Abstract

Application of two-photon selective excitation to isotope separation with high power, high resolution tunable lasers is discussed. A simple kinetic model is given to determine quantum efficiency and separation factor in terms of laser powers and relaxation constants. A numerical example is used to demonstrate the feasibility of the scheme. Results indicate that a high quantum yield is obtainable with the optical technique.

© 1974 Optical Society of America

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References

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  1. A. Mooradian, Am. Phys. Soc. Bull. 18, 1504 (1973).
  2. J. L. Hall, Am. Phys. Soc. Bull. 18, 1504 (1973).
  3. C. B. Moore, Ann. Rev. Phys. Chem. 21, 387 (1971).
    [CrossRef]
  4. V. S. Letokhov, Science 180, 451 (1973).
    [CrossRef] [PubMed]
  5. A. N. Oraevsky, Plenary Lectures, Second General Conference, European Physical Society, Germany (1972).
  6. R. J. Gordon, M. C. Lin, Chem. Phys. Lett. 22, 262 (1973).
    [CrossRef]
  7. N. G. Basov, E. P. Mavkin, A. N. Oraevsky, A. B. Pankratov, A. N. Skachkov, JETP Lett. 14, 165 (1971).
  8. S. W. Mayer, M. A. Kwock, R. W. F. Gross, Appl. Phys. Lett. 17, 516 (1970).
    [CrossRef]
  9. R. V. Ambartzumian, V. S. Letokhov, Chem. Phys. Lett. 13, 446 (1972).
    [CrossRef]
  10. V. S. Letokhov, Chem. Phys. Lett. 15, 221 (1972).
    [CrossRef]
  11. R. V. Ambartzumian, V. S. Letokhov, Appl. Opt. 11, 354 (1972).
    [CrossRef] [PubMed]
  12. R. V. Ambartzumian, V. M. Apatin, V. S. Letokhov, JETP 15, 237 (1972).

1973 (4)

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

R. J. Gordon, M. C. Lin, Chem. Phys. Lett. 22, 262 (1973).
[CrossRef]

A. Mooradian, Am. Phys. Soc. Bull. 18, 1504 (1973).

J. L. Hall, Am. Phys. Soc. Bull. 18, 1504 (1973).

1972 (4)

R. V. Ambartzumian, V. S. Letokhov, Chem. Phys. Lett. 13, 446 (1972).
[CrossRef]

V. S. Letokhov, Chem. Phys. Lett. 15, 221 (1972).
[CrossRef]

R. V. Ambartzumian, V. S. Letokhov, Appl. Opt. 11, 354 (1972).
[CrossRef] [PubMed]

R. V. Ambartzumian, V. M. Apatin, V. S. Letokhov, JETP 15, 237 (1972).

1971 (2)

N. G. Basov, E. P. Mavkin, A. N. Oraevsky, A. B. Pankratov, A. N. Skachkov, JETP Lett. 14, 165 (1971).

C. B. Moore, Ann. Rev. Phys. Chem. 21, 387 (1971).
[CrossRef]

1970 (1)

S. W. Mayer, M. A. Kwock, R. W. F. Gross, Appl. Phys. Lett. 17, 516 (1970).
[CrossRef]

Ambartzumian, R. V.

R. V. Ambartzumian, V. S. Letokhov, Chem. Phys. Lett. 13, 446 (1972).
[CrossRef]

R. V. Ambartzumian, V. S. Letokhov, Appl. Opt. 11, 354 (1972).
[CrossRef] [PubMed]

R. V. Ambartzumian, V. M. Apatin, V. S. Letokhov, JETP 15, 237 (1972).

Apatin, V. M.

R. V. Ambartzumian, V. M. Apatin, V. S. Letokhov, JETP 15, 237 (1972).

Basov, N. G.

N. G. Basov, E. P. Mavkin, A. N. Oraevsky, A. B. Pankratov, A. N. Skachkov, JETP Lett. 14, 165 (1971).

Gordon, R. J.

R. J. Gordon, M. C. Lin, Chem. Phys. Lett. 22, 262 (1973).
[CrossRef]

Gross, R. W. F.

S. W. Mayer, M. A. Kwock, R. W. F. Gross, Appl. Phys. Lett. 17, 516 (1970).
[CrossRef]

Hall, J. L.

J. L. Hall, Am. Phys. Soc. Bull. 18, 1504 (1973).

Kwock, M. A.

S. W. Mayer, M. A. Kwock, R. W. F. Gross, Appl. Phys. Lett. 17, 516 (1970).
[CrossRef]

Letokhov, V. S.

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

R. V. Ambartzumian, V. S. Letokhov, Chem. Phys. Lett. 13, 446 (1972).
[CrossRef]

V. S. Letokhov, Chem. Phys. Lett. 15, 221 (1972).
[CrossRef]

R. V. Ambartzumian, V. M. Apatin, V. S. Letokhov, JETP 15, 237 (1972).

R. V. Ambartzumian, V. S. Letokhov, Appl. Opt. 11, 354 (1972).
[CrossRef] [PubMed]

Lin, M. C.

R. J. Gordon, M. C. Lin, Chem. Phys. Lett. 22, 262 (1973).
[CrossRef]

Mavkin, E. P.

N. G. Basov, E. P. Mavkin, A. N. Oraevsky, A. B. Pankratov, A. N. Skachkov, JETP Lett. 14, 165 (1971).

Mayer, S. W.

S. W. Mayer, M. A. Kwock, R. W. F. Gross, Appl. Phys. Lett. 17, 516 (1970).
[CrossRef]

Mooradian, A.

A. Mooradian, Am. Phys. Soc. Bull. 18, 1504 (1973).

Moore, C. B.

C. B. Moore, Ann. Rev. Phys. Chem. 21, 387 (1971).
[CrossRef]

Oraevsky, A. N.

N. G. Basov, E. P. Mavkin, A. N. Oraevsky, A. B. Pankratov, A. N. Skachkov, JETP Lett. 14, 165 (1971).

A. N. Oraevsky, Plenary Lectures, Second General Conference, European Physical Society, Germany (1972).

Pankratov, A. B.

N. G. Basov, E. P. Mavkin, A. N. Oraevsky, A. B. Pankratov, A. N. Skachkov, JETP Lett. 14, 165 (1971).

Skachkov, A. N.

N. G. Basov, E. P. Mavkin, A. N. Oraevsky, A. B. Pankratov, A. N. Skachkov, JETP Lett. 14, 165 (1971).

Am. Phys. Soc. Bull. (2)

A. Mooradian, Am. Phys. Soc. Bull. 18, 1504 (1973).

J. L. Hall, Am. Phys. Soc. Bull. 18, 1504 (1973).

Ann. Rev. Phys. Chem. (1)

C. B. Moore, Ann. Rev. Phys. Chem. 21, 387 (1971).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. W. Mayer, M. A. Kwock, R. W. F. Gross, Appl. Phys. Lett. 17, 516 (1970).
[CrossRef]

Chem. Phys. Lett. (3)

R. V. Ambartzumian, V. S. Letokhov, Chem. Phys. Lett. 13, 446 (1972).
[CrossRef]

V. S. Letokhov, Chem. Phys. Lett. 15, 221 (1972).
[CrossRef]

R. J. Gordon, M. C. Lin, Chem. Phys. Lett. 22, 262 (1973).
[CrossRef]

JETP (1)

R. V. Ambartzumian, V. M. Apatin, V. S. Letokhov, JETP 15, 237 (1972).

JETP Lett. (1)

N. G. Basov, E. P. Mavkin, A. N. Oraevsky, A. B. Pankratov, A. N. Skachkov, JETP Lett. 14, 165 (1971).

Science (1)

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

Other (1)

A. N. Oraevsky, Plenary Lectures, Second General Conference, European Physical Society, Germany (1972).

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Figures (9)

Fig. 1
Fig. 1

One-dimensional energy surfaces for molecules ABC, AB + C, and A + BC.

Fig. 2
Fig. 2

A schematic diagram of two-photon selective photodissociation and photopredissociation of a molecule.

Fig. 3
Fig. 3

A three-level system illustrating a two-photon selective excitation scheme and competing thermalization processes such as spontaneous decay, collisional deactivation, and resonant energy transfer.

Fig. 4
Fig. 4

Energy diagram of HCl.

Fig. 5
Fig. 5

The quantum efficiency η and the separation factor ξ plotted as a function of time in a medium loss situation. Laser intensity I1 = 1 kW/cm2 and I2 = 10 W/cm2 (——); 103 W/cm2 (– – –) and 105 W/cm2 (– · –). τ2 = 10−3 sec, τ3 = 10−3 sec.

Fig. 6
Fig. 6

The quantum efficiency η and the separation factor ξ plotted as a function of time. Parameters are the same as those in Fig. 5 except τ2 = 10−5 sec.

Fig. 7
Fig. 7

(a)Time evolution of molecular populations in levels 1 and 2 is shown to illustrate explicitly the saturation effect. (b)A case showing that the separation factor is enhanced at the expense of the quantum efficiency as a result of an increase of the relaxation rate in the intermediate level.

Fig. 8
Fig. 8

In a high loss case, both quantum efficiency and separation factor are low and strongly peaked in time.

Fig. 9
Fig. 9

(a)A best utilization of laser radiation to obtain both a high quantum efficiency and a high separation factor is shown. (b)A less desirable case is shown with a low quantum yield.

Equations (22)

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A * τ s A + ћ ω ;
A * + M τ c A + M ;
A * + B τ υ A + B * ;
( / t ) N 1 = ( N 2 N 1 ) W 1 ,
( / t ) N 2 = ( N 2 / τ 2 ) ( N 2 N 1 ) W 1 N 2 W 2 ,
( / t ) N 3 = W 2 N 2 ( 1 / τ 3 ) N 3 ,
W i = ( σ i I i / ћ ω ) = σ i c N P i ,
N ( t ) = 0 N p exp ( P t ) d P ,
N 1 = N 0 , N 2 = 0 , N 3 = 0 .
| P + W 1 W 1 W 1 P + ( 1 / τ 2 ) + W 1 + W 2 | = 0.
P 1,2 = ( a + b ) ± ( a 2 + b 2 ) 1 / 2 ,
a W 1 b 1 2 ( W 2 + 1 / τ 2 ) .
N 1 ( t ) = N 0 / ( P 1 P 2 ) [ ( W 1 P 2 ) exp ( P 1 t ) + ( P 1 W 1 ) exp ( P 2 t ) ] ,
N 2 ( t ) = N 0 W 1 / ( P 1 P 2 ) × [ exp ( P 1 t ) exp ( P 2 t ) ] .
N 3 ( t ) = N 0 W 1 W 2 τ 3 / ( P 2 P 1 ) × ( { [ exp ( P 1 t ) exp ( t / τ 3 ) ] / ( 1 P 1 τ 3 ) } { [ exp ( P 2 t ) exp ( t / τ 3 ) ] / ( 1 P 2 τ 3 ) } ) .
N ˜ 1 ( T ) = N 1 ( t ) / N 0 , N ˜ 2 ( T ) = N 2 ( t ) / N 0 , N ˜ 3 ( T ) = N 3 ( t ) / N 0 , P ˜ 1 = P 1 / W 1 , P ˜ 2 = P 2 / W 1 , τ ˜ 2 = W 1 τ 2 , τ ˜ 3 = W 1 τ 3 , T = W 1 t .
N ˜ 1 ( T ) = 1 / ( P ˜ 1 P ˜ 2 ) [ ( 1 P ˜ 2 ) exp ( P ˜ 1 T ) + ( P ˜ 1 1 ) exp ( P ˜ 2 T ) ] ,
N ˜ 2 ( T ) = 1 / ( P ˜ 1 P ˜ 2 ) [ exp ( P ˜ 2 T ) exp ( P ˜ 1 T ) ] ,
N ˜ 3 ( T ) = W ˜ 2 τ ˜ 3 / ( P ˜ 1 P ˜ 2 ) × ( { [ exp ( P ˜ 2 T ) exp ( T / τ ˜ 3 ) ] / ( 1 P ˜ 2 τ ˜ 3 ) } { [ exp ( P ˜ 1 T ) exp ( T / τ ˜ 3 ) ] / ( 1 P ˜ 1 τ ˜ 3 ) } ) .
ξ ( T ) N ˜ 3 ( T ) = N 3 ( t ) / N 0
η total number of isotopes produced in the final state total number of photons absorbed
η ( T ) = P ˜ 1 P ˜ 2 W ˜ 2 τ ˜ 3 × ( { [ exp ( P ˜ 2 T ) exp ( T / τ ˜ 3 ) ] / ( 1 P ˜ 2 τ ˜ 3 ) } { [ exp ( P ˜ 1 T ) exp ( T / τ ˜ 3 ) ] / ( 1 P ˜ 1 τ ˜ 3 ) } ) / { P ˜ 2 ( P ˜ 2 + W ˜ 2 ) [ exp ( P ˜ 1 T ) 1 ] P ˜ 1 ( P ˜ 1 + W ˜ 1 ) [ exp ( P ˜ 2 T ) 1 ] } .

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