Magdy F. Iskander, Steven C. Olson, Robert E. Benner, and Dawn Yoshida, "Optical scattering by metallic and carbon aerosols of high aspect ratio," Appl. Opt. 25, 2514-2520 (1986)
The iterative extended boundary condition method (IEBCM) is utilized to calculate scattering and absorption by metallic colloids and carbon aerosols in the 0.4-μm < λ < 10-μm optical wavelength range. The colloids and aerosols were modeled by dielectric spheroids of high aspect ratio. The new IEBCM method is found to be suitable for making calculations for particles with aspect ratios as high as 12. Results are presented for silver and aluminum metallic aerosols as well as for atmospheric aerosols such as soot and iron oxides (magnetite). The various parameters used to examine the convergence of the IEBCM solution, such as the number of subdomain expansions and the size of the incremental change in intermediate object sizes used in the iterative process, are discussed. Using the internal field distribution to test the convergence of the results is also found to be more accurate than the traditional procedure which utilizes extinction and scattering cross-section data.
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Comparison between the Basic Features of the Regular (EBCM) and the New Advantages of the New Iterative Technique
Comparison between EBCM and IEBCM
EBCM
IEBCM
Single spherical expansion
Multiple expansions; spherical and mixed
Analytical continuity implicitly assumed
Continuity explicitly enforced
One-step solution
Iterative and requires initial surface fields
Application
Applications
Limited to small and moderate aspect ratios
Small and moderate aspect
Highly elongated objects
Objects of large ∊* and Ka
Composite homogeneous objects whose surface naturally divides into several parts of different geometric shapes.
Table II
Comparison Between the EBCM and IEBCM Results for Elongated Objectsa
a/b = 4
a/b = 5
a/b = 6
a/b = 7
NRANK = 12
NRANK = 20
NRANK = 12
NRANK = 20
NRANK = 12
NRANK = 20
NRANK = 12
NRANK = 20
EBCM
EBCM
IEBCM
EBCM
EBCM
IEBCM
EBCM
EBCM
IEBCM
EBCM
EBCM
IEBCM
a
0.1487
0.1487
0.1434
0.1359
2.3707
0.1457
0.1304
93.920
0.1359
0.1276
3457.8
0.1492
b
0.1300
0.1300
0.1297
0.1259
0.1283
0.1274
0.1243
0.2063
0.1245
0.1234
2.6620
0.1269
c
0.1187
0.1187
0.1187
0.1196
0.1193
0.1197
0.1203
0.1109
0.1203
0.1234
1.2930
0.1210
d
0.1129
0.1129
0.1129
0.1163
0.1163
0.1163
0.1182
0.1167
0.1183
0.1194
0.3070
0.1194
e
0.1146
0.1146
0.1146
0.1176
0.1176
0.1176
0.1192
0.1185
0.1192
0.1202
0.1861
0.1201
f
0.1224
0.1224
0.1224
0.1224
0.1221
0.1225
0.1224
0.1143
0.1224
0.1224
1.1590
0.1226
g
0.1363
0.1363
0.1361
0.1306
0.1329
0.1324
0.1278
0.2087
0.1278
0.1262
3.0900
0.1306
h
0.1592
0.1592
0.1546
0.1434
2.3715
0.1548
0.1358
93.870
0.1359
0.1317
3414.0
0.1611
The results for spheroidal silver colloids are calculated at λ = 0.621 μm, where ∊′ = −17.4 and ∊″ = 2.25. The semimajor axis of the spheroid a = 100 nm, and results were calculated for a/b up to 7. Large field enhancements are not observed from the silver spheroids because of their large sizes which were chosen to test the IEBCM in the regime λ ~ a.
Table III
Comparison Between the EBCM and IEBCM Results for a Spheroidal Soot Particle of Semimajor Axis a = 100 nm and as High an Aspect Ratio as ga
a/b = 4
a/b = 6
a/b = 8
a/b = 9
NRANK = 12
NRANK = 20
NRANK = 12
NRANK = 20
NRANK = 12
NRANK = 20
NRANK = 12
NRANK = 20
EBCM
EBCM
IEBCM
EBCM
EBCM
IEBCM
EBCM
EBCM
IEBCM
EBCM
EBCM
IEBCM
a
0.4162
0.4162
0.4160
0.4156
134.23
0.4108
0.4165
5839.7
0.6174
0.4197
11414.4
.7650
b
0.4509
0.4509
0.4507
0.4343
0.8468
0.4337
0.4274
6.063
0.4543
0.4254
22.819
.4721
c
0.4780
0.4780
0.4780
0.4489
0.4301
0.4489
0.4365
1.6315
0.4377
0.4328
2.036
.4352
d
0.4963
0.4963
0.4963
0.4589
0.4544
0.4589
0.4429
0.7187
0.4429
0.4381
.4722
.4388
e
0.5124
0.5124
0.5124
0.4674
0.4691
0.4674
0.4482
0.5159
0.4482
0.4424
.2287
.4425
f
0.5146
0.5146
0.5146
0.4677
0.4470
0.4677
0.4481
0.9013
0.4490
0.4423
1.1574
.4441
g
0.5146
0.5146
0.5145
0.4662
0.8361
0.4656
0.4467
15.001
0.4711
0.4411
8.1875
.4832
h
0.5118
0.5118
0.5108
0.4629
132.19
0.4581
0.4450
2840.5
0.6401
0.4427
6735.0
.7791
The results were calculated at λ = 0.4 μm where the complex permittivity of soot is ∊* = 1.88 − j0.69.
Tables (3)
Table I
Comparison between the Basic Features of the Regular (EBCM) and the New Advantages of the New Iterative Technique
Comparison between EBCM and IEBCM
EBCM
IEBCM
Single spherical expansion
Multiple expansions; spherical and mixed
Analytical continuity implicitly assumed
Continuity explicitly enforced
One-step solution
Iterative and requires initial surface fields
Application
Applications
Limited to small and moderate aspect ratios
Small and moderate aspect
Highly elongated objects
Objects of large ∊* and Ka
Composite homogeneous objects whose surface naturally divides into several parts of different geometric shapes.
Table II
Comparison Between the EBCM and IEBCM Results for Elongated Objectsa
a/b = 4
a/b = 5
a/b = 6
a/b = 7
NRANK = 12
NRANK = 20
NRANK = 12
NRANK = 20
NRANK = 12
NRANK = 20
NRANK = 12
NRANK = 20
EBCM
EBCM
IEBCM
EBCM
EBCM
IEBCM
EBCM
EBCM
IEBCM
EBCM
EBCM
IEBCM
a
0.1487
0.1487
0.1434
0.1359
2.3707
0.1457
0.1304
93.920
0.1359
0.1276
3457.8
0.1492
b
0.1300
0.1300
0.1297
0.1259
0.1283
0.1274
0.1243
0.2063
0.1245
0.1234
2.6620
0.1269
c
0.1187
0.1187
0.1187
0.1196
0.1193
0.1197
0.1203
0.1109
0.1203
0.1234
1.2930
0.1210
d
0.1129
0.1129
0.1129
0.1163
0.1163
0.1163
0.1182
0.1167
0.1183
0.1194
0.3070
0.1194
e
0.1146
0.1146
0.1146
0.1176
0.1176
0.1176
0.1192
0.1185
0.1192
0.1202
0.1861
0.1201
f
0.1224
0.1224
0.1224
0.1224
0.1221
0.1225
0.1224
0.1143
0.1224
0.1224
1.1590
0.1226
g
0.1363
0.1363
0.1361
0.1306
0.1329
0.1324
0.1278
0.2087
0.1278
0.1262
3.0900
0.1306
h
0.1592
0.1592
0.1546
0.1434
2.3715
0.1548
0.1358
93.870
0.1359
0.1317
3414.0
0.1611
The results for spheroidal silver colloids are calculated at λ = 0.621 μm, where ∊′ = −17.4 and ∊″ = 2.25. The semimajor axis of the spheroid a = 100 nm, and results were calculated for a/b up to 7. Large field enhancements are not observed from the silver spheroids because of their large sizes which were chosen to test the IEBCM in the regime λ ~ a.
Table III
Comparison Between the EBCM and IEBCM Results for a Spheroidal Soot Particle of Semimajor Axis a = 100 nm and as High an Aspect Ratio as ga
a/b = 4
a/b = 6
a/b = 8
a/b = 9
NRANK = 12
NRANK = 20
NRANK = 12
NRANK = 20
NRANK = 12
NRANK = 20
NRANK = 12
NRANK = 20
EBCM
EBCM
IEBCM
EBCM
EBCM
IEBCM
EBCM
EBCM
IEBCM
EBCM
EBCM
IEBCM
a
0.4162
0.4162
0.4160
0.4156
134.23
0.4108
0.4165
5839.7
0.6174
0.4197
11414.4
.7650
b
0.4509
0.4509
0.4507
0.4343
0.8468
0.4337
0.4274
6.063
0.4543
0.4254
22.819
.4721
c
0.4780
0.4780
0.4780
0.4489
0.4301
0.4489
0.4365
1.6315
0.4377
0.4328
2.036
.4352
d
0.4963
0.4963
0.4963
0.4589
0.4544
0.4589
0.4429
0.7187
0.4429
0.4381
.4722
.4388
e
0.5124
0.5124
0.5124
0.4674
0.4691
0.4674
0.4482
0.5159
0.4482
0.4424
.2287
.4425
f
0.5146
0.5146
0.5146
0.4677
0.4470
0.4677
0.4481
0.9013
0.4490
0.4423
1.1574
.4441
g
0.5146
0.5146
0.5145
0.4662
0.8361
0.4656
0.4467
15.001
0.4711
0.4411
8.1875
.4832
h
0.5118
0.5118
0.5108
0.4629
132.19
0.4581
0.4450
2840.5
0.6401
0.4427
6735.0
.7791
The results were calculated at λ = 0.4 μm where the complex permittivity of soot is ∊* = 1.88 − j0.69.
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