Short optical solitons in fibers

The dynamics of short (of the order of a few wave periods) intense optical pulses and interaction of short optical solitons in fibers are considered within the framework of the third-order nonlinear Schrodinger equation. It is shown that an initial pulse tends to one or a few short solitons plus a linear quasiperiodic wave when the third-order linear dispersion and nonlinear dispersion have parameters of the same sign. The number and parameters of the solitons depend on the magnitudes of initial pulse parameters. Interaction of short optical solitons having different amplitudes is accompanied by radiation of part of the wave field from the area of interaction, by an increase of the soliton with larger amplitude, and a decrease of the soliton with a smaller one. (c) 2000 American Institute of Physics.     

Conditional expectation values in quantum mechanics

The general question of defining the expectation value of an operator for a fixed value of another noncommuting observable is considered and explicit expressions are derived. Due to the noncommutivity of operators a unique definition is not possible, and we consider different possible expressions. Special cases which have previously been considered in the literature are shown to be derivable from the methods presented.In honor of Ilya Prigogine on the occasion of his 70th birthday.     

Formation of nonclassical states of vortex solitons in optical fibers with quantum dots

The problem of control for the quantum statistics of dissipative vortex optical solitons when using the Raman scheme of spin-flip transitions in an optical fiber doped with narrow-bandgap semiconductor quantum dots is considered. The possibility of forming individual bounded nonclassical quadrature squeezed light regions appearing within the spatial profile of a formed vortex soliton is demonstrated.     

Heat dissipative solitons in optical fibers

We propose a one-dimensional model governing the propagation of heat waves in an optical fiber (the “fiber fuse”). The model has solutions in the form of high temperature localized waves moving towards the input end of the fiber, fueled by the laser power. These waves can be ignited by local heating at any point along the fiber. The effect of such a wave is irreversible damage to the fiber core. The phenomenon was observed earlier by Hand and Russell, when locally heating a fiber through which CW light of modest intensity was propagating. This induced self-destruction of the optical fiber core.     

On inferring quantum energies and expectation values

A maximum entropy-like inference approach is proposed that yields ground and excited states energies and expectation values without solving Schrödinger's equation. The method is tested with reference to the quartic anharmonic oscillator and other model potentials and yields good results without undue numerical effort.     

Area expectation values in quantum area Regge calculus

Regge calculus generalised to independent area tensor variables is considered. Continuous time limit is found and formal Feynman path integral measure corresponding to the canonical quantisation is written out. Quantum measure in the completely discrete theory is found which possesses the property to lead to the Feynman path integral in the continuous time limit whatever coordinate is chosen as the time. This measure can be well defined by passing to the integration over imaginary field variables (area tensors). Averaging with the help of this measure gives finite expectation values for areas.     

Analysis of enhanced-power solitons in dispersion-managed optical fibers

We analyze pulse propagation in an optical fiber employing a periodic dispersion map. Second-order averaging is used to determine a general evolution equation valid for both return-to-zero and non-return-to-zero pulses in dispersion-managed systems. The equation is then applied to the case of solitons, and an analytic expression for the power enhancement arising from the dispersion management is obtained.     

Velocity of heat dissipative solitons in optical fibers

In the fiber fuse, a pulse of high temperature travels toward the input end of the fiber, where high-power laser light is launched into the fiber. At any point along the fiber, the soliton can be ignited. The fiber core is damaged in the process so that light cannot propagate beyond the hot spot. This phenomenon is an example of a dissipative soliton that can exist only in the presence of an external energy supply and internal loss. We analyze this phenomenon, derive an expression for the velocity of the soliton, and determine its width as functions of the physical parameters of the laser and the fiber material.     

Surface optical solitons in semiconductor quantum dot layers

A theory of optical solitons under the condition of nonlinear coherent interaction of surface TM-modes with a layer of inhomogeneously broadened semiconductor quantum dots is developed. Explicit analytical expressions for a surface soliton (2π-pulse) in the presence of single and biexciton transitions are obtained in the regime of self-induced transparency with realistic parameters which can be reached in current experiments.     

Surface optical solitons in semiconductor quantum dot layers

A theory of optical solitons under the condition of nonlinear coherent interaction of surface TM-modes with a layer of inhomogeneously broadened semiconductor quantum dots is developed. Explicit analytical expressions for a surface soliton (2π-pulse) in the presence of single and biexciton transitions are obtained in the regime of self-induced transparency with realistic parameters which can be reached in current experiments.     

Manifestation of destruction of quantum integrability with expectation and uncertainty values of quantum observables

A method to demonstrate destruction of quantum integrability is presented. The method is based on the calculation (for systems with two degrees of freedom) of the expectation and uncertainty values of energy and another quantum observable which is conservative when the system is integrable. Two kinds of avoided crossings can be shown clearly with this method.     

Diverse chirped optical solitons and new complex traveling waves in nonlinear optical fibers

This paper studies chirped optical solitons in nonlinear optical fibers. However, we obtain diverse soliton solutions and new chirped bright and dark solitons, trigonometric function solutions and rational solutions by adopting two formal integration methods. The obtained results take into account the different conditions set on the parameters of the nonlinear ordinary differential equation of the new extended direct algebraic equation method. These results are more general compared to Hadi et al(2018 Optik 172 545–53) and Yakada et al(2019 Optik197 163108).     

Chern-Simons expectation values and quantum horizons from loop quantum gravity and the Duflo map

We report on a new approach to the calculation of Chern-Simons theory expectation values, using the mathematical underpinnings of loop quantum gravity, as well as the Duflo map, a quantization map for functions on Lie algebras. These new developments can be used in the quantum theory for certain types of black hole horizons, and they may offer new insights for loop quantum gravity, Chern-Simons theory and the theory of quantum groups.     

Generation of high order multi-bound solitons and propagation in optical fibers

We demonstrate experimental generation of multi-bound solitons of up to sextuple in an active FM mode-locked fiber ring laser operating under power saturation in the locking state. The ring laser consists of two booster optical amplifiers operating in saturation regime, an electro-optic phase modulator driven by a sinusoidal electrical wave and a length of dispersive fiber. The periodic phase modulation generates phase chirp of the generated lightwaves in the ring laser. The chirped phase state plays an important role in the phase matching condition for mode-locking as well as the stabilization and the determination of the bound states of multi-solitons. The formation of such high order multi-bound solitons is explained based on the chirping of the phase and the behavior of the optical pulse sequence in the near field region of the dispersive fiber. The propagation of these multi-bound solitons through single mode optical fibers is observed. Experimental and simulation results of bound solitons have been shown to follow similar trends.The propagation of these multi-bound solitons through single mode optical fibers is described. Their mutual interaction through such quadratic phase media shows the influence of the quadratic phase property on the differential phase of individual solitons of the bound group. Simulated results confirm the evolution of the bound solitons over dispersive single mode optical fibers.     

Perturbation of higher-order solitons by fourth-order dispersion in optical fibers

We study analytically and numerically how the radiation emitted by fundamental solitons in the form of dispersive waves is affected by the third and fourth-order dispersions when a higher-order soliton undergoes the fission process inside an optical fiber. Our results show that two dispersive wave sidebands appear in the output spectrum on opposite sides of the input spectrum. The frequencies of these sidebands are set by the relative magnitudes of the third- and fourth-order dispersion parameters, but are not affected much by the Raman process. A well defined phase-matching condition accurately predicts these conjugate frequencies of dispersive wave. The relative amplitudes of these two sidebands are not equal because of the asymmetry induced by the third-order dispersion and higher-order nonlinearities. It is found that with increasing fourth-order dispersion the amplitude of both spectral components eventually saturate and the relative power level associated with one of the components can exceed 10% of the launched power under suitable conditions. This component is the one that will form even in the absence of fourth-order dispersion and its wavelength may lie on the red or the blue side of the launched wavelength depending on the sign of the dispersion slope at this wavelength. It is also observed that soliton order itself significantly influence the peak amplitude of the radiation and play a minor role in determining radiation frequencies. We believe, these results should be of relevance for applications requiring an ultrabroadband optical source and understanding the interesting facts of supercontinuum generation.     

Ultraslow optical solitons in tunnel-coupled double semiconductor quantum well

This paper investigates the nonlinear evolution of the pulse probe field in an asymmetric coupled-quantum well driven coherently by a pulse probe field and two controlled fields. This study shows that, by choosing appropriate physical parameters, self-modulation can precisely balance group velocity dispersion in the investigated system, leading to the formation of ultraslow optical solitons of the probe field. The proposed scheme may lead to the development of the controlled technique of optical buffers and optical delay lines.