Abstract

Effects deriving from the finite spectral line width of an irradiation source are investigated for the resonant excitation process and found to be of particular interest when the irradiation spectral width is comparable with atomic (or molecular) line widths. An application of high current interest is laser isotope separation using relatively broad band but tunable dye lasers for selective excitation. Expressions are derived in systematic fashion for the absorption coefficient and for the yield, taking into account three independent line shapes—the first describing the irradiation source, the other two describing Lorentz and Doppler broadening of the atomic (or molecular) medium. Saturation effects are included, but propagation effects are neglected. It is shown that the customary distinction between homogeneous and inhomogeneous atomic-line broadening must be modified if the irradiation is not monochromatic. A further result of practical importance is that there exists an optimum irradiation line width that maximizes the yield for resonant transfer. In this respect, the relatively broad spectral widths characteristic of dye lasers are to be regarded as an advantageous feature, contrary to what is generally assumed.

© 1975 Optical Society of America

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  1. S. W. Mayer, M. A. Kwok, R. W. F. Gross, and D. J. Spencer, Appl. Phys. Lett. 17, 516 (1970).
    [CrossRef]
  2. E. S. Yeung and C. B. Moore, Appl. Phys. Lett. 21, 109 (1972).
    [CrossRef]
  3. R. V. Ambartsumyan, V. S. Letokhov, G. N. Makarov, and A. A. Puretskii, JETP Lett. 17, 63 (1973).
  4. R. V. Ambartsumyan, V. M. Apatin, and V. S. Letokhov, JETP Lett. 15, 237 (1972).
  5. S. H. Dworetsky and R. S. Hozack, J. Chem. Phys. 59, 3856 (1973).
    [CrossRef]
  6. C. B. Moore, Accounts Chem. Res. 6, 323 (1973).
    [CrossRef]
  7. V. S. Letokhov, Science 180, 451 (1973).
    [CrossRef] [PubMed]
  8. Dye Lasers—Topics in Applied Physics, Vol. 1, edited by F. P. Schaefer (Springer, New York, 1973), Ch. 5.
  9. An article reviewing tunable coherent light sources has been prepared by J. Kuhl and W. Schmidt, Appl. Phys. 3, 251 (1974).
    [CrossRef]
  10. A. Hordvik and P. B. Sackett, Appl. Optics 13, 1060 (1974).
    [CrossRef]
  11. N. Bloembergen and Y. R. Shen, Phys. Rev. 133, A37 (1964).
    [CrossRef]
  12. L. I. Schiff, Quantum Mechanics (McGraw–Hill, New York, 1955), p. 250.
  13. See Eq. (35.21) of Ref. 12, which contains an additional factor of 4π∊0because of the use of unrationalized cgs units.
  14. A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. P., London, 1934).
  15. This result has been exhibited by J. Ostrem and H. Gamo, Proc. IEEE 61, 1656 (1973).
    [CrossRef]
  16. B. H. Armstrong, J. Quant. Spectrosc. Radiat. Transf. 7, 61 (1967).
    [CrossRef]
  17. B. F. Fried and S. D. Conte, The Plasma Dispersion Function (Academic, New York, 1961).

1974 (2)

An article reviewing tunable coherent light sources has been prepared by J. Kuhl and W. Schmidt, Appl. Phys. 3, 251 (1974).
[CrossRef]

A. Hordvik and P. B. Sackett, Appl. Optics 13, 1060 (1974).
[CrossRef]

1973 (5)

S. H. Dworetsky and R. S. Hozack, J. Chem. Phys. 59, 3856 (1973).
[CrossRef]

C. B. Moore, Accounts Chem. Res. 6, 323 (1973).
[CrossRef]

V. S. Letokhov, Science 180, 451 (1973).
[CrossRef] [PubMed]

R. V. Ambartsumyan, V. S. Letokhov, G. N. Makarov, and A. A. Puretskii, JETP Lett. 17, 63 (1973).

This result has been exhibited by J. Ostrem and H. Gamo, Proc. IEEE 61, 1656 (1973).
[CrossRef]

1972 (2)

R. V. Ambartsumyan, V. M. Apatin, and V. S. Letokhov, JETP Lett. 15, 237 (1972).

E. S. Yeung and C. B. Moore, Appl. Phys. Lett. 21, 109 (1972).
[CrossRef]

1970 (1)

S. W. Mayer, M. A. Kwok, R. W. F. Gross, and D. J. Spencer, Appl. Phys. Lett. 17, 516 (1970).
[CrossRef]

1967 (1)

B. H. Armstrong, J. Quant. Spectrosc. Radiat. Transf. 7, 61 (1967).
[CrossRef]

1964 (1)

N. Bloembergen and Y. R. Shen, Phys. Rev. 133, A37 (1964).
[CrossRef]

Ambartsumyan, R. V.

R. V. Ambartsumyan, V. S. Letokhov, G. N. Makarov, and A. A. Puretskii, JETP Lett. 17, 63 (1973).

R. V. Ambartsumyan, V. M. Apatin, and V. S. Letokhov, JETP Lett. 15, 237 (1972).

Apatin, V. M.

R. V. Ambartsumyan, V. M. Apatin, and V. S. Letokhov, JETP Lett. 15, 237 (1972).

Armstrong, B. H.

B. H. Armstrong, J. Quant. Spectrosc. Radiat. Transf. 7, 61 (1967).
[CrossRef]

Bloembergen, N.

N. Bloembergen and Y. R. Shen, Phys. Rev. 133, A37 (1964).
[CrossRef]

Conte, S. D.

B. F. Fried and S. D. Conte, The Plasma Dispersion Function (Academic, New York, 1961).

Dworetsky, S. H.

S. H. Dworetsky and R. S. Hozack, J. Chem. Phys. 59, 3856 (1973).
[CrossRef]

Fried, B. F.

B. F. Fried and S. D. Conte, The Plasma Dispersion Function (Academic, New York, 1961).

Gamo, H.

This result has been exhibited by J. Ostrem and H. Gamo, Proc. IEEE 61, 1656 (1973).
[CrossRef]

Gross, R. W. F.

S. W. Mayer, M. A. Kwok, R. W. F. Gross, and D. J. Spencer, Appl. Phys. Lett. 17, 516 (1970).
[CrossRef]

Hordvik, A.

A. Hordvik and P. B. Sackett, Appl. Optics 13, 1060 (1974).
[CrossRef]

Hozack, R. S.

S. H. Dworetsky and R. S. Hozack, J. Chem. Phys. 59, 3856 (1973).
[CrossRef]

Kuhl, J.

An article reviewing tunable coherent light sources has been prepared by J. Kuhl and W. Schmidt, Appl. Phys. 3, 251 (1974).
[CrossRef]

Kwok, M. A.

S. W. Mayer, M. A. Kwok, R. W. F. Gross, and D. J. Spencer, Appl. Phys. Lett. 17, 516 (1970).
[CrossRef]

Letokhov, V. S.

R. V. Ambartsumyan, V. S. Letokhov, G. N. Makarov, and A. A. Puretskii, JETP Lett. 17, 63 (1973).

V. S. Letokhov, Science 180, 451 (1973).
[CrossRef] [PubMed]

R. V. Ambartsumyan, V. M. Apatin, and V. S. Letokhov, JETP Lett. 15, 237 (1972).

Makarov, G. N.

R. V. Ambartsumyan, V. S. Letokhov, G. N. Makarov, and A. A. Puretskii, JETP Lett. 17, 63 (1973).

Mayer, S. W.

S. W. Mayer, M. A. Kwok, R. W. F. Gross, and D. J. Spencer, Appl. Phys. Lett. 17, 516 (1970).
[CrossRef]

Mitchell, A. C. G.

A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. P., London, 1934).

Moore, C. B.

C. B. Moore, Accounts Chem. Res. 6, 323 (1973).
[CrossRef]

E. S. Yeung and C. B. Moore, Appl. Phys. Lett. 21, 109 (1972).
[CrossRef]

Ostrem, J.

This result has been exhibited by J. Ostrem and H. Gamo, Proc. IEEE 61, 1656 (1973).
[CrossRef]

Puretskii, A. A.

R. V. Ambartsumyan, V. S. Letokhov, G. N. Makarov, and A. A. Puretskii, JETP Lett. 17, 63 (1973).

Sackett, P. B.

A. Hordvik and P. B. Sackett, Appl. Optics 13, 1060 (1974).
[CrossRef]

Schiff, L. I.

L. I. Schiff, Quantum Mechanics (McGraw–Hill, New York, 1955), p. 250.

Schmidt, W.

An article reviewing tunable coherent light sources has been prepared by J. Kuhl and W. Schmidt, Appl. Phys. 3, 251 (1974).
[CrossRef]

Shen, Y. R.

N. Bloembergen and Y. R. Shen, Phys. Rev. 133, A37 (1964).
[CrossRef]

Spencer, D. J.

S. W. Mayer, M. A. Kwok, R. W. F. Gross, and D. J. Spencer, Appl. Phys. Lett. 17, 516 (1970).
[CrossRef]

Yeung, E. S.

E. S. Yeung and C. B. Moore, Appl. Phys. Lett. 21, 109 (1972).
[CrossRef]

Zemansky, M. W.

A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. P., London, 1934).

Accounts Chem. Res. (1)

C. B. Moore, Accounts Chem. Res. 6, 323 (1973).
[CrossRef]

Appl. Optics (1)

A. Hordvik and P. B. Sackett, Appl. Optics 13, 1060 (1974).
[CrossRef]

Appl. Phys. (1)

An article reviewing tunable coherent light sources has been prepared by J. Kuhl and W. Schmidt, Appl. Phys. 3, 251 (1974).
[CrossRef]

Appl. Phys. Lett. (2)

S. W. Mayer, M. A. Kwok, R. W. F. Gross, and D. J. Spencer, Appl. Phys. Lett. 17, 516 (1970).
[CrossRef]

E. S. Yeung and C. B. Moore, Appl. Phys. Lett. 21, 109 (1972).
[CrossRef]

J. Chem. Phys. (1)

S. H. Dworetsky and R. S. Hozack, J. Chem. Phys. 59, 3856 (1973).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transf. (1)

B. H. Armstrong, J. Quant. Spectrosc. Radiat. Transf. 7, 61 (1967).
[CrossRef]

JETP Lett. (2)

R. V. Ambartsumyan, V. S. Letokhov, G. N. Makarov, and A. A. Puretskii, JETP Lett. 17, 63 (1973).

R. V. Ambartsumyan, V. M. Apatin, and V. S. Letokhov, JETP Lett. 15, 237 (1972).

Phys. Rev. (1)

N. Bloembergen and Y. R. Shen, Phys. Rev. 133, A37 (1964).
[CrossRef]

Proc. IEEE (1)

This result has been exhibited by J. Ostrem and H. Gamo, Proc. IEEE 61, 1656 (1973).
[CrossRef]

Science (1)

V. S. Letokhov, Science 180, 451 (1973).
[CrossRef] [PubMed]

Other (5)

Dye Lasers—Topics in Applied Physics, Vol. 1, edited by F. P. Schaefer (Springer, New York, 1973), Ch. 5.

B. F. Fried and S. D. Conte, The Plasma Dispersion Function (Academic, New York, 1961).

L. I. Schiff, Quantum Mechanics (McGraw–Hill, New York, 1955), p. 250.

See Eq. (35.21) of Ref. 12, which contains an additional factor of 4π∊0because of the use of unrationalized cgs units.

A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. P., London, 1934).

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Equations (112)

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ρ ρ 22 ρ 11 ,
i ћ ρ ˙ = 2 μ E ( t ) [ ρ 12 e i ω 0 t ρ 21 e i ω 0 t ] + i ћ T 1 ( ρ ρ 0 ) , i ћ ρ ˙ 12 = μ E ( t ) ρ e i ω 0 t + i ћ T 2 ρ 12
ћ ω 0 W 2 W 1 > 0 ,
μ = μ 12 = μ 21
E ( t ) = E 0 cos ω t ,
ρ 12 = 1 2 μ E 0 e i ( ω ω 0 ) t ћ [ ω ω 0 i T 2 1 ] ρ ,
ρ = ρ 0 1 + L ( ω , ω 0 ) ( I / I s ) ,
L ( ω , ω 0 ) = [ 1 + ( ω ω 0 ) 2 ( T 2 ) 2 ] 1 ,
I = c 0 2 E 0 2 [ rationalized units ] ,
I s = c ћ 2 0 2 μ 2 T 1 T 2 ,
k ω = ω c Im χ ( ω ) .
P = N μ ρ 12 e i ω 0 t + ( complex conj . ) ,
χ ( ω ) = i N μ 2 ρ T 2 0 1 1 + i ( ω ω 0 ) T 2 ,
k ω = k 0 L ( ω , ω 0 ) 1 + L ( ω , ω 0 ) ( I / I s ) ,
k 0 = N ω μ 2 T 2 ( ρ 0 ) ћ c 0 .
I ( z ) = I ( 0 ) exp ( k ω z ) .
I = I ω d ω .
I ω ( z ) = I ω ( 0 ) exp ( k ω z ) ,
ρ = ρ 0 1 + L ( ω , ω 0 ) ( I ω / I s ) d ω
k ω = k 0 L ( ω , ω 0 ) 1 + L ( ω , ω 0 ) ( I ω / I s ) d ω .
L ( ω r , ω 0 ) L ( ω , ω 0 ) I ω d ω I ω d ω ,
k ω = k 0 L ( ω , ω 0 ) 1 + L · ( I / I s ) .
k = d I / d z I ,
I ( z ) = I ω ( z ) d ω ;
I ( z ) = I ω ( 0 ) exp ( k ω z ) d ω .
d I d z = I ω ( z ) k ω d ω 1 + z I ω ( z ) ( d k ω / d I ) d ω .
k = I ω k ω d ω I ω d ω .
k = k 0 L 1 + L · ( I / I s ) ,
lim L = I ω 0 I · π T 2 .
P ( t ) = 2 μ 2 I c 0 ћ 2 sin 2 1 2 ( ω ω 0 ) t ( ω ω 0 ) 2 .
w = π μ 2 I ω 0 ћ 2 c 0 .
k = N π μ 2 ω ћ c 0 · I ω 0 I .
g ( ω 0 ) T 2 * π exp [ ( ω 0 ω 0 ) 2 ( T 2 * ) 2 ] , g ( ω 0 ) d ω 0 = 1.
( Δ ω ) D = ( ln 2 ) 1 / 2 T 2 * .
k ¯ = k 0 d ω 0 g ( ω 0 ) L ( ω r , ω 0 ) 1 + L ( ω r , ω 0 ) ( I / I s )
ρ ¯ = ρ 0 d ω 0 g ( ω 0 ) 1 1 + L ( ω r , ω 0 ) ( I / I s )
I I s · k ¯ k 0 = 1 ρ ¯ ρ 0 .
ρ ¯ 22 = 1 + ρ 0 2 ρ 0 2 · I I s · k ¯ k 0 .
ρ ¯ 22 = 1 2 ( I I s · k ¯ k 0 ) .
( Δ ω ) L ( Δ ω ) D ( Δ ω ) R
I ω = I ω r exp [ ( ω r ω ) 2 T 0 2 ] .
( Δ ω ) R = ( ln 2 ) 1 / 2 T 0
I = I ω r T 0 π .
( Δ ω ) L ( Δ ω ) D or ( Δ ω ) R ( Δ ω ) D .
L ( ω r , ω 0 ) = 1 π exp ( u 2 ) d u 1 + [ ( u + δ ) / c ] 2 ,
δ ( ω r ω 0 ) T 0
c ( T 2 ) 1 / ( T 0 ) 1 .
L ( ω r , ω 0 ) = c Im Z ( δ + i c ) .
L ( ω r , ω 0 ) = F ( c ) G ( δ , c ) ,
F ( y ) = π y exp ( y 2 ) erfc ( y ) ,
G ( x , y ) = Im Z ( x + i y ) Im Z ( i y ) .
lim c 1 F ( c ) = 1.
lim c 1 F ( c ) = π c .
lim δ 1 L ( ω 0 , ω r ) = ( 1 + Δ 2 ) 1 ,
Δ ( ω r ω 0 ) T 2 = δ / c .
lim c 1 L ( ω r , ω 0 ) = ( 1 + Δ 2 ) 1 .
L ( ω r , ω 0 ) = ( 1 + Δ 2 ) 1 ,
k = k 0 [ 1 + Δ 2 + I / I s ] 1 .
lim c 1 ( ω r , ω 0 ) = π c exp ( δ 2 ) .
k = k 0 π c exp ( δ 2 ) .
( Δ ω ) D ( Δ ω ) L and ( Δ ω ) D ( Δ ω ) R .
k ¯ = k 0 π 1 / 2 κ 1 exp ( θ 2 ) J ( I , c ) ,
κ ( T 2 * ) 1 / ( T 0 ) 1 ,
θ ( ω r , ω 0 ) T 2 * ,
J ( I , c ) = d u · c Im Z ( u + i c ) 1 + c ( I / I s ) Im Z ( u + i c ) ,
L ( ω r , ω 0 ) = c Im Z ( u + i c ) .
lim c 1 Im Z ( u + i c ) = c 2 u 2 + c 2 ,
lim c 1 J ( I , c ) = c π / t ,
t ( 1 + I / I s ) 1 / 2 ,
lim c 1 k ¯ = k 0 π a t 1 exp ( θ 2 ) ,
a ( T 2 ) 1 / ( T 2 * ) 1 = c κ 1 .
lim c 1 Im Z ( u + i c ) = π 1 / 2 exp ( u 2 ) .
lim c 1 J ( I , c ) = π c ,
lim κ 1 k ¯ = k 0 π 1 / 2 a exp ( θ 2 ) .
k ¯ = k 0 a t 1 Im Z ( θ + i a t ) .
lim a 1 Im Z ( θ + i a t ) = a t θ 2 + a 2 t 2 ,
lim a 1 k ¯ = k 0 Δ 2 + t 2 .
lim a 1 Im Z ( θ + i a t ) = π 1 / 2 exp ( θ 2 ) ,
lim a 1 k ¯ = k 0 π 1 / 2 a t 1 exp ( θ 2 ) ,
lim c 1 k ¯ = k 0 c ( π 1 + κ 2 ) 1 / 2 exp ( κ 2 θ 2 1 + κ 2 ) .
lim κ 1 k ¯ = k 0 c π 1 / 2 exp ( δ 2 ) .
lim κ 1 k ¯ = k 0 π 1 / 2 a exp ( θ 2 ) .
I ω = I ω r [ 1 + ( ω ω r ) 2 T 0 2 ] 1 ,
L ( ω r , ω 0 ) = γ [ 1 + Δ 1 2 ] 1 ,
γ T 2 1 T 2 1 + T 0 1 ,
Δ 1 ω r ω 0 T 2 1 + T 0 1 .
k = k 0 γ s 2 + Δ 1 2 ,
s 2 1 + γ ( I / I s ) .
k ¯ = k 0 a s 1 Im Z ( θ + i b s ) ,
b T 2 1 + T 0 1 ( T 2 * ) 1 .
lim b 1 k ¯ = k 0 π 1 / 2 a s 1 exp ( θ 2 ) .
lim γ 1 k ¯ = k 0 a t 1 Im Z ( θ + i a t ) ,
lim γ 1 k ¯ = k 0 a Im Z ( θ + i κ 1 ) .
lim γ 1 κ 1 k ¯ = k 0 a π 1 / 2 exp ( θ 2 ) ,
( Δ ω ) R 2 ( 2 θ 2 1 ) ( Δ ω ) D 2 ,
Z ( ζ ) = 2 i exp ( ζ 2 ) i ζ exp ( t 2 ) d t ,
Z ( ζ ) = i π exp ( ζ 2 ) [ 1 + erf ( i ζ ) ] ,
erf ( z ) = 2 π 1 / 2 0 z exp ( t 2 ) d t .
Z ( ζ ) = 1 π d u exp ( u 2 ) u ζ = ζ π d u exp ( u 2 ) u 2 ζ 2 .
Z ( ζ ) ζ 1 [ 1 + 1 / 2 ζ 2 + 3 / 4 ζ 4 + ] .
Re Z ( x , y ) = Re Z ( x , y ) , Im Z ( x , y ) = Im Z ( x , y ) .
Z ( x ) = i π exp ( x 2 ) 2 exp ( x 2 ) 0 x exp ( t 2 ) d t .
Z ( i y ) = i π exp ( y 2 ) [ 1 erf ( y ) ] ,
Z ( ζ ) = i π exp ( ζ 2 ) 2 ζ [ 1 2 ζ 2 / 3 + 4 ζ 4 / 15 8 ζ 6 / 105 + ] .
Im Z ( x , y ) = y π d u exp ( u 2 ) ( u x ) 2 + y 2 .
Im Z ( 0 , y ) = y π d u exp ( u 2 ) u 2 + y 2 = π exp ( y 2 ) [ 1 erf ( y ) ] .
Im Z ( ζ ) = π Re [ exp ( ζ 2 ) erfc ( i ζ ) ] ,
erfc ( z ) = 1 erf ( z ) .
Im Z ( x + i y ) = π exp ( x 2 ) [ cos 2 x y · exp ( y 2 ) erfc ( y ) + 2 π 1 / 2 0 x exp ( t 2 ) sin 2 y ( x t ) d t ] .
K ( x , y ) = y π exp ( t 2 ) d t y 2 + ( x t ) 2 .
Im Z ( x , y ) = π K ( x , y ) .
K ( x , y ) = 1 π 0 exp ( t y t 2 / 4 ) cos ( t x ) d t .