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Strongly scattering media disrupt both the wavefront distribution and the polarization state of the incident light field. Controlling and effectively utilizing depolarization effects are crucial for optical applications in highly scattering environments, such as imaging through dense fog. However, current simulation models have difficulty simulating the evolution of vector light fields within scattering media, posing challenges for studying vector light fields in strongly scattering environments. Here, we propose the Vector Angular Spectrum (VAS) model for simulating the propagation of vector light fields within scattering media. By introducing the angular spectrum distribution of vector light scattering and polarization conversion mechanisms, this model can simulate the depolarization effects of vector light propagating through strongly scattering media. The VAS model has also been used to investigate the focusing of vector scattered light through scattering media. Furthermore, the simulation results of the model have been validated through experiments. The proposed VAS model is expected to play a role in the theoretical research of vector scattered light and optical applications in strongly scattering environments.

To design semiconductor-based optical devices, the optical properties of the used semiconductor materials must be precisely measured over a large band. Transmission spectroscopy stands out as an inexpensive and widely available method for this measurement but requires model assumptions and reconstruction algorithms to convert the measured transmittance spectra into optical properties of the thin films. Amongst the different reconstruction techniques, inverse synthesis methods generally provide high precision but rely on rigid analytical models of a thin film system. In this paper, we demonstrate a novel flexible inverse synthesis method that uses angular spectrum wave propagation and does not rely on rigid model assumptions. Amongst other evaluated parameters, our algorithm is capable of evaluating the geometrical properties of thin film surfaces, which reduces the variance caused by inverse synthesis optimization routines and significantly improves measurement precision. The proposed method could potentially allow for the characterization of "uncommon" thin film samples that do not fit the current model assumptions, as well as the characterization of samples with higher complexity, e.g., multi-layer systems., Comment: 10 pages, 7 figures, 5 tables

In computational optics, numerical modeling of diffraction between arbitrary planes offers unparalleled flexibility. However, existing methods suffer from the trade-off between computational accuracy and efficiency. To resolve this dilemma, we present a novel approach that rigorously and efficiently models wave propagation between two arbitrary planes. This is achieved by rearranging the angular spectrum of the source field, coupled with linear algebraic computations. Notably, our method achieves comparable computational efficiency to the control method for both scalar and vectorial diffraction modeling, while eliminating nearly all numerical errors. Furthermore, we selectively merge the angular spectrum to further enhance the efficiency at the expense of precision in a controlled manner. Thereafter, the time consumption is reduced to at most 3% of that before merging.

We prepare a quasi-non-diffracting Bessel beam defined within an annular angular spectrum with a spatial light modulator. The beam propagates though a strongly scattering media and the transmitted speckle pattern is measured at one point with a Hadamard Walsh basis that divides the ring into $N$ segments ($N=16,64,256, 1024$). The phase of the transmitted beam is reconstructed with 3 step interferometry and the intensity of the transmitted beam is optimized by projecting the conjugate phase at the SLM. We find that the optimum intensity is attained for the condition that the transverse wave vector $k_\perp$ (of the Bessel beam) matches the spatial azimuthal frequencies of the segmented ring $k_\phi$. Furthermore, compared with beams defined on a 2d grid (i.e. Gaussian) a reasonable enhancement is achieved for all the $k_\perp$ sampled with only 64 elements. Finally, the measurements can be done while the scatterer is moving as long as the total displacement during the measurement is smaller than the speckle correlation distance., Comment: 5 pages, 4 figures, submitted to Optics Letters

Digital holography numerically restores three-dimensional image information using optically captured diffractive waves. The required bandwidth is larger than that of hologram pixel at a closer distance in the Fresnel diffraction regime, which results in the formation of aliased replica patterns in digital hologram. From the analysis of sampling phenomenon, the replica functions are revealed to be the components of higher angular spectra of hologram. Undersampled hologram consists of the moire patterns formed by the modulation of original function by complex exponential function. There is a one-to-one correspondence between the replicas in both real and Fourier spaces. The possibility to acquire high-resolution images over a wide field view is explored in terms of the expansion process of angular spectrum by using replicas. Only a low-NA hologram captured over a wide field restores a high-resolution image when using an optimization algorithm. Numerical simulations and optical experiments are performed to investigate the proposed scheme., Comment: 24 figures

Scaling arguments are used to constrain the angular spectrum of distortions on boundaries of macroscopic causal diamonds, produced by Planck-scale vacuum fluctuations of causally-coherent quantum gravity. The small-angle spectrum of displacement is derived from a form of scale invariance: the variance and fluctuation rate of distortions normal to the surface of a causal diamond of radius $R$ at transverse physical separation $c\tau\ll R$ should depend only on $\tau$, with a normalization set by the Planck time $t_P$, and should not depend on $R$. For measurements on scale $R$, the principle leads to universal scaling for variance on angular scale $\Theta$, $\langle\delta\tau^2\rangle_\Theta\simeq\tau\:\!t_p\sim\Theta R\:\!t_P/c$, and angular power spectrum $C_\ell\sim (R\:\!l_P)/\ell^3$ at $\ell\gg1$. This spectrum is consistent with a relational model of holographic noise based on causally coherent virtual null gravitational shocks, a general picture conjectured for all $\ell$. The high $\ell$ scaling is contrasted with that predicted in some other quantum models, which differ by one power of angular wavenumber $\ell$ and are shown to predict excessive blurring of images from distant sources., Comment: 5 pages, 2 figures. PRD accepted version

Mie theory is a powerful method to model electromagnetic scattering from a multilayered sphere. Usually, the incident beam is expanded to its vector spherical harmonic representation defined by beam shape coefficients, and the multilayer sphere scattering is obtained by the T-matrix method. However, obtaining the beam shape coefficients for arbitrarily shaped incident beams has limitations on source locations and requires different methods when the incident beam is defined inside or outside the computational domain or at the scatterer surface. We propose a 3D angular spectrum method for defining beam shape coefficients from arbitrary source field distributions. This method enables the placement of the sources freely within the computational domain without singularities, allowing flexibility in beam design. We demonstrate incident field synthesis and spherical scattering by comparing morphology-dependent resonances to known values, achieving excellent matching and high accuracy. Additionally, we present mathematical proof to support our proposal. The proposed method has significant benefits for optical systems and inverse beam design. It allows for the analysis of electromagnetic forward/backward propagation between optical elements and spherical targets using a single method. It is also valuable for optical force beam design and analysis.

A controllable energy method, which considers the undersampling issue of the transfer function and valid spectral energy of a source signal, is proposed to implement angular spectrum diffraction calculation in near and far fields. The proposed method provides an optimized frequency boundary $f_{CE}$ within which it always keeps controllable energy to be diffracted. The controllable energy angular spectrum method significantly reduces the number of samples while having the same accuracy as previous angular spectrum methods, implying a higher calculation efficiency. The new perspective of analyzing spectral energy is shown to improve the performance of relevant diffraction calculations.

Optical interference is not only a fundamental phenomenon that has enabled new theories of light to be derived but it has also been used in interferometry for the measurement of small displacements, refractive index changes and surface irregularities. In a two-beam interferometer, variations in the interference fringes are used as a diagnostic for anything that causes the optical path difference (OPD) to change; therefore, for a specified OPD, greater variation in the fringes indicates better measurement sensitivity. Here, we introduce and experimentally validate an interesting optical interference phenomenon that uses photons with a structured frequency-angular spectrum, which are generated from a spontaneous parametric down-conversion process in a nonlinear crystal. This interference phenomenon is manifested as interference fringes that vary much more rapidly with increasing OPD than the corresponding fringes for equal-inclination interference; the phenomenon is parameterised using an equivalent wavelength, which under our experimental conditions is 29.38 nm or about 1/27 of the real wavelength. This phenomenon not only enriches the knowledge with regard to optical interference but also offers promise for applications in interferometry., Comment: 16 pages, 6 figures

In this paper we will analyze the propagation of the angular spectrum of the electromagnetic field through a finite length uniaxial crystal. We solve the boundary conditions of the fields at an interface of an isotropic medium and an uniaxial anisotropic medium with the optical axis in an arbitrary direction and soon after we choose the optical axis in a plane formed by the direction of propagation (z-axis) and the x-axis . We show how the couplings occur between the components of the field and in what situations we can give a vector or scalar treatment for the propagation, Comment: 8 pages, 9 figures

Two main methods have been proposed to derive the acoustical radiation force and torque applied by an arbitrary acoustic field on a particle: The first one relies on the plane wave angular spectrum decomposition of the incident field (see [Sapozhnikov and Bailey, J. Acoust. Soc. Am. 133, 661 (2013)] for the force and [Gong and Baudoin, J. Acoust. Soc. Am. 148, 3131 (2020)] for the torque), while the second one relies on the decomposition of the incident field into a sum of spherical waves, the so-called multipole expansion (see [Silva, J. Acoust. Soc. Am. 130, 3541 (2011)] and [Baresh et al., J. Acoust. Soc. Am. 133, 25 (2013)] for the force, and [Silva et al., EPL 97, 54003 (2012)] and [Gong et al., Phys. Rev. Applied 11, 064022 (2019)] for the torque). In this paper, we formally establish the equivalence between the expressions obtained with these two methods for both the force and torque., Comment: 37 pages

Entangled quantum states play an important role in quantum information science and also in quantum mechanics fundamental investigations. Implementation and characterization of techniques allowing for easy preparation of entangled states are important steps in such fields. Here we generated entangled quantum states encoded in photons transversal paths, obtained by pumping a non-linear crystal with multiple transversal Gaussian beams. Such approach allows us to generate entangled states of two qubits and two qutrits encoded in Gaussian transversal path of twin photons. We make a theoretical analyses of this source, considering the influence of the pump angular spectrum on the generated states, further characterizing those by their purity and entanglement degree. Our experimental results reveals that the generated states presents both high purity and entanglement, and the theoretical analysis elucidates how the pump beams profile can be used to manipulate such photonic states., Comment: 6.5 pages +1 page refs. Comments are welcome!

We develop the formal approach to the angular spectrum transfer in parametric down-conversion that allows pumping with a structured beam. The scheme is based on an entangled photon source pumped by a laser beam structured with a vector-vortex polarization profile. This creates a two-photon quantum state exhibiting polarization-dependent transverse correlations that can be accessed through coincidence measurements on the spatially separated photons. The calculated correlations are shown to present a spin-orbit profile typical of vector beams, however, distributed on separate measurement regions. Our approach allows the design of the pump beam vector spatial structure and measurement strategies for potential applications of these entangled states, such as in quantum communication., Comment: 11 pages, 5 figures

The angular spectrum approach (ASA)---a fast, frequency domain method for calculation of the acoustic field---enables passive source localization and modeling forward propagation in homogeneous media with high computational efficiency. Here we show that, if the medium is continuously stratified, a first-order analytical solution may be obtained for the field at arbitrary depth. Our simulations show that the stratified ASA solution enables accurate source localization as compared to the uncorrected ASA (error from 1.2$\pm$0.3 to 0.49$\pm$0.3 wavelengths) at scalings relevant to biomedical ($kL \sim$ 500, where $L$ is the length of the measurement aperture), underwater ($kL \sim$ 800), and atmospheric ($kL \sim$ 10) acoustic applications. Overall the total computation was on the order milliseconds on standard hardware (225$\pm$84 ms, compared with $78\pm63$ ms for the homogeneous ASA formulation over all cases). Collectively, the results suggest the proposed ASA phase correction enables efficient and accurate method for source localization in continuously stratified environments., Comment: arXiv admin note: text overlap with arXiv:1906.08156

In this work, we derive a set of compact analytical formulas expressing the three-dimensional acoustic radiation torque (ART) exerted on a particle of arbitrary shape embedded in a fluid and insonified by an arbitrary acoustic field. This formulation enables direct computation of the ART from the angular spectrum based beam shape coefficients introduced by Sapozhnikov and Bailey [J. Acoust. Soc. Am. 133, 661 (2013)] and the partial wave coefficients. It is particularly well suited to determine the ART exerted on a particle when the acoustic field is known in a source plane.

Self-healing, as an exotic effect, has showed many potential applications. In this paper, we focus on the self-healing effect of Laguerre-Gaussian beams after an obstacle. By taking advantage of angular spectrum theory, we study self-healing limit of the beam against on-axis obstacle. The dependence of self-healing capability on the radius of obstacle is analyzed. Additionally, we briefly discuss the self-healing limit of the beam in an off-axis scenario. Our results indicate that field amplitude of the beam will be healed well when the obstacle is approximately on-axis without oversized radius, perhaps providing advantages for optical communication, imaging, and remote sensing systems., Comment: 14 pages, 7 figures

Ultrasound, alone or in concert with circulating microbubble contrast agents, has emerged as a promising modality for therapy and imaging of brain diseases. While this has become possible due to advancements in aberration correction methods, a range of applications, including adaptive focusing and tracking of the microbubble dynamics through the human skull, may benefit from even more computationally efficient methods to account for skull aberrations. Here, we derive a general method for the angular spectrum approach (ASA) in a heterogeneous medium, based on a numerical marching scheme to approximate the full implicit solution. We then demonstrate its functionality with simulations for (human) skull-related aberration correction and trans-skull passive acoustic mapping. Our simulations show that the general solution provides accurate trans-skull focusing as compared to the uncorrected case for clinically relevant frequencies, apertures, and targets, with the effects of skull attenuation and amplitude shading included. In the case of source localization, our method leads to an average of 75 % error reduction and 40 to 60 % increase in peak intensity, evaluated over the range of frequencies as compared to the homogeneous medium ASA. Overall, total computation times for both focusing and point source localization of the order milliseconds can be attained with this approach. Collectively our findings indicate that the proposed phase correction method based on the ASA could provide a computationally efficient and accurate method for trans-skull transmit focusing and imaging of point scatterers, potentially opening new possibilities for treatment and diagnosis of brain diseases., Comment: 18 pages, 7 figures

We prepare qudits based on angular multimode biphoton states by modulating the pump angular spectrum. The modes are prepared in the Schmidt basis and their intensity distributions do not overlap in space. This allows one to get rid of filtering losses while addressing single modes and to realize a single-shot qudit readout.