrinsic function of self-phase modulation and spectral filtering effects. The loss corresponding to the real part of the eigenvalue decreases with the increase of the filtering order and gradually approaches zero. When the filtering order is large enough, there is a complete balance between spectral filtering effects and self-phase modulation, as well as between parametric gain and uniform loss. The soliton light comb produced at this time has an extremely flat spectrum, and the pulse shape is very close to the theoretical bandwidth-limited Nyquist pulse, so it is also called “Nyquist soliton”.

Figure 1 Physical mechanism of chromatic dispersion solitons. (a) Spectral filtering effects and eigenfunctions of self-phase modulation. The loss corresponding to the real part of the eigenvalue decreases with the increase of the filter order. (b) Schematic diagram of the Nyquist soliton equilibrium. There is a balance between spectral filtering and self-phase modulation, and a balance between parametric gain and uniform loss.

The results were published in Light: Science & Applications under the title “Dispersion-less Kerr solitons in spectrally confined optical cavities.” Xiaoxiao Xue is the first author and corresponding author of this paper, Zheng Xiaoping is the co-corresponding author of this paper, and Philippe Grelu of Bourgogne Franche-Comté University in France is the co-author of this paper.

The researchers built an experimental system for optical fiber ring cavity, used a programmable spectral shaper to accurately control the dispersion and loss in the cavity, and performed stable feedback control on environmental disturbances, and finally successfully captured non-dispersive solitons. The pulse shape and spectral shape of the soliton are precisely in agreement with the theoretical predictions.

The experimentally obtained Nyquist soliton has a near-ideal rectangular spectrum, with 99.6% of the power distributed over a 6 dB bandwidth containing 66,000 comb teeth. At the same time, the researchers observed the structure of soliton molecules formed by the close aggregation of multiple solitons, and the controlled evolution of soliton molecules to monosolon pulses.

The numerical simulation results of the system show that the Nyquist soliton can exist stably in a large parameter interval, and its pulse energy can be continuously increased while keeping the pulse width and spectral shape basically unchanged.

Figure 2: Nyquist soliton molecules and their evolution to monosolitons. (a) The change curve of optical power in the resonator cavity with the optical frequency of the pump. Different power steps correspond to different soliton states within the cavity. (b) Soliton pulse shape (left) vs. spectrum (right) at the 3 power steps marked. Blue: experimental results; Red: Simulation results. The S6 and S3 states are soliton molecules, which contain 6 and 3 solitons, respectively. The S1 state is soliton. Both soliton molecules and monosoliton correspond to the eigenfunctions (gray profile) of spectral filtering effects and self-phase modulation.

Summary and outlook

In this work, the researchers discovered a new mechanism of soliton generation dominated by spectral filtering effect, which achieved flexible regulation of spectral shape by regulating the dispersion and loss of the resonant cavity, and obtained a Nyquist soliton with a flat spectrum. This study deepens people’s understanding of the physical mechanism of photosolon formation and expands the research paradigm of Kerr soliton photocombs. In the future, the concept can be transferred to an integrated microcavity platform to regulate the dispersion and filtering characteristics of the microcavity by designing periodic photonic crystal structures to realize micro-Kerr combs with ideal spectral shapes. (Source: LightScience Applications WeChat public account)

Figure 3: Conceptual diagram of an integrated Kerr comb with a flat spectrum.

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