Dissipative Kerr soliton (DKS) frequency combs—also known as microcombs—have arguably created a new field in cavity nonlinear photonics, with a strong cross-fertilization between theoretical, experimental, and technological research. Spatiotemporal mode-locking (STML) not only adds new degrees of freedom to ultrafast laser technology, but also provides new insights for implementing analogue computers and heuristic optimizers with photonics. Here, we combine the principles of DKS and STML to demonstrate the STML DKS by developing an unexplored ultrahigh-quality-factor Fabry–Pérot (FP) mesoresonator based on graded index multimode fiber (GRIN-MMF). Complementing the two-step pumping scheme with a cavity stress tuning method, we can selectively excite either the eigenmode DKS or the STML DKS. Furthermore, we demonstrate an ultralow noise microcomb that enhances the photonic flywheel performance in both the fundamental comb linewidth and DKS timing jitter. The demonstrated fundamental comb linewidth of 400 mHz and DKS timing jitter of 500 attosecond (averaging times up to 25 μs) represent improvements of 25× and 2.5×, respectively, from the state-of-the-art. Our results show the potential of GRIN-MMF FP mesoresonators as an ideal testbed for high-dimensional nonlinear cavity dynamics and photonic flywheel with ultrahigh coherence and ultralow timing jitter.

the biaxial anisotropy of Nd:YLF crystal, the parameters, such as the stimulated-emission cross section, thermo-optical coefficient and thermo-expansion coefficient, along the a and c axes are different, which leads to a quite different performance of the thermal lens effect for a and c directions. The former studies [5-9] on the thermal effect of Nd:YLF crystal revealed that there is an obvious difference between the thermal lens focal length along a and c axes for both π and σ polarizations. According to Ref.[5], the thermal lens focal lengths of π and σ polarizations along a direction are negative and positive, respectively, for example −100 mm and 300 mm at 12 W end pump power under non-lasing condition. However, along the c direction, the thermal lens focal lengths of the two polarizations are both too weak to be measured. It is interesting that there is a so great difference on the thermal lens focal length between the a and c axes. It is explained by the elliptical pump beam waist and the surmise of that the thermal conductivity for the c axis is twice of the a axis in Ref. [5]. And rarely experimental and theoretical discussions about this phenomenon were made in other papers as far as we know.In our experiment, the same phenomenon as that in the referred papers above is observed, however, some differences are also discovered. The weak thermal lens effect for π polarization along c axis is measured, and the contradiction between the experimental results and the theoretical analysis is discussed. It is found that the complementation among the thermo-optical coefficient, the thermal end bulging and the photoelastic effects contributes to the weak and asymmetry thermal lens effect of Nd:YLF crystal. Experimental measurementsThe experimental setup is shown in Fig. 1. The Nd:YLF crystal is end pumped by a diode laser (LD) with central Abstract The thermal lens effect of Nd:YLF crystal for different polarized beams is experimentally and theoretically studied in this paper. In the experiment, the different thermal lens effects of Nd:YLF crystal along a and c axes for π-and σ-polarized probe beams are observed, and the values of the focal lengths are measured. The theoretical analysis is made to explain the extremely weak thermal lens effect along the c axis, as well as that for the σ-polarized beam. And it is corroborated that the complementation among the thermo-optical coefficient, the thermal end bulging and the photoelastic effects contributes to the weak and asymmetry thermal lens effect of Nd:YLF crystal.

By identifying the similarities between the coupled-wave equations and the parametrically driven nonlinear Schrödinger equation, we for the first time unveil the existence condition of quadratic solitons in continuouswave pumped singly resonant degenerate optical parametric oscillators (SR-DOPOs). Compared to the previously explored doubly resonant DOPOs, quadratic solitons in SR-DOPOs are advantageous in their robustness against perturbations induced by dispersion of the effective third-order nonlinearity and temporal walk-off between the signal and the pump. Terahertz comb bandwidth and femtosecond pulse duration are attainable in an example periodically poled Lithium niobate waveguide resonator in the short-wave infrared. The working principle can be extended to other material platforms, making it a competitive ultrashort pulse and broadband comb source architecture at the mid-infrared.

By identifying the similarities between the coupled-wave equations and the parametrically driven nonlinear Schrödinger equation, we unveil the existence condition of the quadratic soliton mode-locked degenerate optical parametric oscillator in the previously unexplored parameter space of near-zero group velocity mismatch. We study the nature of the quadratic solitons and divide their dynamics into two distinctive branches depending on the system parameters. We find the nonlinear interaction between the resonant pump and signal results in phenomena that resemble the dispersive two-photon absorption and the dispersive Kerr effect. Origin of the quadratic soliton perturbation is identified and strategy to mitigate its detrimental effect is developed. Terahertz comb bandwidth and femtosecond pulse duration are attainable in an example periodically poled lithium niobate waveguide resonator in the short-wave infrared and an example orientation-patterned gallium arsenide free-space cavity in the long-wave infrared. The quadratic soliton mode-locking principle can be extended to other material platforms, making it a competitive ultrashort pulse and broadband comb source architecture at the mid-infrared.

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