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A calculation is presented that shows that Feynman's path integral implies Ostrogradsky's Hamiltonian for nonsingular Lagrangians with second derivatives. The procedure employs the stationary phase approximation to obtain the limiting…
The system of nonlinear Langevin equations was obtained by using Hamiltonian's operator of two coupling quantum oscillators which are interacting with heat bath. By using the analytical solution of these equations, the analytical…
High-quality frequency references are the cornerstones in position, navigation and timing applications of both scientific and commercial domains. Optomechanical oscillators, with direct coupling to continuous-wave light and…
The Hamiltonian description of the self-consistent interaction between an electromagnetic plane-wave and a co-propagating beam of charged particles is considered. We show how the motion can be reduced to a one-dimensional Hamiltonian model…
Molecular optomechanics stems from the description of Raman scattering in the presence of an optical resonator using a cavity optomechanics formalism. We extend the molecular optomechanics formalism to the case of hybrid…
Optical Ising machines promise to solve complex optimization problems with an optical hardware acceleration advantage. Here we study the ground state properties of a nonlinear optical Ising machine realized by spatial light modulator,…
Mirrorless optical parametric oscillator (MOPO) is a consequence of intrinsic feedback provided by the nonlinearity in a medium due to the interaction of a pair of strong counter-propagating fields. As the name suggests, the device doesn't…
Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to…
A new model for the finite one-dimensional harmonic oscillator is proposed based upon the algebra u(2)_{\alpha}. This algebra is a deformation of the Lie algebra u(2) extended by a parity operator, with deformation parameter {\alpha}. A…
We study the groundstates of cold atomic gases on rotating optical lattices, as described by the Bose-Hubbard model in a uniform effective magnetic field. Mapping the bosons to composite fermions leads to the prediction of quantum Hall…
Solitons are non-dispersing localized waves that occur in diverse physical settings. A variety of optical solitons have been observed, but versions that involve both spatial and temporal degrees of freedom are rare. Optical fibers designed…
The phenomenon of pattern formation in nonlinear optical resonators is commonly related to an off-resonance excitation mechanism, where patterns occur due to mismatch between the excitation and resonance frequency. In this paper we show…
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series…
A new device to generate polarization-entangled light in the continuous variable regime is introduced. It consists of an Optical Parametric Oscillator with two type-II phase-matched non-linear crystals orthogonally oriented, associated with…
Dissipative solitons can emerge in a wide variety of dissipative nonlinear systems throughout the fields of optics, medicine or biology. Dissipative solitons can also exist in Kerr-nonlinear optical resonators and rely on the double balance…
We derive model equations for optical pulse propagation in a medium described by a two-level Hamiltonian, without the use of the slowly varying envelope approximation. Assuming that the resonance frequency of the two-level atoms is either…
We study theoretically the spatial evolution of optical beams inside a graded-index fiber exhibiting saturable nonlinearity. Utilizing an approach based on the variational principle, we identify the existence of bistable spatial solitons…
We theoretically investigate interactions between non-degenerate mechanical oscillators mediated by a time-dependent cavity field. We obtain a reduced master equation valid for all optomechanical systems operating in the weak coupling…
Optical oscillators present a powerful optimization mechanism. The inherent competition for the gain resources between possible modes of oscillation entails the prevalence of the most efficient single mode. We harness this 'ultrafast'…
A comprehensive analysis of hybrid TM-TE polarized surface electromagnetic waves supported by different few-layer anisotropic metasurfaces is presented. A generalized 4$\times$4 T-matrix formalism for arbitrary anisotropic 2D layers is…