Scattering and Absorption of Electromagnetic Radiation by Infinite Cylinders

Bert K. Larkin; Stuart W. Churchill

doi:10.1364/JOSA.49.000188

Journal of the Optical Society of America
Vol. 49,
Issue 2,
pp. 188-190
(1959)
•https://doi.org/10.1364/JOSA.49.000188

Scattering and Absorption of Electromagnetic Radiation by Infinite Cylinders

Bert K. Larkin and Stuart W. Churchill

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Bert K. Larkin and Stuart W. Churchill, "Scattering and Absorption of Electromagnetic Radiation by Infinite Cylinders," J. Opt. Soc. Am. 49, 188-190 (1959)

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Abstract

Expressions suitable for machine computation are presented for the scattering and absorbing properties of infinitely long, dielectric, and conducting cylinders. These properties include the amplitude functions, the angular distribution of scattered light, and the scattering and absorbing cross sections for both parallel and perpendicular polarized light. Illustrative calculations were carried out for real indices of refraction of 1.5, 2.0, and 2.5 at circumference to wavelength ratios of 0.5, 1.0, 1.5, 2.0, 3.0, and 4.0.

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m	α	n	Re(B_n)	Im(B_n)	Re(A_n)	Im(A_n)
1.5	0.5	0	−0.0687	0.2530	−0.0000	0.0078
		1	−0.0000	0.0078	−0.0055	0.0741
	1.0	0	−0.4344	0.4957	−0.0185	0.1347
		1	−0.0185	0.1347	−0.0595	0.2366
		2	−0.0000	0.0050	−0.0012	0.0346
		3	−0.0000	0.0001	−0.0000	0.0014
	1.5	0	−0.5361	0.4987	−0.3964	0.4891
		1	−0.3964	0.4891	−0.1572	0.3640
		2	−0.0034	0.0580	−0.0242	0.1536
		3	−0.0000	0.0024	−0.0002	0.0147
	2.0	0	−0.5645	0.4958	−0.8400	0.3666
		1	−0.8400	0.3666	−0.3531	0.4779
		2	−0.1292	0.3354	−0.1464	0.3535
		3	−0.0007	0.0238	−0.0053	0.0728
		4	−0.0000	0.0011	−0.0000	0.0061
	3.0	0	−0.9825	−0.1311	−0.9126	0.2824
		1	−0.9126	0.2824	−0.9993	−0.0258
		2	−0.9961	0.0622	−0.7753	0.4174
		3	−0.4887	0.4999	−0.2946	0.4559
		4	−0.0035	0.0593	−0.0136	0.1159
		5	−0.0000	0.0039	−0.0002	0.0131
		6	−0.0000	0.0002	−0.0000	0.0010
	4.0	0	−0.9165	−0.2773	−0.6820	−0.4657
		1	−0.6820	−0.4657	−0.9702	−0.1701
		2	−0.9982	−0.0420	−0.8667	−0.3398
		3	−0.9581	−0.2004	−0.9981	0.0441
		4	−0.9683	0.1751	−0.5480	0.4977
		5	−0.0151	0.1219	−0.0295	0.1691
		6	−0.0001	0.0094	−0.0005	0.0223
		7	−0.0000	0.0006	−0.0000	0.0022
2.0	0.5	0	−0.4318	0.4953	−0.0004	0.0205
		1	−0.0004	0.0205	−0.0141	0.1181
	1.0	0	−0.8892	0.3138	−0.2709	0.4444
		1	−0.2709	0.4444	−0.1521	0.3591
		2	−0.0000	0.0139	−0.0032	0.0569
	1.5	0	−0.9128	0.2821	−0.9677	−0.1769
		1	−0.9677	−0.1769	−0.5186	0.4996
		2	−0.0650	0.2465	−0.0775	0.2674
		3	−0.0000	0.0072	−0.0006	0.0243
	2.0	0	−0.7671	−0.4227	−0.9331	−0.2499
		1	−0.9331	−0.2499	−0.7966	−0.4025
		2	−0.8193	−0.3848	−0.5681	0.4953
		3	−0.0107	0.1030	−0.0181	0.1333
		4	−0.0000	0.0034	−0.0001	0.0101
2.0	3.0	0	−0.1150	−0.3191	−0.0218	0.1462
		1	−0.0218	0.1462	−0.3018	−0.4590
		2	−0.5535	−0.4971	−0.1173	−0.3217
		3	−0.3510	−0.4773	−0.7604	−0.4268
		4	−0.9530	0.2115	−0.0809	0.2727
		5	−0.0003	0.0165	−0.0006	0.0237
	4.0	0	−0.8404	0.3661	−0.2010	0.4007
		1	−0.2010	0.4007	−0.6982	0.4590
		2	−0.5551	0.4969	−0.0951	0.2934
		3	−0.0071	0.0840	−0.0118	0.1081
		4	−0.1658	−0.3719	−0.0372	−0.1892
		5	−0.0875	−0.2826	−0.9745	0.1576
		6	−0.0082	0.0904	−0.0023	0.0484
		7	−0.0000	0.0027	−0.0000	0.0040
2.5	0.5	0	−0.8809	0.3239	−0.0017	0.0409
		1	−0.0017	0.0409	−0.0213	0.1444
		2	−0.0000	0.0035	−0.0000	0.0044
	1.0	0	−0.9946	0.0735	−0.9865	−0.1152
		1	−0.9865	−0.1152	−0.2504	0.4332
		2	−0.0010	0.0314	−0.0051	0.0714
	1.5	0	−0.7988	−0.4009	−0.6742	−0.4687
		1	−0.6742	−0.4687	−0.8151	−0.3882
		2	−0.8350	−0.3711	−0.1619	0.3683
		3	−0.0003	0.0180	−0.0010	0.0309
	2.0	0	−0.0332	0.1791	−0.4200	−0.4935
		1	−0.4200	−0.4935	−0.0579	−0.2335
		2	−0.2767	−0.4474	−0.4798	−0.4996
		3	−0.5943	−0.4910	−0.0436	0.2041
	3.0	0	−0.9499	−0.2182	−0.7138	0.4520
		1	−0.7138	0.4520	−0.9976	−0.0484
		2	−0.9929	0.0841	−0.1876	0.3904
		3	−0.0368	−0.1882	−0.0544	0.2269
		4	−0.0229	−0.1496	−0.0424	−0.2016
		5	−0.0537	−0.2255	−0.0015	0.0387
		6	−0.0000	0.0022	−0.0000	0.0022
	4.0	0	−0.2767	−0.4474	−0.0533	−0.2246
		1	−0.0533	−0.2246	−0.3072	−0.4613
		2	−0.3441	−0.4751	−0.4100	−0.4918
		3	−0.7944	−0.4041	−0.5070	−0.4999
		4	−0.5970	−0.4905	−0.6163	0.4863
		5	−0.0004	−0.0208	−0.0203	0.1410
		6	−0.0009	−0.0309	−0.0005	−0.0229
		7	−0.0006	−0.0243	−0.0000	0.0071

	m=1.5		m=2.0		m=2.5

α	K_s	B	K_s	B	K_s	B
0.5	0.1596	0.4424	0.9231	0.4320	1.8571	0.3981
1.0	0.6114	0.2235	2.0128	0.0941	4.4669	0.1989
1.5	1.3967	0.0382	3.4262	0.1602	4.2985	0.1121
2.0	2.1768	0.0722	3.9961	0.1056	2.0988	0.1375
3.0	3.6210	0.0520	2.1392	0.3259	2.6237	0.1815
4.0	3.9171	0.0536	1.6822	0.2544	1.9085	0.1427

m	α	n	Re(B_n)	Im(B_n)	Re(A_n)	Im(A_n)
1.5	0.5	0	−0.0687	0.2530	−0.0000	0.0078
		1	−0.0000	0.0078	−0.0055	0.0741
	1.0	0	−0.4344	0.4957	−0.0185	0.1347
		1	−0.0185	0.1347	−0.0595	0.2366
		2	−0.0000	0.0050	−0.0012	0.0346
		3	−0.0000	0.0001	−0.0000	0.0014
	1.5	0	−0.5361	0.4987	−0.3964	0.4891
		1	−0.3964	0.4891	−0.1572	0.3640
		2	−0.0034	0.0580	−0.0242	0.1536
		3	−0.0000	0.0024	−0.0002	0.0147
	2.0	0	−0.5645	0.4958	−0.8400	0.3666
		1	−0.8400	0.3666	−0.3531	0.4779
		2	−0.1292	0.3354	−0.1464	0.3535
		3	−0.0007	0.0238	−0.0053	0.0728
		4	−0.0000	0.0011	−0.0000	0.0061
	3.0	0	−0.9825	−0.1311	−0.9126	0.2824
		1	−0.9126	0.2824	−0.9993	−0.0258
		2	−0.9961	0.0622	−0.7753	0.4174
		3	−0.4887	0.4999	−0.2946	0.4559
		4	−0.0035	0.0593	−0.0136	0.1159
		5	−0.0000	0.0039	−0.0002	0.0131
		6	−0.0000	0.0002	−0.0000	0.0010
	4.0	0	−0.9165	−0.2773	−0.6820	−0.4657
		1	−0.6820	−0.4657	−0.9702	−0.1701
		2	−0.9982	−0.0420	−0.8667	−0.3398
		3	−0.9581	−0.2004	−0.9981	0.0441
		4	−0.9683	0.1751	−0.5480	0.4977
		5	−0.0151	0.1219	−0.0295	0.1691
		6	−0.0001	0.0094	−0.0005	0.0223
		7	−0.0000	0.0006	−0.0000	0.0022
2.0	0.5	0	−0.4318	0.4953	−0.0004	0.0205
		1	−0.0004	0.0205	−0.0141	0.1181
	1.0	0	−0.8892	0.3138	−0.2709	0.4444
		1	−0.2709	0.4444	−0.1521	0.3591
		2	−0.0000	0.0139	−0.0032	0.0569
	1.5	0	−0.9128	0.2821	−0.9677	−0.1769
		1	−0.9677	−0.1769	−0.5186	0.4996
		2	−0.0650	0.2465	−0.0775	0.2674
		3	−0.0000	0.0072	−0.0006	0.0243
	2.0	0	−0.7671	−0.4227	−0.9331	−0.2499
		1	−0.9331	−0.2499	−0.7966	−0.4025
		2	−0.8193	−0.3848	−0.5681	0.4953
		3	−0.0107	0.1030	−0.0181	0.1333
		4	−0.0000	0.0034	−0.0001	0.0101
2.0	3.0	0	−0.1150	−0.3191	−0.0218	0.1462
		1	−0.0218	0.1462	−0.3018	−0.4590
		2	−0.5535	−0.4971	−0.1173	−0.3217
		3	−0.3510	−0.4773	−0.7604	−0.4268
		4	−0.9530	0.2115	−0.0809	0.2727
		5	−0.0003	0.0165	−0.0006	0.0237
	4.0	0	−0.8404	0.3661	−0.2010	0.4007
		1	−0.2010	0.4007	−0.6982	0.4590
		2	−0.5551	0.4969	−0.0951	0.2934
		3	−0.0071	0.0840	−0.0118	0.1081
		4	−0.1658	−0.3719	−0.0372	−0.1892
		5	−0.0875	−0.2826	−0.9745	0.1576
		6	−0.0082	0.0904	−0.0023	0.0484
		7	−0.0000	0.0027	−0.0000	0.0040
2.5	0.5	0	−0.8809	0.3239	−0.0017	0.0409
		1	−0.0017	0.0409	−0.0213	0.1444
		2	−0.0000	0.0035	−0.0000	0.0044
	1.0	0	−0.9946	0.0735	−0.9865	−0.1152
		1	−0.9865	−0.1152	−0.2504	0.4332
		2	−0.0010	0.0314	−0.0051	0.0714
	1.5	0	−0.7988	−0.4009	−0.6742	−0.4687
		1	−0.6742	−0.4687	−0.8151	−0.3882
		2	−0.8350	−0.3711	−0.1619	0.3683
		3	−0.0003	0.0180	−0.0010	0.0309
	2.0	0	−0.0332	0.1791	−0.4200	−0.4935
		1	−0.4200	−0.4935	−0.0579	−0.2335
		2	−0.2767	−0.4474	−0.4798	−0.4996
		3	−0.5943	−0.4910	−0.0436	0.2041
	3.0	0	−0.9499	−0.2182	−0.7138	0.4520
		1	−0.7138	0.4520	−0.9976	−0.0484
		2	−0.9929	0.0841	−0.1876	0.3904
		3	−0.0368	−0.1882	−0.0544	0.2269
		4	−0.0229	−0.1496	−0.0424	−0.2016
		5	−0.0537	−0.2255	−0.0015	0.0387
		6	−0.0000	0.0022	−0.0000	0.0022
	4.0	0	−0.2767	−0.4474	−0.0533	−0.2246
		1	−0.0533	−0.2246	−0.3072	−0.4613
		2	−0.3441	−0.4751	−0.4100	−0.4918
		3	−0.7944	−0.4041	−0.5070	−0.4999
		4	−0.5970	−0.4905	−0.6163	0.4863
		5	−0.0004	−0.0208	−0.0203	0.1410
		6	−0.0009	−0.0309	−0.0005	−0.0229
		7	−0.0006	−0.0243	−0.0000	0.0071

	m=1.5		m=2.0		m=2.5

α	K_s	B	K_s	B	K_s	B
0.5	0.1596	0.4424	0.9231	0.4320	1.8571	0.3981
1.0	0.6114	0.2235	2.0128	0.0941	4.4669	0.1989
1.5	1.3967	0.0382	3.4262	0.1602	4.2985	0.1121
2.0	2.1768	0.0722	3.9961	0.1056	2.0988	0.1375
3.0	3.6210	0.0520	2.1392	0.3259	2.6237	0.1815
4.0	3.9171	0.0536	1.6822	0.2544	1.9085	0.1427

Abstract

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Figures (3)

Tables (2)

Equations (10)

Journal of the Optical Society of America