[en] In this note we provide an alternative way of defining the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive ${\mathrm{\delta <!--\; ??\; -->}}^{\mathrm{\prime <!--\; ???\; -->}}$- interaction, of strength $\mathrm{\beta <!--\; ??\; -->}$, centred at 0 (the bottom of the confining parabolic potential), that was rigorously defined in a previous paper by means of a ‘coupling constant renormalisation’. Here we get the Hamiltonian as a norm resolvent limit of the harmonic oscillator Hamiltonian perturbed by a triple of attractive $\mathrm{\delta <!--\; ??\; -->}$-interactions, thus extending the Cheon–Shigehara approximation to the case in which a confining harmonic potential is present. (paper)

[en] This paper shows the feasibility of a harmonic-oscillation generator using a SNS microbridge biased by a dc voltage in the negative differential resistance range of its I-V characteristic curve. The frequency of the harmonic oscillations of this generator is equal to the resonant frequency of the tank RLC circuit. The principal features of this harmonic generator are discussed

[en] The paper presents a simplified formula of nonlinear regime (NR) approximation [1] for calculation of second-harmonic generation (SHG) efficiency for type I synchronism. The original formula of NR contains the Jacobi elliptic sine, which considerably complicates the calculations. The proposed simplified formula does not contain a Jacobi elliptic sine and calculation of a single graph takes several seconds in even the simplest program for mathematical calculations. At high values of the radiation divergence φ and the length of the crystal L the graphs of SHG efficiency, obtained with using initial and proposed formulas are in good agreement, and the difference in their values is about 10 % and less. Reducing the value of (φ·L) leads to an increase in the difference between results, obtained with using initial and proposed formulas. (paper)

[en] We discuss the role of commuting operators for quantum superintegrable systems, showing how they are used to build eigenfunctions. These ideas are illustrated in the context of resonant harmonic oscillators, the Krall–Sheffer operators, with polynomial eigenfunctions, and the Calogero–Moser system with additional harmonic potential. The construction is purely algebraic, avoiding the use of separation of variables and differential equation theory. (paper)

[en] We report an efficient high order harmonic generation achieved using a two-color laser field. By inserting a second harmonic generation crystal in the path of a converging laser pulse, the overall efficiency for high-order harmonic generation was enhanced by more than an order of magnitude. In addition even-order harmonics were also generated. The 2(2n+1) in order harmonics were very strong and, in particular, the 38th harmonic (21.6 nm) obtained with a single laser shot of 2 mJ, saturated the x-ray CCD of an extreme ultraviolet spectrometer even with an Al filter of 1.5 μm thickness installed in front of the CCD.

[en] The existence of quasi-bi-Hamiltonian structures for the Tremblay–Turbiner–Winternitz (TTW) and the Post–Winternitz (PW) systems is studied. We first recall that the superintegrability of these two systems is related with the existence of certain complex functions endowed with interesting Poisson bracket properties, and then we prove the existence of several quasi-bi-Hamiltonian structures making use of these complex functions. This is done in two steps: first with complex 2-forms (wedge product of the differentials of the complex functions) and then with several real 2-forms. The properties of these geometric structures and the associated recursion operators are also analyzed. The paper can be considered as divided in two parts. In the first part a we study the TTW system (related to the harmonic oscillator) and in the second part we study the PW system (related to the Kepler problem). (paper)

[en] Three-color continuous-variable (CV) entangled beams can be produced by single-pass cascaded sum-frequency processes of third-harmonic generation by quasi-phase-matching technique in only one optical superlattice. Firstly, second-harmonic field is generated by the first double-frequency process of the fundamental field. Then, the third-harmonic field can be generated by the second cascaded sum-frequency process between the second-harmonic and the fundamental fields by quasi-phase-matching technique in the same optical superlattice. By using the quantum stochastic method, we investigated the conversion dynamics of the cascaded sum-frequency processes and the quantum correlation nature among the fundamental, second-harmonic, and third-harmonic fields. The results show that the higher conversion efficiency of third-harmonic generation can be achieved with the larger nonlinear coupling parameter of the second cascaded sum-frequency process. We also show that the fundamental, second-, and third-harmonic beams are CV entangled with each other according to the necessary and sufficient CV entanglement criterion. This scheme of three-color entanglement generation without involving optical cavity is easy to realize in experiment. Moreover, the three-color entangled beams are separated by an octave in frequency which has potential applications in quantum communication and computation networks. (letter)

[en] One of the main obstacles in achieving stable, efficient operation at the cyclotron harmonics in a gyrotron is mode competition with parasitic modes at the fundamental frequency. In this article, the nonlinear dynamics of mode interactions in such a system are studied using a multifrequency, time-dependent model. The results of numerical simulations for a second harmonic gyrotron are presented by considering two starting scenarios: (a) fast voltage rise or an instant turn-on case, and (b) slow voltage rise case. For the first case, it is demonstrated that for a certain range of operating parameters, the presence of a parasitic mode at the fundamental can be helpful in the excitation of the second harmonic operating mode. In the second case, it is found that the unstable operating region increases with the value of the rise time constant of the electrode voltages. Stable, efficient gyrotron operation at the second harmonic is demonstrated using the numerical study

[en] By solving the normalized dimensionless linear Schrödinger-like equation with harmonic potential analytically, we have studied the spatiotemporal Airy Gaussian (AiG) and Airy Gaussian vortex (AiGV) light bullets. The AiG light bullets are composed of the chirped Airy functions in temporal domain and the AiG functions in spatial domain, while AiGV light bullets are AiG light bullets carrying the vortex. By selecting the negative or positive linear chirp we can obtain decelerating or accelerating light bullets, respectively. Combing effects from harmonic potential with the negative quadratic chirp, we can study reversed light bullets in both spatial and temporal domains. (letter)

[en] We propose a scheme for generating three primary colours with a 1064 nm pump wave. Three quasi-phase-matched parametric processes, i.e., second-harmonic generation, optical parametric generation, and sum-frequency generation, are coupled in a single optical superlattice. On the basis of the plane-wave approximation, the coupling process is investigated theoretically. And a special design for a quasiperiodic structure is presented