Sum rules for arbitrary-order harmonic generation susceptibilities

Dispersion theory for harmonic generation susceptibilities is considered with the aid of complex analysis. New sum rules are obtained for the powers of arbitrary-order harmonic generation susceptibilities. The theory is based on the holomorphic properties and asymptotic behaviour of nonlinear susceptibilities. The present sum rules are reportedly important in nonlinear optical spectra analysis. Received 19 September 2002 Published online 31 December 2002     

Effect of cationic polymethacrylates on the rheology and flocculation of microfibrillated cellulose

Using two cationic methacrylate polymers: poly([2-(methacryloyloxy)ethyl] trimethyl ammonium iodide) (PDMQ) and poly[(stearyl methacrylate)-stat-([2-(methacryloyloxy)ethyl] trimethyl ammonium iodide)] (PSMA13Q), we modified microfibrillated cellulose (MFC) water suspensions. The aim was to affect the flocculation and rheological behavior of the MFC suspension. PDMQ is a strongly cationic polymer while PSMA13Q, also a cationic polymer, contains hydrophobic segments. We studied the MFC/polymer suspension rheological properties with a rotational rheometer in oscillatory and flow measurements. To observe structural changes in suspensions at different shear rates, we measured flow curves with transparent outer geometry and photographed the sample with a digital camera. The oscillatory measurements showed that a small amount of the cationic PDMQ in the MFC suspension strengthened the gel, whereas a small amount of amphiphilic PSMA13Q weakened it. Increased amounts of either polymer increased the gel strength. PSMA13Q also changed the rheological character of the MFC suspension turning it more fluid-like. When we photographed the flow curve measurement, we saw a clear change in the floc structure. This floc structure rupture coincided with a transient region in the flow curve.     

The NMR reciprocity theorem for arbitrary probe geometry

It is shown that the NMR reciprocity theorem is a variant of a problem considered by Lorentz in 1895. This formulation is quite general and applies to electric-dipole-based as well as coil-based or resonator-based magnetic resonance probes. The reasoning is related to, but different from, the proof of the reciprocity theorem for radiofrequency networks and for transmit/receive antenna systems in telecommunications. The signal-to-noise ratio of the NMR experiment is also discussed in very general terms.     

3D printed plano-freeform optics for non-coherent discontinuous beam shaping

Optical Review - The design, fabrication, and characterization of freeform optics for LED-based complex target irradiance distribution are challenging. Here, we investigate a 3D printing technology...     

Kramers-Kronig relations and sum rules of negative refractive index media

Negative refractive index media have become a hot topic in physics due to their proposed revolutionary properties, which would have drastic consequences in design of novel optical devices. We show that Kramers-Kronig relations connecting the real and imaginary parts of the complex refractive index of absorbing media are valid even though the real refractive index may take negative value at some spectral range. In addition universal sum rules for linear optical constants of negative index media are also valid. This means that negative refractive index media are not fundamentally different from regular media. Hence, any spectrum measured from negative refractive index media can be analyzed using dispersion relations and sum rules, which have so far provided information on the optical properties of materials.Received: 13 May 2004, Published online: 30 September 2004PACS: 77. Dielectrics, piezoelectrics, and ferroelectrics and their properties - 78.20.Ci Optical constants (including refractive index, complex dielectric constant, absorption, reflection and transmission coefficients, emissivity)     

Phase retrieval of reflectance for nanoparticle optical identification

We present a method for optical identification of dielectric and metal nanoparticles in a liquid matrix using phase retrieval of reflectance with TE- and TM-polarized light. A formula is derived for extracting the effective complex dielectric function of a nanoparticle colloid based on different complex reflectance components. The phase retrieval is performed using the maximum entropy method. We observe excellent accuracy both for dielectric and metallic nanoparticles with volume fractions up to 10%.     

High- and low-adhesive superhydrophobicity on the liquid flame spray-coated board and paper: structural effects on surface wetting and transition between the low- and high-adhesive states

Surface wetting is an important and relevant phenomenon in several different fields. Scientists have introduced a large number of applications where special surface wetting could be exploited. Here, we study wetting phenomena on high- and low-adhesive superhydrophobic liquid flame spray (LFS)-generated TiO₂ coatings on paper and pigment-coated board substrates using water–ethanol solution as a probe liquid. Submicrometer-scale air gaps, which exist on superhydrophobic surfaces below the liquid droplets, were more stable with the ethanol increment than the larger-scale micrometric air gaps. With the droplet ethanol concentration of 15 wt%, static contact angle as high as 155?±?2° was measured on the LFS–TiO₂-coated board. Transition from the low-adhesive wetting state to the high-adhesive state was demonstrated on the LFS–TiO₂-coated paper. The LFS method enables efficient roll-to-roll production of surfaces with special wetting properties on economically viable board and paper substrate materials.     

The effect of wall depletion on the rheology of microfibrillated cellulose water suspensions by optical coherence tomography

Rheology of microfibrillated cellulose (MFC) water suspensions was characterized with a rotational rheometer, augmented with optical coherence tomography (OCT). To the best of the authors’ knowledge, this is the first time the behavior of MFC in the rheometer gap was characterized by this real-time imaging method. Two concentrations, 0.5 and 1 wt% were used, the latter also with 10^?3 and 10^?2 M NaCl. The aim was to follow the structure of the suspensions in a rotational rheometer during the measurements and observe wall depletion and other factors that can interfere with the rheological results. The stepped flow measurements were performed using a transparent cylindrical measuring system and combining the optical information to rheological parameters. OCT allows imaging in radial direction from the outer geometry boundary to the inner geometry boundary making both the shear rate profile and the structure of the suspension visible through the rheometer gap. Yield stress and maximum wall stress were determined by start-up of steady shear and logarithmic stress ramp methods and they both reflected in the stepped flow measurements. Above yield stress, floc size was inversely proportional to shear rate. Below the yield stress, flocs adhered to each other and the observed apparent constant shear stress was controlled by flow in the depleted boundary layer. With higher ionic strength (10^?2 M NaCl), the combination of yield stress and wall depletion favored the formation of vertical, cylindrical, rotating floc structures (rollers) coupled with a thicker water layer originating at the suspension—inner cylinder boundary at low shear rates.     

Modeling and interference-microscopy characterization of graded index transitions in ion-exchange waveguide integrated elements: transitions between annealed surfaces

We employ interference microscopy to characterize in a direct and local way the graded index transitions at the boundaries of integrated optical elements fabricated by multistep ion-exchange processes, a task not yet possible by other technologies. A particular fabrication method based on purely thermal ion-exchange, which allows local single-mode propagation, is investigated. The refractive-index distribution is modeled on the basis of the linear theory of diffusion and adiabatic transitions of the refractive-index profile. Finally, its validity is analyzed by microinterferometry.