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 Physics , 2012, DOI: 10.1103/PhysRevA.87.053852 Abstract: We establish an exact partial differential equation to model Kerr comb generation in whispering-gallery mode resonators. This equation is a variant of the Lugiato-Lefever equation that includes higher-order dispersion and nonlinearity. This spatio-temporal model, whose main variable is the total intracavity field, is significantly more suitable than the modal expansion approach for the theoretical understanding and the numerical simulation of wide-span combs. It allows us to explore pulse formation in which a large number of modes interact cooperatively. This versatile approach can be straightforwardly extended to include higher-order dispersion, as well as other phenomena like Raman, Brillouin and Rayleigh scattering. We demonstrate for the first time that when the dispersion is anomalous, Kerr comb generation can arise as the spectral signature of dissipative cavity solitons, leading to wide-span combs with low pumping.
 Physics , 2014, DOI: 10.1103/PhysRevA.89.013835 Abstract: We report a theoretical study showing that rogue waves can emerge in whispering gallery mode resonators as the result of the chaotic interplay between Kerr nonlinearity and anomalous group-velocity dispersion. The nonlinear dynamics of the propagation of light in a whispering gallery-mode resonator is investigated using the Lugiato-Lefever equation, and we evidence a range of parameters where rare and extreme events associated with a non-gaussian statistics of the field maxima are observed.
 Physics , 2012, DOI: 10.1103/PhysRevLett.109.143902 Abstract: Nonlinear frequency conversion is a well known and widely exploited family of effects in optics, often arising from a Kerr nonlinearity in a crystal medium. Here, we report high stability frequency conversion in the microwave regime due to a $\chi^{(3)}$ nonlinearity in sapphire introduced by a dilute concentration of paramagnetic spins. First, we produce a high stability comb from two microwave fields at 12.029 and 12.037 GHz corresponding to two high $Q$-factor Whispering Gallery (WG) modes within the Electron Spin Resonance (ESR) bandwidth of the Fe$^{3+}$ ion. The resulting comb is generated by a cascaded four-wave mixing effect with a 7.7 MHz repetition rate. Then, by suppressing four-wave mixing by increasing the threshold power, third harmonic generation is achieved in a variety of WG modes coupled to various species of paramagnetic ion within the sapphire.
 Physics , 2008, DOI: 10.1103/PhysRevA.79.041805 Abstract: An optical comb is shown to arise from a whispering gallery mode resonator pumped by two optical frequencies. Two externally excited modes couple due to Kerr nonlinearity to initially empty modes and give rise to new frequency components. This thresholdles process is much more efficient than the previously reported single-pump four-wave mixing. As a result, a few milliwatt pump is sufficient to generate strong secondary fields, that efficiently generate higher-order frequency components and so on, in a cascade process leading to an optical comb.
 Physics , 2015, DOI: 10.1364/OE.23.001594 Abstract: Optical whispering gallery mode (WGM) resonators have been very attracting platforms for versatile Kerr frequency comb generations. We report a systematic study on the material dispersion of various optical materials that are capable of supporting quality factors above $10^9$. Using an analytical approximation of WGM resonant frequencies in disk resonators, we investigate the effect of the geometry and transverse mode order on the total group-velocity dispersion ($GVD$). We demonstrate that the major radii and the radial mode indices play an important role in tailoring the $GVD$ of WGM resonators. In particular, our study shows that in WGM disk-resonators, the polar families of modes have very similar $GVD$, while the radial families of modes feature dispersion values that can differ by up to several orders of magnitude. The effect of these giant dispersion shifts are experimentally evidenced in Kerr comb generation with magnesium fluoride. From a more general perspective, this critical feature enables to push the zero-dispersion wavelength of fluorite crystals towards the mid-infrared (mid-IR) range, thereby allowing for efficient Kerr comb generation in that spectral range. We show that barium fluoride is the most interesting crystal in this regard, due to its zero dispersion wavelength ($ZDW$) at $1.93 \rm{\mu m}$ and an optimal dispersion profile in the mid-IR regime. We expect our results to facilitate the design of different platforms for Kerr frequency comb generations in both telecommunication and mid-IR spectral ranges.
 Physics , 2009, DOI: 10.1063/1.3065024 Abstract: The boundary element method is applied to investigate the optical forces when whispering gallery modes (WGMs) are excited by a total internally reflected wave. Such evanescent wave is particularly effective in exciting the high-$Q$ WGM, while the low angular or high radial order modes are suppressed relatively. This results in a large contrast between the forces on and off resonance, and thus allows for high size-selectivity. We fully incorporate the prism-particle interaction and found that the optical force behaves differently at different separations. Optimal separation is found which corresponds to a compromise between intensity and $Q$ factor.
 Physics , 2011, DOI: 10.1103/PhysRevA.85.014902 Abstract: We study theoretically interference of the long-living quasistationary quantum states of antihydrogen atoms, localized near a concave material surface. Such states are an antimatter analog of the whispering gallery states of neutrons and matter atoms, and similar to the whispering gallery modes of sound and electro-magnetic waves. Quantum states of antihydrogen are formed by the combined effect of quantum reflection from van der Waals/Casimir-Polder (vdW/CP) potential of the surface and the centrifugal potential. We point out a method for precision studies of quantum reflection of antiatoms from vdW/CP potential; this method uses interference of the whispering gallery states of antihydrogen.
 Physics , 2014, DOI: 10.1117/12.2044823 Abstract: Different applications of crystalline whispering gallery mode resonators call for different properties of the resonator host material. We report on our recent study of resonators made out of sapphire, diamond, and quartz crystals and discuss possible applications of these resonators. In particular, we demonstrate Kerr frequency comb generation in sapphire microresonators.
 Physics , 2015, Abstract: Magnons in ferrimagnetic insulators such as yttrium iron garnet (YIG) have recently emerged as promising candidates for coherent information processing in microwave circuits. Here we demonstrate optical whispering gallery modes of a YIG sphere interrogated by a silicon nitride photonic waveguide, with quality factors approaching $10^6$ in the telecom c-band after surface treatments. Moreover, in contrast to conventional Faraday setup, this implementation allows input photon polarized colinearly to the magnetization to be scattered to a sideband mode of orthogonal polarization. This Brillouin scattering process is enhanced through triply resonant magnon, pump and signal photon modes - all of whispering gallery nature - within an "optomagnonic cavity". Our results show the potential use of magnons for mediating microwave-to-optical carrier conversion.
 Physics , 2015, DOI: 10.1126/science.aaa7469 Abstract: Designing high-finesse resonant cavities for electronic waves faces challenges due to short electron coherence lengths in solids. Previous approaches, e.g. the seminal nanometer-sized quantum corrals, depend on careful positioning of adatoms at clean surfaces. Here we demonstrate an entirely different approach, inspired by the peculiar acoustic phenomena in whispering galleries. Taking advantage of graphene's unique properties, namely gate-tunable light-like carriers, we create Whispering Gallery Mode (WGM) resonators defined by circular pn-junctions, induced by a scanning tunneling probe. We can tune the resonator size and the carrier concentration under the probe in a back-gated graphene device over a wide range, independently and in situ. The confined modes, revealed through characteristic resonances in the tunneling spectrum, originate from Klein scattering at pn junction boundaries. The WGM-type confinement and resonances are a new addition to the quantum electron-optics toolbox, paving the way to real-world electronic lenses and resonators.
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