Abstract

Mie’s coefficients an, bn are calculated by using recurrently generated spherical Bessel functions, which are then used to compose the numerators and denominators wn, Wn of the coefficients an, bn. It is demonstrated that recurrent relations can be found directly between the expressions wn, Wn.

© 1976 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  2. P. Chýlek, J. Opt. Soc. Am. 63, 699–706 (1973).
    [CrossRef]
  3. L. S. Rodberg and R. M. Thaler, Introduction to the Quantum Theory of Scattering (Academic, New York, 1967), pp. 73–74.

1973 (1)

Chýlek, P.

Rodberg, L. S.

L. S. Rodberg and R. M. Thaler, Introduction to the Quantum Theory of Scattering (Academic, New York, 1967), pp. 73–74.

Thaler, R. M.

L. S. Rodberg and R. M. Thaler, Introduction to the Quantum Theory of Scattering (Academic, New York, 1967), pp. 73–74.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

J. Opt. Soc. Am. (1)

Other (2)

L. S. Rodberg and R. M. Thaler, Introduction to the Quantum Theory of Scattering (Academic, New York, 1967), pp. 73–74.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (21)

Equations on this page are rendered with MathJax. Learn more.

a n ( α , m ) = w n ( ψ ( α ) , ψ ( m α ) ) / w n ( ζ ( α ) , ψ ( m α ) ) ,
b n ( α , ω ) = W n ( ψ ( α ) , ψ ( m α ) ) / W n ( ζ ( α ) , ψ ( m α ) ) ,
W n ( ψ ( α ) , ψ ( m α ) ) = ψ n ( α ) ψ n ( m α ) - m ψ n ( α ) ψ n ( m α ) ,
w n ( ψ ( α ) , ψ ( m α ) ) = m ψ n ( α ) ψ n ( m α ) - ψ n ( α ) ψ n ( m α ) ;
ψ n + 1 ( x ) = 2 n + 1 x ψ n ( x ) - ψ n - 1 ( x ) ,
ψ n ( x ) = ψ n - 1 ( x ) - n x ψ n ( x ) = n + 1 x ψ n ( x ) - ψ n + 1 ( x ) .
W n + 1 = w n - n + 1 m α d d α W n ,
W n - 1 = w n + n m α d d α W n ,
d d α W n = ( m 2 - 1 ) ψ n ( α ) ψ n ( m α ) .
W n - 1 - W n + 1 = 2 n + 1 m α d d α W n .
n W n + 1 + ( n + 1 ) W n - 1 = ( 2 n + 1 ) w n .
W n = w n - 1 - n m α d d α W n - 1 ,
W n = w n + 1 + n + 1 m α d d α W n + 1 .
( 2 n + 1 ) W n = ( n + 1 ) w n - 1 + n w n + 1 + n ( n + 1 ) m α d d α ( W n + 1 - W n - 1 ) .
d d α ( W n + 1 - W n - 1 ) = 2 n + 1 m α 2 d d α W n - 2 n + 1 m α d 2 d α 2 W n ,
d 2 d α 2 W n = ( m 2 - 1 ) [ ψ n ( α ) ψ n ( m α ) + m ψ n ( α ) ψ n ( m α ) ] = 2 m w n - ( m 2 + 1 ) W n ,
ψ n ( α ) ψ n ( m α ) = ( w n - m W n ) / ( m 2 - 1 ) , ψ n ( α ) ψ n ( m α ) = ( m w n - W n ) / ( m 2 - 1 ) .
n w n + 1 = ( 2 n + 1 ) 2 ( n + 1 ) m α 2 w n - ( n + 1 ) w n - 1 + ( 2 n + 1 ) W n × ( 1 - n ( n + 1 ) m 2 + 1 m 2 α 2 ) - ( n + 1 ) ( 2 n + 1 ) m α 2 W n - 1 .
n w n + 1 + ( n + 1 ) w n - 1 = ( 2 n + 1 ) W n , n W n + 1 + ( n + 1 ) W n - 1 = ( 2 n + 1 ) w n .
w 0 = W 1 = m cos α sin ( m α ) - sin α cos ( m α ) , w 1 = W 0 = cos α sin ( m α ) - m sin α cos ( m α ) ,
W n + 1 = w n , W n + 1 = W n - 1 , w n + 1 = w n - 1 .