Numerical analysis of micro-optics based single photon sources via a combined physical optics and rigorous simulations approach.

The use of 3D printed micro-optical components has enabled the miniaturization of various optical systems, including those based on single photon sources. However, in order to enhance their usability and performance, it is crucial to gain insights into the physical effects influencing these systems via computational approaches. As there is no universal numerical method which can be efficiently applied in all cases, combining different techniques becomes essential to reduce modeling and simulation effort. In this work, we investigate the integration of diverse numerical techniques to simulate and analyze optical systems consisting of single photon sources and 3D printed micro-optical components. By leveraging these tools, we primarily focus in evaluating the impact of different far-field spatial distributions and the underlying physical phenomena on the overall performance of a compound micro-optical system via the direct evaluation of a fiber in-coupling efficiency integral expression.

Introduction to the feature issue on augmented/virtual reality: optics & photonics.

In recent years, augmented/virtual reality (AR/VR) has been attracting attention and investment in both the tech and academic communities, kickstarting a new wave of innovations. In the wake of this momentum, this feature issue was launched to cover the latest advances in this burgeoning field that pertains to optics and photonics. Alongside the 31 research articles being published, this introduction is appended to share with readers the behind-the-issue stories, submission statistics, reading guides, author biographies, and editors' perspectives.

Simultaneous spatio-temporal focusing with pulse front symmetrization.

Simultaneous spatio-temporal focusing of ultrashort pulses is usually performed by single-channel stretcher-compressor geometries where pulse front tilt leads to spatial asymmetry. Here, the basic approach is extended by superimposing two reciprocal sub-beams in a dual-channel stretcher-compressor setup. Spatio-temporal properties of the symmetrized focal zones of few-cycle near-infrared pulses are studied by parametric numerical simulations with physical optics software. Spatial modulations of focal zones depending on focusing conditions appear. Relationships to specific ultrafast interference phenomena are addressed.

Freeform surface for light shaping by iterative design via Fourier domain.

We extend our previous work [Yang et al., Opt. Express29, 3621 (2021)10.1364/OE.415649] and propose an iterative algorithm to design a freeform surface for far-field light shaping. The algorithm alternately performs a wavefront phase design step and a freeform surface construction step. The smooth wavefront phase is designed by the mapping-type Fourier pair synthesis method, and the freeform surface is constructed by using the obtained wavefront phase. The algorithm provides a solid approach that ensures the introduction of the required wavefront phase manipulation for light shaping. Moreover, the related physical effects such as the Fresnel effect and polarization effect are included in the algorithm. We demonstrate the flexibility of the algorithm by examples.

Wavefront phase representation by Zernike and spline models: a comparison.

A comparative analysis of spline and Zernike models is presented for wavefront phase construction. The techniques are analyzed on the basis of representation accuracy, computational costs, and the number of samples used for representation. The strengths and weaknesses of each model over a set of various wavefront phases with different domain shapes are analyzed. The findings show that both models efficiently represent a simple wavefront phase at irregular domain shapes. On the other hand, when complex wavefront phases at irregular domain shapes are represented, the spline model performs much better than the Zernike model. Further, results show that the spline model evaluation speed is significantly faster than the Zernike model.

Antiderivative of gradient data by spline model integration.

Numerous optical techniques describe the local slope of the functions at their discrete positions but do not report the actual functions. However, many applications require the description of the functions, which must be retrieved from the gradients by an integration process. This study shows a spline model function-based integration technique that can construct original functions from irregularly measured gradient data over general shape domains with high accuracy and speed.

Generalized far-field integral.

The propagation of light in homogeneous media is a crucial technology in optical modeling and design as it constitutes a part of the vast majority of optical systems. Any improvements in accuracy and speed are therefore helpful. The far-field integral is one of the most widely used tools to calculate diffraction patterns. As a general rule, this approximate method requires the observation plane located in the far-field region, i.e., a very considerable propagation distance. Only in the well-designed (namely aberration-free) optical system does the far-field integral not suffer from the limitation of the large distance. Otherwise, the far-field integral cannot provide accurate results. In the present work, we generalize the far-field integral to a more general concept with a much more flexible application scope, which allows for the inclusion of aberrations as well. Finally, as an essential part of this generalization, the propagation to arbitrarily oriented planes is also taken into account.

Numerical analysis of tiny-focal-spot generation by focusing linearly, circularly, and radially polarized beams through a micro/nanoparticle.

Obtaining a tiny focal spot is desired for super resolution. We do a vectorial numerical analysis of the linearly, circularly, and radidally polarized electromagnetic fields being focused through a dielectric micro/nanoparticle of size comparable to the wavelength. We find tiny focal spots (up to ∼0.05 λ2) can be obtained behind micro/nanoparticles of various shapes, e.g. spherical, disk-shaped, and cuboid micro/nanoparticles. Furthermore, we also investigate the influence of the misalignment of a real lens system on the tiny focal spots. We find that tiny focal spots can still be generated even though they are distorted due to the misalignment.

Light-shaping design by a fourier pair synthesis: the homeomorphic case.

From a physical-optics point of view, the far-field light-shaping problem mainly requires a Fourier pair synthesis. The Iterative Fourier Transform Algorithm (IFTA) is one of the algorithms capable of realizing this synthesis, however, it may lead to stagnation problems when the fields of the Fourier pair exhibit a homeomorphic behavior. To overcome this problem, we use a mapping-type relation for the Fourier pair synthesis. This approach results in a smooth phase response function in a single step, without requiring an iterative procedure. The algorithm is demonstrated with examples and the results are investigated via physical-optics modeling techniques.

Generalized Debye integral.

The Debye integral is an essential technique in physical optics, commonly used to efficiently tackle the problem of focusing light in lens design. However, this approximate method is only valid for systems that are well designed and with high enough Fresnel numbers. Beyond this assumption, the integral formula fails to provide accurate results. In this work, we generalize the Debye integral to overcome some of its limitations. The theory explicitly includes aberrations and extends the integral to fields on tilted planes in the focal region. We show, using examples, that the new formulas almost reach the accuracy of a rigorous modeling technique while being significantly faster.

Genuine-field modeling of partially coherent X-ray imaging systems.

A genuine representation of the cross-spectral density function as a superposition of mutually uncorrelated, spatially localized modes is applied to model the propagation of spatially partially coherent light beams in X-ray optical systems. Numerical illustrations based on mode propagation with VirtualLab software are presented for imaging systems with ideal and non-ideal grazing-incidence mirrors.

Vectorial physical-optics modeling of Fourier microscopy systems in nanooptics.

Fourier microscopy, which makes direct observation of the angular distribution possible, is widely used in the nanooptics community. The theory of such systems is typically based on ideal lenses. However, the real lenses in the typical complex lens systems have an impact on the image quality in the experiment. Therefore, it is desirable to have a model of the entire system, which is capable of predicting such phenomena, in order to conduct a preliminary detailed analysis of the setup before building it in the lab. In this work, we perform a vectorial physical-optics simulation of Fourier microscopy systems, which considers the real lenses; it also includes the nanostructure (e.g., photonic crystal). The systems are used to image the emission diagram of a single molecule as well as to analyze the angular-spectral property of a photonic crystal. We analyze various effects of the entire systems, e.g., Fresnel effects of the real lens surfaces, diffraction, polarization, chromatic aberration, and the effects of misalignment. We find that the above-mentioned effects have an influence on the final results, which should be taken into account when performing similar real-life experiments.

Light shaping by freeform surface from a physical-optics point of view.

Modeling techniques for light-shaping systems with freeform surface are presented from a physical-optics point of view. We apply the modeling techniques to different light-shaping systems with freeform surfaces designed by "ray mapping method". The simulation results show that the design is not always valid. Diffraction effects occur, especially in paraxial situations. We discuss the accuracy of the design via physical-optics simulation, and find an explanation in the geometric-optics assumption of the design algorithm being sufficient only if the optical system results in homeomorphic behavior for the electric field between the input and target.

k-domain method for the fast calculation of electromagnetic fields propagating in graded-index media.

A conceptually straightforward method for the fast calculation of electromagnetic fields propagating in graded-index media is presented. More specifically, in this method, we convert Maxwell's curl equations into the spatial-frequency domain to obtain an ordinary differential equation (ODE), and subsequently solve the ODE with the 4th-order Runge-Kutta method. Compared to the traditional beam propagation methods, this method deals with vectorial fields accurately, without physical approximations, like the scalar field approximation or the paraxial approximation; numerically, this method takes advantage of the fast Fourier transform and the convolution theorem to achieve an efficient calculation.

Theory and algorithm of the homeomorphic Fourier transform for optical simulations.

The introduction of the fast Fourier transform (FFT) constituted a crucial step towards a faster and more efficient physio-optics modeling and design, since it is a faster version of the Discrete Fourier transform. However, the numerical effort of the operation explodes in the case of field components presenting strong wavefront phases-very typical occurrences in optics- due to the requirement of the FFT that the wrapped phase be well sampled. In this paper, we propose an approximated algorithm to compute the Fourier transform in such a situation. We show that the Fourier transform of fields with strong wavefront phases exhibits a behavior that can be described as a bijective mapping of the amplitude distribution, which is why we name this operation "homeomorphic Fourier transform." We use precisely this characteristic behavior in the mathematical approximation that simplifies the Fourier integral. We present the full theoretical derivation and several numerical applications to demonstrate its advantages in the computing process.

Comparison of aplanatic and real lens focused spots in the framework of the local plane interface approximation.

Tight focusing of various beams is widely used for microscopy, optical tweezers, lithography, optical storage, etc. In literature, the investigation of the tightly focused spot is very often based on an ideal lens, which is aplanatic, by the Debye-Wolf integral. In this work, we formulate the aplanatic lens by interpreting the Gaussian reference sphere as a fictitious surface. In this manner, the formulation of an ideal lens is analogous to the one of a real lens by local plane interface approximation, which is well known. It is straightforward to interpret. And furthermore, we compare the tight focusing of differently polarized beams via ideal and real lenses with circular and annular apertures. We find the focal spot by a well-designed real lens is in good agreement with that of the ideal lens in the case of perfect alignment. But the appearance of misalignment distorts the focal spot. The deformed focal spot is more sensitive in the case of the annular aperture compared with the circular aperture. It is in good agreement with the experimental results in literature. An investigation of the tolerance of misalignment of a specific lens system is also performed.

Isolating the Gouy phase shift in a full physical-optics solution to the propagation problem.

The Gouy phase shift has remained an object of fascination since its discovery by the eponymous scientist at the end of the nineteenth century. The reason behind this uninterrupted interest resides, at least in part, in the fact that the Gouy effect is to be found in the borderland between geometrical optics and diffractive behavior. Using purely mathematical arguments in a full electromagnetic solution to the propagation problem, it is possible to derive a formula where all the physical effects that we know must appear are laid bare, including the Gouy phase. Additionally, by discarding the field information, this formula retrieves the ray-tracing result, and in doing so vindicates the predictions that geometrical optics can make, of the ray mapping and optical path length accretion. The resulting analysis helps overcome the geometrical-physical optics dichotomy in our understanding of the Gouy phenomenon.

Physical-optics propagation through curved surfaces.

Curved surfaces are the basic elements of various optical components and systems such as microscopy systems, diffractive optical elements, freeform components, microlens arrays, etc. In order to model the propagation through curved surfaces fully vectorially and fast, the local plane interface approximation (LPIA) [Appl. Opt.39, 3304 (2000)APOPAI0003-693510.1364/AO.39.003304] is often used. However, the evaluation of the validity and accuracy of this method has, to our knowledge, not yet been fully addressed in the literature. In this work, we compare the field on the curved surface obtained by LPIA with that obtained with the finite element method. We find it is highly accurate even when the size of the curved surface is on the scale of micrometers. We further evaluate the limitation of LPIA in the cases of multi-reflection/transmission and internal resonance.

Application of the semi-analytical Fourier transform to electromagnetic modeling.

The Fast Fourier Transform (FFT) algorithm makes up the backbone of fast physical optics modeling. Its numerical effort, approximately linear on the sample number of the function to be transformed, already constitutes a huge improvement on the original Discrete Fourier Transform. However, even this orders-of-magnitude improvement in the number of operations required can fall short in optics, where the tendency is to work with field components that present strong wavefront phases: this translates, as per the Nyquist-Shannon sampling theorem, into a huge sample number. So much so, in fact, that even with the reduced effort of the FFT, the operation becomes impracticable. Finding a workaround that allows us to evade, at least in part, these stringent sampling requirements is then fundamental for the practical feasibility of the Fourier transform in optics. In this work we propose, precisely, a way to tackle the Fourier transform that eschews the sampling of second-order polynomial phase terms, handling them analytically instead: it is for this reason that we refer to this method as the "semi-analytical Fourier transform". We present here the theory behind this concept and show the algorithm in action at several examples which serve to illustrate the vast potential of this approach.

Non-paraxial idealized polarizer model.

An idealized polarizer model that works without the structural and material information is derived in the spatial frequency domain. The non-paraxial property is fully included and the result takes a simple analytical form, which provides a straight-forward explanation for the crosstalk between field components in non-paraxial cases. The polarizer model, in a 2 × 2-matrix form, can be conveniently used in cooperation with other computational optics methods. Two examples in correspondence with related works are presented to verify our polarizer model.