We utilize the Volume Integral Equation Formulation (VIEF) and the method of moments to calculate the electromagnetic scattering and absorption of aerosol particles with branched-chain structures. Two kinds of polarization of the incident electromagnetic wave were considered: the cross- and end-fire polarizations. The numerical results of internal electric field distribution, absorbed power, and extinction and scattering cross sections, obtained from the VIEF, show excellent agreement with the Mie theory for the special case of spherical particles. Comparison between the results of the VIEF and Iterative Extended Boundary Condition Method for very long oriented (elongated) chains of particles also showed good agreement. After validating the accuracy of the VIEF, the absorption characteristics of three branched-chain structures simulated from microscopic pictures of coagulated smoke aerosol particles were calculated. Results showed that the ratio of absorption in the two polarization cases, Pcross-fire/Pend-fire, for very long oriented chain structures is as high as a factor of 4 at lower frequencies (λ = 10 μm). While in the higher frequency (λ = 0.5-μm) case, the ratio of Pcross-fire/Pend-fire is reduced to 2.0. For branched-chain structures, the ratio of Pcross-fire/Pend-fire decreased with the increase in the number of the side branches. These observations show that the frequency, polarization, and structure factors play important roles in determining the optical characteristics of branched chains of aerosol particles.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
Comparison Between the Results Using the VIEF and Mie Theory for a Spherical Particle of Radius r =0.02 μm, ∊* = 1.75 + j0.3, and λ = 0.5 μm (Visible)
Electric field distribution
Mie theory
VIEF 27 cells, end-fire
VIEF 27 cells, end-fire
VIEF 64 cells, end-fire
VIEF 64 cells, end-fire
a
0.797
0.767
0.832
0.783
0.787
b
0.801
0.777
0.820
0.792
0.806
c
0.804
0.788
0.812
0.806
0.809
d
0.807
0.804
0.804
0.807
0.819
e
0.811
0.804
0.804
0.807
0.819
l
0.812
0.788
0.812
0.809
0.809
g
0.813
0.777
0.820
0.814
0.806
h
0.813
0.767
0.832
0.819
0.787
Pab (W)
0.109 × 10−18
0.101 × 10−18
0.101 × 10−18
0.111 × 10−18
0.111 × 10−18
ECS (m2)
0.827 × 10−16
0.770 × 10−16
0.770 × 10−16
0.842 × 10−16
0.842 × 10−16
SCS (m2)
0.663 × 10−18
0.667 × 10−18
0.667 × 10−18
0.670 × 10−18
0.670 × 10−18
Pab = power absorbed. Note the improved accuracy of the VIEF with the increase in the number of cells from 27 to 64.
Table II
Comparison Between the Results Using the VIEF and Mie Theory for a Spherical Particle of Radius r = 0.02 μm, ∊* = 3 + j1, and λ = 10 μm (IR)
Electric field distribution
Mie theory
VIEF 27 cells, end-fire
VIEF 27 cells, end-fire
VIEF 64 cells, end-fire
VIEF 64 cells, end-fire
a
0.577
0.541
0.628
0.575
0.608
b
0.588
0.552
0.612
0.585
0.594
c
0.588
0.564
0.594
0.585
0.585
d
0.588
0.574
0.574
0.590
0.575
e
0.589
0.578
0.574
0.590
0.575
f
0.589
0.571
0.594
0.585
0.585
g
0.589
0.562
0.612
0.582
0.594
h
0.580
0.551
0.629
0.576
0.608
Pab (W)
0.101 × 10−19
0.973 × 10−20
0.973 × 10−20
0.103 × 10−19
0.103 × 10−19
ECS (m2)
0.760 × 10−17
0.734 × 10−17
0.734 × 10−17
0.777 × 10−17
0.777 × 10−17
SCS (m2)
0.161 × 10−22
0.162 × 10−22
0.162 × 10−22
0.162 × 10−22
0.160 × 10−22
Pab = power absorbed. Note the improved accuracy of the VIEF with the increase in the number of cells from 27 to 64.
Table III
Comparison of Results Using the IEBCM and VIEF for a Spheroidal Model of Elongated Aerosol Particles with Semiminor Axis of 0.02 μm, ∊* = 1.75 + j0.3, λ = 0.5 μm (Visible) for Cross-Fire Polarization; Aspect Ratio was Varied from 3 to 20
Electric field distribution
Aspect ratio 3
Aspect ratio 7
Aspect ratio 11
Aspect ratio 15
Aspect ratio 20
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
a
0.911
0.905
0.938
0.925
0.942
0.930
0.950
0.941
0.953
0 943
b
0.919
0.914
0.943
0.946
0.952
0.952
0.965
0.960
0.967
0.962
c
0.925
0.922
0.962
0.969
0.971
0.972
0.971
0.981
0.973
0.988
d
0.928
0.926
0.970
0.972
0.981
0.983
0.996
0.997
0.996
0.997
e
0.928
0.926
0.970
0.972
0.981
0.983
0.996
0.997
0.996
0997
f
0.925
0.922
0.962
0.969
0.971
0.972
0.971
0.981
0.973
0.988
g
0.919
0.914
0.943
0.946
0.952
0.952
0.965
0.960
0.967
0.962
h
0.911
0.905
0.938
0.925
0.942
0.930
0.950
0.941
0.953
0.943
Pab (W)
0.422 × 10−18
0.420 × 10−18
0.104 × 10−17
0.109 × 10−17
0.187 × 10−17
0.194 × 10−17
0.254 × 10−17
0.270 × 10−17
0.351 × 10−17
0 362 × 10−17
ECS (m2)
0.325 × 10−15
0.325 × 10−15
0.821 × 10−15
0.862 × 10−15
0.150 × 10−14
0·158 × 10−14
0.209 × 10−14
0.223 × 10−14
0.292 × 10−14
0 302 × 10−14
SCS (m2)
0.708 × 10−17
0.737 × 10−17
0.385 × 10−16
0.400 × 10−16
0.955 × 10−16
0.115 × 10−15
0.17 × 10−15
0.195 × 10−15
0.271 × 10−15
0 288 × 10−15
Table IV
Comparison of Results Using the IEBCM and VIEF for a Spheroidal Model of Elongated Aerosol Particles with Semiminor Axis of 0.02 μm, ∊* = 1.75 + j0.3, λ = 0.5 μm (Visible) for End-Fire Polarization; Aspect Ratio was Varied from 3 to 20
Electric field distribution
Aspect ratio 3
Aspect ratio 7
Aspect ratio 11
Aspect ratio 15
Aspect ratio 20
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
a
0.750
0.748
0.745
0.743
0.765
0.759
0.789
0.764
0.788
0.775
b
0.755
0.751
0.748
0.747
0.760
0.762
0.785
0.764
0.783
0.771
c
0.760
0.761
0.751
0.750
0.753
0.761
0.765
0.757
0.779
0.762
d
0.764
0.764
0.754
0.755
0.754
0.758
0.768
0.770
0.776
0.761
e
0.766
0.765
0.755
0.752
0.753
0.754
0.769
0.769
0.763
0.762
f
0.765
0.774
0.751
0.752
0.752
0.755
0.751
0.768
0.776
0.761
g
0.764
0.771
0.745
0.745
0.762
0.760
0.784
0.770
0.785
0.778
h
0.763
0.765
0.732
0.730
0.768
0.760
0.794
0.761
0.795
0.772
Pab (W)
0.291 × 10−18
0.307 × 10−18
0.665 × 10−18
0.666 × 10−18
0.101 × 10−17
0.104 × 10−17
0.132 × 10−17
0.142 × 10−17
0.231 × 10−17
0.209 × 10−17
ECS (m2)
0.224 × 10−15
0.235 × 10−15
0.516 × 10−15
0.519 × 10−15
0.789 × 10−15
0.815 × 10−15
0.101 × 10−14
0.111 × 10−14
0.167 × 10−14
0.163 × 10−14
SCS (m2)
0.426 × 10−17
0.442 × 10−17
0.138 × 10−16
0.168 × 10−16
0.275 × 10−16
0.299 × 10−16
0.383 × 10−16
0.378 × 10−16
0.606 × 10−16
0.583 × 10−16
Table V
Comparison of Results Using the IEBCM and VIEF for a Spheroidal Model of Elongated Aerosol Particles with Semiminor Axis of 0.02 μm, ∊* = 3 + j1, λ = 10 μm (IR) for Cross-Fire Polarization; Aspect Ratio was Varied from 3 to 20
Electric field distribution
Aspect ratio 3
Aspect ratio 7
Aspect ratio 11
Aspect ratio 15
Aspect ratio 20
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
a
0.815
0.781
0.848
0.850
0.900
0.893
0.922
0.921
0.925
0.929
b
0.815
0.808
0.841
0.851
0.905
0.913
0.931
0.930
0.944
0.943
c
0815
0.812
0.852
0.852
0.909
0.925
0.939
0.933
0.945
0.943
d
0.815
0.814
0.855
0.887
0.913
0.926
0.942
0.946
0.954
0.956
e
0.815
0.814
0.855
0.886
0.913
0.926
0.942
0.947
0.954
0.956
f
0.815
0.812
0.852
0.852
0.909
0.925
0.939
0.933
0.945
0.943
g
0.815
0.808
0.851
0.851
0.905
0.913
0.931
0.930
0.944
0.943
h
0.815
0.781
0.848
0.850
0.900
0.893
0.922
0.921
0.925
0.929
Pab (W)
0.557 × 10−19
0.540 × 10−19
0.163 × 10−18
0.175 × 10−18
0.288 × 10−18
0.297 × 10−18
0.420 × 10−18
0.427 × 10−18
0.584 × 10−18
0.591 × 10−18
ECS (m2)
0.420 × 10−16
0.407 × 10−16
0.123 × 10−15
0.132 × 10−15
0.217 × 10−15
0.224 × 10−15
0.317 × 10−15
0.323 × 10−15
0.438 × 10−15
0.446 × 10−15
SCS (m2)
0.278 × 10−21
0.269 × 10−21
0.190 × 10−20
0.203 × 10−20
0.580 × 10−20
0.598 × 10−20
0.121 × 10−19
0.117 × 10−19
0.221 × 10−19
0.216 × 10−19
Table VI
Comparison of Results Using the IEBCM and VIEF for a Spheroidal Model of Elongated Aerosol Particles with Semiminor Axis 0.02 μm, ∊* = 3 + j1, λ = 10 μm (IR) for End-Fire Polarization; Aspect Ratio was Varied from 3 to 20
Electric field distribution
Aspect ratio 3
Aspect ratio 7
Aspect ratio 11
Aspect ratio 15
Aspect ratio 20
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
a
0.514
0.502
0.491
0.490
0.481
0.478
0.483
0.473
0.487
0.472
b
0.514
0.509
0.492
0.491
0.488
0.482
0.487
0.487
0.487
0.482
c
0.514
0.512
0.495
0.493
0.490
0.490
0.489
0.488
0.487
0.487
d
0.515
0.516
0.498
0.500
0.507
0.491
0.488
0.489
0.487
0.491
e
0.515
0.517
0.501
0.503
0.492
0.503
0.489
0.492
0.487
0.490
f
0.515
0.517
0.500
0.504
0.492
0.495
0.488
0.487
0.486
0.486
g
0.515
0.520
0.495
0.495
0.490
0.482
0.490
0.484
0.485
0.482
h
0.516
0.526
0.492
0.496
0.483
0.478
0.488
0.473
0.482
0.472
Pab (W)
0.222 × 10−19
0.232 × 10−19
0.487 × 10−19
0.490 × 10−19
0.747 × 10−19
0.752 × 10−19
0.100 × 10−18
0.101 × 10−18
0.132 × 10−18
0.133 × 10−18
ECS (m2)
0.167 × 10−16
0.175 × 10−16
0.367 × 10−17
0.370 × 10−17
0.563 × 10−16
0.567 × 10−16
0.753 × 10−16
0.760 × 10−16
0.997 × 10−16
0.100 × 10−15
SCS (m2)
0.111 × 10−21
0.122 × 10−21
0.603 × 10−21
0.625 × 10−21
0.142 × 10−20
0.150 × 10−20
0.247 × 10−20
0.274 × 10−20
0.432 × 10−20
0.478 × 10−20
Table VII
Absorbed Power in Watts of Very High Aspect Ratio, a/b = 125 and 250, Elongated Aerosol Particles with Semiminor axis b = 0.02 μm, ∊* = 3 + j1, at IR Frequency (λ = 10 μm): Comparison of IEBCM and VIEF Results
Aspect ratio polarization
a/b = 125
a/b = 250
Cross-fire (× 10−17)
End-fire (× 10−18)
Cross-fire (× 10−17)
End-fire (× 10−17)
IEBCM
0.382
0.806
0.707
0.159
VIEF
0.392
0.785
0.731
0.152
Table VIII
Absorbed Power in Watts of Very High Aspect Ratio, a/b = 125 and 250, Elongated Aerosol Particles with Semiminor axis b = 0.02 μm,∊* = 1.75 + j0.3, at Visible Frequency (λ = 0.5 μm) Comparison of IEBCM and VIEF Results
Aspect ratio polarization
a/b = 125
a/b = 250
Cross-fire (× 10−16)
End-fire (× 10−16)
Cross-fire (× 10−16)
End-fire (× 10−16)
IEBCM
0.225
0.113
0.427
0.224
VIEF
0.229
0.115
0.447
0.226
Table IX
Results of Absorbed Power, Extinction, and Scattering, Cross Sections of the Three Branched Chains of Aerosol Particles Shown in Fig. 5a
The complex permittivity is ∊* = 3 + j1 at the IR frequency (λ = 10 μm). The absorption by 125 spherical particles, each of 0.02-μm radius and of the same complex permittivity at λ = 10 μm is Pab= 0.1208 × 10−17 W. This estimate predicted by Berry and Percival8 lies between the calculated values for cross- and end-fire polarizations.
Table X
Results of Absorbed Power, Extinction, and Scattering, Cross Sections of the Three Branched Chains of Aerosol Particles Shown in Fig. 5a
The complex permittivity is ∊* = 1.75 + j0.3 at the visible frequency (λ = 0.5 μm). The absorption by 125 spherical particles, each of 0.02-μm radius and of the same complex permittivity at λ = 0.5 μm is Pab= 0.1373 × 10−16 W. This estimate predicted by Berry and Percival8 lies between the calculated values for cross- and end-fire polarizations.
Tables (10)
Table I
Comparison Between the Results Using the VIEF and Mie Theory for a Spherical Particle of Radius r =0.02 μm, ∊* = 1.75 + j0.3, and λ = 0.5 μm (Visible)
Electric field distribution
Mie theory
VIEF 27 cells, end-fire
VIEF 27 cells, end-fire
VIEF 64 cells, end-fire
VIEF 64 cells, end-fire
a
0.797
0.767
0.832
0.783
0.787
b
0.801
0.777
0.820
0.792
0.806
c
0.804
0.788
0.812
0.806
0.809
d
0.807
0.804
0.804
0.807
0.819
e
0.811
0.804
0.804
0.807
0.819
l
0.812
0.788
0.812
0.809
0.809
g
0.813
0.777
0.820
0.814
0.806
h
0.813
0.767
0.832
0.819
0.787
Pab (W)
0.109 × 10−18
0.101 × 10−18
0.101 × 10−18
0.111 × 10−18
0.111 × 10−18
ECS (m2)
0.827 × 10−16
0.770 × 10−16
0.770 × 10−16
0.842 × 10−16
0.842 × 10−16
SCS (m2)
0.663 × 10−18
0.667 × 10−18
0.667 × 10−18
0.670 × 10−18
0.670 × 10−18
Pab = power absorbed. Note the improved accuracy of the VIEF with the increase in the number of cells from 27 to 64.
Table II
Comparison Between the Results Using the VIEF and Mie Theory for a Spherical Particle of Radius r = 0.02 μm, ∊* = 3 + j1, and λ = 10 μm (IR)
Electric field distribution
Mie theory
VIEF 27 cells, end-fire
VIEF 27 cells, end-fire
VIEF 64 cells, end-fire
VIEF 64 cells, end-fire
a
0.577
0.541
0.628
0.575
0.608
b
0.588
0.552
0.612
0.585
0.594
c
0.588
0.564
0.594
0.585
0.585
d
0.588
0.574
0.574
0.590
0.575
e
0.589
0.578
0.574
0.590
0.575
f
0.589
0.571
0.594
0.585
0.585
g
0.589
0.562
0.612
0.582
0.594
h
0.580
0.551
0.629
0.576
0.608
Pab (W)
0.101 × 10−19
0.973 × 10−20
0.973 × 10−20
0.103 × 10−19
0.103 × 10−19
ECS (m2)
0.760 × 10−17
0.734 × 10−17
0.734 × 10−17
0.777 × 10−17
0.777 × 10−17
SCS (m2)
0.161 × 10−22
0.162 × 10−22
0.162 × 10−22
0.162 × 10−22
0.160 × 10−22
Pab = power absorbed. Note the improved accuracy of the VIEF with the increase in the number of cells from 27 to 64.
Table III
Comparison of Results Using the IEBCM and VIEF for a Spheroidal Model of Elongated Aerosol Particles with Semiminor Axis of 0.02 μm, ∊* = 1.75 + j0.3, λ = 0.5 μm (Visible) for Cross-Fire Polarization; Aspect Ratio was Varied from 3 to 20
Electric field distribution
Aspect ratio 3
Aspect ratio 7
Aspect ratio 11
Aspect ratio 15
Aspect ratio 20
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
a
0.911
0.905
0.938
0.925
0.942
0.930
0.950
0.941
0.953
0 943
b
0.919
0.914
0.943
0.946
0.952
0.952
0.965
0.960
0.967
0.962
c
0.925
0.922
0.962
0.969
0.971
0.972
0.971
0.981
0.973
0.988
d
0.928
0.926
0.970
0.972
0.981
0.983
0.996
0.997
0.996
0.997
e
0.928
0.926
0.970
0.972
0.981
0.983
0.996
0.997
0.996
0997
f
0.925
0.922
0.962
0.969
0.971
0.972
0.971
0.981
0.973
0.988
g
0.919
0.914
0.943
0.946
0.952
0.952
0.965
0.960
0.967
0.962
h
0.911
0.905
0.938
0.925
0.942
0.930
0.950
0.941
0.953
0.943
Pab (W)
0.422 × 10−18
0.420 × 10−18
0.104 × 10−17
0.109 × 10−17
0.187 × 10−17
0.194 × 10−17
0.254 × 10−17
0.270 × 10−17
0.351 × 10−17
0 362 × 10−17
ECS (m2)
0.325 × 10−15
0.325 × 10−15
0.821 × 10−15
0.862 × 10−15
0.150 × 10−14
0·158 × 10−14
0.209 × 10−14
0.223 × 10−14
0.292 × 10−14
0 302 × 10−14
SCS (m2)
0.708 × 10−17
0.737 × 10−17
0.385 × 10−16
0.400 × 10−16
0.955 × 10−16
0.115 × 10−15
0.17 × 10−15
0.195 × 10−15
0.271 × 10−15
0 288 × 10−15
Table IV
Comparison of Results Using the IEBCM and VIEF for a Spheroidal Model of Elongated Aerosol Particles with Semiminor Axis of 0.02 μm, ∊* = 1.75 + j0.3, λ = 0.5 μm (Visible) for End-Fire Polarization; Aspect Ratio was Varied from 3 to 20
Electric field distribution
Aspect ratio 3
Aspect ratio 7
Aspect ratio 11
Aspect ratio 15
Aspect ratio 20
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
a
0.750
0.748
0.745
0.743
0.765
0.759
0.789
0.764
0.788
0.775
b
0.755
0.751
0.748
0.747
0.760
0.762
0.785
0.764
0.783
0.771
c
0.760
0.761
0.751
0.750
0.753
0.761
0.765
0.757
0.779
0.762
d
0.764
0.764
0.754
0.755
0.754
0.758
0.768
0.770
0.776
0.761
e
0.766
0.765
0.755
0.752
0.753
0.754
0.769
0.769
0.763
0.762
f
0.765
0.774
0.751
0.752
0.752
0.755
0.751
0.768
0.776
0.761
g
0.764
0.771
0.745
0.745
0.762
0.760
0.784
0.770
0.785
0.778
h
0.763
0.765
0.732
0.730
0.768
0.760
0.794
0.761
0.795
0.772
Pab (W)
0.291 × 10−18
0.307 × 10−18
0.665 × 10−18
0.666 × 10−18
0.101 × 10−17
0.104 × 10−17
0.132 × 10−17
0.142 × 10−17
0.231 × 10−17
0.209 × 10−17
ECS (m2)
0.224 × 10−15
0.235 × 10−15
0.516 × 10−15
0.519 × 10−15
0.789 × 10−15
0.815 × 10−15
0.101 × 10−14
0.111 × 10−14
0.167 × 10−14
0.163 × 10−14
SCS (m2)
0.426 × 10−17
0.442 × 10−17
0.138 × 10−16
0.168 × 10−16
0.275 × 10−16
0.299 × 10−16
0.383 × 10−16
0.378 × 10−16
0.606 × 10−16
0.583 × 10−16
Table V
Comparison of Results Using the IEBCM and VIEF for a Spheroidal Model of Elongated Aerosol Particles with Semiminor Axis of 0.02 μm, ∊* = 3 + j1, λ = 10 μm (IR) for Cross-Fire Polarization; Aspect Ratio was Varied from 3 to 20
Electric field distribution
Aspect ratio 3
Aspect ratio 7
Aspect ratio 11
Aspect ratio 15
Aspect ratio 20
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
a
0.815
0.781
0.848
0.850
0.900
0.893
0.922
0.921
0.925
0.929
b
0.815
0.808
0.841
0.851
0.905
0.913
0.931
0.930
0.944
0.943
c
0815
0.812
0.852
0.852
0.909
0.925
0.939
0.933
0.945
0.943
d
0.815
0.814
0.855
0.887
0.913
0.926
0.942
0.946
0.954
0.956
e
0.815
0.814
0.855
0.886
0.913
0.926
0.942
0.947
0.954
0.956
f
0.815
0.812
0.852
0.852
0.909
0.925
0.939
0.933
0.945
0.943
g
0.815
0.808
0.851
0.851
0.905
0.913
0.931
0.930
0.944
0.943
h
0.815
0.781
0.848
0.850
0.900
0.893
0.922
0.921
0.925
0.929
Pab (W)
0.557 × 10−19
0.540 × 10−19
0.163 × 10−18
0.175 × 10−18
0.288 × 10−18
0.297 × 10−18
0.420 × 10−18
0.427 × 10−18
0.584 × 10−18
0.591 × 10−18
ECS (m2)
0.420 × 10−16
0.407 × 10−16
0.123 × 10−15
0.132 × 10−15
0.217 × 10−15
0.224 × 10−15
0.317 × 10−15
0.323 × 10−15
0.438 × 10−15
0.446 × 10−15
SCS (m2)
0.278 × 10−21
0.269 × 10−21
0.190 × 10−20
0.203 × 10−20
0.580 × 10−20
0.598 × 10−20
0.121 × 10−19
0.117 × 10−19
0.221 × 10−19
0.216 × 10−19
Table VI
Comparison of Results Using the IEBCM and VIEF for a Spheroidal Model of Elongated Aerosol Particles with Semiminor Axis 0.02 μm, ∊* = 3 + j1, λ = 10 μm (IR) for End-Fire Polarization; Aspect Ratio was Varied from 3 to 20
Electric field distribution
Aspect ratio 3
Aspect ratio 7
Aspect ratio 11
Aspect ratio 15
Aspect ratio 20
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
IEBCM
VIEF
a
0.514
0.502
0.491
0.490
0.481
0.478
0.483
0.473
0.487
0.472
b
0.514
0.509
0.492
0.491
0.488
0.482
0.487
0.487
0.487
0.482
c
0.514
0.512
0.495
0.493
0.490
0.490
0.489
0.488
0.487
0.487
d
0.515
0.516
0.498
0.500
0.507
0.491
0.488
0.489
0.487
0.491
e
0.515
0.517
0.501
0.503
0.492
0.503
0.489
0.492
0.487
0.490
f
0.515
0.517
0.500
0.504
0.492
0.495
0.488
0.487
0.486
0.486
g
0.515
0.520
0.495
0.495
0.490
0.482
0.490
0.484
0.485
0.482
h
0.516
0.526
0.492
0.496
0.483
0.478
0.488
0.473
0.482
0.472
Pab (W)
0.222 × 10−19
0.232 × 10−19
0.487 × 10−19
0.490 × 10−19
0.747 × 10−19
0.752 × 10−19
0.100 × 10−18
0.101 × 10−18
0.132 × 10−18
0.133 × 10−18
ECS (m2)
0.167 × 10−16
0.175 × 10−16
0.367 × 10−17
0.370 × 10−17
0.563 × 10−16
0.567 × 10−16
0.753 × 10−16
0.760 × 10−16
0.997 × 10−16
0.100 × 10−15
SCS (m2)
0.111 × 10−21
0.122 × 10−21
0.603 × 10−21
0.625 × 10−21
0.142 × 10−20
0.150 × 10−20
0.247 × 10−20
0.274 × 10−20
0.432 × 10−20
0.478 × 10−20
Table VII
Absorbed Power in Watts of Very High Aspect Ratio, a/b = 125 and 250, Elongated Aerosol Particles with Semiminor axis b = 0.02 μm, ∊* = 3 + j1, at IR Frequency (λ = 10 μm): Comparison of IEBCM and VIEF Results
Aspect ratio polarization
a/b = 125
a/b = 250
Cross-fire (× 10−17)
End-fire (× 10−18)
Cross-fire (× 10−17)
End-fire (× 10−17)
IEBCM
0.382
0.806
0.707
0.159
VIEF
0.392
0.785
0.731
0.152
Table VIII
Absorbed Power in Watts of Very High Aspect Ratio, a/b = 125 and 250, Elongated Aerosol Particles with Semiminor axis b = 0.02 μm,∊* = 1.75 + j0.3, at Visible Frequency (λ = 0.5 μm) Comparison of IEBCM and VIEF Results
Aspect ratio polarization
a/b = 125
a/b = 250
Cross-fire (× 10−16)
End-fire (× 10−16)
Cross-fire (× 10−16)
End-fire (× 10−16)
IEBCM
0.225
0.113
0.427
0.224
VIEF
0.229
0.115
0.447
0.226
Table IX
Results of Absorbed Power, Extinction, and Scattering, Cross Sections of the Three Branched Chains of Aerosol Particles Shown in Fig. 5a
The complex permittivity is ∊* = 3 + j1 at the IR frequency (λ = 10 μm). The absorption by 125 spherical particles, each of 0.02-μm radius and of the same complex permittivity at λ = 10 μm is Pab= 0.1208 × 10−17 W. This estimate predicted by Berry and Percival8 lies between the calculated values for cross- and end-fire polarizations.
Table X
Results of Absorbed Power, Extinction, and Scattering, Cross Sections of the Three Branched Chains of Aerosol Particles Shown in Fig. 5a
The complex permittivity is ∊* = 1.75 + j0.3 at the visible frequency (λ = 0.5 μm). The absorption by 125 spherical particles, each of 0.02-μm radius and of the same complex permittivity at λ = 0.5 μm is Pab= 0.1373 × 10−16 W. This estimate predicted by Berry and Percival8 lies between the calculated values for cross- and end-fire polarizations.