Fresnel Diffraction Effects Research Articles

Stochastic ray tracing for Fresnel diffraction

We propose stochastic ray tracing for laser beam propagation in Fresnel diffraction to find the duality between wave and ray representations. We transform from the Maxwell equations to the Schrödinger equation for a monochromatic laser beam in the slowly varying envelope approximation. The stochastic ray tracing method interprets this Schrödinger equation as a stochastic process, of an analogy of Nelson’s stochastic mechanics. It can illustrate the stochastic paths and the wavefront of an optical beam. This ray tracing method includes Fresnel diffraction effects naturally. We show its general theoretical construction and numerical tests for a Gaussian laser beam with diffraction, that stochasticity realizes the beam waist around the Rayleigh range.

Ultrasensitive Near‐Infrared MoTe2 Photodetectors with Monolithically Integrated Fresnel Zone Plate Metalens

AbstractAtomic layers of group‐VI 2D transition metal dichalcogenides (TMDCs) with substantial materials system and unique physicochemical properties have exhibited excellent performances in electronics and optoelectronics. However, photodetectors based on TMDCs suffer from poor sensitivity and optical absorption due to the weak phonon conversion efficiency and optical absorption due to their atomically thin feature. Here, taking advantages of miniaturization and integrability, all‐dielectric TiO2 metalenses are designed based on the Fresnel diffraction effect and integrated with molybdenum ditelluride (MoTe2) photodetectors. Owing to the enhancement of photon utilization efficiency, the corresponding integrated devices exhibit a high responsivity of 135.0 A W–1, an excellent external quantum efficiency of 202.0%, and a specific detectivity of ≈4.05 × 1012 Jones. These results indicate that the optoelectrical properties of 2D materials can be significantly optimized by integration with metalens and will accelerate the evolution of metalens in 2D optoelectronics fields.

A practical criterion for focusing of unstained cell samples using a digital holographic microscope.

Digital holographic microscopy (DHM) is an important technique that may be used for quantitative phase imaging of unstained biological cell samples. Since the DHM technology is not commonly used in clinics or bioscience research labs, at present there is no well-accepted focusing criterion for unstained samples that users can follow while recording image plane digital holograms of cells. The usual sharpness metrics that are useful for auto-focusing of stained cells do not work well for unstained cells as there is no amplitude contrast. In this work, we report a practical method for estimating the best focus plane for unstained cells in the digital hologram domain. The method is based on an interesting observation that for the best focus plane the fringe pattern associated with individual unstained cells predominantly shows phase modulation effect in the form of bending of fringes and minimal amplitude modulation. This criterion when applied to unstained red blood cells shows that the central dip in the doughnut-like phase profile of cells is maximal in this plane. The proposed methodology is helpful for standardizing the usage of DHM technology across different users and application developmentefforts. LAY DESCRIPTION: Digital holographic microscopy (DHM) is slowly but steadily becoming an important microscopy modality and gaining acceptability for basic bio-science research as well as clinical usage. One of the important features of DHM is that it allows users to perform quantitative imaging of unstained transparent cells. Instead of using dyes or fluorescent labelling, DHM systems use quantitative phase as a contrast mechanism which depends on the natural refractive index variation within the cell samples. Since minimal wet lab processing is required in order to image cell samples with a DHM, cells can be imaged in their natural state. While DHM is gaining popularity among users, the imaging protocols across the labs or users need to be standardized in order to make sure that the same quantitative phase parameters are used for tasks such as quantitative phased based cellclassification. One of the important operational tasks for any microscopy work is to focus the sample under study. While focusing comes naturally to users of brightfield microscopes based on image contrast, the focusing is not straightforward when samples are unstained so that they do not offer any amplitude contrast. When performing quantitative phase imaging, defocus can actually change the phase profile of the cell due to near-zone (Fresnel) diffraction effects. So unless a standardized focusing methodology is used, it will be difficult for multiple DHM users (potentially at different sites) to agree on quantitative results out of their phase images. DHM literature has prior works which perform numerical focusing of recovered complex wave-field in the hologram plane to find the best focus plane. However such methods are not user friendly and do not allow user the same focusing experience as in a brightfield microscope. The numerical focusing is therefore a reasonably good method for an optics researcher but not necessarily so for a microscopy technician looking at cell samples with a DHM system in a clinicalsetting. The present work provides a simple focusing criterion for unstained samples that works directly in the hologram domain. The technique is based on an interesting observation that the when an unstained cell sample is in the best-focus plane, its corresponding hologram (or fringe pattern) predominantly shows phase modulation manifested by bending of fringes at the location of the cell. This criterion can be converted into a simple numerical method as we have used to find the best-focus plane using a stack of through focus holograms. We believe that the technique can be used manually by visually observing the holograms or can be converted to an auto-focus algorithm for a motorized DHMsystem.

Writing arbitrary distributions of radiant exposure by scanning a single illuminated spatially random screen

Arbitrary distributions of radiant exposure may be written by transversely scanning a single known spatially-random screen that is normally illuminated by spatially but not necessarily temporally uniform radiation or matter wave fields. The arbitrariness, of the written pattern of radiant exposure, holds up to both (i) a spatial resolution that is dictated by the characteristic transverse length scale of the illuminated spatially random screen, and (ii) a background term that grows linearly with the number of random-illumination patterns. Two classes of the method are developed. The former assumes the distance between the illuminated random mask and the target plane to be sufficiently small that the effects of diffraction may be neglected. The latter accounts for the effects of Fresnel diffraction in the regime of large Fresnel number. Numerical simulations are provided for both variants of the method. Contrast and signal-to-noise ratio are also considered. The method may be parallelized, and is suited to both magnifying and de-magnifying geometries. Possible applications include spatial light modulators and intensity projectors for those matter and radiation wave fields for which such devices do not exist, printing or micro-fabrication in both two and three spatial dimensions, and lithography.

Fabrication of large-scale spherical-cap structure and the application on n-GaN based light-emitting diodes

An under exposure method based on Fresnel diffraction effect in a conventional optical lithography system is used to fabricate large-scale, uniform spherical-cap structures. This method provides an effective roughening technology on the top surface of light-emitting diodes (LEDs) to improve the light extraction efficiency of LEDs. LEDs with high duty cycle spherical-cap structures showed enhanced light output power by 130%–160% compared with the LED with a flat surface. This simple and easy shape control method has potential applications in other optical devices such as organic LEDs, inorganic solar cells, and laser diodes.

Central-Obscuration Removal Plates for Focal-Plane Phase-Mask Coronagraphs with a Centrally-Obscured Telescope

Focal-plane phase-mask coronagraphs, such as eight-octant phase-mask coronagraphs (8OPM), are one of the most promising tools for high contrast observations. However, coronagraphic performance would be degraded when combined with a centrally-obscured telescope. We propose pupil-remapping optics for removing the shade of a secondary mirror to generate a clear, circular pupil for the phase-mask coronagraph. First, we show the design of the pupil-remapping optics, called central-obscuration removal plates (CRPs). Next, we report laboratory experiments on the 8OPM coronagraph using manufactured CRPs. We also evaluate off-axis point-spread functions via both laboratory experiments and numerical simulations. Finally, we evaluate, via numerical simulations, limiting factors for coronagraphic performance, such as phase aberrations introduced by the CRPs, the effect of Fresnel diffraction, and chromatic behavior. The numerical simulations suggest that the phase aberrations could be a dominant limiting factor of the achievable contrast in the current laboratory experiments.

A MODEL OF MULTIPATH PROPAGATION OF MILLIMETER RADIO WAVES OVER THE SEA SURFACE AT STRONG SHADOWINGS

A description is given of an over-sea radio-wave propagation model involving strongly shadowed parts of the sea surface. This model is of great practical consequence, since the present-day imperative of the fundamental science is to explore physical processes occurring during the wave propagation. The currently used calculation of e.m. field over the sea surface with wind-generated waves at low grazing angles are based on the hypothesis that surface roughness (sea waves) results from the perturbation (on the average) of the planar interface and exhibit minor slopes. However, in practice these radio-wave propagation conditions do not occur ever so often. We have investigated an alternative incident that is clearly indicate of strong shadowings. The shadowed surface areas preclude the reflection from quasi-planar near-horizontal, surface elements. The received data provide a totally new insight into the physical processes (mechanisms) during radio-wave scattering under strong shadowing conditions. We have made use of the numerical simulation method to determine the coordinates and the curvature of unshadowed elements which represent the wave crests. The field being reradiated by these elements is shows to be the result of the Fresnel diffraction effect and the reflections from the convex cylindrical surfaces (in the 2-D case under study). As far as Ka-band radio waves (8-mm-wavelength), we have assessed the reradiation-power path-length distribution, angular spectra of waves arriving at the receiving-antenna aperture. The knowledge of these parameters is required to analyze the direction finder operation. The authors of the present paper have revealed and analyzed the characteristic features of path length distribution and the distribution of angles of arrival (at a receiving point) of coherent and noncoherent sea surface-reradiated field components, the latter significantly affecting the accuracy of systems for measuring the angular coordinates of radiation sources, including the new modern methods of spectral evaluation.

Numerical simulations of a new approach for seeing measurement

Using a numerical simulation, a new approach to determine the wave structure function, and therefore the astronomical seeing, is presented and discussed. This method is based on the study of the diffraction pattern produced by a double slit at the focus plane of a telescope. The phase screens are simulated using a fast Fourier transform (FFT) based method and Kolmogorov’s law regarding atmospheric turbulence. From the scattered wave intensity, the wave structure function is calculated by taking into account both phase and amplitude fluctuations. This means that we can obtain a seeing value that is independent of the propagation distance between the turbulent layers and the ground level (Fresnel diffraction effect). Indeed, the seeing is related to the refractive-index structure constant (C 2 n ) inside the turbulent layers and thus should be independent of the aforementioned propagation distance.

Development of Photolithography Process for Printed Circuit Board Using Liquid Crystal Mask in Place of Photomask

In this paper, we present a photolithography method for printed circuit boards using a liquid crystal mask (LCM) in place of a photomask. The LCM photolithography method has the advantage of ease of forming various patterns. There were opaque interpixel regions of the LCMs; the areas on the dry film resist (DFR) located under the interpixel regions of the LCM were not exposed to illumination. The unexposed DFR area could be exposed to illumination by utilizing the Fresnel diffraction effects that were due to a gap maintained between the LCM and the DFR during the exposure process. DFR patterns with a width of 200 µm were obtained successfully using the 160 µm gap between LCM and DFR and three sheets of DFR for the exposure process.

Development of Photolithography Process for Printed Circuit Board Using Liquid Crystal Mask in Place of Photomask

In this paper, we present a photolithography method for printed circuit boards using a liquid crystal mask (LCM) in place of a photomask. The LCM photolithography method has the advantage of ease of forming various patterns. There were opaque interpixel regions of the LCMs; the areas on the dry film resist (DFR) located under the interpixel regions of the LCM were not exposed to illumination. The unexposed DFR area could be exposed to illumination by utilizing the Fresnel diffraction effects that were due to a gap maintained between the LCM and the DFR during the exposure process. DFR patterns with a width of 200 µm were obtained successfully using the 160 µm gap between LCM and DFR and three sheets of DFR for the exposure process.

Study on the Straight Edge Diffraction Effects of Base Model Gaussian Laser Field

Considering that in the nanometer grating deposition the substrate is usually set at the center of the laser beam, the straight edge diffraction occurs. Therefore this paper analyze the straight edge diffraction effect of base model Gaussian laser field, which based on the straight edge Fresnel diffraction effects, using the theory of scalar optical, considering the situation of the actual beam waist and straight edge diffraction side not at the same position, and obtain a general and practical light intensity expression of the base model Gaussian laser under the straight edge diffraction field, and had some model analysis and simulation of its light intensity distribution characteristics.

Experimental Observation of Quantum Talbot Effects

We report the first experimental observation of quantum Talbot effects with single photons and entangled photon pairs. Both the first- and second-order quantum Talbot self-images are observed experimentally. They exhibit unique properties, which are different from those produced by coherent and incoherent classical light sources. In particular, our experiments show that the revival distance of two-photon Talbot imaging is twice the usual classical Talbot length and there is no net improvement in the resolution, due to the near-field effect of Fresnel diffraction, which is different from the case of previous proof-of-principle quantum lithography experiments in the far field.

Sub-wavelength micromachining of silica glass by irradiation of CO2 laser with Fresnel diffraction

We investigated a simple and productive micromachining method of silica glass by ablation using a TEA CO 2 laser (10.6 μm) with a spatial resolution down to sub-wavelength scale. The silica glass was irradiated by the TEA CO 2 laser light through a copper grid mask with square apertures of 20 x 20 μm 2 attached to the silica glass surface. After the irradiation, circular holes with a diameter of several μm were formed on the silica glass surface at the centers of the apertures due to the Fresnel diffraction effect. The minimum diameter of the holes was 3.4 μm. The characteristics of the micromachining are discussed based on the electric field distributions of the CO 2 laser light under the mask using a three-dimensional full-wave electromagnetic field simulation.

Fresnel diffraction effects in Fourier-transform arrayed waveguide grating spectrometer

We present an analysis of Fourier-transform arrayed waveguide gratings in the Fresnel diffraction regime. We report a distinct spatial modulation of the interference pattern referred to as the Moiré-Talbot effect. The effect and its influence in a FT AWG device is explained by deriving an original analytical expression for the modulated field, and is also confirmed by numerical simulations using the angular spectrum method to solve the Fresnel diffraction integral. We illustrate the retrieval of spectral information in a waveguide Fourier-transform spectrometer in the presence of the Moiré-Talbot effect. The simulated device comprises two interleaved waveguide arrays each with 180 waveguides and the interference order of 40. It is designed with a Rayleigh spectral resolution of 0.1 nm and 8 nm bandwidth at wavelength lambda approximately 1.5 mum. We also demonstrate by numerical simulations that the spectrometer crosstalk is reduced from -20 dB to -40 dB by Gaussian apodization.

Novel exposure methods based on reflection and refraction effects in the field of SU-8 lithography

Thick-film photolithography based on SU-8 has gained great interest in the field of microreplication technologies. For replication applications the SU-8 structures themselves or electroplated copies of the resist structures are used as casting or embossing tools. In this paper, a simple estimation model is proposed to predict the sidewall profiles of SU-8. This model is based on the effects of Fresnel diffraction and absorption resulting in useful approximations for the pattern profile of SU-8. Its usefulness is successfully verified by experimental results; the estimated and experimental results show similar trends. In addition, by utilizing this model two exposure methods based on reflection and refraction could be developed which avoid negatively sloped sidewall profiles of SU-8. Using these exposure methods, SU-8 preforms without undercut for the replication of optical waveguides have been achieved.

Fresnel diffraction and polychromatic effects on angle-of-arrival fluctuations

Seeing monitoring in astronomy is widely based on the statistical analysis of angle-of-arrival (AA) fluctuations, which are usually modelled in the framework of the near-field approximation where diffraction through turbulence is ignored. They are consequently believed to be completely independent of wavelength. We discuss in this paper the influence of Fresnel diffraction from distant turbulence layers on multi-wavelength (polychromatic) AA fluctuations. For this purpose we propose a model for polychromatic AA fluctuations in weak turbulence conditions and derive an analytical model for their variance in the case where scintillation is ignored. We also present a numerical simulation that includes scintillation and justifies that this latter may be neglected in the analytical model.

Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination

Analytical expressions for the spatial distribution of the spectral density and intensity of projection images are derived for a broad class of object transmission functions in the case of partially coherent Schell-model-type incident illumination. The expressions are linear with respect to the phase distribution in the transmitted wave. Associated methods for phase retrieval are discussed with the emphasis on a technique that allows simultaneous “automatic” phase retrieval and deconvolution of projection images of homogeneous objects by means of mutual cancellation at a specified defocus distance of the Fresnel diffraction effects and the image blurring due to the point-spread function of the imaging system.

Nulling interferometry : Lommel's integrals applied to a Fresnel's diffraction effect

Nulling Interferometry applied to the search and characterization of earth-like ex- oplanets requires to eliminate the star's contribution at a rejection level (Rej = collected en- ergy/residual energy)larger than 10 6 over a large bandwidth (6 to 18 µm). Nulling test-benches are in development in several laboratories so as to master such high a rejection. One approach relies on a Mach-Zehnder set-up with Achromatic Phase Shifters (APS). One APS concept is based on the focus-crossing property, providing an intrinsically achromatic phase shift by π. Using a confocal configuration for the focus-crossing approach, a Fresnel's diffraction effect de- grades the rejection. Usual optical engineering softwares fail in assessing rejection performance and an analytical approach is needed. We describe the bench optical configuration and the Fres- nel's diffraction effect as well as a possible way for correction. Then we describe the analytical method, based on Lommel's integrals, to evaluate the expectable rejection.

InGaN nano-ring structures for high-efficiency light emitting diodes

A technique based on the Fresnel diffraction effect for the fabrication of nano-scale site-controlled ring structures in InGaN/GaN multi-quantum well structures has been demonstrated. The ring structures have an internal diameter of 500 nm and a wall width of 300 nm. A 1cm−1 Raman shift has been measured, signifying substantial strain relaxation from the fabricated structure. The 9 nm blueshift observed in the cathodoluminescence spectra can be attributed to band filling and/or screening of the piezoelectric field. A light emitting diode based on this geometry has been demonstrated.

Sub‐micron InGaN ring structures for high‐efficiency LEDs

A novel technique based on the Fresnel diffraction effect for the fabrication of sub-micron ring structures in InGaN/GaN multi-quantum well structures has been demonstrated. The ring structures have an external diameter of 1.5 μm and a wall width of 500 nm. A 1 cm−1 Raman shift has been measured, signifying substantial strain relaxation from the fabricated structure. The 5 nm blue shift observed in the cathodoluminescence spectra can be attributed to band-filling and/or screening of the piezoelectric field. A light emitting diode based on this geometry has been demonstrated. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)