Incident Plane Wavefront Research Articles

Ronchi-Hartmann type null screens for testing a plano-freeform surface with a detection plane inside a caustic surface.

We have implemented an exact ray trace through a plano-freeform surface for an incident plane wavefront. We obtain two caustic surfaces and provide the critical points related to the ray tracing process. Additionally, we study the propagation of the refracted wavefronts through the plane-curved surface. Finally, by using the Ronchi-Hartmann type null screen and placing the detection plane within the caustic region, we have evaluated the shape of a plano-freeform optical surface under test, obtaining an RMS difference in sagitta value of 6.3 μm.

Removing Phase Misalignment in the Validation of a Compact Antenna Test Range for 5G mm-Wave UE OTA Testing

Over-the-air (OTA) measurement is mandatory for 5G mm-wave wireless devices. The compact antenna test range (CATR) is the baseline method in the current version of TR 38.810 in 3rd generation partnership project (3GPP) and cellular telecommunications industry association (CTIA) millimeter-wave (mm-Wave) test plan. For CATR, both amplitude and phase variations inside the quiet zone (QZ) could affect the final OTA results significantly and hence need to be characterized carefully. Especially in the phase validation of QZ, even slight misalignments between sampling plane and incident plane wavefront due to the limited precision of the positioner or tolerance in antenna fixture could result in large phase variations, which is not the true phase property of QZ. This letter presents a method to remove the effect of the angular error due to misalignment when measuring the phase variation inside QZ. By adopting the proposed method to the measured phase data, any angular error due to misalignment with respect to the incident plane wavefront will be eliminated mathematically, leaving the true phase variations of QZ only. In the meanwhile, the proposed method can alleviate the requirements of fixture manufacture and alignment precision and reduce the test cost.

Geometric treatment of the radiation captured by the Large Millimeter Telescope (LMT/GTM) and ronchigrams at the caustic region for a static source

The aim of the present work is to determine the reflected light rays, wavefronts, caustic and the ronchigram associated with the reflection phenomenon of a plane wave on a parabolic mirror, in particular on the parabolic antenna of the Large Millimeter Telescope (LMT/GTM). The results presented here are general in the sense that the incident plane wavefront has an arbitrary direction , determined by the angles α and β. We present numerical results for two different cases: () and (). From these results we find that in general the caustic is a surface with a stable singularity of a hyperbolic umbilic type. For these cases we compute the distribution of the reflected light rays at some representative planes, determined by the form and dimensions of the caustic, then assuming that the ronchigrating is placed at those representative planes we compute the associated ronchigram. These results are important because they could describe the behavior of the light emitted by a static pointlike source located far away in the Universe.

Acoustic vortices with high-order orbital angular momentum by a continuously tunable metasurface

Metasurface-based acoustic vortex generators formed by fixed microstructures can only transfer the first-order orbital angular momentum (OAM) at a single frequency in a waveguide. Here, the multiple order acoustic vortices are realized through a helical metasurface design that is geometrically compact, broadband, and tunable. The proposed metasurface consists of matched helices rotating into the corresponding helical channels, allowing us to modulate the reflected phase shifts of the individual units. The units are arranged in a compact circular configuration and then passively transform an incident plane wavefront into the desired spiral wavefront with a controllable topological charge. The reported theoretical, numerical, and experimental results evidence that multiple orders of OAM modes can be continuously generated by using only a single metasurface. The tunable vortex design is relevant to the pragmatic applications of metasurfaces in real-time acoustic communications, spanners, and tweezers.

Huygens principle: exact and approximate wavefronts propagated through conic lenses.

Exact and approximate formulae for refracted wavefronts through singlet lenses are obtained by considering an incident plane wavefront propagating along the optical axis. We provide two different approaches for the wavefronts approximated at the second order based on the Huygens principle and the Malus-Dupin theorem. We have in the first method found a way to use iterative wavelets instead of the usual evaluated integral to arrive at these formulae, showing a physical and mathematical correspondence between both methods. Finally, we introduce a parabolic wavefront into the irradiance transport equation in order to provide an analytical solution for the distribution of illumination.

Generation of acoustic helical wavefronts using metasurfaces

It has been shown that acoustic waves with helical wavefronts can carry angular momentum, which can be transmitted towards a propagating medium. Such a wave field can be achieved by using a planar array of electroacoustic transducers, forming a given spatial distribution of phased sound sources which produce the desired helical wavefronts. Here, we introduce a technique to generate acoustic vortices, based on the passive acoustic metasurface concept. The proposed metasurface is composed of space-coiled cylindrical unit cells transmitting sound pressure with a controllable phase shift, which are arranged in a discretized circular configuration, and thus passively transforming an incident plane wavefront into the desired helical wavefront. This method presents the advantage of overcoming the restrictions on using many acoustic sources, and it is implemented with a transmitting metasurface which can be easily three-dimensionally printed. The proposed straightforward design principle can be adopted for easy production of acoustic angular momentum with minimum complexity and using a single source.

Exact wavefronts and caustic surfaces produced by planar ripple lenses.

We obtain simple exact formulas for both caustic and refracted wavefronts through smooth surfaces by considering an incident plane wavefront propagating along the optical axis, providing a condition for total internal reflection (TIR). On the other hand, a formula to provide the maximum slopes for refracted rays outside of the lens is directly related to the condition to obtain the inflection points on the refracting surface. Demanding simultaneously both conditions can potentially provide the shape for an optimized surface which reduces the gap produced by TIR and to refract efficiently all the light outside of the lens. This has a wide potential in applications on the field of non-imagining systems and illumination.

Huygens’ Principle: Exact wavefronts produced by aspheric lenses

We obtain simple exact formulas for the refracted wavefronts through plano-convex aspheric lenses with arbitrary aspheric terms by considering an incident plane wavefront propagating along the optical axis. We provide formulas for the zero-distance phase front using the Huygens' Principle and the Malus-Dupin theorem. Using the fact that they are equivalent, we have in the second method found a way to use an improper integral, instead of the usual evaluated integral, to arrive at these formulas. As expected, when the condition of total internal reflection is satisfied, there is no contribution to the formation of the refracted wavefront.

Optical Nanoantennas with Tunable Radiation Patterns

We address new optical nanoantenna systems with tunable highly directional radiation patterns. The antenna comprises a regular linear array of metal nanoparticles in the proximity of an interface with high dielectric contrast. We show that the radiation pattern of the system can be controlled by changing parameters of the excitation, such as the polarization and/or incidence angles. In the case of excitation under the total reflection condition, the system operates as a nanoscopic source of radiation, converting the macroscopic incident plane wavefront into a narrow beam of light with adjustable characteristics. We derive also simple analytical formulas which give an excellent description of the radiation pattern and provide a useful tool for analysis and antenna design.

Effect of crack opening and orientation on dispersion and attenuation of antiplane coherent wave

SUMMARY Propagation of antiplane coherent wave in solids containing randomly and uniformly distributed cracks is studied by calculating the associated effective wave number. Attention is focused on the influence of crack opening and orientation. Strip-like cracks or empty elliptical cavities are either mutually parallel or randomly oriented, and their surfaces are stress-free. Different multiple-scattering formulations for the effective wave number, in terms of the farfield displacement scattered by a single crack in the matrix, are compared for various crack systems. They coincide at low crack density and show similar trends when the crack density increases. Simple analytical estimates enable a direct evaluation of the crack density from the speed and attenuation of the coherent wave. In the low- and high-frequency ranges, the effective wave speed and attenuation appear to be mainly governed by the projection of cracks on the incident plane wave front.

Measurement of two-dimensional small angle deviation with a prism interferometer

A new technique for the measurement of two-dimensional small angular deviation is presented. A compound prism, which effectively produces a combination of two right-angled prisms in orthogonal directions, and plane reference surfaces have been utilized for the measurement of the orthogonal components of the angular tilt of an incident plane wavefront. Each orthogonal component of the angular tilt is separately measured from the angular rotation of the resultant wedge fringes between two plane wavefronts generated due to splitting of the incident plane wavefront by the corresponding set of right-angled prism and plane reference surface. The technique is shown to have high sensitivity for the measurement of small angle deviation. A monolithic prism interferometer, which is practically insensitive to vibration, is also proposed. Results obtained for the measurement of a known tilt angle are presented.

Computer modelling of a wavefront diffracted at a concave grating

The problem of monitoring the quality of concave gratings is solved by means of an optical system based on a Wyko interferometer and by computer modelling of the wavefront. The optical system transforms a plane wavefront into a toroidal one with two foci, coinciding with the meridional and sagittal foci of the grating. The aberrations of the grating result from the interference of an incident plane wavefront and a modified diffracted wavefront. The mathematical model gives an interferogram corresponding to an ideally fabricated grating. The difference between the computed and the experimental interferograms indicates that the grating has fabrication errors.

Effects of strain field on light in crack opening interferometry

Crack opening interferometry is a standard technique used to measure the normal opening displacement profile of a crack in a transparent material. This paper calculates how much an incident light ray deflects from a nominally straight line path due to strain induced changes in the index of refraction.It is shown that an incident plane wavefront of light that propagates toward a plane strain crack is split into two linearly polarized light rays: one polarized in a direction parallel to the crack front; the other polarized in the plane perpendicular to the crack front.Assuming linear, elastic mechanical behavior and linear optical behavior in a homogeneous, isotropic medium, the index of refraction of both wavefronts is derived for a Mode I crack in the K-field region. In general, the index of refraction is anisotropic and inhomogeneous. Four new material parameters are identified which characterize crack opening interferometry; values are tabulated for three materials.Using geometrical optics, the paths of both light rays are calculated analytically for a special set of initial conditions and an expression for the total light deflection at the crack flank is obtained.The results show that for some materials and specimen geometries, the absolute deflection of each light ray is large enough to be measured, but the relative deflection (i.e. the difference in deflection between the two light rays) is too small to be measured. The main effect that this phenomenon has on crack opening interferometry is to cause a shift in the apparent position of the crack tip. It is shown that this shift will not affect the interpretation of the interference fringes in terms of crack opening displacement.

The use of diffraction techniques for the study of in-plane distortions of x-ray masks

We describe the use of gratings, placed on boron–nitride membranes and exposed with electron beam lithography, as a method of obtaining both qualitative and quantitative information about x-ray mask in-plane distortions. The mask is placed at an angle α≂arcsin λ/d0 measured with respect to an incident plane wave front (λ=6328 Å for the He–Ne laser and d0=1.0 μm for our grating pitch). A mirror, placed at right angles to the mask, is positioned so that it also intersects the incident plane wave front. Both the resultant diffracted wave front and the reflected diffracted wave front are then collected by a lens system and video camera. The grating is written on all or part of the active area of the mask. The process of developing and patterning the trilayer resist structure and absorber film is identical to that of processing an x-ray mask. Patterned gratings allow us to observe: 1) stage placement errors to <0.1 μm, 2) in-plane errors induced by the mounting fixture, 3) in-plane distortions due to thermal gradients generated at e-beam write-time, 4) in-plane distortions due to the absorber stress. Results indicate that for a 0.9 μm tungsten film the worst-case strain due to the absorber, ∼20 ppm, is seen at visual endpoint; however, complete etching of the interlayer lowers this strain to ∼2–3 ppm.

Microwave Fresnel Zone Plates with Non-Uniform Aperture Excitation

A theoretical study of the variation of relative field amplitude with axial distance has been made for a plane and a spherical microwave zone plate with an incident plane wave front having non-uniform aperture excitation distribution. The results show a sharper focussing property for the non-uniform excitation.

Far-Field Diffraction and Polarization Properties of a Three-Dimensional Hollow, Homogeneous, Isotropic Cone*†

A brief description is given of a theory for computing the form of the far-field diffraction and polarization properties of a hollow, homogeneous, isotropic cone, when it is placed between arbitrarily oriented polarizer and analyzer. For this theory, the incident plane wavefront and circular aperture are normal to the axis of the cone. The solution is an “optical one” for which the circular aperture is large compared with the wavelength, the diffraction properties of the cone in the plane of circular aperture are negligible, and multiple reflections between the cone, circular aperture, and focusing system are neglected. All the multiple reflections which arise inside the cone walls and make contributions to the amplitude and phase in the circular aperture are, however, included. Within these limits, it is possible to compute the radiant flux and form of the far-field diffraction pattern for a cone of arbitrary angle, wall thickness, and optical properties, when it is placed between arbitrarily oriented polarizer and analyzer. In all cases, the symmetry properties of these far-field diffraction patterns can be predicted from the forms of the equations. Computations on the detailed forms of these far-field diffraction patterns have been carried out with an IBM 7090 computer, and three-dimensional models constructed and photographed to show their symmetry properties. It has not been possible experimentally to check these computations because of the problems arising in the making and testing of a cone of the required interferometer quality.

The Optical Performance of Windows with Axial Temperature Gradients

The effect of an axial temperature gradient on the optical performance of a plane parallel window is discussed. It is shown theoretically that an incident plane wave front is not deformed significantly on traversing the window. However, appreciable angular deviation can occur, leading to distortion in the image of an extended object. Experiments which support these results are described and a method is indicated for reducing the effect of air turbulence arising at the window surfaces.