Nonparaxial Propagation Research Articles

Anomalous wavefront control of Lamb wave with metasurfaces via superposed prism resonance

As a special branch of metamaterials characterized by phase discontinuity, elastic metasurfaces have presented extraordinary capacity for elastic wave manipulation. This class of metamaterials has received extensive attention in recent years. In this paper, a subwavelength elastic metasurface with locally resonant prisms is employed to steer the propagation of the A0 Lamb wave. Based on the dispersion curve and transmission ratio, we establish that the resonant feature of prisms is influenced by the diagonal ratio of cross section. By gradually tuning the diagonal ratio of prism cross section, the pattern of resonance modes and the mechanism of resonance superposition are clarified. In this regard, two different resonant modes can be superimposed at a certain frequency. A complete 2 π phase shift that is crucial for redirecting wave propagation can therefore be realized. To have a broader working frequency range, the influence of prism height on the resonance superposed frequency and the effect of plate thickness on the incident flexural wave are explored. Based on the generalized Snell’s law, negative refraction is verified numerically through a metasurface assembled from unit cells with constant phase change. In addition, other wavefront modulations such as eccentric focusing, nonparaxial propagation are also demonstrated. This novel design introduces new degrees of freedom in many engineering applications such as seismic wave protection, structural health monitoring and energy harvesting.

Dual coaxial electric field components in tightly focused circularly polarized Pearcey beams

The optical vortex, with its capacity to carry orbital angular momentum per photon, has garnered significant attention among researchers. Our study showcases the emergence of dual coaxial longitudinal electric field vortices during the non-paraxial propagation of tightly focused circularly polarized Pearcey beams. Our research indicates that combining the self-focusing characteristics of Pearcey beams with the tight focusing effect results in the formation of four focal points. We have achieved controllable adjustment of four distinct focal points. This study also encompasses a detailed numerical analysis of the application in optical trapping, and we investigate and elucidate the trapping strength and corresponding potential energies.

Evaluation of beam convergence driven by spherical gradient refractive index lenses based on nonparaxial beam propagation

Evaluation of beam convergence driven by spherical gradient refractive index lenses based on nonparaxial beam propagation

Exact wave solver for nonparaxial laser beam propagation

Simulations of inertial confinement fusion (ICF) experiments require high-fidelity models for laser beam propagation in a nonuniform plasma with varying index of refraction. We describe a new numerical wave solver that is applicable to centimeter-scale length plasmas encountered in indirect drive ICF applications. The one-way Helmholtz equation (OHE) generalizes the time-harmonic paraxial wave equation to large angles. Here, we present a methodology to numerically evaluate the exact solution to the OHE. This solution is computed by analytically advancing eigenfunctions of the one-way Helmholtz operator along a propagation direction and is applicable to any given index of a refraction profile. We compare our exact method with a commonly used approximate split-step technique for solving the OHE. As a test problem, we consider nonparaxial propagation of Gaussian and speckled beams in a plasma density channel with internal reflection. We find that the split-step approach incurs significant errors compared to the exact solution computed using the novel algorithm.

Correction to: On some novel bright, dark and optical solitons to the cubic-quintic nonlinear non-paraxial pulse propagation model

Correction to: On some novel bright, dark and optical solitons to the cubic-quintic nonlinear non-paraxial pulse propagation model

An efficient nonparaxial and bidirectional wave propagation method for optical fibers & fiber components

We present an efficient method for nonparaxial (i.e., wide angle) and bidirectional wave propagation in optical fibers and fiber components. The method is applicable to all structures such as tapers and fiber gratings which are azimuthally symmetric in respect of the refractive index distribution and the geometry. We use the collocation method to numerically solve the Helmholtz equation as this method allows to take advantage of the symmetry of the structure. This results in reduction of a 3-D propagation problem to a 2-D propagation problem giving a computational advantage by orders of magnitude. The method can also be used to obtain modes with similar computational advantage. The method works for fields of all azimuthal symmetries, i.e., one can treat all LPlm modes. In order to show the applicability of the method we have included examples on obtaining modes (LP and OAM) in step-index and ring core fibers (RCFs), propagation through a tapered RCF and computation of reflection spectra of few-mode fiber Bragg gratings (FM-FBGs).

Behavior of analytical schemes with non-paraxial pulse propagation to the cubic–quintic nonlinear Helmholtz equation

In this paper, the cubic–quintic nonlinear Helmholtz equation which enables a pulse propagates in a planar waveguide with Kerr-like and quintic nonlinearities is studied. By noticing that the system is a non-integrable one, we could to get the diverse of solitary wave solutions by using standard tan(ϕ/2)-expansion technique and the exp(−Ω(η))-Expansion scheme. In particular, four forms of function solution including soliton, bright soliton, singular soliton, periodic wave solutions are investigated. To achieve this, an illustrative example of the Helmholtz equation is provided to demonstrate the feasibility and reliability of the procedure used in this study. The effect of the free parameters on the behavior of acquired figures to some solutions of two nonlinear exact cases was also analyzed due to the nature of nonlinearities. The dynamic properties of the obtained results are shown and analyzed by some density, two and three-dimensional images. We believe that our results will be a way for future research generating optical memories based on the non-paraxial solitons.

Studying near-field propagation of generalized parabolic beams by virtual source method

Generalized parabolic beams have various optical morphologies. They can be used in different research fields, such as component design, aero-optics, and microwave wireless power transmission. Studying the near-field transmission characteristics of these beams is important for improving utilization efficiency. We develop a more accurate theoretical framework to precisely understand the propagation behaviors of complex light fields in the near-field range, especially to break through the limitations of conventional near-axis approximation. This framework fully reveals the propagation mechanism of parabolic beams and their energy transmission modes. Here, based on the principle of independent propagation and the virtual source method, a group of virtual sources are introduced to analyze generalized parabolic beams. These beams can be expanded into the superposition of infinite continuous integer Bessel beams. Then, by combining the Weber integral formula and the Fourier Bessel transform, we rigorously derive an integral expression for generalized parabolic beams during near-field propagation. This expression breaks through the limitation of the traditional paraxial approximation and contains all the key propagation parameters of the family of beams. Based on this integral expression, the intensity distribution and phase characteristics of the generalized parabolic beam along the optical axis are further calculated and analyzed to reveal its energy transfer mode and phase characteristics. By comparing the paraxial approximate solution with the nonparaxial corrected solution for generalized parabolic beams, the far-field propagation of generalized parabolic beams is found to be the same when the propagation distance is sufficiently long. Such simulation results indirectly confirm the correctness of the obtained theoretical solution. The simple paraxial approximation theory can be used conveniently to calculate the far-field propagation of generalized parabolic beams. However, large errors exist when paraxial theory is used to calculate the near-field distribution of generalized parabolic beams. Although calculating nonparaxial propagation is especially complex, the nonparaxial correction solution is necessary when generalized parabolic beams are used in near-field research. Such research results not only deepen the understanding of the propagation mechanism of generalized parabolic beams but also lay a theoretical foundation for studying the precise propagation behaviors of other complex light fields in near-field optics.

Nonparaxial pulse propagation to the cubic–quintic nonlinear Helmholtz equation

In this paper, we study the cubic–quintic nonlinear Helmholtz equation which enables a pulse propagating with Kerr-like and quintic properties further spatial dispersion. By noticing that the system is a nonintegrable one, we could get variety forms of solitary wave solutions by using a generalized [Formula: see text]-expansion method. In particular, we investigate four forms of the function solutions including soliton, bright soliton, singular soliton, periodic wave solutions. To perform this, the demonstrative pattern of the Helmholtz equation is made to show the probability and dependability of the protocol utilized in this research. The effect of the free variables on the behavior of the reached plots to a few achieved solutions for the nonlinear rational exact cases was also explored depending upon the nature of nonlinearities. The dynamical properties of the obtained solutions are analyzed and shown by plotting some density, two and three-dimensional images. We believe that our results would pave a way for future research generating optical memories based on the nonparaxial solitons.

Nonparaxial propagation and the radiation forces of the chirped circular Airy derivative beams.

In this paper, we investigate the nonparaxial propagation dynamics of the chirped circular Airy derivative beams (CCADBs) based on vector angular spectrum method. In the case of nonparaxial propagation, the CCADBs still maintains excellent autofocusing performances. Derivative order and chirp factor are two important physical quantities of the CCADBs to regulate the nonparaxial propagation characteristics, such as focal length, focal depth and K-value. In the nonparaxial propagation model, the radiation force on a Rayleigh microsphere induced the CCADBs are also analyzed and discussed in detail. The results demonstrate that not all derivative order CCADBs can achieve stable microsphere trapping effect. The derivative order and chirp factor of the beam can be used to coarse and fine tune the capture effect of Rayleigh microsphere, respectively. This work will contribute to the more precise and flexible use of circular Airy derivative beams in optical manipulation, biomedical treatment and so on.

Nonparaxial Propagation of Bessel Correlated Vortex Beams in Free Space.

The nonparaxial propagation of partially coherent beams carrying vortices in free space is investigated using the method of decomposition of the incident field into coherent diffraction-free modes. Modified Bessel correlated vortex beams with the wavefront curvature are introduced. Analytical expressions are presented to describe the intensity distribution and the degree of coherence at different distances. The evolution of the intensity distribution during beam propagation for various source parameters is analyzed. The effects of nonparaxiality in the propagation of tightly focused coherent vortex beams are analyzed.

Dipole and quadrupole nonparaxial solitary waves.

The cubic nonlinear Helmholtz equation with third and fourth order dispersion and non-Kerr nonlinearity, such as the self steepening and the self frequency shift, is considered. This model describes nonparaxial ultrashort pulse propagation in an optical medium in the presence of spatial dispersion originating from the failure of slowly varying envelope approximation. We show that this system admits periodic (elliptic) solitary waves with a dipole structure within a period and also a transition from a dipole to quadrupole structure within a period depending on the value of the modulus parameter of a Jacobi elliptic function. The parametric conditions to be satisfied for the existence of these solutions are given. The effect of the nonparaxial parameter on physical quantities, such as amplitude, pulse width, and speed of the solitary waves, is examined. It is found that by adjusting the nonparaxial parameter, the speed of solitary waves can be decelerated. The stability and robustness of the solitary waves are discussed numerically.

Complex source point theory of paraxial and nonparaxial elliptical Gaussian beams.

Using the operator transformation technology, we extend the circular Gaussian beam based virtual (complex) sources method to investigate the paraxial and nonparaxial propagation properties of the elliptical Gaussian beams (EGBs) with planar or cylindrical wavefronts travelling in free space. The paraxial approximation analysis reveals the self-reappearance and self-focusing propagation features for the EGBs with cylindrical wavefront under proper parameter conditions. We further introduce the nonparaxial theory to derive the analytical expressions for the field distribution of an EGB in free space, and confirm that these intriguing propagation features can still be observed with added nonparaxial correction. Comparing with the paraxial approximation results, it is worth noting that there is a clear deviation of the on-axial intensity and phase distributions near the self-focusing position on the basis of nonparaxial correction solution. Our results reveal that the anisotropic diffraction of light propagating through homogeneous medium or free space is possible. The approach in this work can easily be generalized to other beam models with elliptical geometry, which allows us to correctly predict some important information about their near field propagation characteristics for various applications.

Observation of microcavity fine structure

We observe fine structure in the resonance spectra of optical microcavities. We identify the polarization-resolved modes in the spectrum and find that resonance frequencies split in accordance with the theoretical prediction. The observed fine structure is dominantly caused by an optical spin-orbit coupling and non-paraxial propagation and reflection. Both effects are intrinsic, i.e. present in an ideal rotation-symmetric system, and scale inversely proportional to the mirror radius of curvature. For cavities with a small radius of curvature, the influence of fine structure on the resonance spectrum is important and unavoidable and should thus be taken into account.

Detailed analysis for chirped pulses to cubic-quintic nonlinear non-paraxial pulse propagation model

This paper's main focus is on chirped pulses (CP) for a cubic-quintic nonlinear non-paraxial pulse propagation (CQ-NNP-PP) model. Chirped solitons are a relatively new single wave phenomena. The exact CPs generate from the derivative nonlinear Schrödinger equations (NLSE). Chirp is a signal with a changing frequency over time. CPs are used in spread spectrum communications as well as some sonar and radar devices. The propagation of CPs in fibre optics is getting popular due to a wide range of applications in amplification and pulse compression. In an NLSE, the dispersion management (DM) term can influence the velocity of chirp-free nonautonomous soliton but has no effect on its shape. When there is no gain, the classical optical soliton can be expressed with a variable dispersion term and nonlinearity. DM can impact the shape and motion of non autonomous solitons for CPs. We obtain hyperbolic and periodic solutions, as well as a class of solitary wave (SW) solutions such as bright, dark, singular and bell soliton solutions. The governing model will be analyzed with the aid of Jacobian elliptic functions (JEF). We also show accomplished results in 3D and 2D structures.

Ultrafast farfield simulation of non-paraxial computer generated holograms.

The simulation of large-area diffractive optical elements (DOEs) is challenging when non-paraxial propagation and coupling effects between neighboring structures shall be considered. We developed a novel method for the farfield simulation of DOEs, especially computer-generated holograms (CGHs) with lateral feature sizes in the wavelength range. It uses a machine learning approach to predict the optical function based on geometry parameters. Therefore, training data are calculated by physical simulation methods to create a linear regression model. With the trained model a very fast computation of the farfield is possible with high conformity to results of rigorous methods.

Nonparaxial pulse propagation in a planar waveguide with Kerr–like and quintic nonlinearities; computational simulations

This article investigates some novel solitary wave solutions of the cubic-quintic nonlinear Helmholtz equation by implementing two recent analytical (Khater II and generalized exponential methods) techniques. As a result of seeing the nonparaxial effect, this model was developed to show how a pulse propagates in a planar waveguide with Kerr-like and quintic nonlinearities as well as spatial dispersion. When the traditional approximation of a slowly changing envelope fails, this effect takes over. Some novel soliton wave solutions are obtained and formulated in distinct forms such as rational, hyperbolic, and trigonometric forms. The obtained solutions are represented through various figures’ types to show the physical and dynamical behavior of the nonparaxial pulse propagation. The model’s features are demonstrated, such as its intriguing bright, anti-bright, periodic, singular, gray, chirped anti-dark, and dark solitary waves depending upon the nature of nonlinearities. The solutions’ originality is discussed by comparing it with those constructed in recently published articles. All built results are checked their accuracy by putting them back into the original model by employing Mathematica 12.

Depolarization of Vector Light Beams on Propagation in Free Space

Nonparaxial propagation of the vector vortex light beams in free space was investigated theoretically. Propagation-induced polarization changes in vector light beams with different spatial intensity distributions were analyzed. It is shown that the hybrid vector Bessel modes with polarization-OAM (orbital angular momentum) entanglement are the exact solutions of the vector Helmholtz equation. Decomposition of arbitrary vector beams in the initial plane z = 0 into these polarization-invariant beams with phase and polarization singularities was used to analyze the evolution of the polarization of light within the framework of the 2 × 2 coherency matrix formalism. It is shown that the 2D degree of polarization decreases with distance if the incident vector beam is not the modal solution. The close relationship of the degree of polarization with the quantum-mechanical purity parameter is emphasized.

On some novel bright, dark and optical solitons to the cubic-quintic nonlinear non-paraxial pulse propagation model

On some novel bright, dark and optical solitons to the cubic-quintic nonlinear non-paraxial pulse propagation model

Aberrated optical cavities

Optical cavities are an enabling technology of modern quantum science: From their essential role in the operation of lasers to applications as flywheels in atomic clocks and interaction-enhancing components in quantum optics experiments, developing a quantitative understanding of the mode shapes and energies of optical cavities has been crucial for the growth of the field. Nonetheless, the standard treatment using paraxial quadratic optics fails to capture the influence of optical aberrations present in modern cavities with high finesse, small waist, and/or many degenerate modes. In this work, we compute the mode spectrum of optical resonators, allowing for both nonparaxial beam propagation and beyond-quadratic mirrors and lenses. Generalizing prior works, we develop a complete theory of resonator aberrations, including intracavity lenses, nonplanar geometries, and arbitrary mirror forms. Harnessing these tools, we reconcile the near absence of aberration in the work of Schine et al. [N. Schine et al., Nature (London) 534, 671 (2016)] with the strongly evident aberrations in the seemingly similar cavity of Clark et al. [L. W. Clark et al., Nature (London) 582, 41 (2020)]. We further validate our approach by comparison to a family of nonplanar lens cavities realized in the laboratory, finding good quantitative agreement. This work opens prospects for cavities with smaller waists and more degenerate modes.