High- and low-frequency asymptotic consequences of the Kramers-Kronig relations

Summary This paper examines the high- and low-frequency asymptotic consequences of the Kramers-Kronig relations which hold for the real and imaginary parts of the Fourier transform of the response of any linear causal system. By knowing or assuming the high- or low-frequency expansion of one of these functions, the corresponding asymptotic expansion of the other is easily determined, and furthermore the coefficients in this expansion may be determined by evaluating integrals that involve intermediate frequencies. The practical utility of the approach is demonstrated with examples from floating-body hydrodynamics and some new integral relations are derived and exploited.     

The Kramers-Kronig relations method and wave propagation in porous elastic media

Waves of an arbitrary frequency in a porous elastic medium are investigated via the Kramers-Kronig relations method. It is shown that some of the widely accepted theories of wave propagation in random composites may violate the causality and/or linearity of the effective medium.Experimentally observed dynamic effects in random media, such as stop bands and complicated behavior of the dispersion curve, are shown to follow from the K-K relations.     

Damping/cooling sum rules in accelerators

I remark that, when formulated appropriately, the damping sum rules for many beam cooling phenomena are in fact particular instances of the same general sum rule. I draw attention to the formulas of Csonka and of Derbenev and Skrinsky, who both showed that under very general circumstances, the total damping rate for a Hamiltonian system acted on by frictional forces is the divergence in momentum space of the frictional force: the individual formulas for radiation damping, ionization cooling, electron cooling and laser cooling are all special cases of this general formula. This places the damping sum rules in a broader context, and gives a deeper understanding of beam cooling.     

Dispersion relations for testing the validity of linear and nonlinear optical spectra

We exploit efficient dispersion relations, which were developed for terahertz spectroscopy, to show their validity for testing linear and nonlinear optical spectra. As an example, we deal with the measured data for complex reflectivity of a KCl crystal and complex nonlinear susceptibility of a polysilane. It is suggested that the spectral data presented in the literature both for the KCl and the polysilane are consistent with the presented spectra analysis method.     

Molecular orientation of nonlinear optical polymer nanosheets on silica nanoparticle monolayer studied by optical waveguide spectroscopy

The paper describes molecular orientation of nonlinear optical (NLO) polymer monolayer transferred onto a sphere-shaped silica nanoparticle monolayer using optical waveguide spectroscopy. Structurally well-defined hybrid polymer nanoassemblies were constructed through bottom-up approaches: Langmuir–Blodgett technique and immersion method. Silica nanoparticles (SiO₂ NPs, 40–50 nm diameter) were immobilized on a quartz waveguide using cationic polymer Langmuir–Blodgett films (nanosheets) as a template. The SiO₂ NPs took a uniformly distributed monolayer formation without any aggregates, which minimizes light scattering. This allows us to gain reproducible absorption spectra of dye molecules embedded in polymer nanosheet monolayer on the nanoscale rough surface using optical waveguide spectroscopy. The NLO polymer nanosheets containing disperse red 1 (DR) were transferred onto the SiO₂ NP monolayer. The polarized absorption spectra were obtained; the s-light absorption was larger than the p-light absorption, indicating that polymer nanosheets are wrapped around SiO₂ NPs so that DR moieties undergo molecular disorientation not to form H-aggregates. This method provides us with useful information on structure–property relationship between nanoshaped inorganic nanoparticle and organic functional molecules in hybrid nanoassemblies.     

Third order nonlinear optical susceptibility of fluorescein-containing polymers determined by electro-absorption spectroscopy

Novel polymers containing xanthene groups with high dye concentrations were prepared, and their third order nonlinear optical properties were studied by electroabsorption spectroscopy technique. The polymers were amorphous with refractive indices above 1.6 in the non-resonant region. The UV-Visible absorption spectra indicate the fluoresceins molecules in the polymers are H-aggregated. They showed third order nonlinear susceptibility, χ⁽³⁾ (−ω:ω, 0, 0), of 2.5-3.5 × 10⁻¹² esu.     

Compact 50-Hz terawatt Ti:sapphire laser for x-ray and nonlinear optical spectroscopy

We report a high-repetition-rate, compact terawatt Ti:sapphire laser system. The oscillator produces an 82-MHz pulse train consisting of broad-bandwidth pulses of 0.5-nJ/pulse energy and of 9-fs pulse duration. The spectrally shaped, lambda/4 regenerative amplifier supports an 80-nm bandwidth. A single 50-Hz repetition-rate pump laser pumps both the regenerative amplifier and a multiple-pass amplifier. The final output from this laser is a 50-Hz pulse train made from pulses of 53 mJ/pulse energy and of 24-fs pulse duration. For generating ultrafast x-ray pulses, 90% of the energy from the final output of a 28-mm-diameter (1/e2) beam is focused onto an ultrafast x-ray wire target. The energy conversion efficiency from optical (800-nm central wavelength) to x-ray (characteristic lines of K(alpha) from Cu at 8 keV) pulses is estimated to be 7 x 10(-5). This laser system can also generate a lower-peak-power, dual-pulse output that can excite, simultaneously and coherently, Raman modes within an adjustable bandwidth (up to 700 cm(-1)) and at a tunable central vibrational frequency. Preliminary results for the generation of dual-pulse output and ultrafast x rays are presented.     

Linear stress-strain relations in nonlinear elasticity

Summary Nonlinear strain measures which are compatible with the existence of an elastic potential and lead to a linear stress-strain relation are obtained. An unusual property of these measures is their dependence on material parameters. Standard strain measures commonly used in nonlinear elasticity are shown to be consistent with linear stress-strain relations only for particular cases of Poisson's ratio. Corresponding potentials for these cases are presented.     

Design rules for phase-matched terahertz surface electromagnetic wave generation by optical rectification in a nonlinear planar waveguide

The theory of guided waves in metal-dielectric planar multilayer structures is applied to reduce the loss and maximize optical nonlinearity for efficient terahertz-field generation in a surface electromagnetic wave by femtosecond laser pulses confined in a (chi)((2)) nonlinear planar waveguide. For typical parameters of thin-film polymer waveguides and metal-dielectric interfaces, the optimal size of the (chi)((2)) waveguide core providing the maximum efficiency of terahertz plasmon-field generation is shown to be less than the wavelength of the optical pump field.     

Kramers-Kronig analysis of molecular evanescent-wave absorption spectra obtained by multimode step-index optical fibers

Spectral distortions that arise in evanescent-wave absorption spectra obtained with multimode step-index optical fibers are analyzed both theoretically and experimentally. Theoretical analysis is performed by the application of Kramers-Kronig relations to the real and the imaginary parts of the complex refractive index of an absorbing external medium. It is demonstrated that even when the extinction coefficient of the external medium is small, anomalous dispersion of that medium in the vicinity of an absorption band must be considered. Deviations from Beer's law, band distortions, and shifts in peak position are quantified theoretically as a function of the refractive index and the extinction coefficient of the external medium; the effect of bandwidth for both Lorentzian and Gaussian bands is also evaluated. Numerical simulations are performed for two types of sensing sections in commonly used plastic-clad silica optical fibers. These sensors include an unclad fiber in contact with a lower-index absorbing liquid and a fiber with the original cladding modified with an absorbing species. The numerical results compare favorably with those found experimentally with these types of sensing sections.     

Polymer optical fibers and nonlinear optical device principles

Basic principles of the present optoelectronic research activities at Hoechst AG are presented in this contribution. Within the diversified broad band spectrum of optoelectronic materials and applications our interest is focused on new types of polymer optical fibers and nonlinear optical device principles using organic Langmuir–Blodgett films and electrically poled polymers. The basic principles and the limits of the present research and development activities which, have a high market potential are outlined.     

Tip-enhanced optical spectroscopy

Spectroscopic methods with high spatial resolution are essential for understanding the physical and chemical properties of nanoscale materials including biological proteins, quantum structures and nanocomposite materials. In this paper, we describe microscopic techniques which rely on the enhanced electric field near a sharp, laser-irradiated metal tip. This confined light-source can be used for the excitation of various optical interactions such as two-photon excited fluorescence or Raman scattering. We study the properties of the enhanced fields and demonstrate fluorescence and Raman imaging with sub-20 nm resolution.     

Diffusive heat flow and sum rules in the hydrodynamic limit of normal 3He

In earlier work it was shown that a sinusoidal distribution ~cos (x) at time t = 0 will decay as 0, t with the excitation of damped, standing waves of first sound. To consider thermal conduction in a first-sound wave, we modify the solution of the Boltzmann equation by introducing a thermal diffusive pole into the Fourier time and space transform, in such a way that the f-sum and compressibility sum rules remain satisfied. The diffusivity factor D appearing in this pole is determined by the consistency condition that ² T/ t ² calculated in two ways should give the same result. One of these ways proceeds by differentiation of an expression relating the temperature fluctuation T to the quasiparticle momentum distribution, and the other approach utilizes the hydrodynamic equation of energy conservation. Elimination of D from the problem via this consistency condition makes possible an estimate of F ₂ ^s = –2.65 for the Landau parameter, on application of the additional condition that the f-sum rule holds true to terms of fourth order in the wave vector. Use of this value in an expression derived for thermal conductivity gives T = 39.2 ergs/sec cm, in good agreement with experiment.     

Universal relations for nonlinear electroelastic solids

Summary Electro-sensitive elastomers are materials that can support large elastic deformations under the influence of an electric field. There has been growing interest recently in their applications as so-called ``smart materials'. This paper is devoted to the derivation of universal relations in the context of the nonlinear theory of electroelasticity that underpins such applications. Universal relations are equations relating the components of the stress, the electric variables and the deformation that are independent of the constitutive law for a family of materials. For the general constitutive equations of an isotropic electroelastic material derived from a free energy function and for some special cases of these equations, we obtain universal relations, the word ``universal' being relative to the considered class or subclass of constitutive laws. These universal relations are then applied to some controllable states (homogeneous and non-homogeneous) in order to highlight some examples that may be useful from the point of view of experimental characterization of the material properties. Additionally, we examine the (non-controllable) problem of helical shear of a circular cylindrical tube in the presence of a radial electric field, and we find that a nonlinear universal relation that has been obtained previously for an elastic material also holds when the electric field is applied.     

Temperature relations inside bodies in nonlinear heat-conduction processes

An equation has been obtained which allows the unsteady temperature field inside multidimensional bodies to be calculated from known temperatures along the coordinate axes, in nonlinear heat-condition process.     

Femtosecond Z-scan measurements of nonlinear refraction in nonlinear optical crystals

We report an investigation of third-order optical nonlinearities in several nonlinear optical crystals using the Z-scan technique with femtosecond laser pulses at 780 nm wavelength. The crystals studied include LiNbO₃:MgO, KTiOAsO₄, KTiOPO₄, β-BaB₂O₄ and LiB₃O₅, which are extensively used for ultrashort-pulse second-harmonic generation and optical parametric oscillation. The nonlinear refractive index n₂ in these crystals has been determined to be in the range from 10⁻¹⁶ to 10⁻¹⁵ cm²/W. No two-photon absorption has been observed. The experimental results are compared with the two-band model for the bound electronic Kerr nonlinearity. It is shown that the measured n₂ values in β-BaB₂O₄ and LiB₃O₅ are one order of magnitude smaller than those of LiNbO₃:MgO, KTiOAsO₄, KTiOPO₄, which is in agreement with the theoretical prediction.     

Monolayer detection on flat metal surface via surface enhanced Raman spectroscopy and sum frequency generation spectroscopy

Monolayer detection on metal surface requires ultra high sensitivity. Sum Frequency Generation Spectroscopy (SFG) and Surface Enhanced Raman Spectroscopy (SERS) are regarded as two powerful techniques with submolecular sensitivity to detect adsorbents on metal surface. However, in some cases it's still challenge to characterize molecules or groups with relatively high intramolecular symmetry, such as 4-Nitrothiophenol (4NTP), on flat metal surface even combining these two techniques. Basically, this is due to that 4NTP with para-substituted phenol groups is SFG insensitive while flat metal surface is unfavorable to yield strong SERS enhancement. In this concern, a simple and efficient method, silver mirror method, was employed to facilitate the detection of 4NTP SAM on flat gold surface. Silver nanopheres with diameters around 300 nm was fabricated through silver mirror reaction and in situ formed milky overlayer on top of 4NTP SAM adsorbed on gold surface. Significant enhancement on SERS signal can be achieved with such special assembly structure of the "metal-molecule-metal" system. Generally, the silver mirror method provided a complementary approach to facilitate the spectroscopic applications of molecule level detection on various metal surfaces in situ.