We study nonlinear Čerenkov radiation generated from a nonlinear photonic crystal waveguide where the nonlinear susceptibility tensor is modulated by the ferroelectric domain. Nonlinear polarization driven by an incident light field may emit coherently harmonic waves at new frequencies along the direction of Čerenkov angles. Multiple radiation spots with different azimuth angles are simultaneously exhibited from such a hexagonally poled waveguide. A scattering involved nonlinear Čerenkov arc is also observed for the first time. Čerenkov radiation associated with quasi-phase matching leads to these novel nonlinear phenomena.

Single solitons are a special limit of more general waveforms commonly referred to as cnoidal waves or Turing rolls. We theoretically and computationally investigate the stability and accessibility of cnoidal waves in microresonators. We show that they are robust and, in contrast to single solitons, can be easily and deterministically accessed in most cases. Their bandwidth can be comparable to single solitons, in which limit they are effectively a periodic train of solitons and correspond to a frequency comb with increased power. We comprehensively explore the three-dimensional parameter space that consists of detuning, pump amplitude, and mode circumference in order to determine where stable solutions exist. To carry out this task, we use a unique set of computational tools based on dynamical system theory that allow us to rapidly and accurately determine the stable region for each cnoidal wave periodicity and to find the instability mechanisms and their time scales. Finally, we focus on the soliton limit, and we show that the stable region for single solitons almost completely overlaps the stable region for both continuous waves and several higher-periodicity cnoidal waves that are effectively multiple soliton trains. This result explains in part why it is difficult to access single solitons deterministically.

Cnoidal waves are the periodic analog of solitons. Like solitons, they can be generated in microresonators and correspond to frequency combs. The generation of frequency combs in nonlinear microresonators is modeled by the Lugiato–Lefever equation. In this paper, we study the Lugiato–Lefever equation for a microresonator in the anomalous dispersion regime. In the lossless case, we show that the cnoidal waves can be expressed as a combination of Jacobi elliptic functions. These solutions reduce to known soliton-like solutions in particular cases. The properties of cnoidal waves in the realistic lossy case and their potential uses are also discussed.

The mechanical analog of optical frequency combs, phononic frequency combs, has recently been demonstrated in mechanical resonators and has been attributed to coupling between multiple phonon modes. This paper investigates the influence of the mode structure on comb generation using a model of two nonlinearly coupled phonon modes. The model predicts that there is only one region within the amplitude-frequency space where combs exist, and this region is a subset of the Arnold tongue that describes a 2:1 autoparametric resonance between the two modes. In addition, the location and shape of the comb region are analytically defined by the resonance frequencies, quality factors, mode coupling strength, and detuning of the driving force frequency from the mechanical resonances, providing clear conditions for comb generation. These results enable comb structure engineering for applications in areas as broad as sensing, communications, quantum information science, materials science, and molecular science.

Modeling brain stimulation at the microscopic scale may reveal new paradigms for various stimulation modalities. We present the largest map to date of extracellular electric field distributions within a layer L2/L3 mouse primary visual cortex brain sample. This was enabled by the automated analysis of serial section electron microscopy images with improved handling of image defects, covering a volume of 250 × 140 × 90 μm³. The map was obtained by applying a uniform brain stimulation electric field at three different polarizations and accurately computing microscopic field perturbations using the boundary element fast multipole method. We used the map to identify the effect of microscopic field perturbations on the activation thresholds of individual neurons. Previous relevant studies modeled a macroscopically homogeneous cortical volume. Our result shows that the microscopic field perturbations - an 'electric field spatial noise' with a mean value of zero - only modestly influence the macroscopically predicted stimulation field strengths necessary for neuronal activation. The thresholds do not change by more than 10% on average. Under the stated limitations and assumptions of our method, this result essentially justifies the conventional theory of "invisible" neurons embedded in a macroscopic brain model for transcranial magnetic and transcranial electrical stimulation. However, our result is solely sample-specific and is only relevant to this relatively small sample with 396 neurons. It largely neglects the effect of the microcapillary network. Furthermore, we only considered the uniform impressed field and a single-pulse stimulation time course.

We analyze the consequences of dissipative heating in driven Kerr microresonators theoretically and numerically, using a thermal Lugiato-Lefever model. We show that thermal sensitivity modifies the stability range of continuous waves in a way that blocks direct access to broadband frequency-comb-forming waveforms, and we propose a deterministic access path that bypasses the thermal instability barrier. We describe a thermal instability that leads to thermo-optical oscillations via a Hopf bifurcation.