Diffraction of Waves by a Dielectric Parabolic Cylinder*

C. Yeh

doi:10.1364/JOSA.57.000195

Journal of the Optical Society of America
Vol. 57,
Issue 2,
pp. 195-201
(1967)
•https://doi.org/10.1364/JOSA.57.000195

Diffraction of Waves by a Dielectric Parabolic Cylinder

C. Yeh

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C. Yeh, "Diffraction of Waves by a Dielectric Parabolic Cylinder*," J. Opt. Soc. Am. 57, 195-201 (1967)

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Abstract

The exact solution of the diffraction of waves by a dielectric parabolic cylinder is obtained. Results are given in terms of parabolic-cylinder functions. It is found that each expansion coefficient of the scattered or transmitted wave is coupled to all coefficients of the series expansion for the incident wave, even for very thin cylinders. Both polarizations of the incident wave are considered: one with the incident electric vector in the axial direction and the other with the incident magnetic vector in the axial direction. Numerical computations are carried out for the backscattering cross section and the radiation patterns of the scattered wave.

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Equations (41)

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m

n	0	2	4	6	8	10	12
0	1.000	−0.1716	0.1472×10⁻¹	−0.8418×110⁻³	0.3611×10⁻⁴	−0.1239×10⁻⁵	0.3543×10⁻⁷
2	0.1716	1.912	−0.3305	0.2843×10⁻¹	−0.1628×10⁻²	0.6987×10⁻⁴	−0.2399×10⁻⁶
4	0.1472×10⁻¹	0.3305	0.5711	−0.1029	0.8963×10⁻²	−0.5166×10⁻³	0.2226×10⁻⁴
6	0.8418×10⁻³	0.2843×10⁻¹	0.1029	0.6320×10⁻¹	−0.1238×10⁻¹	0.1106×10⁻²	−0.6455×10⁻⁴
8	0.3611×10⁻⁴	0.1628×10⁻²	0.8963×10⁻²	0.1238×10⁻¹	0.3376×10⁻²	−0.7691×10⁻³	0.7152×10⁻⁴
10	0.1239×10⁻⁵	0.6987×10⁻⁴	0.5166×10⁻³	0.1106×10⁻²	0.7691×10⁻³	0.9434×10⁻⁴	−0.2846×10⁻⁴
12	0.3543×10⁻⁷	0.2399×10⁻⁵	0.2226×10⁻⁴	0.6455×10⁻⁴	0.7152×10⁻⁴	0.2846×10⁻⁴	0.1157×10⁻⁵

m

n	1	3	5	7	9	11	13

1	1.970	−0.3381	0.2900×10⁻¹	−0.1659×10⁻²	0.7114×10⁻⁵	−0.2441×10⁻⁵	0.6981×10⁻⁷
3	0.3381	1.217	−0.2138	0.1848×10⁻¹	−0.1061×10⁻²	0.4561×10⁻⁴	−0.1568×10⁻⁵
5	0.2900×10⁻¹	0.2138	0.2104	−0.3296×10⁻¹	0.3459×10⁻²	−0.2005×10⁻³	0.8665×10⁻⁵
7	0.1659×10⁻²	0.1848×10⁻¹	0.3926×10⁻¹	0.1586×10⁻¹	−0.3316×10⁻²	0.3016×10⁻³	−0.1775×10⁻⁴
9	0.7114×10⁻⁴	0.1061×10⁻²	0.3459×10⁻²	0.3316×10⁻²	0.6128×10⁻³	−0.1569×10⁻³	0.1498×10⁻⁴
11	0.2441×10⁻⁵	0.4561×10⁻⁴	0.2005×10⁻³	0.3016×10⁻³	0.1569×10⁻³	0.1200×10⁻⁴	−0.4630×10⁻⁵
13	0.6981×10⁻⁷	0.1568×10⁻⁵	0.8665×10⁻⁵	0.1775×10⁻⁴	0.1498×10⁻⁴	0.4630×10⁻⁵	0.5321×10⁻⁷

Abstract

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Figures (9)

Tables (1)

Equations (41)

Journal of the Optical Society of America