Nonparaxial Regime Research Articles

Effective dissipation and nonlocality induced by nonparaxiality

We investigate beam diffraction and spatial modulation instability of coherent light beams propagating in the non-paraxial regime in a nonlinear Kerr medium. We study the instability of plane wave solutions in terms of the degree of non-paraxiality, beyond the regime of validity of the nonlinear Schroedinger equation. We also numerically analyze the way non-paraxial terms breaks the integrability and affect the periodical evolution of higher order soliton solutions. We discuss non-locality and effective dissipation introduced by the non-linear coupling with evanescent waves.

Study of polarization transformations and interaction of ordinary and extraordinary beams in nonparaxial regime

We study deals with the transformation of a uniformly polarized Bessel beam in a crystal of Iceland spar in nonparaxial regime. The polarization transformations taking place in the crystal are numerically and experimentally investigated. It is shown that these transformations provide the interaction of ordinary and extraordinary beams, which becomes significant only in the nonparaxial regime.

Nonparaxial accelerating Bessel-like beams

A new class of nonparaxial accelerating optical waves is introduced. These are beams with a Bessel-like profile that are capable of shifting laterally along fairly arbitrary trajectories as the wave propagates in free space. The concept expands on our previous proposal of paraxial accelerating Bessel-like beams to include beams with subwavelength lobes and/or large trajectory angles. Such waves are produced when the phase at the input plane is engineered so that the interfering ray cones are made to focus along the prespecified path. When the angle of these cones is fixed, the beams possess a diffraction-free Bessel profile on planes that stay normal to their trajectory, which can be considered as a generalized definition of diffractionless propagation in the nonparaxial regime. The analytical procedure leading to these results is based on a ray optics interpretation of Rayleigh-Sommerfeld diffraction and is presented in detail. The evolution of the proposed waves is demonstrated through a series of numerical examples and a variety of trajectories.

Reflection of Laguerre–Gaussian beams carrying orbital angular momentum: a full Taylor expanded solution

Partial reflection of linearly polarized Laguerre-Gaussian beams incident at a dielectric interface are studied beyond the paraxial regime. Based on the angular spectrum method and Taylor series expansion, we derive exact analytical expressions for the reflected electric field. This result holds in both the paraxial and nonparaxial regimes. The result is then extended to beams of arbitrary polarization and used to analytically calculate the transverse and longitudinal shifts of the beams' center of gravity. Finally, several numerical examples are performed to verify the analytical formulas we derived near the Brewster angle.

Multipath multicomponent self-accelerating beams through spectrum-engineered position mapping

We introduce the concept of spatial spectral phase gradient, and demonstrate, both theoretically and experimentally, how this concept could be employed for generating single- and multipath self-accelerating beams. In particular, we show that the trajectories of the accelerating beams are determined a priori by different key spatial frequencies through direct spectrum-to-distance mapping. In the nonparaxial regime, our results clearly illustrate the breakup of Airy beams from a different perspective, and demonstrate how circular, elliptic, or hyperbolic accelerating beams can be created by judiciously engineering the spectral phase. Furthermore, we found that the accelerating beams still follow the predicted trajectory also for vectorial wave fronts. Our approach not only generalizes the idea of Fourier-space beam engineering along arbitrary convex trajectories, but also offers possibilities for beam or pulse manipulation not achievable through standard direct real-space approaches or by way of time-domain phase modulation.

Propagation properties of high order axially symmetric polarized beams

The paraxial and non-paraxial propagation properties of high order axially symmetric polarized beams are theoretically studied. The mathematical expressions of the propagation fields for such beams are derived based on vectorial Rayleigh–Sommerfeld formulas. Simulation results are presented for different dimensionless perturbation parameters, which shows the beam propagation intensity distribution and evolution behavior are affected largely by the polarization property of such beams, especially in the non-paraxial regime.

Periodic self-accelerating beams by combined phase and amplitude modulation in the Fourier space

We propose and demonstrate the generation of periodic self-accelerating beams through both phase and amplitude modulation in the Fourier space. For small amplitude variations, an accelerating beam still follows a smooth convex trajectory, which can be traced by acting on the spectral phase only. However, large modulations such as those generated from the Heaviside function with a zero amplitude distribution partially modify the convex trajectory due to the appearance of straight-line paths. Furthermore, periodic self-accelerating beams along convex trajectories are realized by employing an array of "spectral wells" in both the paraxial and nonparaxial regimes.

Nonparaxial traveling solitary waves in layered nonlinear media

A large class of exact analytical traveling solitary wave solutions in a variety of inhomogeneous structures consisting of linear and nonlinear layers is obtained. The solutions are related to a spatial resonance condition and describe reflectionless and radiationless beam propagation for arbitrary angles and spatial widths in the nonparaxial regime.

Electron acceleration in vacuum by ultrashort and tightly focused radially polarized laser pulses

Exact closed-form solutions to Maxwell's equations are used to investigate electron acceleration driven by radially polarized laser beams in the nonparaxial and ultrashort pulse regime. Besides allowing for higher energy gains, such beams could generate synchronized counterpropagating electron bunches.

Negative propagation effect in nonparaxial Airy beams

Negative propagation is an unusual effect concerning the local sign change in the Poynting vector components of an optical beam under free propagation. We report this effect for finite-energy Airy beams in a subwavelength nonparaxial regime. This effect is due to a coupling process between propagating and evanescent plane waves forming the beam in the spectral domain and it is demonstrated for a single TE or TM mode. This is contrary to what happens for vector Bessel beams and vector X-waves, for which a complex superposition of TE and TM modes is mandatory. We also show that evanescent waves cannot contribute to the energy flux density by themselves such that a pure evanescent Airy beam is not physically realizable. The break of the shape-preserving and diffraction-free properties of Airy beams in a nonparaxial regime is exclusively caused by the propagating waves. The negative propagation effect in subwavelength nonparaxial Airy beams opens new capabilities in optical traps and tweezers, optical detection of invisibility cloacks and selective on-chip manipulation of nanoparticles.

Physical interpretation of the paraxial estimator

The paraxial estimator (PE) is a parameter quantifying the paraxiality of a light beam. Even if some of its features were previously tackled, key details on its behavior were not fully presented. This paper robustly presents the physical meaning of the PE in a global way, enlarging its interpretation out of the paraxial region what permits to get a first view of the beam propagation dynamics from the value of this parameter. The physical interpretation is given in the spatial domain and in the spectral domain as well. In the first one, the value of PE is related to the competition between the fast oscillations and the remaining oscillations of a propagating field. Looking at spectral domain, the PE deals with the spectral dispersion (or width) of the plane waves forming the field. In this context, a negative value of PE concerns the effective contribution of the evanescent waves what only happens in a strong nonparaxial regime. The PE also accounts the geometric and physical features on the concept of the paraxial approximation in a natural way. An analysis performed for beams propagating through a spherical thin lens reveals that the loss of paraxiality is due to the geometric effect of ray bending by the lens and by another physical effect, concerning the nonideal collimation of the beam.

Polarization description of light fields in terms of meridional and azimuthal vectorial features

Abstract In terms of the radial, azimuthal and longitudinal components of the field, the polarization features of 3D electromagnetic beams are described by defining three local parameters, namely, the so-called 3D degree of meridional polarization, the ratio between meridional and azimuthal contributions and the degree of cross-correlation between meridional and azimuthal field components. At each point Q, the term “meridional” refers to the projection of the electric field vector onto a plane containing the point Q and the longitudinal axis z . These parameters are valid for both paraxial and non-paraxial regimes. Accordingly, they can be used for describing highly-focused fields. The analytical relation among the well-known 3D electromagnetic degree of polarization and the above parameters is also obtained, and several simple cases are considered.

Vectorial structure and beam quality of vector-vortex Bessel–Gauss beams in the farfield

The far-field analytical expressions for the electromagnetic fields of amplitude of vector-vortex beams having a Bessel–Gauss (BG) distribution propagating in free space are obtained based on the vector angular spectrum and the method of stationary phase. The far-field energy flux distributions and the beam quality by the power in the bucket (PIB) in the paraxial and nonparaxial regimes are investigated. The PIB of the vector-vortex BG beams depend on the ratio of the waist width to wavelength and the polarization order. The analyses show that vector-vortex BG beams with low polarization order have better energy focusability in the farfield.

Nonparaxial Propagation of a Radially Polarized Beam Diffracted by an Annular Aperture

Based on the vectorial Rayleigh diffraction integral, the integral formulae of three electromagnetic field components for radially polarized Laguerre—Gaussian beams after diffraction by an annular aperture and the propagation distance in nonparaxial regimes are presented. The diffraction by a circular aperture or a circular disk or propagation in free space can be treated as the special cases of this general result. The numerical simulation shows that the electric field intensity distributions closely depend on both the inner truncation parameters and the outer truncation parameters of the annular aperture, as well as on the ratio of the waist of the incident Laguerre-Gaussian beam to the wavelength.

Changes in the spectral degree of polarization of nonparaxial stochastic electromagnetic pulsed beams

By using the generalized vectorial Rayleigh-Sommerfeld diffraction integral, the analytical expression for the spectral degree of polarization (SDP) of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams (SSSPCEPB) is derived, and used to study the changes in the SDP of SSSPCEPB in the nonparaxial regime. Similar to that of continuous beams, the f parameter and f αα parameter of pulsed beams also play an important role in determining the nonparaxiality of SSSPCEPB. However, the pulse duration and temporal coherence length of the pulse can change the nonparaxiality of SSSPCEPB. The dependence of SDP on the f parameter, pulse duration and temporal coherence length is emphasized and illustrated numerically.

Off-axis metallic diffractive lens for terahertz beams

A diffractive optical element for off-axis focusing of terahertz radiation is presented. It was designed in a nonparaxial regime and manufactured in a metal slab by laser cutting of curved stripes. The optical function of the structure includes focusing and deflecting the illuminating beam of a chosen frequency in a particular place. Therefore, the element acts as both a spatial and a spectral filter; hence it is especially suitable for separating the terahertz signal from a broadband thermal load in passive detection devices. The experimental evaluation of the proposed diffractive lens by means of time-domain spectroscopy is presented and discussed.

Modeling and analyzing ghost images for incoherent optical systems

In a previous paper [Proc. SPIEPSISDG0277-786X7428, 742807 (2009)10.1117/12.828564], a methodology was developed to model and analyze incoherent ghosts that are formed by two reflections in the paraxial regime. In this paper, we extend the previously developed methodology to model and analyze ghost images that are formed by N (even) reflections. Rather than dealing with ghosts as spots of light, we apply the concept that each ghost has a structure in the nonparaxial regime that depends on the optical system parameters. A methodology to determine the fourth-order ghost aberration function is developed. We present new key parameters for ghost image formation, namely the ghost sagittal and tangential image surfaces. An expression for the paraxial ghost image irradiance distribution of the point object at the nominal image plane is derived. Since focused ghosts are the most bothersome ghosts, tools are proposed to identify potential problematic ghosts. Simulation examples are provided and are used to validate the developed methodology.

Ambiguity function and phase-space tomography for nonparaxial fields

A nonparaxial generalization of the ambiguity function that retains several properties of its paraxial counterpart is presented, in both two and three dimensions. This generalization is used to extend into the nonparaxial regime a scheme for the recovery of the coherence properties of scalar partially coherent fields in two-dimensional space.

Nonparaxial solitary waves in anisotropic dielectrics

We account for the vectorial character of electromagnetic waves in the study of nonlinear self-action and transverse localization in dielectric anisotropic media. With reference to uniaxials, we address spatial solitons propagating in the nonparaxial regime in the presence of an arbitrary degree of nonlocality, going from the standard Kerr response to the highly nonlocal case, unveiling various effects, including transverse profile asymmetry and bending of the trajectory, as well as a weak effective nonlocality even in local media.

Wavelength decorrelation of speckle in propagation through a thick diffuser

We present a careful theoretical analysis for the wavelength decorrelation of speckle intensity that occurs when plane-polarized laser illumination is propagated through an optical system consisting of a thick diffuser in cascade with the space-invariant 4F imaging system and a CCD monitoring configuration. Based on Maxwell's equations for propagation into the right half-space, our formulation for a scalar component of the electric field is accurate well inside of the Fresnel zone and in the nonparaxial regime as well. The diffuser is described as an artificial dielectric consisting of tiny dielectric spheres embedded in a host medium and randomly spaced. We model the thick diffusers using a thin multilayer decomposition, and we write computer software describing the output speckle pattern amplitude which results from the propagation of an input plane wave. This model provides a good description for opal milk glass (OMG), and we illustrate the usefulness of this software by two applications. First, for a series of OMG diffusers of varying thickness, we present curves for the wavelength decorrelation of speckle that are found to be in good agreement with earlier experiments by George et al.[Appl. Phys. 7, 157 (1975)]. Also, these results are used to compute internal parameters of these diffusers. Second, using these values, we present some first-order statistics of the intensity for this diffuser series and show that they are in accord with the published literature.