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ELECTROMAGNETIC MODE CONVERSION BY ULTRA-FAST IONIZATION OF GASES AND
CONDENSED MATTER

V.B.Gildenburg, N.V.Vvedenskii

Institute of Applied Physics, Russian Academy of Sciences
E-mail: vved@appl.sci-nnov.ru

Abstract. We study in this paper the effect of shock excitation of leaky
and surface modes by the p-polarized electromagnetic wave incident on the
rapidly ionized gaseous or solid layer. Estimations fulfilled show the
potentialities for applying this effect for generation of X-ray and THz
radiation.

1. Introduction

The phenomena of ionization-induced spectrum conversion of
electromagnetic wave attracts the researchers attention in connection with
the problems of transformation and generation of radiation in some badly
mastered or hardly accessible frequency bands (THz, UV, X-ray). The most
theoretical works concerned these problems dealt with the wave propagation
in quasi-homogeneous time-varying plasma (created by an external ionization
source or by the wave itself) or with the reflection of the normal-incident
wave by moving ionization front or suddenly created plasma [1]. It was
considered also effects of "bulk-to-surface" mode conversion (with
frequency down-shifting) at sudden [2] or slow (adiabatic) [3] creation of
plasma layers. Frequency up-shifting of re-radiated waves caused by
excitation (and following adiabatic conversion) of Langmuir oscillations in
plasma layers was analyzed only for the case of slow ionization [4], when
this effect occurs to be depressed strongly due to collision or radiation
damping of this oscillations.
We study in this paper the effect of shock excitation of natural (leaky
and surface) electromagnetic modes by the p-polarized electromagnetic wave
incident on the rapidly ionized gaseous or solid layer. The model
considered is based on the following assumptions: (i) the ionization leads
to the formation of homogeneous plasma layer with Langmuir frequency which
is much greater than the incident wave frequency, (ii) the time of
ionization (unlike the cases considered in [4, 5]) is much smaller than the
period of plasma oscillations, (iii) the layer thickness is much smaller
than the space scale of the incident wave in plasma. It has been found that
besides the known phenomenon of the symmetric surface waves excitation [2],
the rapid ionization leads to effective generation of low-frequency
antisymmetric surface waves and symmetric leaky waves with strongly up-
shifted (Langmuir) frequency.

2. Formulation of the problem and basic equations

Let the electromagnetic field before plasma creation ([pic]) is given
in Cartesian coordinates as a plane [pic]-polarized wave of frequency [pic]
[pic], [pic],
incident at an angle [pic] on the infinite layer of transparent (unionized
at [pic]) medium, occupying the space between the planes [pic].
At the time instant [pic] the layer is ionized suddenly by some
external source (for example, high intensity laser pulse), so that the
plasma density within the layer grows instantly from 0 to [pic]=const. The
approximation of instant plasma creation, supported by a number of
theoretical and experimental studies [1] is valid if the electron density
rise time is much shorter then the period of plasma oscillation. The
spatiotemporal evolution of the electromagnetic field after the plasma
creation (at [pic]) is governed by Maxwell's equations
[pic], (1)
[pic], (2)
[pic], (3)
with current density equations for the cold collisionless plasma
[pic], [pic]. (4)
Here [pic] is the electron plasma (Langmuir) frequency, [pic] and [pic] are
the [pic] and [pic] components of the electron current density.
Initial conditions (at [pic]) for the field and electron current are
the temporal continuities of [pic], [pic], [pic] and [pic] (newly created
electrons have zero velocity at [pic]). Boundary conditions (at [pic]) are
spatial continuities of [pic] and [pic].
Method of the solution is Laplace transform of Maxwell's and current
density equations:
[pic],
where [pic] is Laplace variable, [pic] is a component of the fields or
current density.

3. Laplace transforms

Applying Laplace transform to equations (1)-(4) gives the following
equations for the electromagnetic field and current density transforms
[pic], [pic], [pic], [pic], [pic]:
[pic]
[pic]
[pic]
[pic], [pic],

Boundary conditions for the Laplace transforms are spatial continuities of
[pic] and [pic] at [pic].
The solution for the transform of the magnetic field inside the plasma
([pic]) has the form
[pic]
[pic]
[pic]
[pic].

4. Thin layer approximation

If the following inequalities are fulfilled
[pic], [pic], [pic],
the magnetic field inside the layer can be presented in the form

[pic],
where symmetric term [pic] does not depend on x , antisymmetric term [pic]
and
[pic]
[pic]
The waves with the frequencies [pic] are the surface waves propagating in
the forward ([pic]) and backward ([pic]) directions, respectively. The
waves with the frequencies [pic] are the leaky waves emitted into vacuum
([pic]). The amplitudes of the these waves are determined by the reduces of
[pic] and [pic] at the corresponding poles ([pic]).
The frequencies and amplitudes of antisymmetric and simmetic waves are

[pic].
[pic], [pic],
[pic][pic],
[pic],
[pic], [pic],
[pic], [pic],
[pic], [pic].
The leaky waves are emitted into vacuum under the angles [pic].



5. Discussion

The phenomenon of leaky wave excitation may have important applications
for development of X-ray and THz lasers.
For example, if [pic] (solid density, multiple ionized plasma), the
basic frequency [pic], [pic], [pic] we find, that the wavelength of leaky
wave [pic] is in soft x rays band. The intensity of x rays radiation in
this case is [pic], where [pic] is the intensity of incident (basic)
radiation.
If [pic] (low density gaseous plasma), the basic frequency [pic],
[pic], [pic] we find, that the wavelength of leaky wave [pic] is in THz
band. The intensity of THz radiation in this case is [pic].
This work was supported by Russian Foundation for Basic Research (Grant
Nos. 02-02-17271 and 04-02-16684) and Russian Science Support Foundation.

References

1. IEEE Trans. on Plasma Science, 1993, v.21, No.1. Special Issue on
Generation of Coherent Radiation Using Plasmas.
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3. V.B. Gildenburg, N.A.Zharova, M.I.Bakunov.//Phys.Rev. E, 2001,
v.63, p.066402.
4. M.I. Bakunov, V.B.Gildenburg, Y.Nishida, N.Yugami.// Phys. Plas
mas, 2001, v.8, p.2987.
5. N.V.Vvedenskii, V.B.Gildenburg.// JETP Lett., 2002, v.76, p.380.