Dynamics of Mandel’shtam–Brillouin induced scattering during self-focusing of a laser
beam
N. E. Andreev and M. V. Chegotov
Scientific-Research Center for the Thermal Physics of Pulsed Actions, Unified Institute of High-Temperature
Physics, Russian Academy of Sciences, 127412 Moscow, Russia
L. M. Gorbunov*
)
P. N. Lebedev Physics Institute, Russian Academy of Sciences, 117924 Moscow, Russia
Submitted 17 August 1998
Zh. E
´
ksp. Teor. Fiz. 115, 1950–1960 June 1999
It is shown that the size of the focal spot has a substantial influence on the dynamics of
Mandel’shtam–Brillouin induced scattering MBIS for the laser beam power near critical for
striction self-focusing. For small focal spots MBIS suppresses self-focusing. An increase
in the size of the focal spot leads to growth of the MBIS pulsations and the steady-state setup
time. For large enough focal spots MBIS arises in the form of regular intense spikes.
Physical processes shaping the dynamics of MBIS are discussed. © 1999 American Institute of
Physics. S1063-77619900306-6
1. INTRODUCTION
In nonlinear optics one of the most widely known pro-
cesses is Mandel’shtam–Brillouin induced scattering
MBIS, in which an incident electromagnetic wave, by in-
teracting with sound waves, creates scattered electromag-
netic waves with shifted frequencies see, e.g., Refs. 1–3.
This process is observed in many material media and is of
great significance for a number of applications. In particular,
it is used for phase conjugation see, e.g., Refs. 4–6. It is
also of great significance for laser nuclear fusion, lowering
the fraction of radiation absorbed in the target see, e.g.,
Ref. 7.
If the laser beam power P exceeds a certain critical value
P
cr
Refs. 8–10, then self-focusing can also take place along
with MBIS. It is well known that in steady state either self-
focusing like filamentation of the laser beam leads to a
growth of MBIS see, e.g., Refs. 11–13 or MBIS suppresses
self-focusing see, e.g., Refs. 14–16. However, the interac-
tion of MBIS and self-focusing can be most uniquely mani-
fested in their simultaneous development in time during a
transitory process. Thus, in Ref. 17 it was shown that be-
cause of self-focusing MBIS acquires the form of periodic
spikes during which the intensity of the scattered radiation
can exceed the intensity of the incident radiation. A non-
monotonic time dependence of MBIS is also indicated by
numerical calculations.
18
The present paper discusses the possibility of modifying
the dynamics of MBIS when the laser beam power exceeds
the critical power of striction self-focusing by varying the
size of the focal spot. It follows from a numerical solution of
the system of nonlinear equations describing the incident
beam and scattered beams and also large-scale perturbations
of the density of the medium associated with self-focusing
that for relatively large focal spots the development of self-
focusing leads to the result that MBIS has the form of peri-
odic intense spikes.
17
As the size of the focal spot is reduced,
self-focusing is suppressed and the spiking character of
MBIS gives way to oscillations about some mean value,
where the amplitude of these oscillations decays with time.
For a fixed focal spot size self-focusing is suppressed that
much more effectively, the higher the initial level of scatter-
ing. In this case, the setting up of steady state takes place
faster. Under conditions in which the initial MBIS reflection
coefficient, calculated in the one-dimensional theory neglect-
ing self-focusing, amounts to several percent, the dynamics
of MBIS approaches the dynamics described by the one-
dimensional nonlinear theory.
19
Numerical calculations of the spatiotemporal variation of
the intensity of the incident and scattered radiation, and also
the density of the medium, have made it possible to interpret
the physical processes responsible for the above-described
MBIS dynamics. These questions, and also experiments in
which MBIS pulsations have been observed, are discussed in
the Conclusion.
2. STATEMENT OF THE PROBLEM, AND BASIC EQUATIONS
Let us consider a planar layer of a nonlinear, transparent
medium, onto which, starting at the time t =0, a beam of
electromagnetic radiation having characteristic width 2 a di-
ameter of the focal spot is incident. We assume that the
radiation power exceeds its critical value for striction pon-
deromotive self-focusing and the thickness of the layer ex-
ceeds the diffraction length. Together with self-focusing, we
consider MBIS in directions close to directly backward.
1
To describe the incident and scattered beams, and also
perturbations of the medium density, we use, respectively,
Maxwell’s equations and the equations of acoustics, in which
we allow for the action of the averaged ponderomotive force
see, e.g., Refs. 2 and 3. We represent the electric field
strength in the medium in the form
JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS VOLUME 88, NUMBER 6 JUNE 1999
1066 1063-7761/99/88(6)/6/$15.00 © 1999 American Institute of Physics