Poisson Spot Research Articles

The Arago–Poisson Spot: New Applications for an Old Concept

Herein, we report some specific properties and applications of the so-called Arago–Poisson spot in optics. This spot results from the diffraction of a plane wave by an occulting disk that leads to a small bright spot in its shadow. We discuss some of the properties of such beams. In particular, we focus on the ultimate size that can be reached for these beams, which depends on the diameter of the disk, the wavelength, and the distance from the disk. We also highlight self-healing and faster-than-light properties. Applications are then proposed. The applications mainly deal with new traps with nanometer sizes dedicated to the trapping of nanoparticles. We also discuss beams that change frequency during propagation and their application for signal delivery in a precise and determined area.

Characteristics of a Gaussian focus embedded within spiral patterns in common-path interferometry with phase apertures

A phase-only method is proposed to transform an optical vortex field into desired spiral diffraction–interference patterns. Double-ring phase apertures are designed to produce a concentric high-order vortex beam and a zeroth-order vortex beam, and the diffracted intensity ratio of two beams is adjustable between 0 and 1. The coherent superposition of the two diffracted beams generates a brighter Airy spot (or Poisson spot) in the middle of the spiral pattern, where the singularity for typical vortex beam is located. Experiments employing circular, triangular, and rectangular phase apertures with topological charges from 3 to 16 demonstrate a stable, compact, and flexible apparatus for vortex beam conversion. By adjusting the parameters of the phase aperture, the proposed method can realize the optical Gaussian tweezer function and the optical vortex tweezer function simultaneously along the same axis or switch the experimental setup between the two functions. It also has potential applications in light communication through turbulent air by transmitting an orbital angular momentum-coded signal with a concentric beacon laser.

Measurement of optical coherence structures of random optical fields using generalized Arago spot experiment

Measurement of optical coherence structures of random optical fields using generalized Arago spot experiment

Frequency changes during the propagation of a light beam

The energy and therefore the frequency of electromagnetic fields are quantities which are generally considered to be conserved in free space propagation. However, we observe here a frequency varying optical wave in free space propagation. The light comes from an Arago spot. Its frequency changes due to the rotational Doppler effect. More precisely, the light diffracted by a two-dimensional asymmetric object carries orbital angular momentum that varies with distance. As the object rotates, the frequency of the diffracted light experiences different rotational Doppler shifts along propagation. It varies in a discrete quantized way as it propagates. It can be adjusted, without violation of the conservation of energy. Since this phenomenon is deeply rooted in the diffraction process, it sheds some new light on this still open issue.

A new laser-based monitoring method for the cryomodule components alignment

Alignment of superconducting cavities is one of the important issues for the China Spallation Neutron Source Phase II (CSNS II) linac. In order to obtain the cavity displacement in the process of cooling down to the liquid helium temperature, a laser-based Poisson Spot Monitor (PSM) system was newly proposed and a verification system in the laboratory was built. The PSM system uses the diffraction spot formed on the CMOS camera after a beam of parallel laser passes through a spherical target to monitor the position of the measured object, where the spherical target is fixed on the monitored object. The displacement during the cooling process of the cryomodule is replaced by the movement of the high-precision two-axis motorized translation stage. A spherical target is fixed on the translation stage as the monitoring object. A beam of parallel laser passes through the spherical monitoring target to form a Poisson spot image on a CMOS camera. The coordinates of the Poisson spot center are obtained through image processing. Through experiments, the PSM system obtained a high accuracy within 5 μm, which meets the displacement monitoring requirement of the CSNS II cryomodule components. The system is fairly simple and able to be constructed without highly specialized parts and can also be used in other high-precision alignment and monitoring fields.

Gravitational Lensing of Continuous Gravitational Waves

Continuous gravitational waves are analogous to monochromatic light and could therefore be used to detect wave effects such as interference or diffraction. This would be possible with strongly lensed gravitational waves. This article reviews and summarises the theory of gravitational lensing in the context of gravitational waves in two different regimes: geometric optics and wave optics, for two widely used lens models such as the point mass lens and the Singular Isothermal Sphere (SIS). Observable effects due to the wave nature of gravitational waves are discussed. As a consequence of interference, GWs produce beat patterns which might be observable with next generation detectors such as the ground based Einstein Telescope and Cosmic Explorer, or the space-borne LISA and DECIGO. This will provide us with an opportunity to estimate the properties of the lensing system and other cosmological parameters with alternative techniques. Diffractive microlensing could become a valuable method of searching for intermediate mass black holes formed in the centres of globular clusters. We also point to an interesting idea of detecting the Poisson–Arago spot proposed in the literature.

Enlightening Arago-Poisson spot using structured light.

We show that structured light can amplify the intensity of an Arago-Poisson bright spot, the cornerstone proof of the wave nature of light, by several orders of magnitude. Specifically, we use a thin annular beam produced by either an axicon-lens combination or two axicons to illuminate an opaque circular obstacle. Experimental results confirm the numerical calculations. By judiciously choosing our scheme's parameters, the bright spot intensity can be higher than that of the original beam, meaning that structured light facilitates "focusing" of light behind an obstacle. This amplification, in addition to didactic elucidation of this classical effect, can find use in optical alignment/metrology, lithography, aberration measurements, as well as in basic science studies of the Arago-Poisson spot in matter waves.

Analytical method for the description of important obstructed optical beams and the Poisson-Arago spot.

In this work, we describe analytically the diffraction of some important beams due to a circular obstacle. In order to obtain the desired results, we deal with the wave equation in paraxial approximation together with the diffraction Fresnel integral and apply the analytical method proposed by Zamboni-Rached et al. [Appl. Opt.51, 3370-3379 (2012)APOPAI0003-693510.1364/AO.51.003370]. As a byproduct of our method, we notice the formation of the Poisson-Arago spot for ordinary beams (plane wave and Gaussian beam) and a reconstruction of the beam for nondiffracting beams (Bessel beam). Then, we pass to a vectorial analysis for better describing the electromagnetic beams.

Experimental investigation of the energy backflow in the tight focal spot

Using two identical microobjectives with a numerical aperture NA = 0.95, we experimentally demonstrate that the on-axis intensity near the tight focal spot of an optical vortex with a topological charge 2 is zero for right-handed circular polarization and nonzero for left-handed circular polarization. This serves to confirm that in the latter case there is a reverse energy flow on the optical axis, as testified by a very weak local maximum (the Arago spot) detected at the center of the measured energy flow distribution, caused by diffraction of the direct energy flow by a 300 nm circle (the diameter of a reverse energy flow tube). The comparison of numerical and experimental intensity distributions shows that it is possible to determine the diameter of the reverse energy flow "tube", which is equal to the distance between the adjacent intensity nulls. For NA = 0.95 and a 532 nm incident wavelength, the diameter of the on-axis reverse energy flow "tube" is measured to be 300 nm. It is also experimentally shown that when an optical beam with second-order cylindrical polarization is focused with a lens with NA = 0.95, there is a circularly symmetric energy flow in the focus with a very weak maximum in the center (the Arago spot), whose distribution is determined by diffraction of the direct energy flow by a 300 nm circular region, where the energy flow is reverse. This also confirms that in this case, there is a reverse energy flow on the optical axis.

Nanometer optical trap based on stimulated emission in evanescence of a totally reflected Arago spot : Nanometer optical trap for fluorescent nanoparticles.

Optical tweezers have paved the way towards the manipulation of particles and living cells at the micrometer range. Its extension towards the nanometer world may create unprecedented potentialities in many areas of science. Following a letter (O. Emile, J. Emile, H. Tabuteau, EPL 129, 58001 (2020)) that reported the observation of the trapping of a single 200nm diameter fluorescent particle in a nanometric volume, we detail here our experimental findings. In particular, the trapping mechanism is shown to be based on the radiation pressure of light in one direction and on the stimulated emission of the particle in the evanescent wave of a nanometer Arago spot on a glass/liquid interface on the other directions. The trapping volume is a 200nm height cylinder whose radius varies with the spreading of the evanescent wave near the spot and can reach 50nm. The calculation of the force and the parameters limiting the lifetime are detailed. Applications to laser trapping of atoms and molecules are also discussed.

Poisson's Spot at New Shapes of Damage of a Circular Disk

Poisson's Spot at New Shapes of Damage of a Circular Disk

Signature of Short-Range van der Waals Forces Observed in Poisson Spot Diffraction with Indium Atoms.

The phase of de Broglie matter waves is a sensitive probe for small forces. In particular, the attractive van der Waals force experienced by polarizable atoms in the close vicinity of neutral surfaces is of importance in nanoscale systems. It results in a phase shift that can be observed in matter-wave diffraction experiments. Here, we observe Poisson spot diffraction of indium atoms at submillimeter distances behind spherical submicron silicon dioxide particles to probe the dispersion forces between atoms and the particle surfaces. We compare the measured relative intensity of Poisson's spot to theoretical results derived from first principles in an earlier communication and find a clear signature of the atom-surface interaction.

Fresnel diffraction of multiple disks on axis

Aims. We seek to study the Fresnel diffraction of external occulters that differ from a single mask in a plane. Such occulters have been used in previous space missions and are planned for the future ESA Proba 3 ASPIICS coronagraph. Methods. We studied the shading efficiency of double on-axis disks and generalized results to a 3D occulter. We used standard Fourier optics in an analytical approach. We show that the Fresnel diffraction of two and three disks on axis can be expressed using a Babinet-like approach. Results are obtained in the form of convolution integrals that can be written as Bessel-Hankel integrals; these are difficult to compute numerically for large Fresnel numbers found in solar coronagraphy. Results. We show that the shading efficiency of two disks is well characterized by the intensity of the residual Arago spot, a quantity that is easier to compute and therefore allows an interesting parametric study. Very simple conditions are derived for optimal sizes and positions of two disks to produce the darkest structure around the Arago spot. These conditions are inspired from empirical experiments performed in the sixties. A differential equation is established to give the optimal envelope for a multiple-disk occulter. The solution takes the form of a simple law, the approximation of which is a conical occulter, a shape already used in the SOHO Mission. Conclusions. In addition to quantifying expected results, the present study highlights unfortunate configurations of disks and spurious diffractions that may increase the stray light. Particular attention is paid to the possible issues of the future occulter spacecraft of ASPIICS.

Mechanism of formation of an inverse energy flow in a sharp focus

A reverse energy flow is theoretically demonstrated to occur in the interference pattern generated by four plane waves with linear polarization. In some regions of the interference pattern, the right-handed triplets of plane-wave vectors k $({k}_{z}g0)$, E, and H (comprising a wave vector and $\mathbf{E}$- and H-field vectors) sum up to form an electromagnetic field described by a right-handed triplet of vectors k $({k}_{z}l0)$, E, and H. It is in these regions that the negative propagation of light occurs. On the optical axis the orbital energy flow, proportional to the light intensity, is shown to be positive, while the spin flow is negative and exceeds the orbital flow in magnitude. That is why the on-axis summary energy flow is negative. The magnitude of the reverse flow on the optical axis is two times lower than that of the intensity. A similar mechanism may apply to the case of sharply focusing a laser beam with second-order polarization or phase singularity. Using two identical micro-objectives with a numerical aperture of 0.95, it has been demonstrated experimentally that the intensity on the optical axis near the focus of an optical vortex with a topological charge of 2 is zero for right circular polarization and nonzero for left circular polarization. This confirms that in the latter case there is the reverse flow of light energy on the optical axis, since in the center of the measured energy flow distribution there is a very weak local maximum (the Arago spot) aroused due to diffraction of the forward flow by a circle with a diameter of 300 nm (the diameter of the tube with the reverse flow). Comparing the numerical and experimental intensity distributions, it is possible to determine the diameter of a ``tube'' with the reverse flow. For a numerical aperture of 0.95 and a wavelength of 532 nm, the diameter of the tube of the reverse flow along the optical axis is 300 nm. It is also shown experimentally that when an optical beam with second-order cylindrical polarization is focused with a numerical aperture of 0.95, there is a circularly symmetric energy flow in the focus with a very weak flow in the center (the Arago spot), whose distribution is determined by diffraction of the forward flux by an $\ensuremath{\sim}300$-nm-diameter circular area, where the energy flow is reverse. This also confirms that in the latter case, there is a reverse energy flow on the optical axis.

Nanoscale optical trap for fluorescent nanoparticles

Optical trapping has offered new potentialities in the manipulation of bacteria, living cells, organelles, or microparticles in micrometric volumes. Its extension to the nanometer scale may create exceptional opportunities in many areas of science. We report here the trapping of a single 100 nm radius particle in a nanometric volume. The trapping relies on stimulated emission of the fluorescent particle in the evanescent wave of a totally reflected Arago spot on a glass-liquid interface. The trapping volume is a 200 nm height and 125 nm radius cylinder. Such a nano-trap, aside from applications in nano-physics, may echo the needs of life scientists to manipulate ever-smaller biological samples.

Experimental analysis of submicrometer optical intensity distributions after an opaque disk.

Generation of subwavelength beam sizes is a fascinating challenge with several implications. The observation of a 120 nm laser spot in the visible part of the spectrum is reported here. It has a size variation of less than 10% in a distance of $ 50\;\unicode{x00B5}{\rm m} $50µm along the axis of propagation. This so-called Arago spot results from the diffraction of the light from a laser diode by the edges of an absorbing disk. Applications are discussed and hollow beams carrying orbital angular momentum with a 400 nm diameter dark spot in the center are evidenced. This paves the way toward atom lithography via atom guiding or new spectroscopy on forbidden transitions.

Vector properties of a circular plate diffracted by the plane wave with sub-wavelength size

The vector diffraction of linearly polarized plane wave passing through a thin circular plate with a sub-wavelength radius is investigated by the finite element method. The transverse distribution and propagating evolution of the diffracted field with different intensity expressions are analyzed and compared. It shows that there are not only the component of the incident polarization, but also those of other two vertical directions in the near-field diffracted region. Regardless of the relationship between the wavelength and the radius of the circular plate, the diffracted field could evolve into a steady annular diffracted pattern, in which there is a central bright spot (so-called Poisson spot). There is an obvious difference of the diffracted properties between two intensity expressions from the square of electric field and the average magnitude of the Poynting vector as the propagation distance is very small, while they can be considered same with a large propagation distance (e.g. more than a wavelength).

Arago spot formation in the time domain

Using the space-time duality, we theoretically and experimentally revisit the Arago spot formation in the time domain and explore the temporal emergence of a bright spot in the time shadow of an initial waveform. We describe the linear regime of propagation using Fresnel’s integrals and show that in the presence of Kerr nonlinearity the Arago spot formation is affected depending on the sign of the dispersion. We finally confirm experimentally the Arago spot formation in the time domain using a telecommunication optical fiber platform.

Wave-optical treatment of the shadow cast by a large gravitating sphere

We study the shadow cast by a large gravitating sphere, similar to our Sun. For this, we consider the gravitational field produced by a static mass monopole within the first post-Newtonian approximation of the general theory of relativity. We study the propagation of a monochromatic electromagnetic wave in the vicinity of a large, opaque, gravitating sphere. To treat the opaque nature of the body and its physical size, we implement fully absorbing boundary conditions and develop a wave-optical treatment of the shadow formed by this object. Based on this approach, we demonstrate that the structure of the shadow is determined by the Schwarzschild radius of the body and its physical size. The shadow's boundary has the shape of a concave rotational hyperboloid bent inward due to the refractive properties of the curved spacetime. We show that there is no light in the shadow. However, even in the presence of gravity and related gravitational bending of photon trajectories there is the bright spot of Arago that is formed behind a perfectly spherical obscuration.

Radio Interferometric Observation of an Asteroid Occultation

Abstract The occultation of the radio galaxy 0141+268 by the asteroid (372) Palma on 2017 May 15 was observed using six antennas of the Very Long Baseline Array (VLBA). The shadow of Palma crossed the VLBA station at Brewster, Washington. Owing to the wavelength used, and the size and the distance of the asteroid, a diffraction pattern in the Fraunhofer regime was observed. The measurement retrieves both the amplitude and the phase of the diffracted electromagnetic wave. This is the first astronomical measurement of the phase shift caused by diffraction. The maximum phase shift is sensitive to the effective diameter of the asteroid. The bright spot at the shadow’s center, the so called Arago–Poisson spot, is clearly detected in the amplitude time-series, and its strength is a good indicator of the closest angular distance between the center of the asteroid and the radio source. A sample of random shapes constructed using a Markov chain Monte Carlo algorithm suggests that the silhouette of Palma deviates from a perfect circle by 26 ± 13%. The best-fitting random shapes resemble each other, and we suggest their average approximates the shape of the silhouette at the time of the occultation. The effective diameter obtained for Palma, 192.1 ± 4.8 km, is in excellent agreement with recent estimates from thermal modeling of mid-infrared photometry. Finally, our computations show that because of the high positional accuracy, a single radio interferometric occultation measurement can reduce the long-term ephemeris uncertainty by an order of magnitude.