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  1. G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483–489 (1991).
    [Crossref]
  2. S. Stein, “Addition theorems for spherical wave functions,”Q. Appl. Math. 19, 15–24 (1961).
  3. O. R. Cruzan, “Translational addition theorems for spherical vector wave functions,”Q. Appl. Math. 20, 33–40 (1962).

1991 (1)

1962 (1)

O. R. Cruzan, “Translational addition theorems for spherical vector wave functions,”Q. Appl. Math. 20, 33–40 (1962).

1961 (1)

S. Stein, “Addition theorems for spherical wave functions,”Q. Appl. Math. 19, 15–24 (1961).

Cruzan, O. R.

O. R. Cruzan, “Translational addition theorems for spherical vector wave functions,”Q. Appl. Math. 20, 33–40 (1962).

Stein, S.

S. Stein, “Addition theorems for spherical wave functions,”Q. Appl. Math. 19, 15–24 (1961).

Videen, G.

J. Opt. Soc. Am. A (1)

Q. Appl. Math. (2)

S. Stein, “Addition theorems for spherical wave functions,”Q. Appl. Math. 19, 15–24 (1961).

O. R. Cruzan, “Translational addition theorems for spherical vector wave functions,”Q. Appl. Math. 20, 33–40 (1962).

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Equations (8)

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g n m u n m ( 3 ) = - R ( ) ( - 1 ) n + m e n m u n m ( 3 ) , h n m u n m ( 3 ) = R ( ) ( - 1 ) n + m f n m u n m ( 3 ) .
E int = n = 0 m = - n n e n m ( - 1 ) n + m + 1 R ( ) M n m ( 3 ) + f n m ( - 1 ) n + m R ( ) N n m ( 3 ) = n = 0 m = - n n { e n m ( - 1 ) n + m + 1 R ( ) × [ n = m C n ( n , m ) M n m ( 1 ) + D n ( n , m ) N n m ( 1 ) ] + f n m ( - 1 ) n + m R ( ) × [ n = m D n ( n , m ) M n m ( 1 ) + C n ( n , m ) N n m ( 1 ) ] } = n = 0 m = - n n n = m ( - 1 ) n + m R ( ) × { [ f n , m D n ( n , m ) - e n , m C n ( n , m ) ] M n m ( 1 ) + [ f n , m C n ( n , m ) - e n , m D n ( n , m ) ] N n m ( 1 ) } ,
C n ( n , m ) = c n ( n , m ) - 2 k d 2 n + 3 n + m + 1 n + 1 c n + 1 ( n , m ) - 2 k d 2 n - 1 n - m n c n - 1 ( n , m ) , D n ( n , m ) = - 2 i k d n ( n + 1 ) m c n ( n , m )
g n m = n = m R ( ) ( - 1 ) n + m [ f n , m D n ( n , m ) - e n , m C n ( n , m ) ] , h n m = n = m R ( ) ( - 1 ) n + m [ f n , m C n ( n , m ) - e n , m D n ( n , m ) ] ,
e n m = { a n m + n = m R ( ) ( - 1 ) n + m × [ f n , m D n ( n , m ) - e n , m C n ( n , m ) ] } Q e n , f n m = { b n m + n = m R ( ) ( - 1 ) n + m × [ f n , m C n ( n , m ) - e n , m D n ( n , m ) ] } Q f n .
E TE inc = n = 0 m = - n n a n m TE [ 1 - R TE ( α ) × exp ( 2 i k d cos α ) ( - 1 ) n + m ] M n m ( 1 ) + b n m TE [ 1 + R TE ( α ) exp ( 2 i k d cos α ) ( - 1 ) n + m ] N n m ( 1 ) , H TE inc = k i ω μ n = 0 m = - n n b n m TE [ 1 + R TE ( α ) × exp ( 2 i k d cos α ) ( - 1 ) n + m ] M n m ( 1 ) + a n m TE [ 1 - R TE ( α ) exp ( 2 i k d cos α ) ( - 1 ) n + m ] N n m ( 1 ) , E TM inc = n = 0 m = - n n a n m TM [ 1 - R TM ( α ) × exp ( 2 i k d cos α ) ( - 1 ) n + m ] M n m ( 1 ) + b n m TM [ 1 + R TM ( α ) exp ( 2 i k d cos α ) ( - 1 ) n + m ] N n m ( 1 ) , H TM inc = k i ω μ n = 0 m = - n n b n m TM [ 1 + R TM ( α ) × exp ( 2 i k d cos α ) ( - 1 ) n + m ] M n m ( 1 ) + a n m TM [ 1 + R TM ( α ) exp ( 2 i k d cos α ) ( - 1 ) n + m ] N n m ( 1 ) .
e n m TE = { [ 1 - R TE ( α ) ( - 1 ) n + m exp ( 2 i k d cos α ) ] a n m TE + R TE ( ) n = m ( - 1 ) n + m [ f n m TE D n ( n , m ) - e n m TE C n ( n , m ) ] } Q e n , e n m TM = { [ 1 - R TM ( α ) ( - 1 ) n + m exp ( 2 i k d cos α ) ] a n m TM + R TM ( ) n = m ( - 1 ) n + m [ f n m TM D n ( n , m ) - e n m TM C n ( n , m ) ] } Q e n , f n m TE = { [ 1 - R TE ( α ) ( - 1 ) n + m exp ( 2 i k d cos α ) ] b n m TE + R TE ( ) n = m ( - 1 ) n + m [ f n m TE C n ( n , m ) - e n m TE D n ( n , m ) ] } Q f n , f n m TM = { [ 1 - R TM ( α ) ( - 1 ) n + m exp ( 2 i k d cos α ) ] b n m TM + R TM ( ) n = m ( - 1 ) n + m [ f n m TM C n ( n , m ) - e n m TM D n ( n , m ) ] } Q f n .
S 1 = n = 0 m = - n n ( - i ) n exp ( i m φ ) × { [ 1 + R TE ( π - ϑ ) ( - 1 ) n + m exp ( - 2 i k d cos ϑ ) ] × f n m TE m sin ϑ P ˜ n m ( cos ϑ ) + [ 1 - R TE ( π - ϑ ) ( - 1 ) n + m × exp ( - 2 i k d cos ϑ ) ] e n m TE ϑ P ˜ n m ( cos ϑ ) } , S 2 = - i n = 0 m = - n n ( - i ) n exp ( i m φ ) × { [ 1 + R TM ( π - ϑ ) ( - 1 ) n + m exp ( - 2 i k d cos ϑ ) ] × e n m TM m sin ϑ P ˜ n m ( cos ϑ ) + [ 1 + R TM ( π - ϑ ) ( - 1 ) n + m × exp ( - 2 i k d cos ϑ ) ] f n m TM ϑ P ˜ n m ( cos ϑ ) } , S 3 = - i n = 0 m = - n n ( - i ) n exp ( i m φ ) × { [ 1 - R TM ( π - ϑ ) ( - 1 ) n + m exp ( - 2 i k d cos ϑ ) ] × e n m TE m sin ϑ P ˜ n m ( cos ϑ ) + [ 1 + R TM ( π - ϑ ) ( - 1 ) n + m × exp ( - 2 i k d cos ϑ ) ] f n m TE ϑ P ˜ n m ( cos ϑ ) } , S 4 = n = 0 m = - n n ( - i ) n exp ( i m φ ) × { [ 1 + R TE ( π - ϑ ) ( - 1 ) n + m exp ( - 2 i k d cos ϑ ) ] × f n m TM m sin ϑ P ˜ n m ( cos ϑ ) + [ 1 - R TE ( π - ϑ ) ( - 1 ) n + m × exp ( - 2 i k d cos ϑ ) ] e n m TM ϑ P ˜ n m ( cos ϑ ) } .

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