Abstract

We discuss some physical effects that take place in multifrequency light fields with a nonzero average cube of the electric field, 〈E3〉 ≠ 0. We calculated the polar asymmetry in electron emission that is due to interference between two-photon ionization by the fundamental radiation (ω) and one-photon ionization by the second-harmonic (2ω) wave. The expression for the quasi-static force, which acts on electrons and is proportional to the average cube of the light field, is derived.

© 1991 Optical Society of America

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References

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  1. U. Osterberg and W. Margulis, “Dye laser pumped by Nd:YAG laser pulses frequency doubled in a glass optical fiber,” Opt. Lett. 11, 516–518 (1986); “Experimental studies on efficient frequency doubling in glass optical fibers,” Opt. Lett. 12, 57–59 (1987).
    [CrossRef] [PubMed]
  2. M. C. Farries, P. St, J. Russell, M. E. Fermann, and D. N. Payne, “Second-harmonic generation in an optical fiber by self-written χ(2)-grating,” Electron. Lett. 23, 322–325 (1987).
    [CrossRef]
  3. R. H. Stolen and H. W. K. Tom, “Self-organized phase-matched harmonic generation in optical fibers,” Opt. Lett. 12, 585–588 (1987).
    [CrossRef] [PubMed]
  4. N. B. Baranova and B. Ya. Zel’dovich, “Extension of holography to multifrequency fields,” Sov. Phys. JETP Lett. 45, 717–720 (1987).
  5. A. Krotkus and W. Margulis, “Investigation of the preparation process for efficient second-harmonic generation in optical fibers,” Appl. Phys. Lett. 52, 1942–1945 (1988).
    [CrossRef]
  6. H. W. K. Tom, R. H. Stolen, G. D. Aumiller, and W. Pleibel, “Preparation of long-coherence-length second-harmonic-generating optical fibers by using mode-locked pulses,” Opt. Lett. 13, 512–516 (1988).
    [CrossRef] [PubMed]
  7. F. Ouellette, K. O. Hill, and D. C. Johnson, “Light-induced erasure of self-organized χ(2) gratings in optical fibers,” Opt. Lett. 13, 515–517 (1988).
    [CrossRef] [PubMed]
  8. M. V. Bergot, M. C. Farries, M. E. Fermann, E. Martin, L. Li, L. J. Peyntz-Wright, P. St, J. Russell, and A. Smithson, “Generation of permanent optically induced second-order nonlinearities in optical fibers by poling,” Opt. Lett. 13, 592–595 (1988).
    [CrossRef] [PubMed]
  9. M. A. Saifi and M. J. Andrejco, “Second-harmonic generation in single-mode and multimode fibers,” Opt. Lett. 13, 773–775 (1988).
    [CrossRef] [PubMed]
  10. W. Margulis, I. C. S. Carvalho, and J. P. von der Weid, “Phase measurement in frequency-doubling fibers,” Opt. Lett. 14, 700–702 (1989).
    [CrossRef] [PubMed]
  11. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1976).
  12. M. V. Antin, “Theory of the coherent photogalvanical effect,” Sov. Phys. Semicond. 23, 1066–1069 (1989).
  13. E. M. Dianov, P. G. Kazansky, and D. Yu. Stepanov, “To the question of photoinduced SHG in optical fibers,” Sov. J. Quantum Electron. 16, 887–888 (1989).
  14. R. J. Glauber, “Coherence and quantum detection,” in Quantum Optics, Proceedings of E. Fermi International School in Physics, 1967, R. J. Glauber, ed. (Academic, New York, 1969), p. 15; R. J. Glauber, “Quantum theory of coherence,” in Proceedings of the 10th Session of the Scottish Universities Summer School in Physics, 1969, S. M. Kay and A. Maitland, eds. (Academic, London, 1970), p. 53.
  15. L. D. Landau and E. M. Lifshitz, Classical Mechanics (Pergamon, Oxford, 1975).
  16. A. V. Gaponov and M. A. Miller, “Potential wells of a charged particle in a high frequency electromagnetic field,” Sov. Phys. JETP 34, 168–169 (1958).
  17. L. S. Brown and T. W. B. Kibble, “Interaction of intense laser beams with electrons,” Phys. Rev. 133, A705–A719 (1964).
    [CrossRef]
  18. H. Schwarz, “The Kapitza–Dirac effect at high laser intensities,” Phys. Lett. 43A, 457–458 (1973).

1989 (3)

W. Margulis, I. C. S. Carvalho, and J. P. von der Weid, “Phase measurement in frequency-doubling fibers,” Opt. Lett. 14, 700–702 (1989).
[CrossRef] [PubMed]

M. V. Antin, “Theory of the coherent photogalvanical effect,” Sov. Phys. Semicond. 23, 1066–1069 (1989).

E. M. Dianov, P. G. Kazansky, and D. Yu. Stepanov, “To the question of photoinduced SHG in optical fibers,” Sov. J. Quantum Electron. 16, 887–888 (1989).

1988 (5)

1987 (3)

M. C. Farries, P. St, J. Russell, M. E. Fermann, and D. N. Payne, “Second-harmonic generation in an optical fiber by self-written χ(2)-grating,” Electron. Lett. 23, 322–325 (1987).
[CrossRef]

R. H. Stolen and H. W. K. Tom, “Self-organized phase-matched harmonic generation in optical fibers,” Opt. Lett. 12, 585–588 (1987).
[CrossRef] [PubMed]

N. B. Baranova and B. Ya. Zel’dovich, “Extension of holography to multifrequency fields,” Sov. Phys. JETP Lett. 45, 717–720 (1987).

1986 (1)

1973 (1)

H. Schwarz, “The Kapitza–Dirac effect at high laser intensities,” Phys. Lett. 43A, 457–458 (1973).

1964 (1)

L. S. Brown and T. W. B. Kibble, “Interaction of intense laser beams with electrons,” Phys. Rev. 133, A705–A719 (1964).
[CrossRef]

1958 (1)

A. V. Gaponov and M. A. Miller, “Potential wells of a charged particle in a high frequency electromagnetic field,” Sov. Phys. JETP 34, 168–169 (1958).

Andrejco, M. J.

Antin, M. V.

M. V. Antin, “Theory of the coherent photogalvanical effect,” Sov. Phys. Semicond. 23, 1066–1069 (1989).

Aumiller, G. D.

Baranova, N. B.

N. B. Baranova and B. Ya. Zel’dovich, “Extension of holography to multifrequency fields,” Sov. Phys. JETP Lett. 45, 717–720 (1987).

Bergot, M. V.

Brown, L. S.

L. S. Brown and T. W. B. Kibble, “Interaction of intense laser beams with electrons,” Phys. Rev. 133, A705–A719 (1964).
[CrossRef]

Carvalho, I. C. S.

Dianov, E. M.

E. M. Dianov, P. G. Kazansky, and D. Yu. Stepanov, “To the question of photoinduced SHG in optical fibers,” Sov. J. Quantum Electron. 16, 887–888 (1989).

Farries, M. C.

Fermann, M. E.

Gaponov, A. V.

A. V. Gaponov and M. A. Miller, “Potential wells of a charged particle in a high frequency electromagnetic field,” Sov. Phys. JETP 34, 168–169 (1958).

Glauber, R. J.

R. J. Glauber, “Coherence and quantum detection,” in Quantum Optics, Proceedings of E. Fermi International School in Physics, 1967, R. J. Glauber, ed. (Academic, New York, 1969), p. 15; R. J. Glauber, “Quantum theory of coherence,” in Proceedings of the 10th Session of the Scottish Universities Summer School in Physics, 1969, S. M. Kay and A. Maitland, eds. (Academic, London, 1970), p. 53.

Hill, K. O.

Johnson, D. C.

Kazansky, P. G.

E. M. Dianov, P. G. Kazansky, and D. Yu. Stepanov, “To the question of photoinduced SHG in optical fibers,” Sov. J. Quantum Electron. 16, 887–888 (1989).

Kibble, T. W. B.

L. S. Brown and T. W. B. Kibble, “Interaction of intense laser beams with electrons,” Phys. Rev. 133, A705–A719 (1964).
[CrossRef]

Krotkus, A.

A. Krotkus and W. Margulis, “Investigation of the preparation process for efficient second-harmonic generation in optical fibers,” Appl. Phys. Lett. 52, 1942–1945 (1988).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Classical Mechanics (Pergamon, Oxford, 1975).

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1976).

Li, L.

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1976).

L. D. Landau and E. M. Lifshitz, Classical Mechanics (Pergamon, Oxford, 1975).

Margulis, W.

Martin, E.

Miller, M. A.

A. V. Gaponov and M. A. Miller, “Potential wells of a charged particle in a high frequency electromagnetic field,” Sov. Phys. JETP 34, 168–169 (1958).

Osterberg, U.

Ouellette, F.

Payne, D. N.

M. C. Farries, P. St, J. Russell, M. E. Fermann, and D. N. Payne, “Second-harmonic generation in an optical fiber by self-written χ(2)-grating,” Electron. Lett. 23, 322–325 (1987).
[CrossRef]

Peyntz-Wright, L. J.

Pleibel, W.

Russell, J.

Saifi, M. A.

Schwarz, H.

H. Schwarz, “The Kapitza–Dirac effect at high laser intensities,” Phys. Lett. 43A, 457–458 (1973).

Smithson, A.

St, P.

Stepanov, D. Yu.

E. M. Dianov, P. G. Kazansky, and D. Yu. Stepanov, “To the question of photoinduced SHG in optical fibers,” Sov. J. Quantum Electron. 16, 887–888 (1989).

Stolen, R. H.

Tom, H. W. K.

von der Weid, J. P.

Zel’dovich, B. Ya.

N. B. Baranova and B. Ya. Zel’dovich, “Extension of holography to multifrequency fields,” Sov. Phys. JETP Lett. 45, 717–720 (1987).

Appl. Phys. Lett. (1)

A. Krotkus and W. Margulis, “Investigation of the preparation process for efficient second-harmonic generation in optical fibers,” Appl. Phys. Lett. 52, 1942–1945 (1988).
[CrossRef]

Electron. Lett. (1)

M. C. Farries, P. St, J. Russell, M. E. Fermann, and D. N. Payne, “Second-harmonic generation in an optical fiber by self-written χ(2)-grating,” Electron. Lett. 23, 322–325 (1987).
[CrossRef]

Opt. Lett. (7)

Phys. Lett. (1)

H. Schwarz, “The Kapitza–Dirac effect at high laser intensities,” Phys. Lett. 43A, 457–458 (1973).

Phys. Rev. (1)

L. S. Brown and T. W. B. Kibble, “Interaction of intense laser beams with electrons,” Phys. Rev. 133, A705–A719 (1964).
[CrossRef]

Sov. J. Quantum Electron. (1)

E. M. Dianov, P. G. Kazansky, and D. Yu. Stepanov, “To the question of photoinduced SHG in optical fibers,” Sov. J. Quantum Electron. 16, 887–888 (1989).

Sov. Phys. JETP (1)

A. V. Gaponov and M. A. Miller, “Potential wells of a charged particle in a high frequency electromagnetic field,” Sov. Phys. JETP 34, 168–169 (1958).

Sov. Phys. JETP Lett. (1)

N. B. Baranova and B. Ya. Zel’dovich, “Extension of holography to multifrequency fields,” Sov. Phys. JETP Lett. 45, 717–720 (1987).

Sov. Phys. Semicond. (1)

M. V. Antin, “Theory of the coherent photogalvanical effect,” Sov. Phys. Semicond. 23, 1066–1069 (1989).

Other (3)

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1976).

R. J. Glauber, “Coherence and quantum detection,” in Quantum Optics, Proceedings of E. Fermi International School in Physics, 1967, R. J. Glauber, ed. (Academic, New York, 1969), p. 15; R. J. Glauber, “Quantum theory of coherence,” in Proceedings of the 10th Session of the Scottish Universities Summer School in Physics, 1969, S. M. Kay and A. Maitland, eds. (Academic, London, 1970), p. 53.

L. D. Landau and E. M. Lifshitz, Classical Mechanics (Pergamon, Oxford, 1975).

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Figures (3)

Fig. 1
Fig. 1

Time dependence of the electrical field [Eq. (1)] at E1 = E2 = 1, Δφ = φ2 − 2φ1 = 45°. The time-averaged field is equal to zero, 〈E〉 = 0, but the asymmetry in the upper direction is evident and is characterized by 〈E3〉 = 0.53 > 0.

Fig. 2
Fig. 2

Photoionization of an atom simultaneously by both one-photon (ħ2ω) and two-photon (2ħω) transitions; ħω0, ionization potential.

Fig. 3
Fig. 3

Possible scheme for experimental observation of electron deflection by ponderomotive force F(3) ~ E3. Waves A, B, and C propagate in the figure plane, λA = 1.06 μm, λB = 10.6 μm, ωC = ωA + ωB, λC ≈ 0.96 μm. The potential grating U(3) ~ 〈E3〉 is localized in the region of the overlapping beams and deflects the electrons. The latter are moving in the z direction, perpendicular to the figure plane.

Equations (36)

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E real ( r , t ) = E 1 cos ( ω t - φ 1 ) + E 2 cos ( 2 ω t - φ 2 ) ,
( E 1 2 ) * E 2 exp ( i Δ k z ) + E 1 2 E 2 * exp ( - i Δ k z ) ,
δ χ ( 2 ) ( z ) = β ( E 1 2 ) * E 2 exp ( i Δ k z ) + c . c . ,
P 2 = χ ( 2 ) E 1 2 exp ( 2 i k 1 z - 2 i ω t ) = β E 1 4 E 2 exp ( i k 2 z - 2 i ω t ) .
H = - 2 2 m ( 1 r 0 + κ ) δ ( 1 ) ( r - r 0 ) + ( p - e c A ( t ) ) 2 / 2 m , A ( t ) = - c [ 2 i E 1 exp ( - i ω t ) + i E 2 exp ( - 2 i ω t ) + c . c . ] / 4 ω ,
ψ ( r , t ) = exp ( i ω 0 t ) ( κ 2 π ) 1 / 2 e - κ r r , κ = ( 2 m ω 0 / ) 1 / 2 ,
ψ k ( r ) = ( 2 π ) - 3 / 2 ( e i kr - 1 κ - i k e - i k r r ) exp ( - i k 2 2 m t ) .
d W ( n ) d o = B f 1 · ( E 2 n ) + f 0 · ( E 1 E 1 ) + f 2 · [ ( E 1 n ) 2 - ( E 1 E 1 ) / 3 ] 2 ,
B = 2 e 2 π m ω 0 1 / 2 ( 2 ω - ω 0 ) 1 / 2 ( 2 ω ) 4 ,             f 1 = i ( 2 ω - ω 0 ) 1 / 2 , f 0 = - ( e 2 2 m ) 1 / 2 4 ( ω 0 - ω ) 3 ω 3 [ ( ω 0 ) 1 / 2 - i ( 2 ω - ω 0 ) 1 / 2 ] × [ ( ω 0 ) 1 / 2 - ( ω 0 - ω ) 1 / 2 ] , f 2 = ( e 2 2 m ) 1 / 2 4 ω 2 ( 2 ω - ω 0 ) .
δ 1 = δ 2 = = 0 , δ 0 = - arctan ( k / κ ) = - arctan [ ( 2 ω - ω 0 ) / ω 0 ] 1 / 2 .
d W ( n ) d o - d W ( - n ) d o = 2 B f 1 f 2 { i ( E 2 n ) [ ( E 1 * n ) 2 - ( E 1 * E 1 * ) / 3 ] + c . c . } - 2 B f 1 f 0 [ i ( E 2 n ) ( E 1 * E 1 * ) exp ( - i δ 0 ) + c . c . ] .
d W ( n ) d o = C 1 ( E 2 E 2 ) + C 2 ( E 2 n ) ( E 2 n )
d W ( n ) d o - d W ( - n ) d o = const ( n · d E 2 / d t ) ( E 1 E 1 ) ,
E ( r , t ) = - 1 c A t ,             H ( r , t ) = rot A .
d p i d t = - H ( p , r , t ) x i , d x i d t = H ( p , r , t ) p i .
H ( p , r , t ) = [ p - ( e / c ) A ( r , t ) ] 2 / 2 m ,
d x i d t = p i m - e m c A i ( r , t ) ,
d p i d t = e m c [ p k - e c A k ( r , t ) ] A k x i .
d 2 x i d t 2 = e E i ( r , t ) + e c [ d r d t × H ( r , t ) ] .
x i ( 1 ) = - e m c - t A i ( r , t ) d t e m - t d t - t d t E i ( r , t ) .
d p ( 2 ) d t = - e 2 2 m c 2 ( AA ) ,
d p i ( 2 ) ¯ d t = - x i ( e 2 2 m c 2 A 2 ¯ ) = - x i ω α e 2 4 m ω α 2 ( E α · E α * ) ,
U = - d · E + E · dd = - ( 1 / 2 ) α E · E ,
d p i ( 3 ) d t = e m c p k ( 2 ) ( t ) A k x i - e 2 2 m c 2 x k ( 1 ) x k ( x i A j 2 ) .
d p i ( 3 ) d t = - e 3 2 m 2 c 3 A k x i - t x k ( A 2 ) d t + e 3 2 m 2 c 3 ( - t A k d t ) 2 x i x k A j 2 .
- A k x i - t x k ( A j 2 ) d t ¯ = A j 2 x k - t A k x i d t ¯ ,
d p i ( 3 ) d t = - U ( 3 ) x i , U ( 3 ) = - e 3 2 m 2 c 3 ( A j 2 ) x k - t A k d t ¯ .
k A = ( ω A / c ) e ^ y , k C = - ( ω C / c ) e ^ y , k B = ( ω B / c ) e ^ x , e A = e A * = e C , e B = e ^ y .
F ( 2 ) ( r , t ) - e 2 4 m ω 2 E A exp ( - i ω A t + i k A y ) + E C exp ( - i ω C t - i k C y ) 2 ,
F ( 2 ) ( r , t ) e 2 m ω c e ^ y E A E C * sin ( ω B t + 2 k y ) .
m r ¨ = F ( 2 ) ( r , t ) + e e ^ y E B cos ( ω B t - k B x ) .
U ( 3 ) U ( 3 ) sin ( 2 k y + k B x ) , U ( 3 ) e 3 λ B 2 λ A 16 π 3 m 2 c 4 E A E B E C .
U A ( 2 ) U C ( 2 ) 10 - 3 eV ,             U B ( 2 ) 10 - 1 eV .
U ( 3 ) 1.84 × 10 - 5 eV , q 1.3 × 10 5 cm - 1 , q · U ( 3 ) 2.4 eV / cm .
α ( 3 ) = Δ v y v 0 = q U ( 3 ) τ m v 0 = q U ( 3 ) L 2 ( m v 0 2 / 2 ) 6.7 × 10 - 4 rad .
α ( 2 ) U ( 2 ) L 2 ( m v 0 2 / 2 ) U ( 2 ) r 2 ( m v 0 2 / 2 ) L ,

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