Optical parametric amplification beyond the slowly varying amplitude approximation

The coupled-wave equations describing optical parametric amplification (OPA) are usually solved in the slowly varying amplitude (SVA) approximation regime, in which the second-order derivatives of the signal and idler amplitudes are ignored and in fact the electromagnetic effects due to exit face of the medium is not involved. Here, an analytical plane-wave solution of these coupled-wave equations in a non-absorbing medium is presented. The solutions are derived beyond the SVA approximation up to order of κ/k (coupling constant over the wave number). The intensity distributions of the signal and the idler waves show a periodic behavior about their corresponding distributions of SVA-adapted solution. This behavior can be explained by the interference of the forward propagating signal (idler) wave and the corresponding backward one resulted from the reflection by the end face of the medium. Furthermore, this interference pattern in the medium can in turn serve as a periodic source for the next generations of the signal and idler waves. Therefore, the superposition of the waves, generated from different points of this periodic source, at the exit face of the medium shows an oscillatory behavior of the transmitted signal (idler) wave in terms of normalized coupling constant, κL. This study also shows that this effect is more considerable for high intensity pump beam, high relative refractive index and short length of the nonlinear medium.      

Isospin dependence of electric-transition probabilities <Emphasis Type="Italic">B</Emphasis>(E2) in the unitary scheme

In a physical basis of the unitary scheme, analytic formulas for the probabilities B(E2κL → κ′L′) and their isospin factors for the (λ0) and (λ2) representations of the SU(3) group were obtained for even-even nuclei. It was shown that the isospin correction must be taken into account at low L and in the case of off-diagonal transitions in κ. The results obtained in the unitary scheme are compared with the results of other models and with experimental data. At high L, the transition probabilities B(E2κL → κ′L′) are markedly smaller in the unitary scheme than in the rotational model, while, for L ≪ λ, these probabilities in the unitary scheme and in the rotational model are close.     

Asymptotic coefficients for atoms and ions

We derive convenient analytical formulas in the effective-range approximation for the asymptotic coefficient C _κ of the radial wave function at infinity and for the average radius of the system. A comparison with the results of numerical calculations (done by the Hartree-Fock method) for multi-electron atoms and ions reveals that this approximation has good accuracy for valence s-electrons in all atoms from hydrogen to uranium. We calculate the values of the scattering lengths and the effective ranges for electron-atom and electron-ion scattering. We also examine the quasiclassical approximation for C _κ. Finally, we discuss the logarithmic increase in the effective ranges of ns states as n→∞. Zh. éksp. Teor. Fiz. 115, 521–541 (February 1999)     

Electromagnetic waves in a randomly inhomogeneous Josephson junction

Spectrum modification and damping of Josephson plasma waves induced by random inhomogeneities of the critical current through the superconductor contact and the averaged Green function of such excitations are analyzed. In the self-consistent approximation that makes it possible to take into account multiple wave scattering on the inhomogeneities, the frequency and damping of averaged waves, as well as position ν _m and peak width Δν of the Fourier transform imaginary part of the averaged Green function, are determined as functions of wavevector k. The evolution of such functions with the variation of the correlation radius and the relative r.m.s. fluctuations of inhomogeneities is studied. The inhomogeneity-induced wave frequency decrease observed in the long wavelength spectral region qualitatively agrees with the ν _m behavior. It is established that in the case of “long-range” inhomogeneities, the linear dependence of damping on k changes to the inversely proportional one, and damping tends to zero as k → 0, while Δν at small k attains its maximal values due to nonuniform broadening. In the presence of “short-range” inhomogeneities, the wave damping and Δν are found to be similar functions of k. The results are compared to the numerical calculation data.     

Spin structure of the “Forward” nucleon charge-exchange reaction <Emphasis Type="Italic">n</Emphasis> + <Emphasis Type="Italic">p</Emphasis> → <Emphasis Type="Italic">p</Emphasis> + <Emphasis Type="Italic">n</Emphasis> and the deuteron charge-exchange breakup

The structure of the nucleon charge-exchange process n + p → p + n is investigated basing on the isotopic invariance of the nucleon-nucleon scattering. Using the operator of permutation of the spin projections of the neutron and proton, the connection between the spin matrices, describing the amplitude of the nucleon charge-exchange process at zero angle and the amplitude of the elastic scattering of the neutron on the proton in the “backward” direction, has been considered. Due to the optical theorem, the spin-independent part of the differential cross section of the process n + p → p + n at zero angle for unpolarized particles is expressed through the difference of total cross sections of unpolarized proton-proton and neutron-proton scattering. Meantime, the spin-dependent part of this cross section is proportional to the differential cross section of the deuteron charge-exchange breakup d + p → (pp) + n at zero angle at the deuteron momentum k _d = 2 k _n (k _n is the initial neutron momentum). Analysis shows that, assuming the real part of the spin-independent term of the “forward” amplitude of the process n + p → p + n to be smaller or of the same order as compared with the imaginary part, in the wide range of neutron laboratory momenta k _n > 700 MeV/c the main contribution into the differential cross section of the process n + p → p + n at zero angle is provided namely by the spin-dependent term.     

High efficiency KTiOAsO4 optical parametric oscillator within a diode-side-pumped two-rod Nd:YAG laser

A high efficiency KTiOAsO₄(KTA) intracavity optical parametric oscillator (IOPO) is demonstrated within a diode-side-pumped acousto-optically (AO) Q-switched two-rod Nd:YAG laser. With a 25-mm-long X-cut KTA crystal, efficient parametric conversions to signal (1.54 μm) and idler (3.47 μm) waves are realized. The highest output power of 15.8 W including 12.7 W signal and 3.1 W idler power is obtained at a repetition rate of 7.5 kHz and a pump power of 208 W, corresponding to an optical-to-optical conversion efficiency of up to 7.6%. The signal pulse duration is 32 ns with a peak power of 53 kW. At a repetition rate of 12.5 kHz and the pump power of 208 W, the highest idler power of 3.4 W is obtained with a peak power of 14 kW and a pulse duration of 19 ns. And the beam quality factors (M ²) of the signal and idler waves are determined to be around 2 and 20, respectively.     

Noncommuting limits of oscillator wave functions

Quantum harmonic oscillators with spring constants k > 0 plus constant forces f exhibit rescaled and displaced Hermite—Gaussian wave functions, and discrete, lower bound spectra. We examine their limits when (k, f) → (0, 0) along two different paths. When f → 0 and then k → 0, the contraction is standard: the system becomes free with a double continuous, positive spectrum, and the wave functions limit to plane waves of definite parity. On the other hand, when k → 0 first, the contraction path passes through the free-fall system, with a continuous, nondegenerate, unbounded spectrum and displaced Airy wave functions, while parity is lost. The subsequent f → 0 limit of the nonstandard path shows the dc hysteresis phenomenon of noncommuting contractions: the lost parity reappears as an infinitely oscillating superposition of the two limiting solutions that are related by the symmetry. The text was submitted by the authors in English. On sabatical leave from Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel. on leave from the Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia.     

Spin squeezing in finite temperature Bose-Einstein condensates: Scaling with the system size

We perform a multimode treatment of spin squeezing induced by interactions in atomic condensates, and we show that, at finite temperature, the maximum spin squeezing has a finite limit when the atom number N →∞ at fixed density and interaction strength. To calculate the limit of the squeezing parameter for a spatially homogeneous system we perform a double expansion with two small parameters: 1/N in the thermodynamic limit and the non-condensed fraction ⟨N _nc⟩/N in the Bogoliubov limit. To test our analytical results beyond the Bogoliubov approximation, and to perform numerical experiments, we use improved classical field simulations with a carefully chosen cut-off, such that the classical field model gives for the ideal Bose gas the correct non-condensed fraction in the Bose-condensed regime.     

Decays of σ, κ, a0(980) and f0(980)

Ratios of coupling constants for these decays are compared with qq̄ predictions and Jaffe’s q²q̄² model. In both models, the predicted ratio g²(κ→Kπ)/g²(σ→ππ) is much too small. Also, for qq̄, the predicted ratio g²(κ→Kη’)/g²(κ→Kπ) is much larger than observed. Both models fail for g²(f₀→KK)/g²(a₀→KK). This ratio requires that f₀ has a dominant KK component. It arises naturally because the f₀ pole lies very close to the KK threshold, giving its wave function a long KK tail. PACS 13.25.Gv, 14.40.Gx, 13.40.Hq     

Dissipative tunneling in nanosystems

A quantum dynamical problem has been analytically solved for a two-level system where localized states L ₀ and R ₀ are strongly coupled with reservoirs of local oscillations {L _n } and {R _n }. It is additionally assumed that the spectra of reservoirs are equidistant and the coupling constants are the same. It has been shown that the evolution of states L ₀ and R ₀ in recurrence cycles depends on three independent factors, which characterize exchange with the two-level system, exchange of L ₀ with {L _n } (R ₀ with {R _n }) and the phonon-induced decay of {L _n } and {R _n }. In addition to coherent oscillations with the frequency of the two-level system, Δ, and dissipative tunneling with a rate Δ²/πC ² (where C is the matrix element of the coupling of L ₀ and R ₀ with L _n and R _n ), a new regime appears where L-R transitions are induced by the partial recovery of the populations of L ₀ and R ₀ in each recurrence cycle due to synchronous transitions from reservoirs. These transitions induce repeating changes in the populations of the states of the two-level system (Loschmidt echo). The number and width of the echo components increase with the cycle number. Evolution becomes irregular because of the mixing of the contributions from pulses of the neighboring cycles, when the cycle number k exceeds the critical value k _c = π² C ². Unlike the populations, their cycle-average values remain regular at k ≫ k _c. When Δ ≪ πC ², the cycle-average populations oscillate with a frequency of ΔΩ/πC ² irrespective of mixing. The frequency of oscillations of the populations of the states {L _n } and {R _n } is approximately nΩ(Δ/2πC ²)², where Ω is the spacing between the neighboring levels of the reservoir and nΩ is the difference between the energies of the states L ₀ and L _n . The appearance of the mentioned low-frequency oscillations is due to the formation of collective states of the two-level system that are “dressed” by the reservoir. The predicted oscillations can be detected by femtosecond spectroscopy methods.     

Statistical dynamics at critical bifurcations in Duffing-van der Pol oscillator

We study the characteristic features of certain statistical quantities near critical bifurcations such as onset of chaos, sudden widening and band-merging of chaotic attractor and intermittency in a periodically driven Duffing-van der Pol oscillator. At the onset of chaos the variance of local expansion rate is found to exhibit a self-similar pattern. For all chaotic attractors the variance Σ_n(q) of fluctuations of coarse-grained local expansion rates of nearby orbits has a single peak. However, multiple peaks are found just before and just after the critical bifurcations. On the other hand, Σ_n (q) associated with the coarse-grained state variable is zero far from the bifurcations. The height of the peak of Σ_n(q) is found to increase as the control parameter approached the bifurcation point. It is maximum at the bifurcation point. Power-law variation of maximal Lyapunov exponent and the mean value of the state variablex is observed near sudden widening and intermittency bifurcations while linear variation is seen near band-merging bifurcation. The standard deviation of local Lyapunov exponent λ(X,L) and the local mean valuex(L) of the coordinatex calculated after everyL time steps are found to approach zero in the limitL → ∞ asL ^-Β. Β is sensitive to the values of control parameters. Further weak and strong chaos are characterized using the probability distribution of ak-step difference quantity δx_k = x_i+k x _i.     

Invasion Percolation and the Incipient Infinite Cluster in 2D

 We establish two links between two-dimensional invasion percolation and Kesten's incipient infinite cluster (IIC). We first prove that the k ^th moment of the number of invaded sites within the box [−n, n]×[−n, n] is of order (n ²π _n ) ^k , for k≥1, where π _n is the probability that the origin in critical percolation is connected to the boundary of a box of radius n. This improves a result of Y. Zhang. We show that the size of the invaded region, when scaled by n ²π _n , is tight. Secondly, we prove that the invasion cluster looks asymptotically like the IIC, when viewed from an invaded site v, in the limit |v|→∞. We also establish this when an invaded site v is chosen at random from a box of radius n, and n→∞. Received: 3 December 2000 / Accepted: 3 December 2002 Published online: 18 February 2003 RID="⋆" ID="⋆" Present address: CWI, PNA 3, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands. E-mail:jarai@cwi.nl Communicated by M. Aizenman     

Four-Vertex Theorems, Sturm Theory and Lagrangian Singularities

We prove that the vertices of a curve γ⊂R ⁿ are critical points of the radius of the osculating hypersphere. Using Sturm theory, we give a new proof of the (2k+2)-vertex theorem for convex curves in the Euclidean space R ^2k . We obtain a very practical formula to calculate the vertices of a curve in R ⁿ . We apply our formula and Sturm theory to calculate the number of vertices of the generalized ellipses in R ^2k . Moreover, we explain the relations between vertices of curves in Euclidean n-space, singularities of caustics and Sturm theory (for the fundamental systems of solutions of disconjugate homogeneous linear differential operators L:C ^∞(S ¹)→C ^∞(S ¹)).     

Development of injection-seeded, pulsed optical parametric generator/oscillator systems for high-resolution spectroscopy

We report the development and application of pulsed optical parametric generator (OPG) and optical parametric oscillator (OPO) systems that are injection seeded with near-infrared distributed feedback diode lasers. The OPG is injection seeded at the idler wavelength without the use of a resonant cavity. Two counter-rotating, beta-barium-borate (β-BBO) crystals are used in the OPG. These crystals are pumped by the third harmonic, 355-nm output of an injection-seeded Nd:YAG laser. An OPO version of the system has also been developed by placing two flat mirrors around the two β-BBO crystals to form a feedback cavity at the signal wavelength. The OPO cavity length is not actively controlled. The output signal beam from the OPG or OPO is amplified using an optical parametric amplifier (OPA) stage with four β-BBO crystals. The frequency bandwidths of the signal and idler laser radiation from OPG/OPA and OPO/OPA systems have been determined to be slightly greater than 200 MHz. The temporal pulses from each system are smooth and near-Gaussian. High-resolution optical absorption measurements of acetylene (C₂H₂) were performed as another check of the frequency spectrum of the idler beam. The frequency-doubled signal output of the OPO/OPA system was used to perform high-resolution, single-photon, laser-induced fluorescence (LIF) spectroscopic studies of the (0,0) vibrational band of the A ²Σ⁺−X ²Π electronic transition of nitric oxide (NO) at low pressure. Excellent agreement was obtained between the theory and the experiment. The signal output of the OPG/OPA system was also used for sub-Doppler, two-photon LIF spectroscopic studies of the same vibration–rotation manifold of NO.This revised version was published online in August 2005 with a corrected cover date.     

Ground State Energy of Large Atoms in a Self-Generated Magnetic Field

We consider a large atom with nuclear charge Z described by non-relativistic quantum mechanics with classical or quantized electromagnetic field. We prove that the absolute ground state energy, allowing for minimizing over all possible self-generated electromagnetic fields, is given by the non-magnetic Thomas-Fermi theory to leading order in the simultaneous Z → ∞, α → 0 limit if Z α ² ≤ κ for some universal κ, where α is the fine structure constant.     

12 W mid-infrared output,singly resonant,continuous-wave optical parametric oscillator pumped by a Yb<Superscript>3+</Superscript>-doped fiber amplifier

We report a continuous-wave singly resonant optical parametric oscillator (SRO) with more than 12 W of idler power at 3414 nm when it was operated at 30°C. The SRO was directly pumped by a single-frequency, ytterbium-doped fiber laser with 49 W linear polarization pump powers, and based on 50 mm long periodically poled MgO:LiNbO₃ crystal (PPMgLN) in two-mirror linear cavity with 30.5 μm grating period. It’s pump power at threshold was 5.4 W. The slope-efficiency and quantum-limited performance reached 26 and 79.2%, respectively. The beam polarization matched the e → e + e interaction in crystal. The idler waves were temperature tuned in the range of 3654 to 3811 nm and 3248 to 3414 nm based on two 50 mm long PPMgLN with 29.5 and 30.5 μm grating period. To the best of our knowledge, this is the highest continuouswave mid-IR output obtained for a fiber laser pumped optical parametric oscillator (OPO).     

On the High Density Behavior of Hamming Codes with Fixed Minimum Distance

We discuss the high density behavior of a system of hard spheres of diameter d on the hypercubic lattice of dimension n, in the limit n→∞, d→∞, d/n = δ. The problem is relevant for coding theory, and the best available bounds state that the maximum density of the system falls in the interval 1 ≤ ρ V _d ≤ exp (n κ(δ)), being κ(δ) > 0 and V _d the volume of a sphere of radius d. We find a solution of the equations describing the liquid up to an exponentially large value of ρ = ρ V _d , but we show that this solution gives a negative entropy for the liquid phase for ρ >rsimn. We then conjecture that a phase transition towards a different phase might take place, and we discuss possible scenarios for this transition. PACS: 05.20.Jj, 64.70.Pf, 61.20.Gy     

A Maximum Entropy Method Based on Piecewise Linear Functions for the Recovery of a Stationary Density of Interval Mappings

Let S:[0,1]→[0,1] be a nonsingular transformation such that the corresponding Frobenius-Perron operator P _S :L ¹(0,1)→L ¹(0,1) has a stationary density f ^∗. We propose a maximum entropy method based on piecewise linear functions for the numerical recovery of f ^∗. An advantage of this new approximation approach over the maximum entropy method based on polynomial basis functions is that the system of nonlinear equations can be solved efficiently because when we apply Newton’s method, the Jacobian matrices are positive-definite and tri-diagonal. The numerical experiments show that the new maximum entropy method is more accurate than the Markov finite approximation method, which also uses piecewise linear functions, provided that the involved moments are known. This is supported by the convergence rate analysis of the method.     

Wigner Surmise for Domain Systems

In random matrix theory the spacing distribution functions p ⁽ⁿ⁾(s) are well fitted by the Wigner surmise and its generalizations. In this approximation the spacing functions are completely described by the behavior of the exact functions in the limits s→0 and s→∞. Most non equilibrium systems do not have analytical solutions for the spacing distribution and correlation functions. Because of that, we explore the possibility to use the Wigner surmise approximation in these systems. We found that this approximation provides a first approach to the statistical behavior of complex systems, in particular we use it to find an analytical approximation to the nearest neighbor distribution of the annihilation random walk.     

Coherent inelastic processes on nuclei at ultrarelativistic energies

The coherent inelastic processes of the type a → b, which may take place in the interaction of hadrons and γ quanta with nuclei at very high energies (the nucleus remains the same), are theoretically investigated. For taking into account the influence of the nucleus matter, the optical model, based on the conception of the refraction index, is used. Analytical formulas for the effective cross section σ _coh (a → b) are obtained, taking into account that, at ultrarelativistic energies, the main contribution into σ _coh (a → b) is provided by very small transferred momenta in the vicinity of the minimal longitudinal momentum transferred to the nucleus. It is shown that the cross section σ _coh (a → b) may be expressed through the “forward” amplitudes of inelastic scattering f _a+N+b+N (0) and elastic scattering f _a+N+a+N(0), f _b+N+b+N(0) on a separate nucleon, and it depends on the ratios L _a /R and L _b /R (L _a and L _b are the mean lengths of the free path in the nucleus matter for the particles a and b, respectively, and R is the nucleus radius). In particular, when L _a /R ≫ 1, but L _b /R ≪ 1 (or L _a /R ≪ 1, but L _b /R ≫ 1), σ _coh (a → b) is equal to the ratio of the “forward” cross sections of inelastic scattering a + N → b + N and elastic scattering of the particle b (or a) on a nucleon, multiplied by the cross section of scattering on the “black” nucleus πR ². When both conditions L _a /R ≫ 1 and L _b /R ≫ 1 are satisfied, σ _coh (a → b) is proportional to the factor R ⁴/k ², where k is the initial energy of particle a in the laboratory frame. The text was submitted by the authors in English.