Spherical Wavefront Research Articles

Geometric propagation of an axially symmetric optical wavefront in a homogeneous medium

We obtain a Taylor series neighbor expansion that allows the geometric propagation of an axially symmetric wavefront in such a way that the change in shape of the wavefront is determined as an explicit function of coordinates. We then apply the expansion to the propagation of conicoids in particular. The theory is applied to the propagation of a general conicoidal, a spherical, and a paraboloidal wavefront. Application of the theory to the general conicoid leads to a proof of the invariance of the product of radius of curvature and conic constant for short propagation distances in homogeneous media. For the case of the spherical wavefront, the intuitive result is obtained (i.e. the wavefront remains spherical).

Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification

We present a numerical method for reconstructing large objects using a convolution method with an adjustable magnification. The method is based on the image locations and magnification relations of holography when the illuminating beam is a spherical wavefront. A modified version of the angular spectrum transfer function is proposed that allows the filtering in the spatial frequency spectrum. Experimental results confirm the suitability of the proposed method.

Amplification of short light pulses with a spherical wavefront

The propagation of a conical light beam through an optical amplifier is considered. The theoretical analysis is based on an analogue of the system of Frantz—Nodvik equations taking into account the specific character of spherical waves. The conditions of applicability of reduced equations (in slowly-varying amplitude approximation) for describing spherical waves propagating in a nonlinear medium are formulated. The peculiarities of amplification for different values of the beam divergence are compared. The change in the transverse structure of a diverging beam, which appears due to the amplification saturation, is studied.

Analysis of the optical field on the human retina from wavefront aberration data

Wave aberrations in the human eye are usually known with respect to the ideal spherical wavefront in the exit pupil. Using Kirchhoff's diffraction theory, we have derived a diffraction integral to compute the optical field on the retina from the wave aberration data. We have proposed a numerical algorithm based on the Stamnes-Spjelkavik-Pedersen (SSP) method to solve that integral. We have shown which approximations are admissible to reduce the complexity of the diffraction integral. In addition, we have compared our results with those of the conventional procedure used to compute intensities on the retina. We have found significant differences between our results and the conventional ones.

Numerical simulation for explosion wave propagation of combustible mixture gas

A two-dimensional multi-material code was indigenously developed to investigate the effects of duct boundary conditions and ignition positions on the propagation law of explosion wave for hydrogen and methane-based combustible mixture gas. In the code, Young’s technique was employed to track the interface between the explosion products and air, and combustible function model was adopted to simulate ignition process. The code was employed to study explosion flow field inside and outside the duct and to obtain peak pressures in different boundary conditions and ignition positions. Numerical results suggest that during the propagation in a duct, for point initiation, the curvature of spherical wave front gradually decreases and evolves into plane wave. Due to the multiple reflections on the duct wall, multi-peak values appear on pressure—time curve, and peak pressure strongly relies on the duct boundary conditions and ignition position. When explosive wave reaches the exit of the duct, explosion products expand outward and forms shock wave in air. Multiple rarefaction waves also occur and propagate upstream along the duct to decrease the pressure in the duct. The results are in agreement with one-dimensional isentropic gas flow theory of the explosion products, and indicate that the ignition model and multi-material interface treatment method are feasible.

Random phase plate for wavefront sensing via phase retrieval and a volume speckle field

A random phase plate is prepared by illuminating a photoresist plate with a fully developed speckle field and using the developed phase plate (DPP) as a diffuser. Wavefront sensing is implemented using phase retrieval based on the recording of speckle intensity patterns at various distances from the DPP and the wave propagation equation. The effects of the roughness height of the DPP on the phase retrieval are investigated. From simulations a roughness height of lambda/10 results in a speckle field that yields good phase reconstruction for the spherical test wavefront incident on the DPP. From the experiments different portions of the DPP that received varying exposures are examined. A section of the phase plate with a characteristic roughness height facilitated the generation of a speckle field that is optimum for the phase retrieval algorithm. Thus a random phase plate with varying roughness height allows optimized measurements of wavefronts with different curvatures. Analytical expressions describing the second-order intensity statistics (fourth-order field statistics) for a field traversing a specific diffuser are presented. This DPP will not give rise to a fully developed speckle field, but knowing the statistics of the depth of the DPP will facilitate a rigorous treatment of the problem.

Jumps Across an Outgoing Spherical Shock Wave Front

The shock jump conditions have been used since Rankine published in 1870 and Hugoniot in 1889. However, these conditions, in which the geometrical effect is never included, may not be correctly applied to material responses caused by a spherical wave front. Here, a geometrical effect on jumps in radial particle velocity and radial stress across an outgoing spherical wave front is examined. Two types of jump equations are derived from the conservation laws of mass and momentum. The first equations of Rankine–Hugoniot (RH) type show that the geometrical effect may be neglected at distances of movement of the rear of the wave front that are more than ten times as long as the effective wave front thickness. Furthermore, using four conditions required to satisfy the RH jump conditions, which are contained in the RH type equations, a method is developed to judge the applicability of the RH jump conditions to the jumps. The second type equations for spherical wave fronts of general form are obtained by expressing a volumetric strain wave ε in the wave front by more general wave forms. In the neighborhood of the center of the wave front, for ε<0.09, radial particle velocity in the jump in any materials is inversely proportional to the square of a dimensionless distance from the center to the rear, and for ε<0.04, radial stress in the jump in some viscous fluids and solids is inversely proportional to the distance. In conclusion, an outgoing spherical wave front attenuates greatly near the center due to the geometrical effect as well as rarefaction waves overtaking from behind, while the geometrical effect is negligible at the specified positions that are distant from the center.

A working method for prototyping solid immersion blazed-phase diffractive optics for near-infrared laser microscopy

This paper reports on the design, fabrication and evaluation of solid immersion blazed-phase diffractive optics for near-infrared radiation of wavelength 1064 nm. The practical application of enhancing the analysis of integrated circuits using scanning laser microscopy through the silicon substrate is demonstrated. A general design technique using computer generated holography (CGH) is developed to create a numerical program that calculates the structure required for spherical wavefront reconstruction through a silicon substrate into any user-defined pattern. Fabrication of the blazed-phase structure with a diffraction efficiency of 87.9% is achieved in a single-process step by using a combination of the focused ion beam to implant gallium atoms according to the phase pattern, followed by reactive-ion etching using CHF3 chemistry. The implant conditions and etch times are experimentally adjusted to achieve a continuous blazed-phase profile with the required height of 440 nm with a minimum implant spacing of 140 nm. The imaging capability of the solid immersion blazed-phase lens is compared to a binary-phase lens with a diffraction efficiency of 38.8%, where the more efficient blazed design results in a corresponding improvement with image contrast. The complete technique is then extended to the reconstruction of multiple focal points and ring patterns, to produce analysis techniques that use phase contrast to produce differential images between each focal point from the same diffractive optic. Analysis results are presented that demonstrate lateral resolutions up to 3.5 times better than without the diffraction optic and the capability of selectively removing of specific spatial frequencies from repetitive integrated circuits.Corrections were made to equation 2.9 in this article on 11 March 2008. The corrected electronic version is identical to the print version.

BANDWIDTH CONSIDERATIONS FOR A MICROSTRIP REFLECTARRAY

The paper describes a theoretical investigation into a limited bandwidth operation of a microstrip reflectarray. Two main factors limiting the bandwidth are considered. One is related to the requirement of phase compensation to convert a spherical wavefront launched by a feed into a planar wavefront. The other one is linked to the limited phasing range of microstrip antenna elements. The two factors contribute to the reflectarray phasing errors that in turn reduce its gain as a function of frequency. Simple formulas for an upper bound of gain bandwidth are derived, assuming the phase compensation by the elements is independent of frequency changes and verified against the results produced by other researchers. It is shown that the phase errors incurred in the path equalization to obtain conversion from spherical to planar wavefronts have a more profound effect on the reduction of operational bandwidth of the reflectarray than the phase truncation implemented on the required phase from each element.

Axial Resolution Enhancement by 4Pi Confocal Fluorescence Microscopy with Two-Photon Excitation

Confocal fluorescence microscopy and two-photon microscopy have become important techniques for the three-dimensional imaging of intact cells. Their lateral resolution is about 200-300 nm for visible light, whereas their axial resolution is significantly worse. By superimposing the spherical wave fronts from two opposing objective lenses in a coherent fashion in 4Pi microscopy, the axial resolution is greatly improved to approximately 100 nm. In combination with specific tagging of proteins or other cellular structures, 4Pi microscopy enables a multitude of molecular interactions in cell biology to be studied. Here, we discuss the choice of appropriate fluorescent tags for dual-color 4Pi microscopy and present applications of this technique in cellular biophysics. We employ two-color fluorescence detection of actin and tubulin networks stained with fluorescent organic dyes; mitochondrial networks are imaged using the photoactivatable fluorescent protein EosFP. A further example concerns the interaction of nanoparticles with mammalian cells.

The location of Microseismic events and the Propagation of Ray path and gridded traveltimes for depth migration using locally spherical wavefronts

An efficient algorithm is presented that estimates the apparent source of a microseismic event from the first arrival clock-times at four receiver locations in a 3D volume. Wavefronts are assumed to be locally spherical in a constant velocity medium. Applications for identifying the apparent source range from monitoring hazardous geological sites, estimating the distribution of well fraccing material, the monitoring of sequestered CO2, or global positioning from satellite data. The clock-time of the source may also be estimated, extending applications to Kirchhoff depth migrations in which traveltimes on a grid may be computed directly, or may be estimated from traveltimes computed along raypaths. The traveltimes at additional grid points can be computed from the apparent source. In heterogeneous media, wavefronts may have an arbitrary shape, but can be considered to be circular over a small region in the neighbourhood of the known points. The velocity in this region is assumed to be constant and may be extended, without error, to enclose the apparent source point.

Super focusing of optical beams

It was commonly believed that the spherical wavefront aberration of an optical beam always leads to a lower maximum focused intensity along the optical axis. It was shown recently both theoretically and experimentally that this was only true for high Fresnel number systems. In low Fresnel number focusing systems a properly chosen spherical wavefront aberration can increase the maximum focused intensity. In this paper, we call this 'super focusing'. To investigate the characteristics of the super focusing, an improved axial intensity formula has been newly derived for Gaussian beams with spherical aberrations. Based on this formula, several examples of axial intensity distributions are shown. The cause of the super focusing is considered based on these intensity distributions and the derived formulae.

La cinématique relativiste sous-jacente à l'ellipse de Poincaré

What is the Lorentz transformation (LT) of a spherical wavefront (a set of simultaneous events)? According to Einstein (1905) the LT produces a spherical wavefront whilst according to Poincaré (1908) the LT produces an ellipsoidal wavefront (the events are no longer simultaneous). What is the LT of a plane wavefront (a set of simultaneous events)? According to Einstein the LT is a space transversal (to the direction of propagation) plane wavefront. According to Poincaré, the LT is a non transversal spacetime wavefront (the tangent plane to the ellipsoid). We show that this contrast between Einstein's and Poincaré's theory of wavefronts is not connected with the electromagnetic fields but with electromagnetic potentials. Poincaré's explicit choice is the Lorenz gauge while Einstein's implicit choice is the transverse gauge. In other words, the convention of synchronization of clocks with light signals is not the same. We show that Poincaré's elongated ellipse in the system of the source is not only a direct explanation of the null result of Michelson's experiment but also a direct explanation of the non null Sagnac's experiment. The fruitless historical polemics of priority between Poincaré and Einstein has been replaced by a very current scientific problematic about the best implementation of simultaneity in the GPS system. To cite this article: Y. Pierseaux, C. R. Physique 8 (2007).

Determining parent radius and conic of an off-axis segment interferometrically with a spherical reference wave

A simple interferometric method is presented for determining the parent radius of curvature (ROC) and conic constant (CC) of a conic surface. This method compares the test surface with a spherical reference wavefront having a ROC equal to the local sagittal, medial, or tangential ROC. The measured wavefront aberrations, particularly the astigmatism and coma, and local radii are used to determine the parent ROC and CC. This method does not require null optics or knowledge of the surface coordinate where the measurement is made.

Formation of speckle interferograms characterizing transverse and longitudinal displacements of a light-scattering surface

The speckle-interferometer sensitivity to transverse or longitudinal displacements of a flat diffusively scattering surface is analyzed for the case of double-exposure recording of a speckle photography. It is shown that the interference pattern characterizing the transverse displacement of a scatterer is localized in the far-field diffraction region, and the interferometer sensitivity depends both on the value and sign of curvature of the spherical wavefront of coherent radiation used in the speckle-photography recording stage. The interference pattern charactering the longitudinal displacement of the scatterer is localized in the near-field diffraction region and in order to record it, spatial filtering of the diffraction field should be performed. The experimental data obtained agree with theory.

A millimetre-wave bandpass filter–lens array

A filter–lens array (FLA) is a planar array of bandpass integrated antenna–filter–antenna (AFA) elements which are stagger-tuned in the vicinity of a centre frequency, so as to provide the phase shift required for transforming spherical and planar wavefronts. Due to the filtering response of the AFA elements, FLA presents a bandpass gain and can act as a combination of a conventional lensarray and a filter. An FLA structure is demonstrated with f/D=1.25 and 8.2% bandwidth at 35 GHz. This FLA is composed of 137 AFA elements and fabricated on two three-inch glass wafers ($\epsilon_{r}=4.45$). A gain of 25.6 dBi and a total efficiency of 45% have been measured at 35 GHz. The Ka-band FLA shows a low-loss scanning performance for up to at least ±30° in the H-plane and ±20° in the E-plane.

Computer simulation of enhanced backscattering from randomly distributed spherical scatterers at 30 GHz and comparison with measurement

This paper presents a computer simulation of backscattering enhancement from randomly distributed spherical water scatterers at 30 GHz, corresponding to laboratory measurements. Because of the finiteness in the scattering volume size, we adopt a very simple direct simulation method, together with a sampling of the scattering paths for triple scattering and higher to minimize computer time. The spherical wavefront and the directivity functions of transmitting and receiving antennas are taken into account. The simulation results agree favorably with measurements. Some of the knowledge on the detailed characteristics of enhanced backscattering is also obtained.

Nucleation and Collapse of Scroll Rings in Excitable Media

We describe a novel nucleation mechanism of scroll rings in three-dimensional reaction-diffusion systems with anomalous dispersion. The vortices form after the collision of two spherical wave fronts from a third, trailing wave that only partially annihilates in the wake of its predecessor. Depending on the relative positions of the three relevant wave sources, one obtains untwisted or twisted scroll rings. The formation of both vortex structures is demonstrated for a modified Belousov-Zhabotinsky reaction.

Wave front design by acoustic contrast control

A way to design and generate desired wave fronts using multiple sound sources is proposed. In principle, any kind of wave front can be described as a sum of orthogonal basis functions, and the wave front of a specific shape can be generated by focusing multiple sources’ energy on a single basis function. Once the sound field is decomposed into a set of orthogonal functions, we can apply a conventional focusing algorithm to generate a desired wave front. Extending the concept of energy focusing, we can also generate a wave front packet, whose energy is concentrated on a group of orthogonal functions rather than single component. This enables us to generate a wave front within a desired bound. For this purpose, we employ acoustic contrast control, which focuses sound energy on a selected group of orthogonal functions by enhancing the energy difference between the focal region and others. Various example cases demonstrate how the proposed method can generate a group of planar and spherical wave fronts propag...

Gravimètre à cavité d'ondes de matière

We describe a matter-wave cavity based gravimeter closed on one end by periodic Gaussian Raman pulses. The gravimeter sensitivity increases quickly with the number of cycles experienced by the condensate inside the cavity. The matter wave is refocused thanks to a spherical wavefront for the Raman pulses. This technique opens the way to experimental realizations of controllable atom optics devices such as condensate lenses or convergent mirrors.