Abstract

The theory relating measurements to two-photon absorption cross sections to generated four-wave mixing signals is developed. It is shown that these cross sections can be measured relative to a reference signal. This work is applicable to measurements in other diatomic and polyatomic molecules.

© 1985 Optical Society of America

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References

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  1. M. D. Levenson and N. Bloembergen, J. Chem. Phys. 60, 1323 (1974).
    [Crossref]
  2. M. D. Levenson, IEEE J. Quantum Electron. QE-10, 110 (1974).
    [Crossref]
  3. H. Lotem, R. T. Lynch, and N. Bloembergen, Phys. Rev. A 14, 1748 (1976).
    [Crossref]
  4. R. M. Hochstrasser, G. R. Meredith, and H. P. Trommsdorf, Chem. Phys. Lett. 53, 423 (1978).
    [Crossref]
  5. J. Burris and T. J. McIlrath, “Experimental method for the determination of two-photon cross sections using four-wave mixing,” J. Opt. Soc. Am. B 2, 1307–1312 (1985).
    [Crossref]
  6. T. J. McIlrath, R. Hudson, A. Aikin, and T. D. Wilkerson, Institute for Physical Science and Technology Tech. Note BN-856 (University of Maryland, College Park, Md., June1977).
  7. R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1973).
  8. C. C. Wang, Phys. Rev. 152, 149 (1966).
    [Crossref]
  9. J. Burris, Ph.D. dissertation (Department of Physics, University of Maryland, College Park, Md., 1982).
  10. P. N. Butcher, Nonlinear Optical Phenomena, Bull. 200 (Engineering Experimental Station, Ohio State University, Columbus, Ohio, 1965).
  11. D. C. Hanna, M. A. Yuratich, and D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, New York, 1979).
    [Crossref]
  12. A. Weber, ed., Raman Spectroscopy of Gases and Liquids (Springer-Verlag, New York, 1979), Chap. VII.
    [Crossref]
  13. G. C. Bjorklund, IEEE J. Quantum Electron. QE-11, 287 (1975).
    [Crossref]
  14. Y. M. Yiu, T. J. McIlrath, and R. Mahon, Phys. Rev. A 20, 2470 (1979).
    [Crossref]
  15. J. B. Halpern, H. Zacharias, and R. Wallenstein, J. Mol. Spectrosc. 79, 1 (1980).
    [Crossref]

1985 (1)

1980 (1)

J. B. Halpern, H. Zacharias, and R. Wallenstein, J. Mol. Spectrosc. 79, 1 (1980).
[Crossref]

1979 (1)

Y. M. Yiu, T. J. McIlrath, and R. Mahon, Phys. Rev. A 20, 2470 (1979).
[Crossref]

1978 (1)

R. M. Hochstrasser, G. R. Meredith, and H. P. Trommsdorf, Chem. Phys. Lett. 53, 423 (1978).
[Crossref]

1976 (1)

H. Lotem, R. T. Lynch, and N. Bloembergen, Phys. Rev. A 14, 1748 (1976).
[Crossref]

1975 (1)

G. C. Bjorklund, IEEE J. Quantum Electron. QE-11, 287 (1975).
[Crossref]

1974 (2)

M. D. Levenson and N. Bloembergen, J. Chem. Phys. 60, 1323 (1974).
[Crossref]

M. D. Levenson, IEEE J. Quantum Electron. QE-10, 110 (1974).
[Crossref]

1966 (1)

C. C. Wang, Phys. Rev. 152, 149 (1966).
[Crossref]

Aikin, A.

T. J. McIlrath, R. Hudson, A. Aikin, and T. D. Wilkerson, Institute for Physical Science and Technology Tech. Note BN-856 (University of Maryland, College Park, Md., June1977).

Bjorklund, G. C.

G. C. Bjorklund, IEEE J. Quantum Electron. QE-11, 287 (1975).
[Crossref]

Bloembergen, N.

H. Lotem, R. T. Lynch, and N. Bloembergen, Phys. Rev. A 14, 1748 (1976).
[Crossref]

M. D. Levenson and N. Bloembergen, J. Chem. Phys. 60, 1323 (1974).
[Crossref]

Burris, J.

Butcher, P. N.

P. N. Butcher, Nonlinear Optical Phenomena, Bull. 200 (Engineering Experimental Station, Ohio State University, Columbus, Ohio, 1965).

Cotter, D.

D. C. Hanna, M. A. Yuratich, and D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, New York, 1979).
[Crossref]

Halpern, J. B.

J. B. Halpern, H. Zacharias, and R. Wallenstein, J. Mol. Spectrosc. 79, 1 (1980).
[Crossref]

Hanna, D. C.

D. C. Hanna, M. A. Yuratich, and D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, New York, 1979).
[Crossref]

Hochstrasser, R. M.

R. M. Hochstrasser, G. R. Meredith, and H. P. Trommsdorf, Chem. Phys. Lett. 53, 423 (1978).
[Crossref]

Hudson, R.

T. J. McIlrath, R. Hudson, A. Aikin, and T. D. Wilkerson, Institute for Physical Science and Technology Tech. Note BN-856 (University of Maryland, College Park, Md., June1977).

Levenson, M. D.

M. D. Levenson, IEEE J. Quantum Electron. QE-10, 110 (1974).
[Crossref]

M. D. Levenson and N. Bloembergen, J. Chem. Phys. 60, 1323 (1974).
[Crossref]

Lotem, H.

H. Lotem, R. T. Lynch, and N. Bloembergen, Phys. Rev. A 14, 1748 (1976).
[Crossref]

Loudon, R.

R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1973).

Lynch, R. T.

H. Lotem, R. T. Lynch, and N. Bloembergen, Phys. Rev. A 14, 1748 (1976).
[Crossref]

Mahon, R.

Y. M. Yiu, T. J. McIlrath, and R. Mahon, Phys. Rev. A 20, 2470 (1979).
[Crossref]

McIlrath, T. J.

J. Burris and T. J. McIlrath, “Experimental method for the determination of two-photon cross sections using four-wave mixing,” J. Opt. Soc. Am. B 2, 1307–1312 (1985).
[Crossref]

Y. M. Yiu, T. J. McIlrath, and R. Mahon, Phys. Rev. A 20, 2470 (1979).
[Crossref]

T. J. McIlrath, R. Hudson, A. Aikin, and T. D. Wilkerson, Institute for Physical Science and Technology Tech. Note BN-856 (University of Maryland, College Park, Md., June1977).

Meredith, G. R.

R. M. Hochstrasser, G. R. Meredith, and H. P. Trommsdorf, Chem. Phys. Lett. 53, 423 (1978).
[Crossref]

Trommsdorf, H. P.

R. M. Hochstrasser, G. R. Meredith, and H. P. Trommsdorf, Chem. Phys. Lett. 53, 423 (1978).
[Crossref]

Wallenstein, R.

J. B. Halpern, H. Zacharias, and R. Wallenstein, J. Mol. Spectrosc. 79, 1 (1980).
[Crossref]

Wang, C. C.

C. C. Wang, Phys. Rev. 152, 149 (1966).
[Crossref]

Wilkerson, T. D.

T. J. McIlrath, R. Hudson, A. Aikin, and T. D. Wilkerson, Institute for Physical Science and Technology Tech. Note BN-856 (University of Maryland, College Park, Md., June1977).

Yiu, Y. M.

Y. M. Yiu, T. J. McIlrath, and R. Mahon, Phys. Rev. A 20, 2470 (1979).
[Crossref]

Yuratich, M. A.

D. C. Hanna, M. A. Yuratich, and D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, New York, 1979).
[Crossref]

Zacharias, H.

J. B. Halpern, H. Zacharias, and R. Wallenstein, J. Mol. Spectrosc. 79, 1 (1980).
[Crossref]

Chem. Phys. Lett. (1)

R. M. Hochstrasser, G. R. Meredith, and H. P. Trommsdorf, Chem. Phys. Lett. 53, 423 (1978).
[Crossref]

IEEE J. Quantum Electron. (2)

M. D. Levenson, IEEE J. Quantum Electron. QE-10, 110 (1974).
[Crossref]

G. C. Bjorklund, IEEE J. Quantum Electron. QE-11, 287 (1975).
[Crossref]

J. Chem. Phys. (1)

M. D. Levenson and N. Bloembergen, J. Chem. Phys. 60, 1323 (1974).
[Crossref]

J. Mol. Spectrosc. (1)

J. B. Halpern, H. Zacharias, and R. Wallenstein, J. Mol. Spectrosc. 79, 1 (1980).
[Crossref]

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

Phys. Rev. (1)

C. C. Wang, Phys. Rev. 152, 149 (1966).
[Crossref]

Phys. Rev. A (2)

Y. M. Yiu, T. J. McIlrath, and R. Mahon, Phys. Rev. A 20, 2470 (1979).
[Crossref]

H. Lotem, R. T. Lynch, and N. Bloembergen, Phys. Rev. A 14, 1748 (1976).
[Crossref]

Other (6)

J. Burris, Ph.D. dissertation (Department of Physics, University of Maryland, College Park, Md., 1982).

P. N. Butcher, Nonlinear Optical Phenomena, Bull. 200 (Engineering Experimental Station, Ohio State University, Columbus, Ohio, 1965).

D. C. Hanna, M. A. Yuratich, and D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, New York, 1979).
[Crossref]

A. Weber, ed., Raman Spectroscopy of Gases and Liquids (Springer-Verlag, New York, 1979), Chap. VII.
[Crossref]

T. J. McIlrath, R. Hudson, A. Aikin, and T. D. Wilkerson, Institute for Physical Science and Technology Tech. Note BN-856 (University of Maryland, College Park, Md., June1977).

R. Loudon, The Quantum Theory of Light (Clarendon, Oxford, 1973).

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Equations (36)

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d I d z = - [ α + β I G ( 2 ) ] I ,
R = σ ( 2 ) n 2 G ( 2 ) ( Ref .6 )
β = 2 N σ ( 2 ) ω ,
k 2 c 2 ω 2 = 1 + 4 π χ ,
k c ω = η + i κ
η 2 - κ 2 = 1 + 4 π Re [ χ ( 1 ) + χ ( 3 ) E 2 + ]
2 η κ = 4 π Im [ χ ( 1 ) + χ ( 3 ) E 2 + ] ,
χ = χ ( 1 ) + χ ( 2 ) E + χ ( 3 ) E 2 +
Re χ ( 1 ) Re χ ( 3 ) E 2 ,
κ = 4 π 2 Im χ ( 3 ) η 1 2 c ,
K = 2 ω c κ = 8 π 2 ω 1 I η 1 2 c 2 Im χ ( 3 ) .
β = K / I ,
β = 8 π 2 ω 1 Im χ ( 3 ) η 1 2 c 2 .
σ ( 2 ) = 4 π 2 ω 1 2 Im χ ( 3 ) η 1 2 c 2 ( Ref .9 ) ,
Re χ ( 1 ) 2 π I η 1 c Re χ ( 3 ) ,
ρ i = χ i j ( 1 ) E j + χ i j k ( 2 ) E j E k + χ i j k l ( 3 ) E j E k E l + ,
J 4 = ( 1.58 × 10 - 4 ) k 0 4 k 1 2 k 2 k 4 2 k N 2 χ 2 J 1 2 J 2 F 2 W ,
F 2 = 8 9 k 4 2 k π 3 k 0 4 1 b 3 χ 2 E 1 2 E 2 2 0 ( 2 π R ) E 4 2 d R ,
k 0 = 2 π λ 4 ,             k i = 2 π η i λ i ,
k ¯ = 2 k ¯ 1 - k ¯ 2 ,
I 4 ω I CARS = G ( 2 ) N NO 2 F 2 χ ( 3 ) 4 ω 2 G ( 2 ) N N 2 2 F 2 χ CARS ( 3 ) 2 = N NO 2 χ 4 ω ( 3 ) 2 N N 2 2 χ CARS ( 3 ) 2 .
( d σ d Ω ) R = 4 ω 2 4 n 2 Γ Im χ peak ( 3 ) c 4 η 1 N             ( Ref .12 ) ,
χ CARS ( 3 ) = η 1 c 4 N 2 η 2 ω 2 4 ( d σ d Ω ) R 1 [ ω J - ( ω 1 - ω 2 ) - i Γ J / 2 ]
χ 4 ω ( 3 ) 2 = I 4 ω I CARS N N 2 2 N NO 2 | η 1 c 4 2 η 2 ω 2 4 × ( d σ d Ω ) R 1 ω J - ( ω 1 - ω 2 ) - i Γ / 2 | 2 = I 4 ω I CARS N N 2 2 N NO 2 ( η 1 c 4 2 η 2 ω 2 4 ) 2 ( d σ d Ω ) R 2 × | J P J ω J - ( ω 1 - ω 2 ) - i Γ J / 2 | 2
χ ( 3 ) ( - ω 1 ; ω 1 , ω 1 , - ω 1 ) ,
χ ( 3 ) ( - ω 4 ; ω 1 , ω 1 , - ω 2 ) ,
2 ω 1 - ω 2 - ω J ω 1 - ω J .
χ ( 3 ) ( - χ 1 ; ω 1 , ω 1 - ω 1 ) 2 = I 4 ω I CARS N N 2 2 N NO 2 ( η 1 c 4 2 η 2 ω 2 4 ) 2 ( d σ d Ω ) R 2 × | J P J ω J - ( ω 1 - ω 2 ) - i Γ J / 2 | 2 ( 2 ω 1 - ω 2 - ω J ω 1 - ω J ) 2 .
χ ( 3 ) = J E V R J ω J - 2 ω 1 - i Γ J / 2 ,
χ ( 3 ) 2 = E 2 V 2 ( J R J P J ω J - 2 ω 1 - i Γ J / 2 ) 2 = I 4 ω I CARS N N 2 2 N NO 2 ( η 1 c 4 2 η 2 ω 2 4 ) 2 ( d σ d Ω ) R 2 × | J P J ω J - ( ω 1 - ω 2 ) - i Γ J / 2 | 2 × ( 2 ω 1 - ω 2 - ω J ω 1 - ω J ) 2 ,
σ ( 2 ) = 4 π 2 ω 1 2 Im χ ( 3 ) ( - ω 1 ; ω 1 , ω 1 - ω 1 ) c 2 η 1 2
σ ( 2 ) = 8 π 3 e 4 ω 1 2 2 c 2 η 1 2 g ( 2 ω 1 - ω f ) M μ l 2
σ 0 = 8 π 2 e 4 ω 1 2 2 c 2 η 1 2 M μ l 2 .
I 4 ω d ω = G ( 2 ) N NO 2 F 2 χ 4 ω ( 3 ) 2 d ω
I CARS d ω = G ( 2 ) N N 2 2 F 2 χ CARS 2 d ω ,
E 2 V 2 ( J R J P J ω J - ω - i Γ J / 2 ) 2 d ω = I 4 ω d ω I CARS d ω N N 2 2 N NO 2 ( η 1 c 4 2 η 2 ω 2 4 ) 2 ( d σ d Ω ) R 2 × ( 2 ω 1 - ω 2 - ω J ω 1 - ω J ) 2 × | J P J ω J - ( ω 1 - ω 2 ) - i Γ J / 2 | 2 d ω ,

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