Related papers: The multi-resonant Lugiato-Lefever model
We analyze photo-refractive incoherent soliton beams and their interactions in Kerr-like nonlinear media. The field in each of M incoherently interacting components is calculated using an integrable set of coupled nonlinear Schrodinger…
A convenient for practical use new theoretical approach describing a nonlinear frequency response of the multi-resonant nonlinear ring cavities (RC) to an intense monochromatic wave action is developed. The approach closely relates the…
We derive a general theory of linear coupling and Kerr nonlinear coupling between modes of dielectric optical resonators from first principles. The treatment is not specific to a particular geometry or choice of mode basis, and can…
In recent years, essential progress has been made in the nonlinear stability analysis of periodic Lugiato-Lefever waves against co-periodic and localized perturbations. Inspired by considerations from fiber optics, we introduce a novel…
We analyze the impact of pump depletion in the generation of cavity solitons in a singly-resonant parametrical oscillator that includes a $\chi^{(3)}$ nonlinear section. We find an analytical expression that provides the soliton existence…
We propose a comprehensive model describing the Kerr nonlinear dynamics of an electric field in a cylindrical microresonator with an effective radius variation, coupled to a radiation source. The proposed system of equations for coupled…
In this work we investigate an optomechanical system consisting of two cavities coupled to the same mechanical resonator. We consider each cavity being weakly pumped as well as a small tunneling rate between the cavities. In such…
In this paper, we consider the resonance problem for the cubic nonlinear Helmholtz equation in the subwavelength regime. We derive a discrete model for approximating the subwavelength resonances of finite systems of high-contrast resonators…
We use Maxwell's equations to derive several models describing the interaction of the multi-mode fundamental field and its second harmonic in a ring microresonator with quadratic nonlinearity and quasi-phase-matching. We demonstrate how…
We consider optical 1D envelope solitons in Kerr dielectric with cubic non-linearity and use two solitons configurations for modelling entangled states of photons. We calculate spin, momentum and energy of solitons on the basis of…
In this work, we study the bifurcation structures and the stability of multidimensional localized states within coherently driven Kerr optical cavities with parabolic potentials in 1D, 2D, and 3D systems. Based on symmetric considerations,…
Soliton crystals are periodic patterns of multi-spot optical fields formed from either time or space entanglements of equally separated identical high-intensity pulses. These specific nonlinear optical structures have gained interest in…
We present a general approach to excite robust dissipative three-dimensional and high-order solitons and breathers in passively driven nonlinear cavities. Our findings are illustrated in the paradigmatic example provided by an optical Kerr…
We study a generic cavity-QED system where a set of (artificial) two-level dipoles is coupled to the electric field of a single-mode LC resonator. This setup is used to derive a minimal quantum mechanical model for cavity QED, which…
Optical soliton molecules are bound states of solitons that arise from the balance between attractive and repulsive effects. Having been observed in systems ranging from optical fibers to mode-locked lasers, they provide insights into the…
Emergent phenomena are ubiquitous in nature and refer to spatial, temporal, or spatiotemporal pattern formation in complex nonlinear systems driven out of equilibrium that is not contained in the microscopic descriptions at the…
We consider an optical resonator containing a photonic crystal fiber and driven coherently by an injected beam. This device is described by a generalized Lugiato-Lefever equation with fourth order dispersion. We use an asymptotic approach…
We consider the quantum measurement properties of a driven cavity with a Kerr-type nonlinearity which is used to amplify a dispersively coupled input signal. Focusing on an operating regime which is near a bifurcation point, we derive…
We discover multipole-mode solitons supported by the surface between two distinct periodic lattices imprinted in Kerr-type nonlinear media. Such solitons are possible because the refractive index modulation at both sides of the interface…
Two-mode nonlinear coherent states are introduced in this paper. The pair coherent states and the two-mode Perelomov coherent states are special cases of the two-mode nonlinear coherent states. The exponential form of the two-mode nonlinear…