Optical scattering and absorption by branched chains of aerosols

Magdy F. Iskander; H. Y. Chen; J. E. Penner

doi:10.1364/AO.28.003083

Applied Optics
Vol. 28,
Issue 15,
pp. 3083-3091
(1989)
•https://doi.org/10.1364/AO.28.003083

Optical scattering and absorption by branched chains of aerosols

Magdy F. Iskander, H. Y. Chen, and J. E. Penner

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Magdy F. Iskander, H. Y. Chen, and J. E. Penner, "Optical scattering and absorption by branched chains of aerosols," Appl. Opt. 28, 3083-3091 (1989)

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Abstract

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, P_cross-fire/P_end-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 P_cross-fire/P_end-fire is reduced to 2.0. For branched-chain structures, the ratio of P_cross-fire/P_end-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.

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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
P_ab (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

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
P_ab (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

Electric field distribution	Aspect ratio 3		Aspect ratio 7		Aspect ratio 11		Aspect ratio 15		Aspect ratio 20
Electric field distribution	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
P_ab (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

Electric field distribution	Aspect ratio 3		Aspect ratio 7		Aspect ratio 11		Aspect ratio 15		Aspect ratio 20
Electric field distribution	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
P_ab (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

Electric field distribution	Aspect ratio 3		Aspect ratio 7		Aspect ratio 11		Aspect ratio 15		Aspect ratio 20
Electric field distribution	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
P_ab (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

Aspect ratio polarization	a/b = 125		a/b = 250
Aspect ratio polarization	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

Aspect ratio polarization	a/b = 125		a/b = 250
Aspect ratio polarization	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

		Fig. 5(a)	Fig. 5(b)	Fig. 5(c)
P_ab (W)	Cross-fire	0.365 × 10⁻¹⁷	0.306 × 10⁻¹⁷	0.279 × 10⁻¹⁷
P_ab (W)	End-fire	0.796 × 10⁻¹⁸	0.808 × 10⁻¹⁸	0.803 × 10⁻¹⁸
ECS (m²)	Cross-fire	0.275 × 10⁻¹⁴	0.231 × 10⁻¹⁴	0.210 × 10⁻¹⁴
ECS (m²)	End-fire	0.601 × 10⁻¹⁵	0.609 × 10⁻¹⁵	0.605 × 10⁻¹⁵
SCS (m²)	Cross-fire	0.753 × 10⁻¹⁸	0.609 × 10⁻¹⁸	0.522 × 10⁻¹⁸
SCS (m²)	End-fire	0.121 × 10⁻¹⁸	0.128 × 10⁻¹⁸	0.152 × 10⁻¹⁸

		Fig. 5(a)	Fig. 5(b)	Fig. 5(c)
P_ab (W)	Cross-fire	0.219 × 10⁻¹⁶	0.200 × 10⁻¹⁶	0.171 × 10⁻¹⁶
P_ab (W)	End-fire	0.118 ×10⁻¹⁶	0.117 ×10⁻¹⁶	0.116 × 10⁻¹⁶
ECS (m²)	Cross-fire	0.186 × 10⁻¹³	0.169 × 10⁻¹³	0.145 × 10⁻¹³
ECS (m²)	End-fire	0.924 × 10⁻¹⁴	0.924 × 10⁻¹⁴	0.923 × 10⁻¹⁴
SCS (m²)	Cross-fire	0.204 × 10⁻¹⁴	0.182 × 10⁻¹⁴	0.161 × 10⁻¹⁴
SCS (m²)	End-fire	0.357 × 10⁻¹⁵	0.390 × 10⁻¹⁵	0.465 × 10⁻¹⁵

Electric field distribution	Aspect ratio 3		Aspect ratio 7		Aspect ratio 11		Aspect ratio 15		Aspect ratio 20
Electric field distribution	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
P_ab (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

Electric field distribution	Aspect ratio 3		Aspect ratio 7		Aspect ratio 11		Aspect ratio 15		Aspect ratio 20
Electric field distribution	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
P_ab (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

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Applied Optics