Population trapping in the Jaynes-Cummings model with a Kerr nonlinearity in the cavity

Abstract

An electromagnetic field state is found which maintains the population inversion of the atom stationary during the interaction with the field through a Jaynes-Cummings model (JCM) with a Kerr type nonlinearity in the cavity. The condition of stationarity of the population inversion includes the phase coupling of atomic dipole with the field. We have shown that the Kerr nonlinearity in the cavity field significantly modifies the photon statistics of the trapped field state through an intensity dependent detuning in the field compared to the normal JCM trapping state. We have also demonstrated the novel features of sub-Poissonian character and the squeezing of the trapped field state. The dynamics of the initial trapped field is studied in terms of squeezing and the Q-function.     

Analytical study of optical solitons in media with Kerr and parabolic-law nonlinearities

The nonlinear optical transmission equation was investigated in the presence of detuning, inter-modal dispersion, time- and space-modulated external potentials, and dissipation. Optical solitons, triangular periodic solutions, and Jacobian elliptic periodic solutions are constructed with the aid of the self-similarity transformation and Jacobian elliptic equation expansion methods. The conditions for analytical solutions to exist are obtained. Both Kerr-law as well as parabolic-law nonlinear media are considered.     

The characteristics of Kerr lens mode-locked Nd:YVO4 laser with a symmetrical z-shaped cavity

In this paper, a diode-pumped CW Kerr lens mode-locked Nd:YVO₄ laser is demonstrated in the megahertz (MHz) oscillations mode-locked regime for the first time. Considered the beam mode size in the laser crystal and the Kerr lens sensitivity, an effective laser system with a symmetrical z-shaped cavity is strictly designed by the ABCD matrix and experimentally researched. The laser system can be self-starting without the need of any additional components. When an incident pump power is of 8 W, the maximum output power is 1.65 W, with a slope efficiency of 23.8%. The mode-locked repetition rate and pulse width are 530 MHz and 15.1 ps, respectively.     

Spectrum of a Micromaser with Kerr Nonlinearity

Abstract

We analyse the spectrum of a micromaser with a Kerr-type nonlinearity in its cavity. We show that the intracavity Kerr nonlinearity has significant effects on the spectrum leading to narrowing of the subnatural linewidth and frequency-shifts.     

Electromagnetic solitons in a superlattice with parabolic miniband

Using a microscopic approach and the Maxwell equations, it is shown that extremely short optical pulses (soliton analogs) exist in superlattices with parabolic minibands. Mechanisms responsible for changes in the shape of extremely short optical pulses are considered. It is established that the parameters of these electromagnetic solitons depend on the temperature.

     

Two-dimensional motion in a Bell-constrained plate

The so-called Bell constraint has been used for several years in plasticity theory and has additionally been the subject to several investigations within an elastic context. In this paper the effects of the Bell constraint on the propagation of harmonic waves in a finitely deformed elastic plate are considered. Strong ellipticity conditions are first derived for the unbounded case, and are shown to be dependent on the scalar multiplier associated with the Bell constraint. The dispersion relation, associated with harmonic wave propagation in a plate composed of such a material with zero incremental surface traction, is derived in respect of an arbitrary strain energy function. Asymptotic expansions are then obtained for high and low wave number. These expansions, which give phase speed as a function of wave number, harmonic number and pre-stress, are shown to give excellent agreement with numerical solutions.     

Two-dimensional buoyant jet in a current

Summary When an effluent is discharged into a current at or near the bed, it may be advantageous to have the effluent flowing along the bed for some distance, thickening en route, so that it will have become diluted sufficiently before it reaches the surface. This can be achieved provided the effluent is discharged from a narrow long slot into the ambient current; the effluent plume then flows near the bed due to the pressure drop on the lee side of the emerging effluent.To confirm that this type of effluent flow could exist, laboratory experiments were conducted in which warm water at about 76° C was discharged vertically upwards from a slot 1 cm wide into an ambient current at a temperature of about 12° C. It was observed that the discharged effluent rose a short distance above the slot, due to its initial momentum, and then re-attached itself to the rigid floor, continuing along the floor as it slowly thickened. The temperature and its fluctuation, the velocity and the thickness of the layer, were measured for various ratio of the ambient velocity to the jet velocity and densimetric Froude numbers at the slot. It was found that flow in the layer at a certain distance from the slot is dynamically similar, and that the measured data can be described by non-dimensional similarity functions in the density and velocity field. It was also shown, both theoretically and experimentally, that the depth and the dilution factor, based on the maximum temperature of the under-flowing layer, increases linearly with down-stream distance from the slot.It was further found that the coefficient of skin friction depends on Richardson number and that the coefficient remains constant for a given flow condition.Notation C ₁,C ₂ constant coefficients equation (2.12) - C _f coefficient of skin friction - F ₀ densimetric Froude number equation (4.9) - F _x,F _y components of the buoyancy force inx andy direction - f ₁(),f ₂(),g ₁()g ₂(),g ₁₂() universal functions equation (2.4) - g– acceleration due to gravity - I ₁,I ₂ integrals of functionf ₁() andf ₂() equation (2.15) - h– characteristic thickness of the underflowing layer - h ₀ depth of the warm layer at section A-A (Fig. 1) - H depth of the ambient current - n index associated with raw data - N total number of digitized data - p pressure - R ratio of the ambient velocity to the jet velocity - R _e Reynolds number based at the slot - R _i Richardson number equation (2.12) - T local arithmetic mean value of temperature - T ₀ temperature of the jet at slot exit - T _a temperature of the ambient current - T _m maximum temperature at each section - t _n instantaneous point temperature - t time - root-mean-square of temperature - U local mean velocity in the mean flow direction - U _a average mean velocity of the ambient current (see Fig. 1) - U ₀ jet velocity at the slot exit - U _* shear velocity - V local mean velocity in the vertical direction - velocity fluctuation ofU andV component respectively - w slot width - X ₀ non-dimensional distance from the virtual origin - x, y system of co-ordinates (Fig. 1) - relevant length scale at which the temperature excess is half of its maximum value - non-dimensional transverse distance - angle of inclination of the rigid boundary - ratio between the length scale and the characteristic thicknessh - kinematic viscosity - local mass density - ₀ mass density at slot exit - _a mass density of the ambient current - ₀ mass density excess at the slot exit - _m maximum of mass density excess at each section - ₀ shear stress at rigid boundary - ₁, ₂, ₁, ₂ universal functions equations (4.5, 4.6, 4.7, 4.8)     

Interaction of bright-dark solitons in a silicon-on-insulator optical waveguide

In this paper, we use a distributed Fourier transform to simulate the interaction effects of bright and dark solitons numerically through a nonlinear coupled-wave Schrödinger equation satisfied by the TE and TM mode direction of silicon-on-insulator waveguides. The simulation shows that an increase in the relative polarization angle of bright and dark solitons reduces the influence of bright solitons on dark solitons but increases the influence of dark solitons on bright solitons when the nonlinear effect is constant. At the appropriate polarization angle, the dark soliton will show a quasi-soliton waveform under the influence of a bright soliton. When the power is similar, the interaction is most obvious. An increase in the bright soliton pulse width can increase its effective transmission distance and is greatly affected by dark solitons at short distances. A change in the dark soliton pulse width has little effect on the interaction. Changing the delay difference can change the position and peak of a quasi-soliton in a dark soliton. An appropriate delay difference can improve the effective transmission distance of the bright soliton and increase its stability in a short distance.     

Ultrafast optical Kerr gate imaging in a poly-disperse turbid medium

The influence of the size parameter of the scatterers on ultrafast optical Kerr gate (OKG) imaging is investigated in highly scattering poly-disperse turbid media. The results show that in a poly-disperse turbid medium, which in our case, is a suspension of two different sized mono-disperse microspheres, the temporal and spatial behaviors of the light pulses transmitted through it are dominated by the smaller microspheres. The contrasts of the OKG images for the poly-disperse microsphere sample are closer to the contrasts of the OKG images for the smaller sized mono-disperse microsphere sample.     

Two-dimensional temperature distribution in a ceramic-based electrode

A study has been made of the thermal processes in the electrode units in an MHD channel; generalized relationships between the geometrical parameters of the blocks and the parameters of the working body have been derived.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 1, pp. 116–123, January, 1977.     

Temporal solitons in second-harmonic generation with a noncollinear phase-mismatching scheme

A noncollinear second-harmonic-generation scheme that includes two gratings and a nonlinear optical crystal generates temporal solitons with a noncollinear phase mismatch and frequency-chirped laser pulses. At 180-fs pulse duration, 25-GW/cm2 fundamental intensity, -7647.3-m(-1) wave-vector mismatch, 66-fs delay time, and +/-3.07163 x 10(25) s(-2) frequency-chirp rates, temporal solitons with durations from 139 to 155 fs and Gaussian shapes can be obtained. The corresponding conversion efficiency is greater than 40%.     

Modification of Kerr nonlinearity in a four-level quantum system near a plasmonic nanostructure

We present a theoretical study for the Kerr nonlinearity of a four-level double-V-type quantum system near a two-dimensional array of metal-coated dielectric nanospheres. In the quantum system under study one V-type transition is influenced by the interaction with surface plasmons while the other V-type transition interacts with free-space vacuum. The quantum system interacts with a linearly polarized weak laser field that couples the lowest state with the upper states in the free-space transitions. We show that the Kerr nonlinearity is strongly influenced by the presence of the plasmonic nanostructure and is particularly sensitive to the distance between the quantum system and the plasmonic nanostructure.     

Kerr effect enhancement in ferromagnetic films

The enhancement of the Kerr magneto-optic effect by overcoating a ferromagnetic film with a dielectric film is studied. It is treated as an impedance-matching problem for the light wave. Closed form solutions are obtained for the polar Kerr effect. The same analysis, with modifications, can be applied to the longitudinal Kerr effect. The effect of the dielectric thickness on the enhancement is continuously monitored with a laser beam (λ = 6328Å) during the dielectric film deposition. The amplification of the longitudinal Kerr signal with SiO films on iron film is of the order of five, and the enhancement varies periodically as a function of dielectric thickness. The experimentally observed period, 1600Å, agrees well with the calculated value. The sense ofB-Hloops, which also varies periodically as a function of the dielectric thickness, is explainable in terms of the phase factor which appears in the difference between the reflection coefficients.     

Phase Properties of the Displaced Number State in a Kerr Medium

Abstract

Influences of the interaction of the displaced-number-state field with a Kerr medium on phase properties of the field are investigated. The interaction brings about the symmetrical splitting of the phase probability distribution (PPD) sometimes. Collapses and revivals have also been found in the long-time behaviours of the Hermitian, cosine and sine phase operators at high intensities. In terms of the PPD, the origin for generating these revivals has been revealed.     

Phase Properties of Elliptically Polarized Light Propagating in a Kerr Medium

Abstract

Phase properties of elliptically polarized light propagating through a nonlinear Kerr medium are considered within the framework of the Pegg-Barnett Hermitian phase formalism. The joint phase probability distribution function for the phases of two orthogonal modes describing elliptical polarization of the field is calculated and its evolution discussed and illustrated graphically. The marginal phase probability distribution for the individual phases are also calculated and discussed. Analytical formulae for phase expectation values and variances are derived for the individual phases as well as for the phase difference. It is shown that in the course of propagation the correlation between the phases of the two modes builds up. This correlation is responsible for lowering phase difference variance. The expressions for the sine and cosine functions and their variances of the individual phases as well as the phase difference are obtained and discussed. The effect of randomization of individual phases and the phase difference, which is a purely quantum effect, is shown to appear during propagation. The relation between phase randomization and degradation of the degree of polarization of the light is established.     

Kerr nonlinearity and optical multi-stability in a four-level Y-type atomic system

The nonlinear response to applied fields of a four-level Y-type atomic system is investigated. The effect of laser intensity and quantum interference induced by spontaneous emission on optical bistability, optical multi-stability and Kerr nonlinearity is then discussed. It is found that the threshold of the optical bistability can substantially be reduced by the quantum interference. So, an enhanced Kerr nonlinearity with reduced absorption can be achieved.     

Photon filters in a microwave cavity

Abstract

In an earlier paper we concluded that time-dependent parameters in the atom-mode interaction can be utilized to modify the quantum field in a cavity. When an atom shoots through the cavity field, it is expected to experience a trigonometric time dependence of its coupling constant. We investigate the possibilities this offers to modify the field. As a point of comparison we use the solvable Rosen-Zener model, which has parameter dependences roughly similar to the ones expected in a real cavity. We do confirm that by repeatedly sending atoms through the cavity, we can obtain filters on the photon states. Highly non-classical states can be obtained. We find that the Rosen-Zener model is more sensitive to the detuning than the case of a trigonometric coupling.     

Adiabatic state preparation in a cavity

Abstract

The paper discusses the single-mode Jaynes-Cummings model with time-dependent parameters. Solvable models for two-level systems are utilized to consider the changes in the photon distribution effected by the passage of atoms through the cavity. It is suggested that such systems may be used as filters to modify the photon distribution. The effect can be enhanced by repeatedly sending new atoms through the cavity. We show that such filters can cut out either small or large photon numbers. It is also shown that the method can be used to narrow down photon distributions and in this way achieve highly non-classical sub-Poissonian states. Some limitations and applications of the method are presented.     

布里渊光纤环形腔的克尔效应

针对布里渊光纤环形腔(BFRR)的克尔效应发生机理,首先研究了考虑克尔效应的腔谐振特性,理论推导出一阶斯托克斯出射光强发生光学双稳态的可能性.实验证明,入射光为440 μW左右时30 m短腔的一阶斯托克斯光会发生光学双稳态,双稳态的特性和腔耦合器的光强耦合系数及插入损耗有关.然后对布里渊光纤陀螺中的BFRR克尔效应进行了探讨,重点研究了谐振偏离对于陀螺输出非线性以及动态工作范围的影响.提出了一种全新的双环布里渊光纤陀螺方案,为布里渊光纤陀螺的克尔效应误差抑制提供了一种潜在的解决途径.     

Two-dimensional wave propagation in a micropolar thermo-elastic layer

The object of the present paper is to investigate the 2-dimensional thermo-elastic wave propagation in a micropolar solid layer. The wave velocity equation for the thermo-elastic Rayleigh wave in the micropolar medium has been deduced from the above theory and in the limiting case the wave velocity equation so obtained is in agreement with the corresponding classical problem when the thermal and micropolar effects are vanishingly small.