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.     

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.     

Harmonic mixing by weakly pinned charge density waves

Third order harmonic mixing voltageE ₀ in case of frequency matching, =₂–₁=0, and third order pseudo harmonic mixing currentj() in the detuned case, 0, are evaluated for the one-dimensional Fukuyama-Lee-Rice model for weakly pinned charge density waves in the region of sub-threshold bias electric fields. After a perturbation expansion of the phase response to the ac driving fields the impurity averaging is performed diagrammatically. Specific statistical properties of the charge density wave phase in the weak pinning limit and a non-trivial result for the pinning of the static phase are utilized to expressE ₀ andj() in terms of the dielectric function (). A recent evaluation of () within the self-consistent Born approximation is used to present the results explicitly in a number of diagrams. In comparison to the overdamped anharmonic oscillator the following differences are found: Randomness leads to interference contributions which increase the amplitudes and decrease the phase shifts. The more realistic form for () at lower frequencies lead to a downward shift in the maximum ofj() when ₁ is decreased below the cross-over frequency _c . The present theory retains inertia in the dynamical equations and remains valid for frequencies near and above the pinning frequency. It fails, however, for small frequencies _{1 c} due to the neglect of metastable states and screening.     

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.     

Linear and non-linear ac response of the stochastic classical model for sliding charge density waves

A comprehensive study of the ac response properties of the classical stochastic model for sliding charge density waves (CDW) in quasi one-dimensional metals is made by numerically solving the associated Fokker-Planck equation. Above the conductivity threshold a noise mechanism is indispensable to give finite line widths to the resonances of the applied ac signal of frequency with the narrow band noise frequency _OSC inherent in the model. In the present investigation a current noise of strengthT _N proportional to the CDW current is used in the Fokker-Planck equation in order to model the broad band current noise frequently observed above threshold. The present model thus incorporates three characteristic frequency scales: _OSC,T _N ,and a crossover frequency _OSC. Results are evaluated for the ac conductivity (;E ₀,E ) as function of frequency , dc bias electric fieldE ₀ and ac signal field strengthE . ForE 0 the linear ac response is obtained by a separate treatment of the Fokker-Planck equation. The resonances near =_OSC are studied in detail. Strong ac signals reduce the response at the fundamental resonance and lead to a harmonic interference structure nearn=_OSC. The overall agreement of the present results with recent measurements of the linear ac response is not good. In reality our results seem to be superimposed on a background not reproduced by the classical model with one cross over frequency. However, the peak in Im (;E ₀,E =0) vs.E ₀, when the narrow band noise frequency is near , is well reproduced. The spectral width of this peak which corresponds to the inductive dip in the susceptibility is studied as function of current noise strengthT _N .The results stress the need for a complete Fokker-Planck treatment sinceT _N is not simply related to the line width.     

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     

Third-order nonlinear susceptibilities of dye solutions determined by third-harmonic generation

The third-order nonlinear susceptibilities _xxx ⁽³⁾ (–₃; ₁, ₁, ₁) versus concentration are determined for rhodamine 6G, fuchsin, and methylene blue in methanol. Third-harmonic generation of a modelocked Nd-glass laser is applied. The real and imaginary part of the nonlinear susceptibility are measured. A resonance enhancement due to absorption bands is observed.     

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.     

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.     

Electromagnetic wave excitation in a dense plasma (ωPe>ωBe) by “tail” electrons

We consider the possibility of electromagnetic wave generation in a plasma with _Pe>_Be by tail electrons which scatter on anomalous Doppler resonance of potential waves with _2Be. These oscillations, organized into periodic waves, resonantly excite potential waves of harmonic frequencies ₁=s·_2Pe, s=2, 3, .., easily transformable to electromagnetic radiation. A coherent mechanism for solar radio flares is developed.Deceased.Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 118–122, July, 1994.     

Dynamic scaling for spin glasses near the de Almeida-Thouless line

We calculate the dynamic local susceptibility () of an Ising spin glass near the de Almeida-Thouless (AT) line within the soft spin dynamics for the Sherrington-Kirkpatrick model. We find a crossover from analytic behaviour of () at =0 above the AT line to a power law behaviour ()(–i) ^v on the AT line and discuss the analytic properties of the crossover function. The frequencyscale is proportional to ^1/v , where measures the distance from the AT line. We determine the spectrum of relaxation times which diverge as ^1–1/v . The average relaxation time diverges as ^–1/v wherev1/2. In addition we determine the absolute frequency scale and prove the consistency of the ansatz of Sompolinsky and Zippelius ()–(0)(–i) ^v at and below the AT line.     

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     

Structure factor of substitutional sequences

We study the structure factor for a large class of sequences of two elementsa andb such that longer sequences are generated from shorter ones by a simple substitution rulea ₁(a, b) andb ₂(a, b), where the's are some sequences ofa's andb's. Such sequences include periodic and quasiperiodic systems (e.g., the Fibonacci sequence), as well as systems such as the Thue-Morse sequence, which are neither. We show that there are values of the frequency at which the structure factors of these sequences have peaks that scale withL, the size of the system likeL ⁽⁾. For a given sequence a simple one- or two-dimensional dynamical iterative map of the variable can easily be abstracted from the substitution algorithm. The basin of attraction of a given fixed point or limit cycle of this map is a set of values of at which there are peaks of the structure factor all of which share the same value of. Furthermore, only those values of which are in the basin of attraction of the origin can have()=2. All other peaks will grow less rapidly withL. We show how to construct many sequences which, like the Thue-Morse sequence, have noL ² peaks. Other qualitative features of the structure factors are presented. Our approach unifies the treatment of a large class of apparently very diverse systems. Implications for the band structure of these systems as well as for the analysis of sequences with more than two elements are discussed.     

CW coherent VUV radiation generated by resonant sum-frequency mixing in metal vapors

Resonant third-order sum-frequency mixing of continuous-wave visible and ultraviolet laser light is investigated in the metal vapors of Sr, Ca, Mg, and Zn. The laser radiation (with the frequencies ₁, ₂, and ₃) is generated by single-mode dye- and argonion lasers. The third-order nonlinear susceptibility is enhanced by tuning the laser frequencies 2₁ or ₁+₂ to a two-photon resonance. The wavelength of the generated coherent VUV radiation (with the frequency _VUV=3₁, _VUV=2₁+₂ or _VUV=₁+₂+₃) is tunable in spectral regions between 133 and 217 nm. For most conversion processes an additional enhancement of the nonlinearity is provided by an autoionizing level or by a highly excited state close to E=_VUV. With laser powers of 0.2–3 W the power of the generated sum frequencies is in the range of 5×10⁵–6×10¹⁰ photons s^–1 (0.5 pW–60 nW).     

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.     

Cubic nonlinear tensor of a ferromagnet

The nonlinear properties of a ferromagnet are studied. Many-time retarded Green's functions are used to obtain an expression for the cubic nonlinearity tensor with allowance for spatial dispersion of a uniaxial ferromagnet. The components due to the dipole-dipole interaction of the spins and also due to the anisotropy energy are found. A comparative analysis is made of the different components of the cubic nonlinearity tensor in both the nonresonance case and for various resonances, in particular when ₀, 3 2w₀, 2 ₀, 3 ₀ for the case in tripling of the frequency. Here, is the frequency of the incident wave and ₀ is the frequency of uniform precession. It is shown that in the non-resonance case the largest components are those that are nonvanishing when no allowance is made for spatial dispersion; in the resonance cases the largest components are those due to the dipole-dipole interaction of the ferromagnetism spins.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 53–58, December, 1973.     

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.     

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.     

Static and Vibrational Properties of Transition Metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is proposed to study the equation of state by incorporating the s-d hybridization effects. Very recently proposed screening function due to Sarkar et al has been used to obtain the screened form factor. The equations of state for Cu, Ta, Mo, W and Pt have been studied up to the pressure of 1000 GPa. The vibrational properties such as phonon dispersion curves (in q and r space), phonon density of states, mode Grüneisen parameters, maximum frequency _max, mean frequency , ^21/2 = (/ ^-1)^1/2 and fundamental frequency ² and static properties such as dynamical elastic constants of rhodium and iridium are also calculated. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has confirmed our formulation.