Abstract

A microscopic model is given to explain the irreversible changes in glass fibers caused by simultaneous irradiation with 1064- and 532-nm light. The model involves an excitation of Ge E′ defects by photons of the fourth harmonic. A quantum-mechanical formalism is developed that is especially suited to describe a system under the influence of radiation fields.

© 1990 Optical Society of America

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References

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  1. U. Österberg, W. Margulis, “Dye laser pumped by Nd:YAG laser pulses frequency doubled in a glass optical fiber,” Opt. Lett. 11, 516 (1986).
    [CrossRef] [PubMed]
  2. R. H. Stolen, H. W. K. Tom, “Self-organized phase-matched harmonic generation in optical fibers,” Opt. Lett. 12, 585 (1987).
    [CrossRef] [PubMed]
  3. N. B. Baranova, B. Ya. Zel’dovich, “Extension of holography to multifrequency fields,” JETP Lett. 45, 717 (1987).
  4. W. Margulis, Departamento de fisica PUC-Rio de Janeiro 22452 Brazil (personal communication).
  5. This order-of-magnitude estimate results from the usual formula for second-order susceptibilities, assuming matrix elements of the dipole operator of the order of one elementary charge times 1 or 2 Å and EI of the order of 109V m−1.
  6. A. Krotkus, W. Margulis, “Investigations of the preparation process for efficient second-harmonic generation in optical fibers,” Appl. Phys. Lett. 52, 1942 (1988).
    [CrossRef]
  7. F. Ouellette, K. O. Hill, D. C. Johnson, “Light-induced erasure of self-organized χ(2)gratings in optical fibers,” Opt. Lett. 13, 515 (1988).
    [CrossRef] [PubMed]
  8. Ya. B. Zel’dovich, “Scattering and emission of a quantum system in a strong electromagnetic wave,” Sov. Phys. Usp. 16, 427 (1974).
    [CrossRef]
  9. The terms that were dropped in this approximation need not always be small; however, they add nothing new in the present context. They correspond to transitions that violate conservation of stroboscopic energy by integer multiples of ℏωI. The possibility of excitation by four-photon absorption, which was mentioned at the end of Section 2, can be described by these terms.

1988 (2)

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

F. Ouellette, K. O. Hill, D. C. Johnson, “Light-induced erasure of self-organized χ(2)gratings in optical fibers,” Opt. Lett. 13, 515 (1988).
[CrossRef] [PubMed]

1987 (2)

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

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

1986 (1)

1974 (1)

Ya. B. Zel’dovich, “Scattering and emission of a quantum system in a strong electromagnetic wave,” Sov. Phys. Usp. 16, 427 (1974).
[CrossRef]

Baranova, N. B.

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

Hill, K. O.

Johnson, D. C.

Krotkus, A.

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

Margulis, W.

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

U. Österberg, W. Margulis, “Dye laser pumped by Nd:YAG laser pulses frequency doubled in a glass optical fiber,” Opt. Lett. 11, 516 (1986).
[CrossRef] [PubMed]

W. Margulis, Departamento de fisica PUC-Rio de Janeiro 22452 Brazil (personal communication).

Österberg, U.

Ouellette, F.

Stolen, R. H.

Tom, H. W. K.

Zel’dovich, B. Ya.

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

Zel’dovich, Ya. B.

Ya. B. Zel’dovich, “Scattering and emission of a quantum system in a strong electromagnetic wave,” Sov. Phys. Usp. 16, 427 (1974).
[CrossRef]

Appl. Phys. Lett. (1)

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

JETP Lett. (1)

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

Opt. Lett. (3)

Sov. Phys. Usp. (1)

Ya. B. Zel’dovich, “Scattering and emission of a quantum system in a strong electromagnetic wave,” Sov. Phys. Usp. 16, 427 (1974).
[CrossRef]

Other (3)

The terms that were dropped in this approximation need not always be small; however, they add nothing new in the present context. They correspond to transitions that violate conservation of stroboscopic energy by integer multiples of ℏωI. The possibility of excitation by four-photon absorption, which was mentioned at the end of Section 2, can be described by these terms.

W. Margulis, Departamento de fisica PUC-Rio de Janeiro 22452 Brazil (personal communication).

This order-of-magnitude estimate results from the usual formula for second-order susceptibilities, assuming matrix elements of the dipole operator of the order of one elementary charge times 1 or 2 Å and EI of the order of 109V m−1.

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Figures (2)

Fig. 1
Fig. 1

Born-Oppenheimer potential curves for the ground state and the first excited state of the atomic system.

Fig. 2
Fig. 2

Fluxes due to absorption and spontaneous emission.

Equations (26)

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P = 0 [ χ ( 1 ) E + χ ( 2 ) EE + χ ( 3 ) EEE + ] .
Δ E ± = ½ D ± G · E G cos β ± ,
n n + = 0.08 + ( 0.8 ) 1.7 × 10 4 0.08 ( 0.8 ) 1.7 × 10 4 1.003 .
U t n , 0 = ( U T ) n .
= i 1 T ln ( U T ) ;
U t n , 0 = exp ( i t n ) .
¯ n | n ( n + ω I N n ) n | ,
U T = U T o i 0 T U T , t o 1 ( t ) U t , 0 o d t U T o + Δ U T ,
Pr ( i f ) = | f | ( U T ) N | i | 2 .
Pr ( i f ) = | n = 0 N 1 f | ( U T o ) n Δ U T ( U T o ) N 1 n | i | 2 = | exp [ i ( f i ) T N ] 1 exp [ i ( f i ) T ] 1 | 2 | f | Δ U T | i | 2 .
Pr ( i f ) 2 π N 1 2 δ ( f i T ) × | 0 T f ( t ) | 1 ( t ) | i ( t ) d t | 2 ,
| n ( t ) U t , 0 o | n .
ph = k , α ω k a k , α a k , α
1 = k , α l g l m l p l · e k , α ( c k 2 0 L 3 ) 1 / 2 ( a k , α + a k , α ) ,
| n ( t ) = m | m exp [ i ( m + ω I N m ) t ] [ δ n m + m n ( t ) ] ,
f ( t ) | 1 | i ( t ) = exp [ i ω I ( N f N i ) t ] f | 1 | i + small corrections due to the perturbation ( t ) ¯ .
Pr ( i f ) 2 π N T δ [ ( f + N f ω I ) ( i + N i ω I ) ] × | f | 1 | i | 2 .
T exp { i 0 T [ I ( t ) + λ G ( t ) ] d t } = exp { i T ¯ } ,
0 T U T , t I G ( t ) U t , 0 I d t = 0 T exp [ i ( T t ) ¯ I ] ¯ G ( 1 ) × exp ( i t ¯ I ) d t ,
exp ( i n I T ) 0 T n I ( t ) | G ( t ) | n I ( t ) d t = exp ( i n I T ) n I | ¯ G ( 1 ) | n I ,
Δ n = 1 T 0 T n I ( t ) | G ( t ) | n I ( t ) d t .
G ( t ) = l g l m l p l · A G sin ( ω G t ) + l g l 2 m l A G · A I sin ( ω I t φ ) sin ( ω G t ) .
± I ( t ) | l g l m l p l · A G | ± I ( t ) = d D ± d t · A G + l g l m l A 1 · A G sin ( ω I t φ ) .
Δ Ē ± = 1 T 0 T D ± ( t ) · E G ( t ) d t .
D ± ( t ) = D ± 0 + D ± I cos ( ω I t α ± ) + D ± G cos ( ω G t β ± ) + ,
Δ Ē ± = ½ D ± G · E G cos β ± .

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