Theoretical calculations supported by numerical simulations show that utilization of the nonlinear dependence of the index of refraction on intensity makes possible the transmission of picosecond optical pulses without distortion in dielectric fiber waveguides with group velocity dispersion. In the case of anomalous dispersion (∂2ω/∂k2>0) discussed here [the case of normal dispersion (∂2ω/∂k2<0) will be discussed in a succeeding letter], the stationary pulse is a ``bright'' pulse, or envelope soliton. For a typical glass fiber guide, the balancing power required to produce a stationary 1‐ps pulse is approximately 1 W. Numerical simulations show that above a certain threshold power level such pulses are stable under the influence of small perturbations, large perturbations, white noise, or absorption.

1.
A. Hasegawa and F. Tappert, Appl. Phys. Lett. (to be published).
2.
C.
Gloge
,
Appl. Opt.
10
,
2442
(
1971
).
Google Scholar
Crossref
Search ADS
PubMed
 
3.
R. Y.
Chiao
,
E.
Garmire
, and
C. H.
Townes
,
Phys. Rev. Lett.
13
,
479
(
1964
). For fused quartz, n2 is caused by the electronic Kerr effect which has a response time of about 10−15 s.
Google Scholar
Crossref
Search ADS
 
4.
The normalization of R is taken to be ∫ 0∞R2(r)2πrdr = S, where S is the geometrical cross‐sectional area.
5.
V. I.
 
Karpman
 and
E. N.
 
Krushkal
,
Zh. Eksp. Teor. Fiz.
 
55
,
530
(
1968
)
Google Scholar
 
[
V. I.
 
Karpman
 and
E. N.
 
Krushkal
,
Sov. Phys.‐JETP
 
28
,
277
(
1969
)];
Google Scholar
 
T. Taniuti and N. Yajima, J. Math. Phys. (to be published). For the guided mode, the derivation is somewhat intricate and will be published elsewhere.
See also J. W. Van Dam, Nagoya University Institute of Plasma Physics Report No. PPS136, 1972 (unpublished).
6.
For example, for the HE11 mode this factor is given by α11≈4 ∫ 01x[(J0(p1x̄)]4dx/[J1(p1)]−2, where J0 and J1 are Bessel functions and p1 is the first root of J0.
7.
A. Hasegawa and F. D. Tappert (unpublished).
8.
V. J.
 
Karpman
,
Zh. Eksp. Teor. Fiz. Pis’ma Red.
 
6
,
829
(
1967
)
Google Scholar
 
[
V. J.
 
Karpman
,
JETP Lett.
 
6
,
277
(
1967
)];
Google Scholar
 
L. A.
 
Ostrovskii
,
Zh. Eksp. Teor. Fiz.
 
51
,
1189
(
1966
)
Google Scholar
 
[
L. A.
Ostrovskii
,
Sov. Phys.‐JETP
24
,
797
(
1967
)].
Google Scholar
 
9.
V. E.
 
Zakharov
 and
A. B.
 
Shabat
,
Zh. Eksp. Teor. Fiz.
 
61
,
118
(
1971
)
Google Scholar
 
[
V. E.
Zakharov
 and
A. B.
Shabat
,
Sov. Phys.‐JETP
34
,
62
(
1972
)].
Google Scholar
 
10.
F. D.
 
Tappert
 and
C. N.
 
Judice
,
Phys. Rev. Lett.
 
29
,
1308
(
1972
);
Google Scholar
Crossref
Search ADS
 
R. H.
Hardin
 and
F. D.
Tappert
,
SIAM Rev. (Soc. Ind. Appl. Math.)
15
,
423
(
1973
).
Google Scholar
 
This content is only available via PDF.
© 1973 American Institute of Physics.
1973
American Institute of Physics
You do not currently have access to this content.