On the Derivation of the Integral Equation for the Propagation of Light in Dielectric Crystals

1971 ◽  
Vol 49 (10) ◽  
pp. 1384-1395 ◽  
Author(s):  
J. Vlieger
Keyword(s):  
Integral Equation ◽  
Light Wave ◽  
Dipole Moments ◽  
Incident Light ◽  
Phenomenological Theory ◽  
Dipole Interaction ◽  
Dielectric Tensor ◽  
Simple Lattice ◽  
Propagation Of Light ◽  
Set Up

A new derivation is given of the integral equation for the macroscopic polarization set up in a dielectric crystal by an incident light wave. The molecules are assumed to lie on the points of a perfect, simple lattice and to interact only via the retarded dipole–dipole interaction. The derivation is based on a direct averaging of the microscopic equations for the dipole moments induced by the incident wave and the dipole fields. The averaging is a space averaging with a weight function with a width Δ satisfying [Formula: see text], where a is the lattice constant and λ the wavelength of the incident field. The derivation is an application of Nijboer and De Wette's method for the evaluation of lattice sums.In contrast to the more indirect derivation given earlier by Hoek, (i) the present derivation is not based on an expansion in powers of the molecular polarizability, α, so that, e.g., there is no limitation to frequencies outside the resonance regions, and (ii) the integral equation is shown to be valid everywhere in the crystal except in a macroscopically negligible boundary layer of thickness Δ rather than λ. The latter improvement is crucial in the presence of superradiance.The integral equation is shown to be equivalent to the usual wave equation derived from Maxwell's phenomenological theory supplemented by the appropriate constitutive equations. An explicit expression is derived for the frequency dependent dielectric tensor in terms of rapidly convergent lattice sums.

scholarly journals All organic multiferroic magnetoelectric complexes with strong interfacial spin-dipole interaction

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Yuying Yang ◽  
Zhiyan Chen ◽  
Xiangqian Lu ◽  
Xiaotao Hao ◽  
Wei Qin
Keyword(s):  
Magnetic Field ◽  
Light Intensity ◽  
Room Temperature ◽  
Incident Light ◽  
Dipole Interaction ◽  
Interfacial Interaction ◽  
Magnetoelectric Coupling ◽  
Incident Light Intensity ◽  
Organic Ferromagnets ◽  
Magnetoelectric Coefficient

AbstractThe organic magnetoelectric complexes are beneficial for the development on flexible magnetoelectric devices in the future. In this work, we fabricated all organic multiferroic ferromagnetic/ferroelectric complexes to study magnetoelectric coupling at room temperature. Under the stimulus of external magnetic field, the localization of charge inside organic ferromagnets will be enhanced to affect spin–dipole interaction at organic multiferroic interfaces, where overall ferroelectric polarization is tuned to present an organic magnetoelectric coupling. Moreover, the magnetoelectric coupling of the organic ferromagnetic/ferroelectric complex is tightly dependent on incident light intensity. Decreasing light intensity, the dominated interfacial interaction will switch from spin–dipole to dipole–dipole interaction, which leads to the magnetoelectric coefficient changing from positive to negative in organic multiferroic magnetoelectric complexes.

scholarly journals Formation of half-period surface relief gratings in azobenzene containing polymer films

2020 ◽  
Vol 126 (9) ◽  
Author(s):  
Joachim Jelken ◽  
Carsten Henkel ◽  
Svetlana Santer
Keyword(s):  
Polymer Film ◽  
Polymer Films ◽  
Surface Relief ◽  
Incident Light ◽  
Glassy State ◽  
Polarized Light ◽  
Half Period ◽  
Polarization Distribution ◽  
Linearly Polarized ◽  
Set Up

Abstract We study the peculiar response of photo-sensitive polymer films irradiated with a certain type of interference pattern where one interfering beam is S-polarized, while the second one is P-polarized. The polymer film, although in a glassy state, deforms following the local polarization distribution of the incident light, and a surface relief grating (SRG) appears whose period is half the optical one. All other types of interference patterns result in the matching of both periods. The topographical response is triggered by the alignment of photo-responsive azobenzene containing polymer side chains orthogonal to the local electrical field, resulting in a bulk birefringence grating (BBG). We investigate the process of dual grating formation (SRG and BBG) in a polymer film utilizing a dedicated set-up that combines probe beam diffraction and atomic force microscopy (AFM) measurements, and permits acquiring in situ and in real-time information about changes in local topography and birefringence. We find that the SRG maxima appear at the positions of linearly polarized light (tilted by 45° relative to the grating vector), causing the formation of the half-period topography. This permits to inscribe symmetric and asymmetric topography gratings with sub-wavelength period, while changing only slightly the polarization of one of the interfering beams. We demonstrate an easy generation of sawtooth profiles (blazed gratings) with adjustable shape. With these results, we have taken a significant step in understanding the photo-induced deformation of azo-polymer films.

scholarly journals Directionality of light absorption and emission in representative fluorescent proteins

2020 ◽  
Vol 117 (51) ◽  
pp. 32395-32401
Author(s):  
Jitka Myšková ◽  
Olga Rybakova ◽  
Jiří Brynda ◽  
Petro Khoroshyy ◽  
Alexey Bondar ◽  
...  
Keyword(s):  
Light Wave ◽  
Fluorescent Proteins ◽  
Dipole Moments ◽  
Biological Processes ◽  
Transition Dipole ◽  
X Ray ◽  
Emission Transition ◽  
Transition Dipole Moments ◽  
Fluorescent Molecules ◽  
Incoming Light

Fluorescent molecules are like antennas: The rate at which they absorb light depends on their orientation with respect to the incoming light wave, and the apparent intensity of their emission depends on their orientation with respect to the observer. However, the directions along which the most important fluorescent molecules in biology, fluorescent proteins (FPs), absorb and emit light are generally not known. Our optical and X-ray investigations of FP crystals have now allowed us to determine the molecular orientations of the excitation and emission transition dipole moments in the FPs mTurquoise2, eGFP, and mCherry, and the photoconvertible FP mEos4b. Our results will allow using FP directionality in studies of molecular and biological processes, but also in development of novel bioengineering and bioelectronics applications.

Radiation Field of a Uniformly Moving Charge in an Anisotropic Medium

1974 ◽  
Vol 29 (5) ◽  
pp. 687-692
Author(s):  
G. P. Sastry ◽  
S. Datta Majumdar
Keyword(s):  
Radiation Field ◽  
Anisotropic Medium ◽  
Point Charge ◽  
Potential Distribution ◽  
Asymptotic Form ◽  
Dielectric Tensor ◽  
Arbitrary Direction ◽  
Hankel Functions ◽  
Anisotropic Fields ◽  
Set Up

Abstract Fourier integrals are set up for the field of a point charge moving uniformly in an arbitrary direction in a uniaxial medium anisotropic in ε only. The integrals break up into several parts two of which yield the ordinary and extraordinary cones with uniform azimuthal potential distribution. The remaining integrals neither contribute to the energy radiated nor affect the size and the shape of the cones, but merely distort the field within the cones. The integrals are evaluated exactly in the non-dispersive case and closed expressions for the potential are obtained. In the dispersive case, the radiation field is determined by using the asymptotic form of the Hankel functions occurring in the integrand. The resulting expressions exhibit the high azimuthal asymmetry characteristic of anisotropic fields. From the expressions derived for a pure dielectric the potential in a doubly anisotropic medium is obtained, without a fresh calculation, by making appropriate substitutions for the coordinates of the field point and the components of the dielectric tensor.

Designed Formation of Nanocomposites via Dipole Interaction

2006 ◽  
Author(s):  
David Salac ◽  
Wei Lu
Keyword(s):  
Molecular Diffusion ◽  
Field Model ◽  
Dipole Moments ◽  
Phase Field Model ◽  
Dipole Interaction ◽  
Intermolecular Forces ◽  
Molecular Organization ◽  
Layer By Layer ◽  
Alignment Structure ◽  
Combined Actions

The formation of designed nanocomposites by multiple layers of adsorbate molecules is studied. We consider the presence of two types of molecules in each layer, which are characterized by different dipole moments. The nanostructures are characterized by the non-uniform distribution of the two molecules. A phase field model is developed to simulate the molecular diffusion and patterning under the combined actions of dipole moments, intermolecular forces, entropy, and external electric field. The study reveals self-alignment, structure conformation and the possibility to reduce the domain sizes via a layer by layer approach. It is also shown that the structure in a layer may define the roadway for molecules to travel on top it. This combined with electrodes embedded in the substrate gives much flexibility to guide the molecular organization and fabrication of designed nanocomposites.

A 1D MODEL FOR A CLOSED RIGID FILAMENT IN STOKES FLOW

2009 ◽  
Vol 19 (06) ◽  
pp. 911-937
Author(s):  
PH. CAUSSIGNAC
Keyword(s):  
Integral Equation ◽  
Fluid Velocity ◽  
Single Layer ◽  
Numerical Convergence ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Convergence Results ◽  
1D Model ◽  
Resistance Matrix ◽  
Set Up

We adapt an existing asymptotic method to set up a one-dimensional model for the fall of a closed filament in an infinite fluid in the Stokes regime. Starting from the single-layer integral representation of the fluid velocity around the filament, we get, for a very slender filament, a Fredholm integral equation on the filament centerline. From this equation, we can compute the drag and force acting on the filament and consequently the resistance matrix. The integral equation is discretized with a collocation method. The study of a scalar model problem yields existence and uniqueness results together with an error estimate for the discretization scheme. Then, we compare the resistance matrix of thin ideal knots obtained from the discretization of the present model to a boundary element method; numerical convergence results and a good agreement of both methods validate our model.

A relativistic formula for the scattering of mesons under the influence of radiation damping

1943 ◽  
Vol 39 (3) ◽  
pp. 168-172 ◽  
Author(s):  
S. T. Ma
Keyword(s):  
Integral Equation ◽  
Quantum Theory ◽  
Cross Section ◽  
Radiation Damping ◽  
Theoretical Expression ◽  
Free Electrons ◽  
Relativistic Formula ◽  
Complete Detail ◽  
Charged Mesons ◽  
Set Up

It has recently been pointed out by Heitler(1) that the well-known discrepancy between the theoretical expression and the experimental results for the cross-section of scattering of charged mesons by nuclear particles can be removed by a proper consideration of the effect of radiation damping in the quantum theory. The radiation damping in quantum theory was first considered in complete detail for free electrons by Waller(2). A rigorous deduction of the integral equation set up by Waller was given by Heitler on the basis of a method developed by Góra. An alternative rigorous derivation of the integral equation has also been given by Wilson(3). Exact solutions of the integral equation for the simple scattering of mesons by nuclear particles have been found by Heitler in the non-relativistic approximation. An exact solution has not so far been given for physical problems in which the integral equations are complicated, but Wilson has given a general approximate formula for the scattering cross-section, which should be valid for all problems.

scholarly journals Analysis of the light intensity dependence of the growth ofSynechocystisand of the light distribution in a photobioreactor energized by 635 nm light

PeerJ ◽  
2018 ◽  
Vol 6 ◽  
pp. e5256 ◽  
Author(s):  
Alessandro Cordara ◽  
Angela Re ◽  
Cristina Pagliano ◽  
Pascal Van Alphen ◽  
Raffaele Pirone ◽  
...  
Keyword(s):  
Light Intensity ◽  
Photosynthetic Activity ◽  
Genetic Manipulation ◽  
Incident Light ◽  
Red Light ◽  
Clear Correlation ◽  
Heterogeneous Distribution ◽  
Cultivation System ◽  
Modelling Studies ◽  
Set Up

Synechocystisgathered momentum in modelling studies and biotechnological applications owing to multiple factors like fast growth, ability to fix carbon dioxide into valuable products, and the relative ease of genetic manipulation.Synechocystisphysiology and metabolism, and consequently, the productivity ofSynechocystis-based photobioreactors (PBRs), are heavily light modulated. Here, we set up a turbidostat-controlled lab-scale cultivation system in order to study the influence of varying orange–red light intensities onSynechocystisgrowth characteristics and photosynthetic activity.Synechocystisgrowth and photosynthetic activity were found to raise as supplied light intensity increased up to 500 μmol photons m−2s−1and to enter the photoinhibition state only at 800 μmol photons m−2s−1. Interestingly, reverting the light to a non-photo-inhibiting intensity unveiledSynechocystisto be able to promptly recover. Furthermore, our characterization displayed a clear correlation between variations in growth rate and cell size, extending a phenomenon previously observed in other cyanobacteria. Further, we applied a modelling approach to simulate the effects produced by varying the incident light intensity on its local distribution within the PBR vessel. Our model simulations suggested that the photosynthetic activity ofSynechocystiscould be enhanced by finely regulating the intensity of the light incident on the PBR in order to prevent cells from experiencing light-induced stress and induce their exploitation of areas of different local light intensity formed in the vessel. In the latter case, the heterogeneous distribution of the local light intensity would allowSynechocystisfor an optimized usage of light.

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