Annular Aperture Research Articles

Generalization of Zernike polynomials for regular portions of circles and ellipses.

Zernike polynomials are commonly used to represent the wavefront phase on circular optical apertures, since they form a complete and orthonormal basis on the unit circle. Here, we present a generalization of this Zernike basis for a variety of important optical apertures. On the contrary to ad hoc solutions, most of them based on the Gram-Schmidt orthonormalization method, here we apply the diffeomorphism (mapping that has a differentiable inverse mapping) that transforms the unit circle into an angular sector of an elliptical annulus. In this way, other apertures, such as ellipses, rings, angular sectors, etc. are also included as particular cases. This generalization, based on in-plane warping of the basis functions, provides a unique solution and what is more important, it guarantees a reasonable level of invariance of the mathematical properties and the physical meaning of the initial basis functions. Both, the general form and the explicit expressions for most common, elliptical and annular apertures are provided.

Effect of annular apodization and pupil beam parameter in the focal region of high NA lens

Focusing properties of the radially polarized axisymmetric Bessel-modulated Gaussian beam with quadratic radial dependence (QBG beam) and annular aperture are investigated theoretically by vector diffraction theory. Simulation results show that the intensity distribution in the focal region of the radially polarized axisymmetric QBG beam can be adjusted considerably by small beam parameter (μ) and annular aperture (δ). When μ increases, the focal spot may change to focal hole and changes focal pattern remarkably. On introducing annular aperture, focus can split or extends along the optical axis for different μ. In this paper, we have shown the generation of the focal spot, dark focal spot, focal split and increase in focal depth in the axial direction of the incident beam propagating through the aligned optical system.

Side lobe suppression of a Bessel beam for high aspect ratio laser processing

Bessel beams can be used for high aspect ratio laser drilling and for eliminating the need to precisely position materials along the propagation direction during laser drilling and cutting. However, Bessel beams have side lobes that can damage the materials subjected to these beams. This paper discusses optical suppression of side lobes. A method is proposed to suppress these side lobes, and the method is based on interference between two Bessel beams with different wave vectors. The effectiveness of this method is confirmed both theoretically and experimentally by realizing a superposed Bessel beam; using a He–Ne laser (λ=633nm) and an annular binary aperture placed in front of a convex lens, this beam has a 1/e2 radius of 44μm.

Tight focusing effect of annular obstructed incident beam in the focal region of high NA lens

Focusing properties of the azimuthally polarized axisymmetric Bessel-modulated Gaussian beam with Quadratic Bessel Gaussian (QBG beam) and annular aperture are investigated theoretically by vector diffraction theory. Simulation results show that the intensity distribution in focal region of the azimuthally polarized axisymmetric QBG beam can be shifted along optical axis considerably by changing parameter (C). On introducing annular aperture (δ), focal pattern at the focus extends along optical axis. In this paper, we have shown the generation of focal hole and focal shifting in the axial direction of incident beam propagating through aligned optical system which is suitable for application such as optical manipulation and optical trapping.

Nonparaxial propagation and focusing properties of azimuthal-variant vector fields diffracted by an annular aperture.

Based on the vectorial Rayleigh-Sommerfeld integrals, the analytical expressions for azimuthal-variant vector fields diffracted by an annular aperture are presented. This helps us to investigate the propagation behaviors and the focusing properties of apertured azimuthal-variant vector fields under nonparaxial and paraxial approximations. The diffraction by a circular aperture, a circular disk, or propagation in free space can be treated as special cases of this general result. Simulation results show that the transverse intensity, longitudinal intensity, and far-field divergence angle of nonparaxially apertured azimuthal-variant vector fields depend strongly on the azimuthal index, the outer truncation parameter and the inner truncation parameter of the annular aperture, as well as the ratio of the waist width to the wavelength. Moreover, the multiple-ring-structured intensity pattern of the focused azimuthal-variant vector field, which originates from the diffraction effect caused by an annular aperture, is experimentally demonstrated.

Effect of dielectric interface on the tight focusing properties of radially polarized annular multi Gaussian beams

A super-length optical needle (44 $$\lambda )$$ of strong transversally polarized field with homogeneous intensity along the optical axis and sub-diffraction beam size (0.48 $$\lambda )$$ can be generated by focusing a radially polarized beam through a dielectric interface with an annular high numerical aperture (NA) lens. Moreover, the focal shifts induced by the mismatch of the refractive indices across the interface has been found. The dependence of focal shifts and spot size of the focused field on the probe depth and NA of the objective is also analyzed in detail by numerical calculations using vector diffraction theory. Such kind of non-diffracting optical needle may have applications in atom-optical experiments, such as with atom trap and atom switches.

Tight focusing of a double-ring-shaped, azimuthally polarized beam through a dielectric interface.

We investigate the tight focusing properties of a double-ring-shaped, azimuthally polarized vector beam (DRS-APVB) by use of vectorial Debye theory. It is shown that a dark channel with an ultralong depth of focus (~106λ) and subwavelength focal holes (~0.5λ) can be generated by focusing a DRS-APVB through a dielectric interface with an annular high-numerical aperture (NA) objective lens. The influence of the NA of the objective, the relative refractive indices of two dielectric media, and the probe depth of the system on the focusing properties of the dark channel has been studied in detail. Such a non-diffracting dark channel could find potential applications in atom optical experiments, such as with atomic lenses, atom traps, and atom switches.

Effect of annular obstruction on tight focusing of partially coherent radially polarized Vortex beam

Based on vectorial Debye theory, the effect of annular apodization of tightly focused partially coherent radially polarized vortex beams in the focal field of high NA lens is studied. The intensity distribution in the focal region is illustrated by numerical calculations. It is found that the focal depth of the generated focal segment strongly dependent on the source coherence length for unobstructed case and the presence of annular aperture reduces the variation of focal depth with source coherence length.

Design and simulation of high resolution optical imaging system based on near-field using solid immersion lens with NA = 2.2

In this work, by changing annular aperture zones transmittance, we could get a spot size smaller than any reported one by utilizing annular aperture. Where, by dividing the annular aperture to more than three zones and utilizing of Sony corporation Produced SIL that has NA higher than 2, we could improve imaging resolution for radial polarization (RP); also we could decrease the FWHM from around to near . Here, the FWHM variation, according to the refractive index changing, has decreased to zero for RP. After that, circular polarization (CP) has been introduced to get a spot size less than . This image resolution improving can be applied to enhance optical data storage, microscopes and lithographic and other high accurate optical systems.

Shaping of spherical light intensity based on the interference of tightly focused beams with different polarizations

We consider the shaping of spherical intensity distributions based on the interference of counter-propagating tightly focused vortex beams with different polarizations. The formation of 3D distributions is performed using a simple method of optimization of the width and position of the single annular aperture. The optimum parameters for the narrow aperture are calculated analytically. In addition the wide aperture parameters are numerically adjusted. It is shown that depending on the polarization, the additional vortex phase and/or phase shift in the beams allow to form either solid light balls or light spheres of subwavelength radius. They consist of the various electric field components. • 3D spherical intensity distributions are formed using tightly focused vortex beams. • The presence of the vortex phase expands opportunities of the 3D creation. • The optimal choice of the annular diaphragm provides spherical creations. • Radial polarization provides the highest quality, but circular one is easier to implement.

Point spread function measurement of an X-ray beam focused by a multilayer zone plate with narrow annular aperture

The experimental procedure for obtaining the point spread function (PSF) of a focusing beam generated using an X-ray multilayer zone plate (MZP) with a narrow annular aperture has been developed. It was possible to reconstruct the PSF by applying the tomographic process to the measured dataset consisting of line spread functions (LSFs) in every radial direction on the focal plane. The LSFs were measured by a knife-edge scanning method of detecting scattered intensity. In the experimental work, quasi-monochromatic undulator radiation with a first harmonic energy of 20 keV was directly focused without a monochromator by the MZP, and the PSF was measured using this procedure. As a result, a near diffraction-limited focused beam size of 46 nm full width at half-maximum was obtained.

Effect of annular obstruction and numerical aperture in the focal region of high NA objective lens

In this article, based on the vector diffraction theory, the effect of annular apodization and numerical aperture in the focal region of tightly focused azimuthally polarized Bessel Gaussian beam by high NA lens is investigated numerically. The results show that our proposed system generates a longitudinally polarized beam in sub wavelength focal spot having large uniform focal depth of incident beam with annular aperture for lower NA. Such kind of subwavelength focal segment may find wide applications in optical traps, biological applications, atmospheric sciences and optical manipulation technology.

SFM-FDTD analysis of triangular-lattice AAA structure: Parametric study of the TEM mode

This theoretical work reports a parametric study of enhanced transmission through annular aperture array (AAA) structure arranged in a triangular lattice. The effect of the incidence angle in addition to the inner and outer radii values on the evolution of the transmission spectra is carried out. To this end, a 3D Finite-Difference Time-Domain code based on the Split Field Method (SFM) is used to calculate the spectral response of the structure for any angle of incidence. In order to work through an orthogonal unit cell which presents the advantage to reduce time and space of computation, special periodic boundary conditions are implemented. This study provides a new modeling of AAA structures useful for producing tunable ultra-compact devices.

Negative refraction of a single-layer metamaterial inserted with dual-coaxial waveguides array

Single-layer metamaterials consisting of a hexagonal close-packed array of Ag/GaP/Ag/GaP/Ag dual coaxial waveguides are investigated by simulation, focusing on both the negative-index property and transmission performance at visible frequencies. Numerical simulations indicate that the negative index mode, the same as the one identified in the Ag/GaP/Ag coaxial waveguides arrays (Nat. Mater. 9, 407, 2010) perfectly conserves and exhibits two negative index bands centered at 400 and 800THz, respectively. The transmission peaks of the Fabry–Perot resonance at 400THz and the transmission intensity of the resonance at 800THz are closely related to the thickness of the silver film. Moreover, the coupling of the two coaxial waveguides can dominate the negative refraction and optical transmission of the constructed metamaterial, only by changing the distance of the two annular apertures. The present configuration can provide more approaches to tune its properties than the single coaxial waveguide array.

Sub-λ/10 spot size in semiconductor solid immersion lens microscopy

The angular spectrum of radially polarized Laguerre–Gaussian beams was tailored by an annular aperture in a semiconductor solid immersion lens microscope. The radii of two concentric rings in the amplitude aperture were optimized by a multi-objective particle swarm optimization algorithm. A GaAs solid immersion lens with NA=3.4 was used in the numerical calculation and a spot size of 98nm (<λ/10) at a wavelength of 1064nm illumination was obtained.

Slanted annular aperture arrays as enhanced-transmission metamaterials: Excitation of the plasmonic transverse electromagnetic guided mode

We present here the fabrication and the optical characterization of slanted annular aperture arrays engraved into silver film. An experimental enhanced transmission based on the excitation of the cutoff-less plasmonic guided mode of the nano-waveguides (the transmission electron microscopy mode) is demonstrated and agrees well with the theoretical predicted results. By the way, even if it is less efficient (70% → 20%), an enhanced transmission can occur at larger wavelength value (720 nm–930 nm) compared to conventional annular aperture arrays structure by correctly setting the metal thickness.

Characteristics of Electromagnetic Pulse Coupling into Annular Apertures

Electromagnetic pulse (EMP) coupling into the annular apertures can disturb or damage much electronic equipment. To enhance electronic system’s capability of anti-electromagnetic interference, the finite difference time domain method (FDTD) was employed to study the characteristics of electromagnetic pulse coupling into the cavity enclosures with annular apertures. The coupling characteristics of annular apertures with different shapes (rectangle, square and circle) were discussed. It shows that, in the case of the same aperture area, the coupling energy of electromagnetic pulse into the circular annular aperture is smaller than that into the rectangular and the square ones. To the rectangular annular aperture, while the polarization direction of the incident electromagnetic pulse is perpendicular to the long side of the rectangular annular aperture, the coupling energy is larger when the aspect ratio of the rectangular annular aperture is larger. The coupling effect of incident pulse with short pulse width is obviously better than the one with longer pulse width. The resonance phenomenon of the coupled waveform occurs in the cavity. DOI: http://dx.doi.org/10.11591/telkomnika.v11i11.3544

Active control of terahertz multimode resonance transmission through subwavelength metal annular aperture arrays

Ultrafast optical properties of U-shaped annular aperture arrays (UAAAs) fabricated on a silicon substrate were investigated for varying photodoping levels of the silicon from the back to front interfaces of the sample. Experimental data demonstrate that the transmission modulation depth of the multimode resonance can be realized about 90% under optical power 60 mW, and the off switch of these resonance peaks transmission can be also simultaneously achieved within several picoseconds. Such plasmonic structure is able to be used for ultrafast optical modulators, active terahertz plasmonics, and ultrafast optical off switch.

Engineering the smallest 3D symmetrical bright and dark focal spots

A simple roadmap is established for the construction of the smallest three-dimensional (3D) isotropic focal spots. It is achieved in a 4Pi configuration by imposing a restriction/condition of equal transverse and longitudinal spot sizes to determine the position of an annular aperture and then optimize its size. The calculations were performed for cylindrically symmetric radial, azimuthal, and circular polarizations for the cases of in-phase and out-of-phase counter-propagating beams as well as when a vortex was added to the beams. A diffraction-limited bright 3D isotropic spot containing solely longitudinal or transverse electric field components is obtained, while the 3D dark spot can be formed from one of two complementary combinations, each containing both transverse and longitudinal field components.

Study of Zernike polynomials of an elliptical aperture obscured with an elliptical obscuration: reply

In our previous paper [Appl. Opt.51, 8490 (2012)] we considered the Zernike polynomials for a unit annular ellipse aperture. In that paper many equations were used and were solved by MATLAB language and by hand, and many times these rewritten equations had some written mistakes. In the Diaz and Mahajan comment [Appl. Opt.52, 5962 (2013)] on the work, some remarks were true and others were not. In this reply, we will discuss their comment in detail.