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Huygens-Fresnel Principle in Superspace  [PDF]
Henrique de A. Gomes
Physics , 2006,
Abstract: We first roughly present a summary of the optico-mechanical analogy, which has always been so profitable in physics. Then we put forward a geometrodynamical formulation of gravity suitable to our intentions, both formally and conceptually. We present difficulties in some approaches to canonically quantize gravity which can be amended by the idea put forward in this paper, which we introduce in the last section. It consists basically in trying to find an intermediary between the quantization step going from the classical superhamiltonian constraint to the Wheeler-DeWitt equation. This is accomplished by inputting interference beyond the WKB approximation, through a type of Huygens-Fresnel Principle (HFP) in superspace.
Huygens-Fresnel principle for molecular continuum wave function  [PDF]
A. S. Baltenkov
Physics , 2010,
Abstract: The asymptotic behavior of the molecular continuum wave function has been analyzed within a model of non-overlapping atomic potentials. It has been shown that the representation of the wave function far from a molecule as a plane wave and single spherical wave emitted by the molecular center cannot be corrected. Because of the multicenter character of the problem, the asymptotic form of the wave function according to the Huygens-Fresnel principle must contain N spherical waves with centers at the nuclei of the N atoms that form the molecule. A method of partial waves for a spherically non-symmetrical target is considered for the simplest multicenter target formed by two non-overlapping potentials. The results are compared with those obtained within the single spherical wave approximation. It has been shown that the use of this approximation is intrinsically conflicting, which is a direct consequence of refusal from the Huygens-Fresnel picture of the wave scattering process.
Huygens-Fresnel principle for N-photon states of light  [PDF]
E. Brainis
Physics , 2010,
Abstract: We show that the propagation of a N-photon field in space and time can be described by a generalized Huygens-Fresnel integral. Using two examples, we then demonstrate how familiar Fourier optics techniques applied to a N-photon wave function can be used to engineer the propagation of entanglement and to design the way the detection of one photon shapes the state of the others.
Discontinuous Electromagnetic Fields Using Huygens Sources For Wavefront Manipulation  [PDF]
Michael Selvanayagam,George V. Eleftheriades
Physics , 2013,
Abstract: We introduce the idea of discontinuous electric and magnetic fields at a boundary to design and shape wavefronts in an arbitrary manner. To create this discontinuity in the field we use electric and magnetic currents which act like a Huygens source to radiate the desired wavefront. These currents can be synthesized either by an array of electric and magnetic dipoles or by a combined impedance and admittance surface. A dipole array is an active implementation to impose discontinuous fields while the impedance/admittance surface acts as a passive one. We then expand on our previous work showing how electric and magnetic dipole arrays can be used to cloak an object demonstrating two novel cloaking schemes. We also show how to arbitrarily refract a beam using a set of impedance and admittance surfaces. Refraction using the idea of discontinuous fields is shown to be a more general case of refraction using phase discontinuities.
Huygens-Fresnel-Kirchhoff construction for quantum propagators with application to diffraction in space and time  [PDF]
Arseni Goussev
Physics , 2012, DOI: 10.1103/PhysRevA.85.013626
Abstract: We address the phenomenon of diffraction of non-relativistic matter waves on openings in absorbing screens. To this end, we expand the full quantum propagator, connecting two points on the opposite sides of the screen, in terms of the free particle propagator and spatio-temporal properties of the opening. Our construction, based on the Huygens-Fresnel principle, describes the quantum phenomena of diffraction in space and diffraction in time, as well as the interplay between the two. We illustrate the method by calculating diffraction patterns for localized wave packets passing through various time-dependent openings in one and two spatial dimensions.
Wave-front engineering by Huygens-Fresnel principle for nonlinear optical interactions in domain engineered structures  [PDF]
Yi-qiang Qin,Chao Zhang,Yong-yuan Zhu
Physics , 2007, DOI: 10.1103/PhysRevLett.100.063902
Abstract: The wave-front engineering for nonlinear optical interactions was discussed. Using Huygens-Fresnel principle we developed a general theory and technique for domain engineering with conventional quasi-phase-matching structures being the special cases. By Fourier analysis we put forward the concept of local quasi-phase matching, which suggests that the quasi-phase matching is fulfilled only locally not globally. Experiments on focal effect of second-harmonic wave agreed well with the theoretical prediction. The proposed scheme combines three optical functions: generation, focusing and beam splitting of second-harmonic wave, thus making the device more compact. Further the proposed scheme can be used to perform the integration of multi-functional optical properties in nonlinear photonics, as well as expand the use of nonlinear optical devices.
Nonlinear optical properties in double-sided nonlinear media with Z-scan technique based on the Huygens--Fresnel principle
Nonlinear optical properties in double-sided nonlinear media with Z-scan technique based on the Huygens-Fresnel principle

Ouyang Qiu-Yun,Zhang Xue-Ru,Jiang Li,Chang Qing,Wang Yu-Xiao,Song Ying-Lin,
欧阳秋云
,张学如,蒋 礼,常 青,王玉晓,宋瑛林

中国物理 B , 2006,
Abstract: We present a theoretical model to analyse the propagation of a Gaussian laser beam through double-sided nonlinear media. This model is based on the Huygens--Fresnel diffraction integral method. This theoretical model is not only consistent with the cascade structure model for a small nonlinear phase-shift but also can be used for a large nonlinear phase-shift. It has been verified that it is suitable to characterize the double-sided nonlinear media compared with the cascade structure model. A good agreement between the experimental data and the results from the theoretical model is obtained. It will be useful for the design of multi-sided nonlinear materials.
In Vitro Assessment of Optical Properties of Blood by Applying the Extended Huygens-Fresnel Principle to Time-Domain Optical Coherence Tomography Signal at 1300?nm  [PDF]
Dan P. Popescu,Michael G. Sowa
International Journal of Biomedical Imaging , 2008, DOI: 10.1155/2008/591618
Abstract: A direct method for the measurement of the optical attenuation coefficient and the scattering anisotropy parameter based on applying the extended Huygens-Fresnel principle to optical coherence tomography images of blood is demonstrated. The images are acquired with a low-power probing beam at the wavelength of 1300 nm. Values of 12.15 mm?1 and 0.95 are found for the total attenuation coefficient and the scattering anisotropy factor, respectively. Also, as a preliminary step, the optical refraction index is determined with a precision of two decimal numbers directly from optical coherence images. The total attenuation coefficient and the scattering anisotropy factor are determined with precisions within experimental error margins of 5% and 2%, respectively. Readable OCT signal is obtained for a maximum propagation of light into blood of 0.25 mm. At the maximum probed depth, the measured signal is almost 103 smaller than its initial intensity when entering the sample.
Non-Uniform Dispersion of the Source-Sink Relationship Alters Wavefront Curvature  [PDF]
Lucia Romero, Beatriz Trenor, Jose M. Ferrero, C. Frank Starmer
PLOS ONE , 2013, DOI: 10.1371/journal.pone.0078328
Abstract: The distribution of cellular source-sink relationships plays an important role in cardiac propagation. It can lead to conduction slowing and block as well as wave fractionation. It is of great interest to unravel the mechanisms underlying evolution in wavefront geometry. Our goal is to investigate the role of the source-sink relationship on wavefront geometry using computer simulations. We analyzed the role of variability in the microscopic source-sink relationship in driving changes in wavefront geometry. The electrophysiological activity of a homogeneous isotropic tissue was simulated using the ten Tusscher and Panfilov 2006 action potential model and the source-sink relationship was characterized using an improved version of the Romero et al. safety factor formulation (SFm2). Our simulations reveal that non-uniform dispersion of the cellular source-sink relationship (dispersion along the wavefront) leads to alterations in curvature. To better understand the role of the source-sink relationship in the process of wave formation, the electrophysiological activity at the initiation of excitation waves in a 1D strand was examined and the source-sink relationship was characterized using the two recently updated safety factor formulations: the SFm2 and the Boyle-Vigmond (SFVB) definitions. The electrophysiological activity at the initiation of excitation waves was intimately related to the SFm2 profiles, while the SFVB led to several counterintuitive observations. Importantly, with the SFm2 characterization, a critical source-sink relationship for initiation of excitation waves was identified, which was independent of the size of the electrode of excitation, membrane excitability, or tissue conductivity. In conclusion, our work suggests that non-uniform dispersion of the source-sink relationship alters wavefront curvature and a critical source-sink relationship profile separates wave expansion from collapse. Our study reinforces the idea that the safety factor represents a powerful tool to study the mechanisms of cardiac propagation in silico, providing a better understanding of cardiac arrhythmias and their therapy.
RAY TRACING USING ORDINAL WAVEFRONT RECONSTRUCTION METHOD
有序波前重建法的射线追踪

ZHAO LIANFENG,
赵连锋
,朱介寿,曹俊兴,郑圻森

地球物理学报 , 2003,
Abstract: A new method, is presented the ordinal wavefront reconstruction method to calculate minimum traveltimes and ray paths. In the previous traveltime calculation methods the source is taken as center and the calculation is made layer upon layer and step by step. It would result in acquiring half-baked wavefront information. In this paper, the ordinal wavefront reconstruction method is used in calculating minimum traveltimes according to actual wavefront surfaces' order. The calculating strategy is to take calculation point as center. The fore-node coordinate of the minimum traveltimes of the calculating point is logged directly, at the same time, the minimum traveltimes and ray paths are calculated. This is a kind of synchronous global algorithm. This method has its advantages, such as simple principle, easy implementation, no limit by different velocities, and fast computation etc.. The numerical experiments show that the ordinal wavefront reconstruction method has higher calculation precision and running efficiency.
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