Evaluation of Hankel functions with complex argument and complex order

Paknys, R.

doi:10.1109/8.142635

Cited by 35 publications

(20 citation statements)

References 6 publications

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“…For the deep lit side, it is observed that the Pekeris function P m ,e{í', T) is defined as in (37a), and is well behaved for £' <C 0; but for the coupled Pekeris integral P C *(£',T) the function in (37b) does not work properly in the deep lit region, because the main contributions there come from the saddle point v s = A; i0 6sin/3, which is far from the transition region, where the Watson's representation of Hankel functions [24] fail. On the other hand, Olver's asymptotic formulas [24] are used here for the Hankel functions in the coefficient A c n in (14b). Moreover, the large argument asymptotic approximation for the Hankel functions [19] when used in (20) also fails, and, therefore, Debye's formulas [25] are applied instead.…”

Section: Lit Part Of Transition Regionmentioning

confidence: 99%

A Canonical UTD Solution for Electromagnetic Scattering by an Electrically Large Impedance Circular Cylinder Illuminated by an Obliquely Incident Plane Wave

Aguilar

Pathak

Sierra‐Pérez

2013

IEEE Trans. Antennas Propagat.

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Abstract-A uniform geometrical theory of diffraction (UTD) solution is developed for the canonical problem of the electromagnetic (EM) scattering by an electrically large circular cylinder with a uniform impedance boundary condition (IBC), when it is illuminated by an obliquely incident high frequency plane wave. A solution to this canonical problem is first constructed in terms of an exact formulation involving a radially propagating eigenfunction expansion. The latter is converted into a circumferentially propagating eigenfunction expansion suited for large cylinders, via the Watson transform, which is expressed as an integral that is subsequently evaluated asymptotically, for high frequencies, in a uniform manner. The resulting solution is then expressed in the desired UTD ray form. This solution is uniform in the sense that it has the important property that it remains continuous across the transition region on either side of the surface shadow boundary. Outside the shadow boundary transition region it recovers the purely ray optical incident and reflected ray fields on the deep lit side of the shadow boundary and to the modal surface diffracted ray fields on the deep shadow side. The scattered field is seen to have a cross-polarized component due to the coupling between the TE¡. and TM¡. waves (where z is the cylinder axis) resulting from the IBC. Such cross-polarization vanishes for normal incidence on the cylinder, and also in the deep lit region for oblique incidence where it properly reduces to the geometrical optics (GO) or ray optical solution. This UTD solution is shown to be very accurate by a numerical comparison with an exact reference solution.

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Section: Lit Part Of Transition Regionmentioning

confidence: 99%

A Canonical UTD Solution for Electromagnetic Scattering by an Electrically Large Impedance Circular Cylinder Illuminated by an Obliquely Incident Plane Wave

Aguilar

Pathak

Sierra‐Pérez

2013

IEEE Trans. Antennas Propagat.

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“…The expansion for H (2) λ (λz) can be obtained by changing the sign of i in (A-2). Here, we use the first two terms to obtain more accurate numerical results, which is different from [9] employing only the leading term. In (A-2), the important parameter ξ should be treated carefully and the branch is chosen so that ξ is real when z is positive, i.e.,…”

Section: The Asymptotic Expansion Of the Airy Function Ismentioning

confidence: 99%

“…Kim [7], and Shim and Kim [8] used the Watson transformation to analyze the scattering of a coated sphere. Paknys [9], and Paknys and Jackson [10] studied a variety of asymptotic expansions of Hankel functions and used the Watson transformation to explain the behaviors of complex waves. Li and Chew [11] gave a new residue series solution of Watson transformation.…”

Section: Introductionmentioning

confidence: 99%

High Frequency Scattering by an Impenetrable Sphere

Sha

Chew²

2009

PIER

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Abstract-The high frequency scattering of a scalar plane wave from an impenetrable sphere with a diameter of several thousand wavelengths is treated by the Sommerfeld-Watson transformation, the saddle-point technique (SPT), and the numerical steepest descent method (NSDM). Both the near and far fields for the sphere are computed within the observation angle range of 0 to 180 degree. First, with the aid of the Watson transformation, the fast-convergent residue series replacing the slow-convergent Mie series is derived. Second, a new algorithm for finding the zeros of the Hankel functions is developed. Third, a novel NSDM, which is adaptive to frequency and is hence frequency independent, is proposed to overcome the breakdown of the traditional SPT in the transition region. Numerical results show that when the observation angle is very small, the Mie series solution of the near-field will not be accurate due to error accumulation. Furthermore, using the proposed methods, the CPU times for both the near-field and far-field calculations are frequency independent with controllable error. This work can be used to benchmark future works for high-frequency scattering.

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“…By applying Olver's uniform representation for Bessel and Hankel functions of complex order [12], the sought poles ] for the two analyzed cases are found by plotting the denominators of (5) as functions of complex variable and searching for their zeros. The calculated loci of poles in complex ]-plane are illustrated in Figure 2, while the exact values of the poles with smallest imaginary part (i.e., the propagation coefficients of the dominant creeping waves) are summarized in Table 1.…”

Section: Application To Human Body Modelmentioning

confidence: 99%

An Insight into Creeping Electromagnetic Waves around the Human Body

Ivšić

Bonefačić

Šipuš

et al. 2017

Wireless Communications and Mobile Computing

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The electromagnetic wave propagation around human body torso is modelled by considering elementary electric and magnetic dipoles over an infinite muscle-equivalent cylinder. The poles in the spectral domain Green's function with smallest imaginary part are found to correspond to creeping wave propagation coefficients which predict the general trend in propagation around human body. In addition, it was found that axial magnetic field component is crucial for communication via creeping waves since it generates modes with smaller field decay compared to axial electric field. The developed model may thus serve as a practical guideline in design of on-body wearable antennas. The theoretical considerations are verified with simulations and measurements on the prototype of PIFA antenna placed on the human body.

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Evaluation of Hankel functions with complex argument and complex order

Cited by 35 publications

References 6 publications

A Canonical UTD Solution for Electromagnetic Scattering by an Electrically Large Impedance Circular Cylinder Illuminated by an Obliquely Incident Plane Wave

A Canonical UTD Solution for Electromagnetic Scattering by an Electrically Large Impedance Circular Cylinder Illuminated by an Obliquely Incident Plane Wave

High Frequency Scattering by an Impenetrable Sphere

An Insight into Creeping Electromagnetic Waves around the Human Body

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