Abstract

The general S-matrix theory of multiphoton ionization is presented. The freedom in the form of the S matrix is discussed and exploited to derive a form that uses the exact dressed state as the initial state of the process. This results in a new S-matrix form, which is then evaluated in an approximate form. The numerical result is identical with a previously obtained one but radically different from that obtained by using the Keldysh–Faisal–Reiss theories.

© 1990 Optical Society of America

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References

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  1. Y. Gontier, N. K. Rahman, and M. Trahin, Phys. Rev. A 37, 4694 (1988).
    [CrossRef] [PubMed]
  2. P. Kruit, J. Kimman, H. G. Muller, and M. J. van der Wiel, Phys. Rev. A 28, 248 (1983);M. H. Mittleman, Phys. Rev. A 29, 2245 (1984).
    [CrossRef]
  3. M. H. Mittleman, Phys. Rev. 122, 1930 (1961).
    [CrossRef]
  4. M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, New York, 1965).
  5. L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).
  6. J. Abranyos and M. H. Mittleman, “Low-frequency theory of multiphoton ionization,” submitted to Phys. Rev. A.
  7. P. B. Corkum, N. H. Burnett, and F. Brunei, Phys. Rev. Lett. 62, 1959 (1989).
    [CrossRef]
  8. I. J. Berson, J. Phys. B 8, 3078 (1975).
    [CrossRef]
  9. J. Javanainen and J. H. Eberly, J. Phys. B 21, L93 (1988).
    [CrossRef]
  10. K. C. Kulander, Phys. Rev. A 38, 778 (1988).
    [CrossRef] [PubMed]

1989 (1)

P. B. Corkum, N. H. Burnett, and F. Brunei, Phys. Rev. Lett. 62, 1959 (1989).
[CrossRef]

1988 (3)

Y. Gontier, N. K. Rahman, and M. Trahin, Phys. Rev. A 37, 4694 (1988).
[CrossRef] [PubMed]

J. Javanainen and J. H. Eberly, J. Phys. B 21, L93 (1988).
[CrossRef]

K. C. Kulander, Phys. Rev. A 38, 778 (1988).
[CrossRef] [PubMed]

1983 (1)

P. Kruit, J. Kimman, H. G. Muller, and M. J. van der Wiel, Phys. Rev. A 28, 248 (1983);M. H. Mittleman, Phys. Rev. A 29, 2245 (1984).
[CrossRef]

1975 (1)

I. J. Berson, J. Phys. B 8, 3078 (1975).
[CrossRef]

1965 (1)

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

1961 (1)

M. H. Mittleman, Phys. Rev. 122, 1930 (1961).
[CrossRef]

Abranyos, J.

J. Abranyos and M. H. Mittleman, “Low-frequency theory of multiphoton ionization,” submitted to Phys. Rev. A.

Berson, I. J.

I. J. Berson, J. Phys. B 8, 3078 (1975).
[CrossRef]

Brunei, F.

P. B. Corkum, N. H. Burnett, and F. Brunei, Phys. Rev. Lett. 62, 1959 (1989).
[CrossRef]

Burnett, N. H.

P. B. Corkum, N. H. Burnett, and F. Brunei, Phys. Rev. Lett. 62, 1959 (1989).
[CrossRef]

Corkum, P. B.

P. B. Corkum, N. H. Burnett, and F. Brunei, Phys. Rev. Lett. 62, 1959 (1989).
[CrossRef]

Eberly, J. H.

J. Javanainen and J. H. Eberly, J. Phys. B 21, L93 (1988).
[CrossRef]

Goldberger, M. L.

M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, New York, 1965).

Gontier, Y.

Y. Gontier, N. K. Rahman, and M. Trahin, Phys. Rev. A 37, 4694 (1988).
[CrossRef] [PubMed]

Javanainen, J.

J. Javanainen and J. H. Eberly, J. Phys. B 21, L93 (1988).
[CrossRef]

Keldysh, L. V.

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

Kimman, J.

P. Kruit, J. Kimman, H. G. Muller, and M. J. van der Wiel, Phys. Rev. A 28, 248 (1983);M. H. Mittleman, Phys. Rev. A 29, 2245 (1984).
[CrossRef]

Kruit, P.

P. Kruit, J. Kimman, H. G. Muller, and M. J. van der Wiel, Phys. Rev. A 28, 248 (1983);M. H. Mittleman, Phys. Rev. A 29, 2245 (1984).
[CrossRef]

Kulander, K. C.

K. C. Kulander, Phys. Rev. A 38, 778 (1988).
[CrossRef] [PubMed]

Mittleman, M. H.

M. H. Mittleman, Phys. Rev. 122, 1930 (1961).
[CrossRef]

J. Abranyos and M. H. Mittleman, “Low-frequency theory of multiphoton ionization,” submitted to Phys. Rev. A.

Muller, H. G.

P. Kruit, J. Kimman, H. G. Muller, and M. J. van der Wiel, Phys. Rev. A 28, 248 (1983);M. H. Mittleman, Phys. Rev. A 29, 2245 (1984).
[CrossRef]

Rahman, N. K.

Y. Gontier, N. K. Rahman, and M. Trahin, Phys. Rev. A 37, 4694 (1988).
[CrossRef] [PubMed]

Trahin, M.

Y. Gontier, N. K. Rahman, and M. Trahin, Phys. Rev. A 37, 4694 (1988).
[CrossRef] [PubMed]

van der Wiel, M. J.

P. Kruit, J. Kimman, H. G. Muller, and M. J. van der Wiel, Phys. Rev. A 28, 248 (1983);M. H. Mittleman, Phys. Rev. A 29, 2245 (1984).
[CrossRef]

Watson, K. M.

M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, New York, 1965).

J. Phys. B (2)

I. J. Berson, J. Phys. B 8, 3078 (1975).
[CrossRef]

J. Javanainen and J. H. Eberly, J. Phys. B 21, L93 (1988).
[CrossRef]

Phys. Rev. (1)

M. H. Mittleman, Phys. Rev. 122, 1930 (1961).
[CrossRef]

Phys. Rev. A (3)

Y. Gontier, N. K. Rahman, and M. Trahin, Phys. Rev. A 37, 4694 (1988).
[CrossRef] [PubMed]

P. Kruit, J. Kimman, H. G. Muller, and M. J. van der Wiel, Phys. Rev. A 28, 248 (1983);M. H. Mittleman, Phys. Rev. A 29, 2245 (1984).
[CrossRef]

K. C. Kulander, Phys. Rev. A 38, 778 (1988).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

P. B. Corkum, N. H. Burnett, and F. Brunei, Phys. Rev. Lett. 62, 1959 (1989).
[CrossRef]

Sov. Phys. JETP (1)

L. V. Keldysh, Sov. Phys. JETP 20, 1307 (1965).

Other (2)

J. Abranyos and M. H. Mittleman, “Low-frequency theory of multiphoton ionization,” submitted to Phys. Rev. A.

M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, New York, 1965).

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Equations (45)

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S q , i = lim t ( χ q Ψ i ( + ) ) ,
S q , i = lim t ( Ψ q ( ) , ϕ i ) ,
( i t H ) Ψ = 0 ,
S q , i = d t d t d t ( Ω q ( ) , Ψ i ( + ) ) + lim t ( Ω q ( ) , Ψ i ( + ) ) ,
lim t Ω q ( ) χ q .
( i t H f ) Ω q ( ) = 0 ,
S q , i = i d t ( Ω q ( ) , V f Ψ i ( + ) ) ,
V f = H H f .
S q , i = i d t ( Ψ q ( ) , V i Ω i ( + ) ) ,
( i t H i ) Ω i ( + ) = 0 ,
lim x Ω i ( + ) ϕ i
V i = H H i .
Ω i ( + ) = p i Ψ i ( + ) ,
i t P i Ψ i ( + ) = H i P i Ψ i ( + ) .
i t P i Ψ i ( + ) = P i H Ψ i ( + ) ,
H i P i Ψ i ( + ) = P i H Ψ i ( + ) .
S q i = i d t ( Ψ q ( ) , [ H , P i ] Ψ i ( + ) ) .
H A = 1 2 m ( P + e A ) 2 + V ( r ) + H Field
A A + Λ , Ψ e i e Λ Ψ ,
exp [ i a ( r ) ] υ ( r , r ) exp [ i a ( r ) ] ,
a ( r ) = e r d r A ( r )
Ψ E = exp ( i e r A ) Ψ A ,
H E = exp ( i e r A ) H A exp ( i e r A ) = P 2 2 m + V ( r ) + H Field e r E ,
E = i [ H F , A ] .
| n = ( 2 π ) 1 / 2 e i n β , 0 β < 2 π ,
n = i β ,
a = e i β ( i β ) 1 / 2 , a + = ( i β ) 1 / 2 e i β .
Ψ e i M β Ψ ,
n M + 1 i β , a e i β ( M i β ) 1 / 2 , a + ( M i β ) 1 / 2 e + i β ,
A = A 0 ( x ̂ cos ξ / 2 cos β + ŷ sin ξ / 2 sin β ) , E = E 0 ( x ̂ cos ξ / 2 sin β ŷ sin ξ / 2 cos β ) , E 0 = ω A 0 .
P i = exp [ i e r A ( β ) ] π π d β 2 π exp [ i e r A ( β ) ] ,
[ P + e A , P i ] = [ V ( r ) , P i ] = 0
[ H F , P i ] = [ e r E , P i ] .
Ψ q ( ) χ q ,
χ q = exp i [ q r ( q + U p ) t α 0 q R q sin ( β ϕ q ) U p 2 ω cos ξ sin 2 β ] [ 1 2 π exp ( i N β + i N ω t ) ] ,
q = q 2 / 2 m , U p = e 2 E 0 2 / 4 m ω 2 , α 0 = e E 0 / m ω 2 .
R q = [ 1 2 ( 1 + cos ξ cos 2 ϕ q ) ] 1 / 2 .
Ψ i ( + ) = exp [ i e r A ( β ) ] Φ i ( + ) ,
( i t H E ) Φ i ( + ) = 0 .
{ W n ¯ ( E ) [ P 2 2 m + V ( r ) e r E ] } ϕ n = 0 ,
Φ i ( + ) = ϕ 0 ( r ) exp i [ ( W 0 1 4 α s E 0 2 ) t + α s E 0 2 8 ω cos ξ sin 2 β ] × ( 1 2 π ) .
S q i = 2 π i δ ( q + U p W 0 + 1 4 α S E 0 2 N ω ) T q i ( N ) ,
T q i ( N ) = π π d β d β ( 2 π ) 2 exp i [ ( N β + Z sin ( β ϕ q ) + U p 2 ω cos ξ sin 2 β + ν sin 2 β ] × d 3 r exp { i r [ r + e r ( β ) ] } u o ( r ) e r [ E ( β ) E ( β ) ] ,
Z = α 0 q R q , ν = 1 8 ω α s E 0 2 cos ξ ,
α 0 / a 0 = e E 0 / m ω 2 a 0 = 2 ( I / I 0 ) 1 / 2 ( R q / ω ) 2 ,

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