Abstract

The third-order nonlinear susceptibility responsible for laser-induced birefringence and dichroism is calculated for atomic resonance lines with arbitrary values of total angular momentum J. Several types of polarization spectroscopy are interpreted in terms of this nonlinear susceptibility.

© 1978 Optical Society of America

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References

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  1. P. D. Maker and R. W. Terhune, “Study of Optical Effects due to an Induced Polarization Third Order in the Electric Field Strength,” Phys. Rev. A 137, 801 (1965); C. C. Wang, “Self-Focusing of Optical Beams in Liquids,” Phys. Rev. 152, 149 (1966).
    [Crossref]
  2. D. Heiman, R. W. Hellwarth, M. D. Levenson, and G. Martin, “Raman-Induced Kerr Effect,” Phys. Rev. Lett. 36, 189 (1976); M. D. Levenson and J. J. Song, “Raman-Induced Kerr Effect with Elliptical Polarization,” J. Opt. Soc. Am. 66, 641 (1976).
    [Crossref]
  3. C. Wieman and T. W. Hänsch, “Doppler-Free Laser Polarization Spectroscopy,” Phys. Rev. Lett. 36, 1170 (1976); R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser Polarization Spectroscopy,” SPIE J. 113, 80 (1977).
    [Crossref]
  4. M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974).
  5. A. Dienes, “Theory of Nonlinear Effects in a Gas Laser Amplifier. I. Weak Signals,” Phys. Rev. 174, 400 (1968).
    [Crossref]
  6. J.-C. Keller and C. Delsart, “Observation of Doppler-Free Laser Induced Birefringence using Interferences of Polarized Light,” Opt. Commun. 20, 147 (1977); “Doppler-Free Laser-Induced Dichroism and Birefringence,” in Laser Spectroscopy III, edited by J. L. Hall and J. L. Carlsten (Springer-Verlag, Berlin, 1977).
    [Crossref]
  7. S. Saikan, “J-Dependence of Intensity-Dependent Polarization Change,” Appl. Phys. (to be published).
  8. T. Hänsch and P. Toshek, “Theory of a Three-Level Gas Laser Amplifier,” Z. Phys. 236, 213 (1970).
    [Crossref]

1977 (1)

J.-C. Keller and C. Delsart, “Observation of Doppler-Free Laser Induced Birefringence using Interferences of Polarized Light,” Opt. Commun. 20, 147 (1977); “Doppler-Free Laser-Induced Dichroism and Birefringence,” in Laser Spectroscopy III, edited by J. L. Hall and J. L. Carlsten (Springer-Verlag, Berlin, 1977).
[Crossref]

1976 (2)

D. Heiman, R. W. Hellwarth, M. D. Levenson, and G. Martin, “Raman-Induced Kerr Effect,” Phys. Rev. Lett. 36, 189 (1976); M. D. Levenson and J. J. Song, “Raman-Induced Kerr Effect with Elliptical Polarization,” J. Opt. Soc. Am. 66, 641 (1976).
[Crossref]

C. Wieman and T. W. Hänsch, “Doppler-Free Laser Polarization Spectroscopy,” Phys. Rev. Lett. 36, 1170 (1976); R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser Polarization Spectroscopy,” SPIE J. 113, 80 (1977).
[Crossref]

1970 (1)

T. Hänsch and P. Toshek, “Theory of a Three-Level Gas Laser Amplifier,” Z. Phys. 236, 213 (1970).
[Crossref]

1968 (1)

A. Dienes, “Theory of Nonlinear Effects in a Gas Laser Amplifier. I. Weak Signals,” Phys. Rev. 174, 400 (1968).
[Crossref]

1965 (1)

P. D. Maker and R. W. Terhune, “Study of Optical Effects due to an Induced Polarization Third Order in the Electric Field Strength,” Phys. Rev. A 137, 801 (1965); C. C. Wang, “Self-Focusing of Optical Beams in Liquids,” Phys. Rev. 152, 149 (1966).
[Crossref]

Delsart, C.

J.-C. Keller and C. Delsart, “Observation of Doppler-Free Laser Induced Birefringence using Interferences of Polarized Light,” Opt. Commun. 20, 147 (1977); “Doppler-Free Laser-Induced Dichroism and Birefringence,” in Laser Spectroscopy III, edited by J. L. Hall and J. L. Carlsten (Springer-Verlag, Berlin, 1977).
[Crossref]

Dienes, A.

A. Dienes, “Theory of Nonlinear Effects in a Gas Laser Amplifier. I. Weak Signals,” Phys. Rev. 174, 400 (1968).
[Crossref]

Hänsch, T.

T. Hänsch and P. Toshek, “Theory of a Three-Level Gas Laser Amplifier,” Z. Phys. 236, 213 (1970).
[Crossref]

Hänsch, T. W.

C. Wieman and T. W. Hänsch, “Doppler-Free Laser Polarization Spectroscopy,” Phys. Rev. Lett. 36, 1170 (1976); R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser Polarization Spectroscopy,” SPIE J. 113, 80 (1977).
[Crossref]

Heiman, D.

D. Heiman, R. W. Hellwarth, M. D. Levenson, and G. Martin, “Raman-Induced Kerr Effect,” Phys. Rev. Lett. 36, 189 (1976); M. D. Levenson and J. J. Song, “Raman-Induced Kerr Effect with Elliptical Polarization,” J. Opt. Soc. Am. 66, 641 (1976).
[Crossref]

Hellwarth, R. W.

D. Heiman, R. W. Hellwarth, M. D. Levenson, and G. Martin, “Raman-Induced Kerr Effect,” Phys. Rev. Lett. 36, 189 (1976); M. D. Levenson and J. J. Song, “Raman-Induced Kerr Effect with Elliptical Polarization,” J. Opt. Soc. Am. 66, 641 (1976).
[Crossref]

Keller, J.-C.

J.-C. Keller and C. Delsart, “Observation of Doppler-Free Laser Induced Birefringence using Interferences of Polarized Light,” Opt. Commun. 20, 147 (1977); “Doppler-Free Laser-Induced Dichroism and Birefringence,” in Laser Spectroscopy III, edited by J. L. Hall and J. L. Carlsten (Springer-Verlag, Berlin, 1977).
[Crossref]

Lamb, W. E.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974).

Levenson, M. D.

D. Heiman, R. W. Hellwarth, M. D. Levenson, and G. Martin, “Raman-Induced Kerr Effect,” Phys. Rev. Lett. 36, 189 (1976); M. D. Levenson and J. J. Song, “Raman-Induced Kerr Effect with Elliptical Polarization,” J. Opt. Soc. Am. 66, 641 (1976).
[Crossref]

Maker, P. D.

P. D. Maker and R. W. Terhune, “Study of Optical Effects due to an Induced Polarization Third Order in the Electric Field Strength,” Phys. Rev. A 137, 801 (1965); C. C. Wang, “Self-Focusing of Optical Beams in Liquids,” Phys. Rev. 152, 149 (1966).
[Crossref]

Martin, G.

D. Heiman, R. W. Hellwarth, M. D. Levenson, and G. Martin, “Raman-Induced Kerr Effect,” Phys. Rev. Lett. 36, 189 (1976); M. D. Levenson and J. J. Song, “Raman-Induced Kerr Effect with Elliptical Polarization,” J. Opt. Soc. Am. 66, 641 (1976).
[Crossref]

Saikan, S.

S. Saikan, “J-Dependence of Intensity-Dependent Polarization Change,” Appl. Phys. (to be published).

Sargent, M.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974).

Scully, M. O.

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974).

Terhune, R. W.

P. D. Maker and R. W. Terhune, “Study of Optical Effects due to an Induced Polarization Third Order in the Electric Field Strength,” Phys. Rev. A 137, 801 (1965); C. C. Wang, “Self-Focusing of Optical Beams in Liquids,” Phys. Rev. 152, 149 (1966).
[Crossref]

Toshek, P.

T. Hänsch and P. Toshek, “Theory of a Three-Level Gas Laser Amplifier,” Z. Phys. 236, 213 (1970).
[Crossref]

Wieman, C.

C. Wieman and T. W. Hänsch, “Doppler-Free Laser Polarization Spectroscopy,” Phys. Rev. Lett. 36, 1170 (1976); R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser Polarization Spectroscopy,” SPIE J. 113, 80 (1977).
[Crossref]

Opt. Commun. (1)

J.-C. Keller and C. Delsart, “Observation of Doppler-Free Laser Induced Birefringence using Interferences of Polarized Light,” Opt. Commun. 20, 147 (1977); “Doppler-Free Laser-Induced Dichroism and Birefringence,” in Laser Spectroscopy III, edited by J. L. Hall and J. L. Carlsten (Springer-Verlag, Berlin, 1977).
[Crossref]

Phys. Rev. (1)

A. Dienes, “Theory of Nonlinear Effects in a Gas Laser Amplifier. I. Weak Signals,” Phys. Rev. 174, 400 (1968).
[Crossref]

Phys. Rev. A (1)

P. D. Maker and R. W. Terhune, “Study of Optical Effects due to an Induced Polarization Third Order in the Electric Field Strength,” Phys. Rev. A 137, 801 (1965); C. C. Wang, “Self-Focusing of Optical Beams in Liquids,” Phys. Rev. 152, 149 (1966).
[Crossref]

Phys. Rev. Lett. (2)

D. Heiman, R. W. Hellwarth, M. D. Levenson, and G. Martin, “Raman-Induced Kerr Effect,” Phys. Rev. Lett. 36, 189 (1976); M. D. Levenson and J. J. Song, “Raman-Induced Kerr Effect with Elliptical Polarization,” J. Opt. Soc. Am. 66, 641 (1976).
[Crossref]

C. Wieman and T. W. Hänsch, “Doppler-Free Laser Polarization Spectroscopy,” Phys. Rev. Lett. 36, 1170 (1976); R. E. Teets, F. V. Kowalski, W. T. Hill, N. Carlson, and T. W. Hänsch, “Laser Polarization Spectroscopy,” SPIE J. 113, 80 (1977).
[Crossref]

Z. Phys. (1)

T. Hänsch and P. Toshek, “Theory of a Three-Level Gas Laser Amplifier,” Z. Phys. 236, 213 (1970).
[Crossref]

Other (2)

S. Saikan, “J-Dependence of Intensity-Dependent Polarization Change,” Appl. Phys. (to be published).

M. Sargent, M. O. Scully, and W. E. Lamb, Laser Physics (Addison-Wesley, London, 1974).

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Figures (1)

FIG. 1
FIG. 1

Optical arrangements used to detect laser-induced optical anisotropy.

Equations (29)

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χ 1122 ( 3 ) ( - ω , ω , ω , - ω ) = χ i i j j ( 3 ) ( - ω , ω , ω , - ω ) , χ 1212 ( 3 ) ( - ω , ω , ω , - ω ) = χ i j i j ( 3 ) ( - ω , ω , ω , - ω ) , χ 1221 ( 3 ) ( - ω , ω , ω , - ω ) = χ i j j i ( 3 ) ( - ω , ω , ω , - ω ) ,
χ 1111 ( 3 ) ( - ω , ω , ω , - ω ) = χ i i i i ( 3 ) ( - ω , ω , ω , - ω ) = χ 1122 ( 3 ) + χ 1221 ( 3 ) + χ 1212 ( 3 ) ,
P i ( 3 ) ( ω ) = j 6 0 [ χ 1122 ( 3 ) ( - ω , ω , ω , - ω ) E i ( ω ) A j ( ω ) A j * ( ω ) + χ 1212 ( 3 ) ( - ω , ω , ω , - ω ) E j ( ω ) A i ( ω ) A j * ( ω ) + χ 1221 ( 3 ) ( - ω , ω , ω , - ω ) E j ( ω ) A j ( ω ) A i * ( ω ) ] ,
[ P x P y ] = 0 [ 6 ( χ 1122 ( 3 ) + χ 1212 ( 3 ) + χ 1221 ( 3 ) ) A x 2 + 6 χ 1122 ( 3 ) A y 2 ,             6 ( χ 1212 ( 3 ) A x A y * + χ 1221 ( 3 ) A x * A y ) 6 ( χ 1212 ( 3 ) A y A x * + χ 1221 ( 3 ) A y * A x ) ,             6 ( χ 1122 ( 3 ) + χ 1212 ( 3 ) + χ 1221 ( 3 ) ) A y 2 + 6 χ 1122 ( 3 ) A x 2 ] [ E x E y ] ,
S = 1 2 ( 1 1 - ) ,             = ( χ 1212 e - i ϕ + χ 1221 e i ϕ χ 1212 e i ϕ + χ 1221 e - i ϕ ) 1 / 2 .
χ 1 , 2 = 3 A 2 [ 2 χ 1122 + χ 1212 + χ 1221 ± ( χ 1212 2 + χ 1221 2 + χ 1212 χ 1221 cos 2 ϕ ) 1 / 2 ] ,
( A x , A y ) = ( A / 2 ) ( 1 , e i ϕ )
[ P x P y ] = 0 [ 3 ( 2 χ 1212 ( 3 ) + χ 1221 ( 3 ) ) A x 2 + 6 χ 1212 ( 3 ) A y 2 ,             3 χ 1221 ( 3 ) A x * A y 3 χ 1221 ( 3 ) A y * A x ,             3 ( 2 χ 1212 ( 3 ) + χ 1221 ( 3 ) A y 2 + 6 χ 1212 A x 2 ) ] [ A x A y ] .
[ P + P - ] = 0 [ 6 χ 1212 ( 3 ) A + 2 + 6 ( χ 1212 ( 3 ) + χ 1221 ( 3 ) ) A - 2 ,             0 0 ,             6 χ 1212 ( 3 ) A - 2 + 6 ( χ 1212 ( 3 ) + χ 1221 ( 3 ) ) A + 2 ] [ A + A - ] .
χ 1 = 6 A 2 ( χ 1122 ( 3 ) + χ 1212 ( 3 ) ) ,             χ 2 = 6 A 2 ( χ 1122 ( 3 ) + χ 1221 ( 3 ) ) , Δ χ = χ 1 - χ 2 = 6 A 2 ( χ 1212 ( 3 ) - χ 1221 ( 3 ) ) .
χ 1 = 6 A 2 ( χ 1122 ( 3 ) + χ 1212 ( 3 ) + χ 1221 ( 3 ) ) ,             χ 2 = 6 A 2 χ 1122 ( 3 ) , Δ χ = 6 A 2 ( χ 1212 ( 3 ) + χ 1221 ( 3 ) ) .
χ 1 = 6 A + 2 χ 1212 ( 3 ) + 6 A - 2 ( χ 1212 ( 3 ) + χ 1221 ( 3 ) ) , χ 2 = 6 A - 2 χ 1212 ( 3 ) + 6 A + 2 ( χ 1212 ( 3 ) + χ 1221 ( 3 ) ) , Δ χ = 6 ( A - 2 - A + 2 ) χ 1221 ( 3 ) = 6 A 2 sin ϕ χ 1221 ( 3 ) .
E = ½ [ e ˆ + ( A + e i ( ± k Z - ω t ) + E + e i ( k Z - ω t ) ) + e ˆ - ( A - e i ( ± k Z - ω t ) + E - e i ( k Z - ω t ) ) ] + c · c ,
V a , b = - 1 2 P a , b [ ( A + e i ( ± k Z - ω t ) + E + e i ( k Z - ω t ) ) δ a , b - 1 + ( A - e i ( ± k Z - ω t ) + E - e i ( k Z - ω t ) ) δ a , b + 1 ] ,
χ ( 1 ) = 2 N π P 2 K u 0 M = - J J ( P M - 1 , M ) 2 f ( ξ )
f ( ξ ) = i e - ξ 2 - 2 π e - ξ 2 0 ξ e x 2 d x , ξ = ω - ω 0 K u ,
χ 1122 ( 3 ) = χ 1212 ( 3 ) = B g ( ξ ) M ( P M - 1 , M ) 4 , χ 1221 ( 3 ) = B g ( ξ ) M ( P M - 1 , M ) 2 [ ( P M + 1 , M ) 2 + ( P M - 1 , M - 2 ) 2 - ( P M - 1 , M ) 2 ] ,
B = - N P 4 π γ a b 3 3 K u 0 γ γ a γ b ,
g ( ξ ) = i e - ξ 2 - ( γ K u ) 2 ξ e - ξ 2 ,
χ 1122 ( 3 ) = B h ( η ) M ( P M - 1 , M ) 2 ( ( P M - 1 , M ) 2 + γ b - γ a 2 γ a b ( P M - 1 , M - 2 ) 2 + γ a - γ b 2 γ a b ( P M + 1 , M ) 2 ) , χ 1212 ( 3 ) = B h ( η ) M ( P M - 1 , M ) 2 ( ( P M - 1 , M ) 2 + γ a - γ b 2 γ a b ( P M - 1 , M - 2 ) 2 + γ b - γ a 2 γ a b ( P M + 1 , M ) 2 ) , χ 1221 ( 3 ) = B h ( η ) M ( P M - 1 , M ) 2 ( ( P M - 1 , M - 2 ) 2 + ( P M + 1 , M ) 2 - ( P M - 1 , M ) 2 ) ,
h ( η ) = i / ( 1 + i η ) ,             η ( ω 0 - ω ) / γ
T = ( ½ ) F exp ( - α l ) [ cosh β l - cos ( δ l + 2 θ ) ]
α = ( K / 2 ) ( 2 χ ( 1 ) + χ 1 ( 3 ) + χ 2 ( 3 ) ) , β = ( K / 2 ) ( χ 1 ( 3 ) - χ 2 ( 3 ) ) = ( K / 2 ) I m Δ χ , δ = ( K / 2 ) ( χ 1 ( 3 ) - χ 2 ( 3 ) ) = ( K / 2 ) R e Δ χ ,
Δ χ = 6 A 2 B g ( ξ ) × M ( P M - 1 , M ) 2 [ 2 ( P M - 1 , M ) 2 - ( P M + 1 , M ) 2 - ( P M - 1 , M - 2 ) 2 ] = K 1 f 1 ( J ) ( ½ )             Δ J = 0 ( J J ) = K 1 f 2 ( J ) 2 J 2 - 1 2             Δ J = ± 1 ( J J - 1 )
Δ χ = 6 A 2 B h ( η ) M ( P M - 1 , M ) 2 ( 2 ( P M - 1 , M ) 2 - 2 γ a γ a + γ b ( P M + 1 , M ) 2 - 2 γ b γ a + γ b ( P M - 1 , M - 2 ) 2 ) = K 2 f 1 ( J ) ( ½ )             Δ J = 0 = K 2 f 2 ( J ) 2 J 2 - r J - 1 2             Δ J = ± 1 ,
K 1 = 6 A 2 B g ( ξ ) ,             K 2 = 6 A 2 B h ( η ) , f 1 ( J ) = 6 J ( J + 1 ) ( 2 J + 1 ) ,             f 2 ( J ) = 6 J ( 2 J - 1 ) ( 2 J + 1 ) , r = ± γ a - γ b γ a + γ b
Δ χ = 6 A 2 B g ( ξ ) M ( P M - 1 , M ) 2 [ ( P M + 1 , M ) 2 + ( P M - 1 , M - 2 ) 2 ] = K 1 f 1 ( J ) ( 2 J - 1 ) ( 2 J + 3 ) 10             Δ J = 0 = K 1 f 2 ( J ) 2 J 2 + 3 10             Δ J = ± 1
Δ χ = 6 A 2 B h ( ξ ) M ( P M - 1 , M ) 2 ( 2 γ a γ a + γ b ( P M - 1 , M - 2 ) 2 + 2 γ b γ a + γ b ( P M + 1 , M ) 2 ) = K 2 f 1 ( J ) ( 2 J - 1 ) ( 2 J + 3 ) 10             Δ J = 0 = K 2 f 2 ( J ) 2 J 2 - 5 r J + 3 10             Δ J = ± 1.
Δ χ = 6 A 2 B sin ϕ g ( ξ ) M ( P M - 1 , M ) 2 [ ( P M + 1 , M ) 2 + ( P M - 1 , M - 2 ) 2 - ( P M - 1 , M ) 2 ] = K 1 f 1 ( J ) ( J + 2 ) ( J - 1 ) 5             Δ J = 0 = K 1 f 2 ( J ) - 2 ( J + 1 ) ( J - 1 ) 5             Δ J = ± 1.