Application of Non-Linear Optical Methods to Plasma Diagnostics

The application of non-linear optical methods nowadays allows the measurement of an increasing number of specific plasma quantities which were previously not amenable to diagnostics. Among those are state resolved measurements of molecular density distributions, sensitive measurement of light atomic radical densities, electric field measurements, and determination of quenching rates. In this paper an overview of the available techniques and trends is given. Some selected topics are discussed in more detail. Since the early days of plasma physics the emission of light from the discharge has always been a very valuable tool for the study of basic phenomena. This is still true'today where emission spectroscopy is finding wide application not only in research but also in process monitoring in industrial applications [1,2,3]. The sensitivity of the spectra to changes of the discharge conditions and the relatively modest experimental requirements have contributed to this development. However, to obtain an unambiguous picture of the physical conditions that lead to the measured spectra turns out to be often very difficult and one has to be very carehl when drawing conclusions. This is partly due to the complexity of the problem and partly to the lack of reliable atomic and molecular cross-sections [4]. Laser spectroscopy often allows a more direct interpretation of the measured data and in addition can be a more sensitive probe with, at the same time, better spatial and temporal resolution. Although for most laser techniques the experimental requirements are more demanding, many methods have become standard in plasma diagnostics. Examples are the determination of electron and ion distributions and densities by Thomson scattering, laser induced fluorescence spectroscopy for the measurement of neutral particle densities and ion drift velocities, and IR-absorption spectroscopy by laser diodes for the measurement of molecular populations in the ground states [5-101. These techniques have in common that the generated signal is proportional to the laser intensity and to the number of particles involved as long as saturation is avoided. Therefore they are called linear laser spectroscopy. For practical applications it might also be important that only a single laser system is required. Although these techniques are very powefil diagnostic tools, there are certain technical and basic physical limitations, e.g. available laser wavelengths or powers, selection rules for dipole transitions or absorption of gases in the VW. Nonlinear laser spectroscopy techniques allow some of these constraints to be overcome. In addition to serving as a diagnostic tool nonlinear optical techniques can also be applied to the generation of radiation necessary for linear as well as nonlinear spectroscopy. It is the aim of this paper to give an overview of the available techniques and to discuss briefly some examples of their applications to plasma diagnostics. However, in this frame it is not the intention to give a complete review of experiments and applications of nonlinear optics in plasma physics or to discuss all variants and aspects of a particular technique. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1997413 JOURNAL DE PHYSIQUE IV In the following a brief introduction to nonlinear spectroscopy will be given that leads to the classification of the basic phenomena into certain groups. For every group examples of application to plasma diagnostics will then be discussed in more detail. 2 SOME BASIC PIUNCIPPLES OF NONLINEAR LASER SPECTROSCOPY IN PLASMAS Nonlinear optical phenomena in the plasma itself (free electrons), like e.g. harmonic generation, parametric amplification, and phase conjugation, have been the subject of intense research especially in connection with laser induced plasmas and laser fusion [ll-161. However, in the framework of this paper nonlinear phenomena are defined to be connected to the interaction of the laser beams with neutral particles, i.e. with bound electrons. It is hrther assumed that no strong gradients are present and that the medium can be considered as isotropic. Thls assumption is justified in most cases of low as well as high temperature plasma applications. The interaction of radiation with matter is described by Maxwell's equations together with the susceptibility tensor [17-181. The susceptibility times the electric fields acts as the source term in the wave equations. This means that the electric fields of the laser beams are inducing a polarization in the medium and that this polarization generates a wave at the sum or difference of the frequencies of the incoming waves. As a consequence of the isotropy only nonlinear optical phenomena of third or higher odd order in the susceptibility are possible. Phenomena well known from optical crystals like frequency doubling are not possible in a plasma. With increasing order of the nonlinear effect the interaction efficiency is drastically reduced atrd therefore only third order effects or combinations of third and first order techniques have found application in plasma spectroscopy so far. In general four groups of nonlinear phenomena can be distinguished. As in linear spectroscopy the real and imaginary part of the susceptibility describe the refractive index and .the absorption of radiation, respectively. Although nonlinear in the intensity they are still linear with respect to the particle density. The most important example is two-photon absorption. Nonlinear dispersion as an isolated phenomenon is of no importance for plasma diagnostics. While absorption and dispersion are still similar to what is known from linear spectroscopy the following group has no such counterparts and a more detailed introduction will be given. The third group comprises phenomena based on the square of the absolute value of the susceptibility. These spectroscopic techniques are called four-wave mixing and they depend quadratically on the particle density. Probably the best known example is coherent anti-Stokes Raman scattering (CARS). No energy is dissipated in the medium but it acts like a "catalyst" for the generation of radiation, i.e. the sum of the photon energy of the incoming laser beams and the generated signal wave is conserved. Therefore the frequency of the signal wave can be only the sum or difference of the generating laser frequencies. The generated signal wave is highly directed with a low divergence like a laser beam and makes application especially favorable in cases of high radiation background. The reason for this directionality is the conservation of momentum. Since the atoms or molecules do not absorb photons the momentum of the photons has also to be conserved. In other words the sum of the k-vectors of the four waves involved has to be zero. Since the k-vector times the interaction length gives the phase of a wave this condition is called phase-matching. As a consequence propagation of the signal wave is only possible in a certain direction defined by the directions of the laser beams. Dispersion in the medium can change the value of the k-vectors and therefore for given frequencies this can restrict propagation to certain directions. This is especially pronounced in the VW and close to atomic or molecular one-photon resonances where dispersion is strong and is an important effect for the generation of VUV radiation by frequency mixing or high-order anti-Stokes Raman scattering. However, atomic and molecular resonances also greatly enhance the efficiency of four-wave mixing. For example the CARS technique is taking advantage of two-photon resonances to selectively probe vibrational and rotational levels. Since four-wave mixing generates radiation, it has found application as a direct diagnostic technique as well as a method for the efficient conversion of tunable laser radiation to frequencies that can not be generated otherwise. This radiation can then be again applied to linear or non-linear plasma spectroscopy. As a fourth group one may consider applications that are a combination of linear and nonlinear techniques like e.g. laser induced fluorescence among excited states after a previous two-photon excitation of the atom. Nonlinear spectroscopic techniques in plasma diagnostics are therefore either based on nonlinear absorption, four-wave mixing, or a combination of linear and nonlinear methods. Examples for these groups will be given in the following. In addition to be a spectroscopic technique, four-wave mixing is also applied to the generation of VW radiation for linear spectroscopy. 3 APPLICATIONS TO THE GENERATION OF RADIATION FOR LINEAR SPECTROSCOPY Without going into the details of the nonlinear processes two examples from high and low temperature plasmas should be mentioned. Here the radiation is generated by nonlinear optics but the spectroscopy is still linear. The selected examples show applications of the two most common methods for generation of laser radiation in the vacuum ultraviolet (VUV). For the detection of atomic hydrogen in the boundary layers of the tokamak experiment TEXTOR Bogen and Mertens developed a frequency tripling cell for the generation of coherent radiation at Lyman-a [19, 201. The frequency tripling cell filled with a mixture of krypton and argon converts radiation at 364.68 nm coming from a dye laser down to the third harmonic at 121.56 nm. The generated radiation is used for the measurement of atomic hydrogen densities by laser induced fluorescence spectroscopy. With particles at room temperature densities of the order of less than lo8 cm-3 could be detected. The population of the vibrational and rotational states of molecular hydrogen and deuterium in the electronic ground state is of great importance for the understanding of the formation of negative ions in magnetic multi-cusp sources. These populations can be measured with high sensitivity by absorption spectroscopy. However, tunable radiation in the W V in the spectral range between 120 nm and 140 nrn is required. This radiation has been generated in an experiment performed by Wagner and Dobele by stimulated anti-Stokes Raman scattering [21]. Population of vibrational levels between v = 2 and v = 6 could be investigated. In this case a cell filled with molecular hydrogen converts the pump radiation coming from a dye laser to a series of anti-Stokes orders spectrally displaced from the pump frequency by an integer number of the Raman-transition frequency of 4155 cm-'. Up to 15 anti-Stokes orders have been reported in the literature [22,23]. Recently the generation of very high anti-Stokes orders at short VUV wavelengths between 120 nm and 140 nm has been greatly improved by the combination of two Raman-cells (Fig. 1) [24,25]. Tunable dye-laser radiation around 370 nm is first passing through a high pressure Raman-cell filled with hydrogen. There a small amount of radiation at the wavelength of the first Stokes-order is generated. The