Laser-near-field-based Atomic Lens: Quantum Wave Optics Consideration

Abstract

This paper examines the focusing of an atomic beam by the near field of laser radiation diffracted by a small aperture. The wave properties of the atom are taken into consideration within the framework of an approximate Schrödinger equation. The possibility is demonstrated of focusing an atomic beam into a spot some 3 nm across, the atomic and laser beam characteristics being quite acceptable. The main contribution to the spot size is shown to be from spherical aberrations and diffraction effects, the chromatic aberrations of the atomic beam with a 5% velocity distribution broadening having a lesser effect.     

Sensing a wave front by use of a diffraction grating

A method is presented to sense the wave front at the exit of an optical surface. This method uses a set of diffracted rays generated when a He-Ne laser impinges on a rectangular diffraction grating. The grating was placed near the curvature center of the surface to be tested. After they are reflected in the test surface, the diffracted rays have the information of the slopes of the wave front, like in the Hartmann test. The Hartmann pattern was registered near the curvature center and captured with a CCD camera. The slopes for each ray are measured from the experimental pattern, and they are compared with the ideal ones simulated in a computer. The evaluation was carried out by use of Seidel polynomials to obtain the information of the aberrations of a mirror 53 cm in diameter.     

Ray scattering by an arbitrarily oriented spheroid. II. Transmission and cross-polarization effects

Transmission of an arbitrarily polarized plane wave by an arbitrarily oriented spheroid in the short-wavelength limit is considered in the context of ray theory. The transmitted electric field is added to the diffracted plus reflected ray-theory electric field that was previously derived to obtain an approximation to the far-zone scattered intensity in the forward hemisphere. Two different types of cross-polarization effects are found. These are (a) a rotation of the polarization state of the transmitted rays from when they are referenced with respect to their entrance into the spheroid to when they are referenced with respect to their exit from it and (b) a rotation of the polarization state of the transmitted rays when they are referenced with respect to the polarization state of the diffracted plus reflected rays.     

Linear focusing by a plane grating with curved grooves

We study the field diffracted by a plane grating with curved (parabolic) grooves. We will demonstrate that when a monochromatic plane wave is incident on a grating with parabolic grooves the diffracted field has a focal line whose position depends on the curvature radius of the parabolas and the incidence angle of the light onto the grating. The effect described has potential applications in grating-based devices for focusing light without requiring any additional optics.     

Ray scattering by an arbitrarily oriented spheroid. I. Diffraction and specular reflection

Diffraction and reflection of an arbitrarily polarized plane wave by an arbitrarily oriented spheroid in the short-wavelength limit are considered in the context of ray theory. A closed-form solution for both diffraction and reflection is obtained, and the polarization character of the diffracted plus reflected electric field is obtained. It is found that the magnitude of the reflected electric field is multivalued for forward scattering. This is interpreted in terms of the variation of the spheroid's Gaussian curvature at the points where grazing ray incidence occurs.     

Quantitative phase microscopy using dual-plane in-line digital holography

We present detailed theoretical evaluation and thorough experimental investigation of quantitative phase imaging using our previously demonstrated dual-plane in-line digital holographic microscopy technique [Opt. Lett. 35, 3426 (2010)]. This evaluation is based on the recording of two interferograms at slightly different planes and numerically reconstructing the object information. The zero-order diffracted wave is eliminated by using the method of subtraction of average intensity of the entire hologram, and the twin-image diffracted wave is removed by Fourier domain processing of the two recorded holograms. Experiments are performed using controlled amplitude and phase objects and human muscle cells to demonstrate the potential of this technique.     

Some properties of the optical resonances in a single subwavelength slit

Diffraction of TM-polarized waves by a slit in a thick screen of infinite conductivity is treated. The case of an arbitrary incident beam wave is considered. We study the resonances that appear when the wavelength of the incident beam wave is larger than the slit width, i.e., the subwavelength regime where a one-mode model for the slit can be considered. High anomalous values (resonances) of the transmission coefficient, the angular diffracted energy, and the magnetic field within the slit are analyzed. A simple linear relationship to determine the resonant wavelengths is proposed. We show that the transmission coefficient, the normal diffracted energy, and the magnetic field within the cavity are linear functions of the resonant wavelength and the thickness of the screen. Additionally and surprisingly, we reveal that under certain conditions the incident beam wave via the diffraction can give a suppressed light transmission; i.e., a minimum in the transmission is obtained where a maximum is expected.     

Three-dimensional electromagnetic diffraction of a Gaussian beam by a perfectly conducting half-plane

Formulas are derived for the diffraction of a three-dimensional electromagnetic Gaussian beam by a perfectly conducting half-plane. The beam can be incident from any direction, and the main component of the electric field can point in any direction on the plane of the beam waist. The center of the beam waist is on the edge of the half-plane. The incident beam is constructed as a superposition of plane waves, and the total diffracted field is obtained from a superposition of the diffracted fields that are due to each plane wave. Physical constraints that limit the size and direction of the beam relative to the half-plane are described and incorporated into the theory. The scattered field in the far zone is obtained by asymptotic evaluation of the general formulas. Graphical results for the near-field as well as far-field patterns are presented and discussed.     

Strip theory for underwater vehicles in water of finite depth

This paper addresses the need to know the unsteady forces and moments on an underwater vehicle in finite-depth water, at small enough submergences for it to be influenced by sea waves. The forces are those due to the waves themselves, as well as the radiation forces due to unsteady vehicle motions. Knowledge of these forces and the mass distribution of the vehicle allow solution of the equations of motion at a single-frequency. Since the theory is linear, any incident wave field can be decomposed into the sum of many individual single-frequency sinusoidal waves. The motions due to each frequency component can then be added together to obtain the total predicted vehicle motions. The wave forces are due to the undisturbed sea wave plus those due to the diffracted wave necessary to satisfy boundary conditions on the vehicle. The long-used strip theory for ships, with the inviscid-flow approximation, is modified for finite depth and inclusion of lift forces on the vehicle fins. The two-dimensional solutions for the forces on each strip are found by a different method than is commonly used for strip theory. This form of the theory is easier to deal with and requires much less computing time than a fully three-dimensional approach. Experiments are conducted and their results are compared with the theory. Excellent agreement is found between the theoretical and experimental wave forces, including the diffracted wave. It is shown that inclusion of the forces on the fins not only improves the theoretical wave forces, but also brings the results of theory for the radiation forces and moments due to vehicle motions much closer to the experimental values that the theory without inclusion of fin lift forces.     

Conditions for correction of linear and quadratic field-dependent aberrations in plane-symmetric optical systems

The Abbe sine condition and the recently developed pupil astigmatism conditions provide a powerful set of relationships for describing imaging systems that are free from aberrations that have linear and quadratic dependence on field, to all orders in the pupil. We have proved both of these conditions and applied them to axisymmetric imaging systems. We now extend our approach to plane-symmetric systems. Still using Hamilton's characteristic functions, we derive the general sine conditions and the pupil astigmatism conditions that describe plane-symmetric systems that are free of all aberrations with linear and quadratic field dependence.     

Reflection volume holographic scanners with field-curvature corrections

A new type of polygonal holographic scanner that combines a reflection volume hologram with a computer-generated hologram (CGH) is described. The scanner is free from the aberration of field curvature. Such a scanning system can allow for a compact folded version of the scanner and Bragg diffraction into only a single order. The equations expressing the spatial-variable image distance are derived and are fit to the phase function designated by polynomials incorporated into a CGH in terms of the least-squares method. A reflection scanner with field-curvature correction is made by interfering a diffracted wave front from this CGH with a spherical wave front having scanning focal power through a second plane hologram. Experiments demonstrating the feasibility of this scanner are presented. Raster-scan patterns using a multifaceted scanner are shown. Helpful data on the diffraction efficiency and the spectrally diffracted intensity of reflection holograms are also presented.     

Algorithm study of Collins formula and inverse Collins formula

In the study of a diffraction field of a light wave passing through a symmetrical paraxial optical system, the Collins formula and its inverse are convenient for calculation. The algorithm study of the Collins formula demonstrates that both a single fast Fourier transform algorithm and a double fast Fourier transform algorithm can be used in diffraction calculation. But, whichever algorithm is adopted, only by meeting some specific conditions can the amplitude and phase distributions of a diffracted wave be calculated correctly. Based on the Nyquist sampling theorem, the indispensable conditions to calculate a diffraction field accurately are presented.     

Self-pumped phase-conjugate interferometer with a photorefractive iron-doped lithium-niobate crystal

A single object wave is amplitude divided by a beam splitter into two waves of equal intensity that are made to interfere at the back surface of an iron-doped lithium-niobate crystal so that the normal to the back surface is the angular bisector of the input waves. The interference results in the formation of a phase grating (Bragg grating) in the volume of the crystal. These waves are diffracted at the Bragg grating on both the front focal plane and the back focal plane of the crystal. The wave diffracted in the back focal plane from the Bragg grating and counterpropagating to the incident wave is observed to be the phase conjugate of the input object wave. The wave diffracted in the front focal plane of the Bragg grating is incorporated into the design of an interferometer to measure a specific in-plane displacement of the object wave. It is theoretically evaluated and experimentally demonstrated that interferometers such as those that incorporate conjugate-wave pairs are highly sensitive.     

混凝土表面开口裂缝对近表面声波影响

基于混凝土近表面不同波型的声速,分析开口裂缝对声波的影响。有限元仿真结果表明,激励源辐射的初始纵波P经裂缝端点衍射产生纵波P-P与横波P-T,P-T以一定的角度射向混凝土表面经模式转换产生纵波P-T-P;初始横波T在裂缝端点衍射产生纵波T-P与横波T-P;初始瑞利波R在裂缝端点衍射后除了产生纵波R-P与横波R-S外继续沿着固体表面传播(R-R)。在此基础上,基于变型波到达接收阵元的时刻定量检测裂缝的深度,检测结果较单面平测法具有更高的信噪比与检测精度,可辅助单面平测法更精确地定量检测混凝土开口裂缝的深度。     

Criteria for correction of quadratic field-dependent aberrations

Aberrations of imaging systems can be described by using a polynomial expansion of the dependence on field position, or the off-axis distance of a point object. On-axis, or zero-order, aberrations can be calculated directly. It is well-known that aberrations with linear field dependence can be calculated and controlled by using the Abbe sine condition, which evaluates only on-axis behavior. We present a new set of relationships that fully describe the aberrations that depend on the second power of the field. A simple set of equations is derived by using Hamilton's characteristic functions and simplified by evaluating astigmatism in the pupil. The equations, which we call the pupil astigmatism criteria, use on-axis behavior to evaluate and control all aberrations with quadratic dependence on the field and arbitrary dependence on the pupil. These relations are explained and are validated by using several specific optical designs.     

Hartmann-Shack technique and refraction across the horizontal visual field

We compared refractions across the horizontal visual field, based on different analyses of wave aberration obtained with a Hartmann-Shack instrument. The wave aberrations had been determined for 6-mm-diameter pupils up to at least the sixth Zernike order in five normal subjects [J. Opt. Soc. Am. A 19, 2180 (2002)]. The polynomials were converted into refractions based on 6-mm pupils and second-order Zernike aberrations (6 mm/2nd order), 3-mm pupils and second-order aberrations (3 mm/2nd order), 1-mm pupils and second-order aberrations (1 mm/2nd order), and 6-mm pupils with both second- and fourth-order aberrations (6 mm/4th order). The 3-mm/2nd-order and 6-mm/2nd-order refractions differed by as much as 0.9 D in mean sphere on axis, but the differences reduced markedly toward the edges of the visual field. The cylindrical differences between these two analyses were small at the center of the visual field (<0.3 D) but increased into the periphery to be greater than 1.0 D for some subjects. Much smaller differences in mean sphere and cylinder were found when 3-mm/2nd-order refractions and either the 1-mm/2nd-order refractions or the 6-mm/4th-order refractions were compared. The results suggest that, for determining refractions based on wave aberration data with large pupils, similar results occur by either restricting the analysis to second-order Zernike aberrations with a smaller pupil such as 3 mm or using both second- and fourth-order Zernike aberrations. Since subjective refraction is largely independent of the pupil size under photopic conditions, objective refractions based on either of these analyses may be the most useful.     

Theoretical analysis of the transient response for a stationary inplane crack subjected to dynamic impact loading

The problem considered here is the plane strain response of an elastic solid containing a half plane crack subjected to suddenly applied concentrated point forces acting at a finite distance from the crack tip. Attention is focused on the time-dependent full field solutions in the transient process. It was found by Freund that at the instant that the Rayleigh wave reaches the crack tip, the stress intensity factor jumps to the appropriate static value. We find in this study that the full field stresses will approach to the appropriate static value upon arrival of the shear wave diffracted by the Rayleigh wave from the crack tip.     

Diffraction of elastic waves by an elliptic crack

The integral equation method is used to obtain the scattered field of a normally incident plane wave from an elliptic crack embedded in an isotropic elastic medium. It is shown that the determination of the diffracted field depends on the solution of integro-differential equation. A formal power series solution, in the low frequency limit, is obtained. Expressions are derived for the scattered amplitudes and the dynamic stress intensity factor.     

Measuring ocular aberrations in the peripheral visual field using Hartmann-Shack aberrometry

We have used the Hartmann-Shack technique previously to measure ocular aberrations along the horizontal meridian of the visual field. This requires considerable modifications from the technique for measuring the aberrations corresponding to the fovea. We now further develop the technique so that it can be used for any meridian of the visual field. Allowance is made for any auxiliary optics placed in front of the eye to compensate for the limited range of the Hartmann-Shack technique and for the case where aberrations are estimated at a wavelength other than the measuring wavelength. Zernike wave aberrations are converted to peripheral refractions. Examples are presented showing the developments, and we discuss change in wave aberrations when converting from a circular to an elliptical pupil.