Off-axis Propagation Research Articles

Off-axis propagation algorithm for partial reconstruction of wide-angle computer-generated holograms.

A method for reconstruction of partial off-axis areas of arbitrary size for wide-angle viewing computer generated holograms is presented. Proposed method employs paraxial spherical phase factors and modified propagation kernels. This significantly reduces the numerical space-bandwidth product needed for off-axis wave field calculations, which makes it an efficient propagation method. As a result, propagated wavefields of high-off axis and large size output windows can be obtained. To that end, a phase-space analysis for obtaining the proper condition for implementing spatial-frequency zero-padding for accurate wavefield propagation is carried out. Hence, suppression of aliased components and high spatial resolution is possible. Nevertheless, proposed algorithm faces a computer memory bottleneck when reconstructing very large off-axis areas due to too extensive zero-padding needed. To solve this problem, a memory optimized tiling implementation is introduced. Utility of the developed propagation tools are proven by partial reconstructions from a high-resolution hologram. The size of the reconstructions areas ranges from 100 × 100 mm2 up to 550 × 550 mm2.

Shifted band-extended angular spectrum method for off-axis diffraction calculation.

The shifted band-extended angular spectrum method (Shift-BEASM) is proposed to calculate free-space diffraction between two parallel planes with an off-axis offset. Off-axis numerical propagation is useful for simulating non-paraxial and large-scale fields. The proposed Shift-BEASM allow us to calculate the off-axis diffraction in a wide propagation range by extending the effective bandwidth using the nonuniform fast Fourier transform. The calculation accuracy is higher than that of existing techniques, such as the shifted-Fresnel method and shifted band-limited angular spectrum method, not only in the near field but also in the far field. Numerical examples and accuracy as well as theoretical formulation are presented to confirm validity of the proposed method.

Off-Axis Vortex Beam Propagation through Classical Optical System in Terms of Kummer Confluent Hypergeometric Function

The analytical solution for the propagation of the laser beam with optical vortex through the system of lenses is presented. The optical vortex is introduced into the laser beam (described as Gaussian beam) by spiral phase plate. The solution is general as it holds for the optical vortex of any integer topological charge, the off-axis position of the spiral phase plate and any number of lenses. Some intriguing conclusions are discussed. The higher order vortices are unstable and split under small phase or amplitude disturbance. Nevertheless, we have shown that off-axis higher order vortices are stable during the propagation through the set of lenses described in paraxial approximation, which is untypical behavior. The vortex trajectory registered at image plane due to spiral phase plate shift behaves like a rigid body. We have introduced a new factor which in our beam plays the same role as Gouy phase in pure Gaussian beam.

Alleviating Orbital-Angular-Momentum-Mode Dispersion Using a Reflective Metasurface

Electromagnetic waves carrying orbital angular momentum (OAM) have attracted much interest due to their capacity to enhance communication capabilities. In this work, the OAM-mode-dispersion (OMD) phenomenon is analyzed by decomposing the vortex wave into a series of plane waves based on the spectral-domain method. Specifically, the OMD phenomenon induced by off-axis transmission is analyzed in detail, which clearly demonstrates that the vortex wave with a single OAM mode is spread to multiple OAM modes after off-axis propagation. To avoid the performance degradation of the OAM system due to OMD (e.g., interchannel crosstalk and signal-to-noise ratio reduction), a method for alleviating the OMD based on the reflective metasurface is proposed to transmit or receive the vortex waves with multiple OAM modes. Theoretical formulas for the phase distribution are developed in order to construct the metasurface. As proof-of-concept demonstrations, two metasurface prototypes are designed, fabricated, and measured to verify the proposed method in the radio-frequency range. The experimental results agree very well with the full-wave simulation results, validating the design methodology.

Spacing dependent interaction of vortex dipole and induced off-axis propagations of optical energy

Discussed analytically is the dynamics of a vortex dipole embedded in an elliptic Gaussian beam. Two opposite charged vortices of the vortex dipole can repel or attract each other, depending on whether their initial spacing larger or smaller than the critical value. While, stable vortex dipole with invariant spacing is predicated to exist at critical initial spacing. The critical spacing is dramatically related with the host elliptic beam. Furthermore, the dynamics of the vortex dipole can result in an off-axis propagation of optical beams, with propagating directions normal to the orientations of the vortex dipole. The optical beam exhibits larger off-axis velocity when the vortex dipole is parallel to the major axis of the host elliptic beam. The off-axis velocity can be further enhanced by increasing the ellipticity of host beams. The theoretical results can provide a controllable approach to change the propagating directions of optical beams by adjusting the initial spacing of vortex dipoles.

Type-II Dirac point and extreme dispersion in one-dimensional plasmonic-dielectric crystals with off-axis propagation

Dirac cones exhibit linear crossing dispersion, which results in extraordinary topological properties in the energy bands. When the dispersion around the Dirac points is tilted, type-II or type-III Dirac points are present, which lead to intriguing transport phenomena. With the off-axis wave vector, a two-dimensional (2D) momentum space for one-dimensional (1D) crystals can be constructed. In this work, we revealed that the band structure in the extended 2D momentum space of carefully designed 1D plasmonic-dielectric crystals can be tuned to be highly tilted, forming type-II Dirac cones. In particular, an approximately upright dispersion can be achieved, which is referred to as a class-II Dirac point. Gapless interface states occur across the interface between two connected lattices formed by two distinct inversion-symmetry-broken crystals (i.e., type A and type B). The tilt of the band structure has a crucial influence on the formation of interface states and their sensitivity to the period, which results from the extraordinary properties of the surface impedance in the bulk gap. More importantly, class-II Dirac points exhibit peculiar topological properties. The wavelength area is divided into two regions, each of which can only support interface states for one configuration, type-AB or type-BA connections. Our results show that type-II Dirac points, especially those that are class II, have an underlying impact on the surface impedance and determine the existence of interface states.

Theoretical study on 252 terahertz Gaussian beam shaping based on an off-axis transmissive all-dielectric metasurface

An off-axis transmissive all-dielectric square metasurface with a side length of 55 mm is designed and studied in this paper. It can shape the 2.52 terahertz Gaussian beam into a rigorous plane wave (we define the required field-quality of the rigorous plane wave region: peak-to-peak amplitude ripple less than 1 dB and phase ripple less than 10°). The metasurface is composed of silicon cylindrical resonators whose phase modulation can almost span over the entire 2π range and the poly (4-methyl-1-pentene) substrate. The diameters of the resonators are from 11 to 35 μm and the heights of them are all 60 μm. The working range of the obtained plane wave is calculated by the physical optics integral formula when the off-axis angle is 22°. The results show that when the off-axis propagation distance is 1050 mm, the area satisfying the plane wave condition is 17×20 mm2, and the diffraction efficiency (we define the diffraction efficiency: the ratio of the total light field energy on the target plane to the total energy of light field that is just after the metasurface along the propagation of incident light) of the rigorous plane wave region cross-section is 23.4%. In addition, a random silicon cylinder diameter fabrication error within ± 4.5 μm is taken into account for the actual fabrication condition. The error satisfies the normal distribution with a mean of 0 μm and a standard deviation of 3 μm. The influence of the fabrication error on the shaping result is studied. We anticipate that the whole study will have certain pragmatic applications in some fields, such as enlarging the capture area of terahertz optical tweezers.

Numerical simulation of capillary helium and helium−oxygen atmospheric pressure plasma jets: propagation dynamics and interaction with dielectric

Atmospheric pressure plasma jets (APPJs) can be generated in capillary tubes flowing with pure helium and with admixtures of oxygen into the pure helium. The jet exiting the tube can be used for a variety of applications through surface interaction. In this study, a two-dimensional axi-symmetric model has been developed to provide insight into the evolution of capillary helium plasma jets with and without oxygen admixtures and their interaction with a dielectric surface placed normal to the jet axis. The model considers the gas mixing of helium and ambient air and the analytical chemistry between helium, nitrogen and oxygen species. Experiments were performed in conditions similar to those of the simulations in order to get qualitative agreement between them. The numerical and experimental results show that the evolution of the helium plasma jet is strongly affected by the introduction of oxygen admixtures. In particular, it was observed that the addition of oxygen admixtures in the helium gas promotes plasma bullet propagation on the axis of symmetry of the tube (in contrast to off-axis propagation for the pure helium plasma jet). On the other hand, the presence of the dielectric surface (a slab placed in front of the tube exit) forces the plasma bullet to spread radially. Furthermore, the plasma bullet speed decreases when the helium plasma jet is operated in the presence of oxygen admixtures. The numerical results also showed that He/O2 plasma jets induced much higher electric fields on the dielectric surface in comparison to the pure helium plasma jet.

Investigating the non-radially polarized component of terahertz wave emission during single-colour femtosecond laser filamentation in air

Recently, simultaneous emission of radially and non-radially polarized terahertz (THz) pulses during single-colour femtosecond laser filamentation has been reported. In this work, the latter radiation has been specifically investigated, instead of the well-studied THz radial polarization. Briefly, cut-back measurements have verified that the ellipticity of the generated THz pulse with non-radial polarization decreased (became more linearly polarized) with the increasing filament length. The underlying mechanism responsible for this phenomenon is the existence of a propagation effect of THz wave along the filament plasma channel. In this case, the resulted off-axis propagation of THz wave inside the plasma column played a dominant role on the generated non-radial THz polarization, rather than the expected on-axis THz birefringence induced by the high laser intensity. This discovery will greatly renew the understanding of THz emission from plasma sources.

Enhancement in electro-optic properties of dynamic scattering systems through addition of dichroic dyes

Electro-optic properties of dynamic scattering in homeotropically aligned pure and dichroic dye doped nematic liquid crystal samples are examined. The optical properties of the two systems are quantified using transmission properties of scattered and unscattered as a function of amplitude and frequency of an applied voltage. Auto-correlation of the scattered signal at different applied voltages is used to compare the decay times in the two systems. Lastly, histogram of the scattered signal reveals a wavevector dependent large light scattering event. The dye doped system shows a significant enhancement of light blocking property in both normal and off-axis light propagation. The characteristics of the system are compared to other scattering technologies. The results suggest that dye doped system can overcome shortcomings in scattering based devices used for near eye applications.

Driver-witness electron beam acceleration in dielectric mm-scale capillaries

We investigated a corrugated mm-scale capillary as a compact accelerating structure in the driver-witness acceleration scheme, and suggested a methodology to measure the acceleration of the witness bunch. The accelerating fields produced by the driver bunch and the energy spread of the witness bunch in a corrugated capillary and in a capillary with a constant inner radius were measured and simulated for both on-axis and off-axis beam propagation. Our simulations predicted a change in the accelerating field structure for the corrugated capillary. Also, an approximately twofold increase of the witness bunch energy gain on the first accelerating cycle was expected for both capillaries for the off-axis beam propagation. These results were confirmed in the experiment, and the maximum measured acceleration of $170\text{ }\text{ }\mathrm{keV}/\mathrm{m}$ at 20 pC driver beam charge was achieved for off-axis beam propagation. The driver bunch showed an increase in energy spread of up to 11%, depending on the capillary geometry and beam propagation, with a suppression of the longitudinal energy spread in the witness bunch of up to 15%.

A damage-based model for mixed-mode crack propagation in composite laminates

A model for the off-axis crack propagation in laminated fibre reinforced polymer composites subjected to multiaxial fatigue loadings is presented. On the basis of several observations reported in the literature, the crack propagation phenomenon can be seen as the result of a series of micro-scale events occurring ahead of the crack tip within a process zone. The mixed mode loading condition defines the type of the micro-scale events which occur in the process zone and lead to fatigue crack propagation. Based on this evidence and by using a multiscale approach to determine the micro-scale stress fields in the matrix, two simple parameters are defined for predicting the crack growth rate through a Paris-like law. By extracting the proposed parameters from experimental data obtained from the literature, it is demonstrated that the crack propagation data are all included into two Paris-like scatter bands covering the whole mode-mixity range.

Fatigue damage and stiffness evolution in composite laminates: a damage-based framework

A damage-based design procedure has been developed by the authors to predict the damage evolution and the stiffness degradation in polymeric composite laminates under fatigue loading. For a safe and reliable design against fatigue degradation and failure, the initiation of the main damage mechanisms (off-axis cracks, delamination and fiber failure) as well as their evolution are considered and suitable models are proposed for the quantitative assessment of the lifetime associated to each mechanism. In parallel, the stiffness degradation deriving from the damage evolution over the fatigue life is properly described. After the illustration of the overall damage-based strategy, the paper discusses in details the analysis and modelling of the off-axis crack initiation and propagation. The initiation of cracks in the off axis plies has been proved to be the consequence of a damage process occurring at the microscopic scale since the early stages of fatigue. On this basis, crack initiation prediction is based on the use of local stress parameters: Local Hydrostatic Stress, LHS, and Local Maximum Principal Stress, LMPS, depending on the local degree of multiaxiality of the stress state and accounting for the statistical distribution of the local laminate strength. The propagation phase is then quantified by using a conventional fracture mechanics approach. The model has been implemented in a Matlab procedure for the quantitative evaluation of the crack density in each ply of a laminate during its entire fatigue life. The knowledge of the crack density trend allows the description of the laminate stiffness evolution taking advantage of another model recently developed by the authors, valid for a generic laminate configuration and accounting for the interaction between cracks in the neighbouring plies.

A stochastic multiaxial fatigue model for off-axis cracking in FRP laminates

A model to predict off-axis crack evolution in multidirectional laminates subjected to multiaxial loading is proposed. The model applies multi-scale stress and local fracture mechanics analyses to distinguish between two microscopic damage mechanisms, which govern the damage evolution, as well as determining the magnitude of the damage evolution rate associated with each microscopic damage mechanism. The multi-scale analysis is based on the GLOB-LOC off-axis crack damage model, which is extended to include substantial new capabilities such as the influence of crack face sliding interaction and prediction of variations in the stress field due to the local crack density. The extension of the GLOB-LOC model introduces physically based multiaxial fatigue criteria for off-axis crack initiation and mixed-mode off-axis crack propagation. The extended GLOB-LOC model is implemented and it is demonstrated that good predictions are obtained for the damage evolution under various multiaxial stress conditions. Furthermore it is shown that the model only requires input from two different multiaxial stress states to obtain the material parameters for a given FRP ply.

Annealing effect on threading dislocations in a GaN grown on Si substrate

Effect of rapid thermal annealing (RTA) on crystal defects in a GaN layer grown on a (111)Si substrate was investigated by photoluminescence (PL) and transmission electron microscopy (TEM) analyses. The PL spectra suggested that the density of gallium vacancy is not changed by the heat treatment up to 700°C. In the TEM specimen, we had dislocation half loops generated by off-axis propagation of the threading dislocation. We found that the half-loop of c-type dislocation shrinks/moves by a repetitive RTA at 600–700°C. In contrast, we could find no remarkable changes in the a-type or a+c-type dislocations.

Quantum polarization fluctuations of partially coherent dark hollow beams in non-Kolmogorov turbulence atmosphere**Project supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 61405205).

Non-classical polarization properties of dark hollow beams propagating through non-Kolmogorov turbulence are studied. The analytic equation for the polarization degree of the quantization partially coherent dark hollow beams is obtained. It is found that the polarization fluctuations of the quantization partially coherent dark hollow beams are dependent on the turbulence factors and beam parameters with the detection photon numbers. Furthermore, an investigation of the changes in the on-axis propagation point and off-axis propagation point shows that the polarization degree of the quantization partially coherent dark hollow beams presents oscillation for a short propagation distance and gradually returns to zero for a sufficiently long distance.

Design of off-axis mirrors for the phase-induced amplitude apodization complex mask coronagraph

The phase-induced amplitude apodization complex mask coronagraph (PIAACMC) provides an efficient way to control diffraction propagation effects caused by the central obstruction/segmented mirrors of the telescope. PIAACMC can be optimized in a way that takes into account both chromatic diffraction effects caused by the telescope obstructed aperture and the tip-tilt sensitivity of the coronagraph. As a result, unlike classic phase-induced amplitude apodization (PIAA), the PIAACMC mirror shapes are often slightly asymmetric even for an on-axis configuration and require more care in calculating off-axis shapes when an off-axis configuration is preferred. A method to design off-axis PIAA mirror shapes given an on-axis mirror design is presented. The algorithm is based on geometrical ray tracing and is able to calculate off-axis PIAA mirror shapes for an arbitrary geometry of the input and output beams. The method is demonstrated using the third generation PIAACMC design for WFIRST-AFTA telescope. Geometrical optics design issues related to the off-axis diffraction propagation effects are also discussed.

Light propagation analysis using a translated plane angular spectrum method with the oblique plane wave incidence.

A novel angular spectrum method was proposed to numerically analyze off-axis free-space light propagation on a translated plane to an arbitrary angle. Utilizing a shifted angular spectrum method based on an oblique incident plane wave assumption, a generalized light propagation formulation was obtained in a wide range of both tilt angles and sampling intervals, which overcame the limitations of prior attempts. A detailed comparison of the proposed angular spectrum method with prior methods is numerically presented for diffractive optics and computer-generated holograms. The validity of the proposed method was confirmed experimentally by reconstructing a digital holographic image using a spatial light modulator.

Modified shifted angular spectrum method for numerical propagation at reduced spatial sampling rates.

The shifted angular spectrum method allows a reduction of the number of samples required for numerical off-axis propagation of scalar wave fields. In this work, a modification of the shifted angular spectrum method is presented. It allows a further reduction of the spatial sampling rate for certain wave fields. We calculate the benefit of this method for spherical waves. Additionally, a working implementation is presented showing the example of a spherical wave propagating through a circular aperture.

Off-axis phonon and photon propagation in porous silicon superlattices studied by Brillouin spectroscopy and optical reflectance

Brillouin light scattering experiments and optical reflectance measurements were performed on a pair of porous silicon-based optical Bragg mirrors which had constituent layer porosity ratios close to unity. For off-axis propagation, the phononic and photonic band structures of the samples were modeled as a series of intersecting linear dispersion curves. Zone-folding was observed for the longitudinal bulk acoustic phonon and the frequency of the probed zone-folded longitudinal phonon was shown to be dependent on the propagation direction as well as the folding order of the mode branch. There was no conclusive evidence of coupling between the transverse and the folded longitudinal modes. Two additional observed Brillouin peaks were attributed to the Rayleigh surface mode and a possible pseudo-surface mode. Both of these modes were dispersive, with the velocity increasing as the wavevector decreased.