Vector Plane Wave Spectrum Research Articles

Propagation of arbitrarily polarized terahertz Bessel vortex beam in inhomogeneous unmagnetized plasma slab

On the basis of vector plane wave spectrum expansion, the reflection and transmission characteristics of an arbitrarily polarized terahertz Bessel vortex beam by an inhomogeneous unmagnetized plasma slab are investigated. Magnitude profiles of electric field components in the transverse plane, which is perpendicular to the central axes of the reflected and transmitted beams, as well as the weight distributions of orbital angular momentum (OAM) states, are displayed for both homogeneous and inhomogeneous unmagnetized plasma slabs. The results indicate that the magnitude profiles of electric field components for both the reflected and transmitted beams have a serious distortion which is more distinct for the inhomogeneous plasma slab, resulting in diverse patterns which are different from those of the incident beam. Compared with the incident beam, many adjacent OAM states are derived in both the reflected and transmitted beams. For the incidences of both the x- and circular-polarizations, the weight of the predominant OAM state in the reflected beam for the homogeneous plasma slab is greater than that for the inhomogeneous plasma slab but contrary to this conclusion for the transmitted beam. The deformation of OAM states cannot be reflected by the patterns of the field distribution directly. Polarization has few effects on the weight of OAM states of the transmitted beams to the same plasma slab. The weight of the predominant OAM state in the transmitted beam rises with an increase in the incident angle, which is contrary to the conclusion in the reflected beam.

Analysis of the influence of diattenuation on optical imaging system by using the theory of vector plane wave spectrum

In most of the researches of polarization aberration, the influence of diattenuation is not large enough to affect imaging quality evidently. However, the modulation transfer function decreases when optical elements with complex planar dielectric structures and low transmittance, such as beam-splitter and optical modulator, are introduced into an imaging system. In this paper, a vector optical model in Descartes coordinate system is proposed based on the concept of vector plane wave spectrum (VPWS). The results of calculation show that the VPWS model is consistent with Debye model. Compared with Debye vector diffraction integral, the VPWS method is more suitable to the description of the PA introduced by planar optical device with opaque mask, such as larger surface quantum-confined-stark-effect electro-absorption modulator, which is used to modulate the light collected by optical antenna of time-of-flight (TOF) depth system or modulating-retroreflector free-space-optical communication system. In order to simplify the calculation and obtain the conclusion of the change in imaging quality directly, the formula of optical transfer function is decomposed into three parts (TE component, TM component and the correlation of them) instead of polynomial expansion of pupil function. The influences of diattenuation on MTF is studied globally and locally in a range of cut-off frequency of optical imaging system (2NA/ ). Allowance of diattenuation is analysed by numerical calculation, and a mathematical expression is derived. The result shows that the change of diattenuation can be neglected when the spatial frequency v is less than 0.2NA/, and the range of allowance decreases with the increase of spatial frequency. According to numerical calculation shown in Fig.7 and the derived formulas (15) and (16), the ratios of reflection/transmission coefficient of s-light and p-light D should range respectively from 0.63 to 1.6(0.2NA/ v 0.8NA/) and from 0.9 to 1.11(v0.8NA/ ) when the MTF is required to be not less than 90% of the value in ideal diffraction-limited system. The range of allowance becomes larger gradually with the increase of angle n between the normal of optical interface n and the optical axis of imaging system z. If a polarization beam splitter is considered, D,n sin-1 NA should be greater than 1-3.

Almost pure TM or TE component far field in vector cosine-Gaussian beams

The vectorial structure of cosine-Gaussian beams (cGBs) is investigated in the far field regime based on the vector plane wave spectrum and the method of stationary phase. The energy flux densities of TE or TM term and the ratio of the energy flux of TE or TM term in the whole beam are demonstrated. It is found that the spot configurations of the energy flux densities associated with the TE and TM terms depend on the polarization angle and the beam parameter of the incident cGB. And the far field may be entirely transverse magnetic or transverse electric under appropriate polarization angle and beam parameter.

Scattering from cylinders using the two-dimensional vector plane wave spectrum: addendum

The solution for the vector plane wave spectrum scattering from multiple cylinders by Pawliuk and Yedlin [J. Opt. Soc. A28, 1177 (2011)] only provided the single scattering coefficients for the TM polarization case. The TE solution is similar except for the form of the single scattering coefficients. Here we describe the single scattering coefficients for both polarizations and three types of cylinders: dielectrics, perfect electric conductors, and perfect magnetic conductors.

Scattering from cylinders using the two-dimensional vector plane wave spectrum

The two-dimensional vector plane wave spectrum (VPWS) is scattered from parallel circular cylinders using a boundary value solution with the T-matrix formalism. The VPWS allows us to define the incident, two-dimensional electromagnetic field with an arbitrary distribution and polarization, including both radiative and evanescent components. Using the fast Fourier transform, we can quickly compute the multiple scattering of fields that have any particular functional or numerical form. We perform numerical simulations to investigate a grating of cylinders that is capable of converting an evanescent field into a set of propagating beams. The direction of propagation of each beam is directly related to a spatial frequency component of the incident evanescent field.

Vectorial structure of helical hollow Gaussian beams in the far field

The analytical vectorial structure of helical hollow Gaussian beam (HHGB) is investigated in the far field based on the vector plane wave spectrum and the method of stationary phase. The energy flux distributions of HHGB in the far-field, which is composed of TE term with the electric field transverse to the propagation axis, and TM term with the magnetic field transverse to the propagation axis, are demonstrated. The physics pictures of HHGB is illustrated from the vectorial structure, which is important to understand the theoretical aspects of both scalar and vector HHGB propagation.

Analytical vectorial structure of hollow Gaussian beams in the far field

The analytical vectorial structure of HGB is investigated in the far field based on the vector plane wave spectrum and the method of stationary phase. The energy flux distributions of HGB in the far-field, which is composed of TE term and TM term, are demonstrated. The physics pictures of HGB is illustrated from the vectorial structure, which is important to understand the theoretical aspects of both scalar and vector HGB propagation.

Analytical structure of the TE and TM terms of paraxial Gaussian beam in the near field

The description of paraxial Gaussian beam is directly started from the Maxwell’s equations. According to the vector plane wave spectrum representation of Maxwell’s equations and the vectorial structure of electromagnetic beam, the analytical TE and TM terms of paraxial Gaussian beam are presented by means of mathematical techniques in the near field. The influence of linearly polarized angle on the components of the TE and TM terms is investigated. The structural light intensities are depicted in the near field. As the vectorial structures are not orthogonal in the near field, there is a crossed light intensity in the paraxial Gaussian beam. This research reveals the abundant internal structure of paraxial Gaussian beam in the near field.

Resolution of aplanatic systems with various semiapertures, viewed from the two sides of the diffracting aperture

With the vector plane-wave spectrum and stationary phase method, a rigorous vector diffraction model of an aplanatic system when the polarized point source is at an arbitrary location on the optical axis is presented. The computer simulation is used to discuss in detail the effects of various angular semiapertures on the object and image sides on the resolution. Results show that angular semiapertures on the object and image sides have an obvious effect on the resolution and image fields, which indicates that the classical Wolf theory [Proc. R. Soc. London, Ser. A253, 358 (1959)] cannot be applied to the study of imaging properties of an aplanatic system when the point source is not located at infinity in the direction of the axis.

Imaging theory of an aplanatic system with a stratified medium based on the method for a vector coherent transfer function

A simple formalism relating image fields to object fields, similar to that of the scalar and paraxial case, is presented for an aplanatic system obeying the sine condition, which shows that the vector plane-wave spectrum of image fields is equal to the product of the vector coherent transfer function due to the x- and y-polarized point electric field source and the scalar spectrum of the corresponding transverse object fields. Utilizing this formula and dyadic Green's function, a rigorous imaging theory of an aplanatic system for the point electric current source through a stratified medium is readily developed.

Vector plane wave spectrum of an arbitrary polarized electromagnetic wave

By using the method of modal expansions of the independent transverse fields, a formula of vector plane wave spectrum (VPWS) of an arbitrary polarized electromagnetic wave in a homogenous medium is derived. In this formula VPWS is composed of TM- and TE-mode plane wave spectrum, where the amplitude and unit polarized direction of every plane wave are separable, which has more obviously physical meaning and is more convenient to apply in some cases compared to previous formula of VPWS. As an example, the formula of VPWS is applied to the well-known radially and azimuthally polarized beam. In addition, vector Fourier-Bessel transform pairs of an arbitrary polarized electromagnetic wave with circular symmetry are also derived.