Spectral superbroadening of self-focused picosecond laser pulses in D2O

Intense picosecond light pulses of a mode-locked Nd: glass laser at _L =1054 nm (fundamental wavelength) and _SH =527 nm (second harmonic wavelength) are passed through a sample of D₂O under self-focusing conditions. Spectrally structured superbroadened, spatially bell-shaped emission in the forward direction is obtained. Primary generation processes are pump-pulse-degenerate stimulated parametric four-photon interaction (₁ + _{1 3} + ₄) and stimulated Raman scattering (_{1 R} + ), which occur concurrently (₁= _L or _SH angular pump frequency, #x03C9; _R first Stokes frequency, #x03C9; signal frequency, #x03C9;₃ signal frequency, #x03C9;₄ idler frequency). The parametric four-photon interaction occurs under collinear non-phase-matched conditions and under longitudinally phase-matched, transversally non-phase-matched (erenkov-like) conditions. Subsequent interaction processes are pump-pulse-nondegenerate four-photon interaction of the type ₁ + _{R 3} + ₄, coherent antiStokes Raman scattering (CARS, ₁ + ₁ – _{4 3}), inverse Raman scattering ( _A + ₁ + ), and cascading light up-conversion of the type ₁ + _(i) – _{R (i+1)}.     

Excited-state absorption and third-order optical nonlinearities in symmetric π-electron organic molecules

Excited-State Absorption (ESA), Two-Photon Absorption (TPA) and the third-order polarizability (;,, – ) have been investigated for a model dichloride derivative of a symmetrically substituted benzylidene analine (SBAC), using a multielectron configuration-interaction procedure. The calculations indicate that SBAC exhibits ESA across the visible region of the spectrum, but that it is not as extensive as for molecules such as the phthalocyanines. The magnitude of the third-order polarizability is dominated by resonance enhancement from a very strongA _g B _u one-photon absorption. The calculated off-resonance value for (;,, – ) suggests that SBAC is a potential candidate for ultrafast switching applications.     

The modular group and super-KMS functionals

Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical ₂ grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.     

Low frequency limits of third-order harmonic coefficients for atomic hydrogen in any level of discrete energy spectrum

In this paper the analytical expression is derived for the third-order optical harmonic coefficients x _abcd ^v (,,) of the atomic hydrogen at very low frequencies 0 in many level of the discrete energy spectrum.The author expresses his thank to Prof. Nguyen Van Hieu for suggesting the problem and fruitful discussions.     

Calculation of the dispersion of the third-order optical nonlinearity in C60 films

Using wave functions determined from ground-state local-density calculations, we have calculated the wave-dispersed free response of the optical nonlinear polarizability ⁽³⁾(–3;,,), for the C₆₀ molecule and ⁽³⁾(–3;,,) i.e. Third-Harmonic Generation (THG) for films using a sum-over-states approach. The influence of screening was determined by applying an external static electric field in separate selfconsistent calculations to evaluate induced dipole moments which was used to determine the static linear and nonlinear polarizabilities. The polarizabilities calculated in the static limit were used to determine an effective screening parameter which was, in turn, used together with an RPA approach to calculate screened wave-dispersed, third-order nonlinear optical properties such as ⁽³⁾(–3;,,) and ⁽³⁾(–3;,,). Comparing evaluated polarizabilities with experimental values we found that the non-resonant free polarizability compares well in absolute magnitude with experimental results. Inclusion of screening results in a polarizability about two orders of magnitude below the experimental values.Paper presented at the 129th WE-Heraeus-Seminar on Surface Studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994     

Stochastic linear maps and transition probability

Some aspects of the transition probability P(, ) between states , on unital ^*-algebras are discussed. It is shown that P increases under the action of any stochastic linear map T, i.e., P(T, T)P(, ). Some properties of P are derived in starting from a recently-proved characterization of the quantity in question.     

Some exact models for nonspherical collapse.I

Evolution of incoherent matter distributions with cylindrical, pseudoplanar, and toroidal symmetries is considered. The system is described in terms of the scale factora (R, T) and the anisotropy factor (R, T) of the (x², x³ surfaces. A number of exact solutions is obtained under the assumptions=(a), =(R), and=(T) and their physical properties are breifly discussed. In particular, the solution with=(T) is noncollapsing and describes a matter distribution with unchanging density.     

Spectral properties of random Schrödinger operators with unbounded potentials

We investigate spectral properties of random Schrödinger operators H = - + _n()(1 + |n|) acting onl ²(Z ^d), where _n are independent random variables uniformly distributed on [0, 1].Research partially supported by a Sloan Doctoral Dissertation Fellowship and NSERC under grant OGP-0007901Research partially supported by NSF grant DMS-9101716     

Lifshitz tails for periodic plus random potentials

We prove that the integrated density of states () for a potentialW =V _per +V has Lifshitz tails where V_per is a periodic potential with reflection symmetry andV is a random potential, e.g., of the formV =q _i ()f(x–i).research partially supported by DFG.research partially supported by USNSF under grant No. MCS-81-20833.     

Four-wave mixing in CO via the C 1Σ+ (υ′=0) state

Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (_VUV=2₁–₂) of pulsed dye laser radiation in carbon monoxide (CO). The frequency ₁ was tuned to the C ¹⁺(=0)X ¹⁺(=0) two-photon transition, while the dye laser frequency ₂ was scaned around 17650 cm^–1 which corresponds to the A ¹(=7)«C ¹⁺(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A ¹(=7) state and (ii) that the off-resonance excitation in the C ¹⁺(=0)X ¹⁺(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed.     

Extensible Embeddings of Black-Hole Geometries

Removing a black hole conic singularity by means of Kruskal representation is equivalent to imposing extensibility on the Kasner–Fronsdal local isometric embedding of the corresponding black hole geometry. Allowing for globally non-trivial embeddings, living in Kaluza–Klein-like M ₅ × S ₁ (rather than in standard Minkowski M ₆ ) and parametrized by some wave number k, extensibility can be achieved for apparently forbidden frequencies in the range ₁ (k) ₂ (k). As k 0, _{1, 2} (0) _H (e.g., _H = 1/4M in the Schwarzschild case) such that the Hawking–Gibbons limit is fully recovered. The various Kruskal sheets are then viewed as slices of the Kaluza–Klein background. Euclidean k discreteness, dictated by imaginary time periodicity, is correlated with flux quantization of the underlying embedding gauge field.     

Averaged electron Green function and CDW pinning in one-dimensional random potential

The averaged retarded electron Green functionG ⁺(,k) in 1d disordered metal is calculated using the Berezinsky diagram technique. Using the Gorkov's theory it is shown, that the substitution of inG ⁺ (,k) by the square of the external frequency atk=0 gives the dependence of Fröhlich conductivity _F(). This dependence describes the impurity pinning of CDW in 1d disordered metals. The good agreement of this dependence with experimental data Zeller et al. about _F() in quasi-1d conductor KCP is found     

Radiation damping of waves in a cold magnetized two-component plasma

It is shown in this paper that the damping decrements of electromagnetic waves with right circular polarization and the decrements of plasma oscillations near the cyclotron and hybrid frequencies in a strong magnetic field _eBpe are proportional to the square of the cyclotron frequencies _eB and _iB. In a weak magnetic field _eBpe the damping decrements of all modes are proportional to the square of the plasma oscillation frequencies _pe, _pi. Taking account of ions results in a nonzero damping decrement for electromagnetic waves with left circular polarization.Deceased.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, p. 8–11, October, 1982.In conclusion, I am grateful to L. S. Kuz'menkov and P. Polyakov for constant attention to the research and for useful remarks.     

Third order nonlinear optical difference frequency generation in KH2PO4, TiO2, LiNbO3, CaCO3, ZnO and CdS

Third-order nonlinear optical susceptibilities of different crystals have been measured relative to LiNbO₃ by observing collinear phase-matched difference frequency generation ₁=2 ₂– ₄. The two incident light waves have been produced by a ruby laser ( ₂, ₂=694.3 nm) and by induced Raman scattering ( ₄, ₄=765.8 nm). With noncollinear phase-matching the number of nonlinear processes and the possibilities to determine nonlinear coefficients is much larger than in the collinear case. Therefore the theory of Raman-type third order interactions has been extended to noncollinear propagation of the interacting waves. The theory has been tested experimentally for CdS.     

Some exact models for nonspherical collapse. III

The gravitational nonradiative collapse of dust configurations in the presence of electromagnetic field is analyzed in terms of exact dynamical solutions for a wide range of spacetime symmetries: cylindrical, pseudoplanar, toroidal, and also spherical, planar, and pseudospherical [when the anisotropy factor of the (x ²,x ³) surfaces,(R, T), is replaced by a massless scalar field]. The condition that the collapse is nonradiative leaves three possibilities for the coordinate dependence of(R,T) (i)=(a),a (R, T) being the scale factor of the (x ²,x ³) surfaces, (ii)=(T), and (iii)=(R). Almost all (in the meaning indicated in the text) solutions for charged dust with=(a) and for dust in the external electromagnetic field with=(T) and=(R) have been obtained and discussed. A wideranging discussion concerning the topics of papers I–III is given. Special attention is paid to the question of horizon existence and formation and also the perspective of extension of the techniques developed onto the more realistic case of axial symmetry.     

Entanglement of Resonantly Coupled Field Modes in Cavities with Vibrating Boundaries

We study time dependence of various measures of entanglement (covariance entanglement coefficient, purity entanglement coefficient, normalized distance coefficient, entropy coefficients) between resonantly coupled modes of the electromagnetic field in ideal cavities with oscillating boundaries. Two types of cavities are considered — a three-dimensional cavity possessing eigenfrequencies ₃ = 3₁, whose wall oscillates at the frequency _w = 2₁, and a one-dimensional (Fabry–Perot) cavity with an equidistant spectrum _n = n₁ where the distance between perfect mirrors oscillates at the frequencies ₁ and 2₁. The behavior of entanglement measures in these cases turns out to be completely different, although all three coefficients demonstrate qualitatively similar time dependences in each case (except some specific situations where the covariance entanglement coefficient based on traces of covariance submatrices seems to be essentially more sensitive to entanglement than other measures, which are based on determinants of covariance submatrices). Different initial states of the field, namely, vacuum, squeezed vacuum, thermal, Fock, and even/odd coherent states, are considered.     

A relationship between asymmetric Lévy-stable distributions and the dielectric susceptibility

This paper, as a complement to the work of Montroll and Bendler, is concerned with the Lévy-stable distributions and their connection to the dielectric response of dipolar materials in the frequency domain. The necessary and sufficient condition for this connection is found. The presented probabilistic analysis is based on the mathematically correct representation of the meaning of the relaxation function of a system of dipoles and shows why the same form of a distribution of relaxation rates, namely, the completely asymmetric Lévy-stable distribution, should apply in all different relaxing systems. This is in contrast to the traditional definition of the relaxation function, expressed as a weighted average of exponential relaxation functions, which does not explain the universality of the dielectric relaxation law. It also follows from the present considerations that not only is the imaginary part () of the dielectric susceptibility directly related to the Lévy-stable distribution (as was found by Montroll and Bendler), but so is the real part(). As a consequence the relation()/()=cot(n/2) for> _p and 0<n<1, implied by experimental results, is obtained.     

The efficient inject of high microwave powers into the overdense magnetoactive plasma in the waveguide

On the boundary vacuum — a dense magnetoactive plasma, an incident RHCP (right hand circularly polarized) wave is strongly reflected if ₀ ² / ² 1 and _ce/ > 1;, ₀, _ce are the ncident wave frequency, the plasma frequency and the electron cyclotron frequency, respectively. This reflection strongly lowers the efficiency of the plasma heating by microwaves. Our experimental study shows that a suitable matching system consisting of dielectric plates, placed in front of the plasma, can ensure practically complete transfer of the RHCP wave energy into a dense plasma. The experiment was carried out in the S band waveguide (=12·7 cm) with the power of the order of l kW.The authors wish to thank to the director of the Institute of Plasma Physics Dr. J.Váa for his interest in this work.     

The proper formula for relative entropy and its asymptotics in quantum probability

Umegaki's relative entropyS(,)=TrD (logD –logD ) (of states and with density operatorsD andD , respectively) is shown to be an asymptotic exponent considered from the quantum hypothesis testing viewpoint. It is also proved that some other versions of the relative entropy give rise to the same asymptotics as Umegaki's one. As a byproduct, the inequality TrA logAB TrA(logA+logB) is obtained for positive definite matricesA andB.     

Theoretical investigation of noncollinear phase-matched parametric four-photon amplification of ultrashort light pulses in isotropic media

The amplification of light signals (angular frequency _S in some isotropic media (D₂O, fused silica, and Schott type SF10 glasses) by noncollinear phase-matched parametric four-photon interaction ₁+_2S+₁ is studied theoretically. Computer simulations are carried out for fundamental and second-harmonic pump pulses of a mode-locked Nd: glass laser. Degenerate interaction (wavelength ₁=₂=1054nm or 527 nm) and nondegenerate interaction (₁=1054nm, ₂=527 nm are considered. Characteristic phase-matching parameters and gain parameters versus wavelength are determined. Limitations by spectral bandwidth, optical absorption, optical damage, self-phase modulation, self-focusing and stimulated Raman scattering are analysed.