Hänsch--Couillaud locking of Mach--Zehnder interferometer for carrier removal from a phase-modulated optical spectrum

We describe and analyse the operation and stabilization of a Mach--Zehnder interferometer, which separates the carrier and the first-order sidebands of a phase-modulated laser field, and which is locked using the H\"ansch--Couillaud method. In addition to the necessary attenuation, our interferometer introduces, via total internal reflection, a significant polarization-dependent phase delay. We employ a general treatment to describe an interferometer with an object which affects the field along one path, and we examine how this phase delay affects the error signal. We discuss the requirements necessary to ensure the lock point remains unchanged when phase modulation is introduced, and we demonstrate and characterize this locking experimentally. Finally, we suggest an extension to this locking strategy using heterodyne detection.

A Phase-field Model for Computer Simulation of Lamellar Structure Formation in y-TiAI

In the present paper, a phase-field model is developed to simulate the formation and evolution of lamellar microstructure in γ-TiAl alloys. The mechanism of formation of TiAl lamellae proposed by Denquin and Naka is incorporated into the model. The model describes the formation and evolution of the face-centered cubic (fcc) stacking lamellar zone followed by the subsequent appearance and growth of the γ-phase, involving both the chemical composition change by atom transfer and the ordering of the fcc lattice. The thermodynamics of the model system and the interaction between the displacive and diffusional transformations are described by a non-equilibrium free energy formulated as a function of concentration and structural order parameter fields. The long-range elastic interactions, arising from the lattice misfit between the α, fcc (A1) and the various orientation variants of the γ-phase are taken into account by incorporating of the elastic strain energy into the total free energy. Simulation studies based on the model successfully predicted some essential features of the lamellar structure. It is found that the formation and evolution of the lamellar structure are predominantly controlled by the minimization of the elastic energy of the interfaces between the different fcc stacking groups, low-symmetry product phase γ and the high-symmetry α-phase, as well as between the various orientation variants of the product phase.

Channelled Waves in Anisotropic Mesh Metamaterials

Channelled waves in 2-D periodic anisotropic L-C mesh metamaterials have been investigated. Circuit simulation and the newly developed analytical model of a unit cell have demonstrated full qualitative agreement for both lossless and lossy cases. Isofrequencies for a lattice unit cell and the circuit simulations of finite meshes have shown that propagating waves are channelled from a point source as pencil beams which can travel only along specific trajectories. The beam direction varies with frequency, and at the resonance frequency, the phase and group velocities of the travelling wave are orthogonal. The effect of losses was explored, and it was shown that losses cause qualitative changes of the channelled wave type. It was proven that the channelled waves do not follow the laws of geometrical optics (Snell's law, specular reflection, etc.) at the interfaces of L-C meshes but are governed by the conditions of phase synchronism and impedance matching. Only in the special case of dual L-C and C-L meshes with the interface parallel to the axis of rectangular grid excited at the resonance frequency (X=1) do the channels follow the trajectories of optical rays. A planar mesh test cell has been designed and used for retrieving the unit cell L-C parameters from the S-parameter measurements.

Phase-resolved emission spectroscopy of a hydrogen rf discharge for the determination of quenching coefficients

Collisional effects can have strong influences on the population densities of excited states in gas discharges at elevated pressure. The knowledge of the pertinent collisional coefficient describing the depopulation of a specific level (quenching coefficient) is, therefore, important for plasma diagnostics and simulations. Phase resolved optical emission spectroscopy (PROES) applied to a capacitively coupled rf discharge excited with a frequency of 13.56 MHz in hydrogen allows the measurement of quenching coefficients for emitting states of various species, particularly of noble gases, with molecular hydrogen as a collision partner. Quenching coefficients can be determined subsequent to electron-impact excitation during the short field reversal phase within the sheath region from the time behavior of the fluorescence. The PROES technique based on electron-impact excitation is not limited â?? in contrast to laser techniques â?? by optical selection rules and the energy gap between the ground state and the upper level of the observed transition. Measurements of quenching coefficients and natural fluorescence lifetimes are presented for several helium (3 1S,4 1S,3 3S,3 3P,4 3S), neon (2p1 ,2p2 ,2p4 ,2p6), argon (3d2 ,3d4 ,3d18 and 3d3), and krypton (2p1 ,2p5) states as well as for some states of the triplet system of molecular hydrogen.

Spectroscopic measurements of phase-resolved electron energy distribution functions in RF-excited discharges

The reliable measurement of the electron energy distribution function (EEDF) of plasmas is one of the most important subjects of plasma diagnostics, because this piece of information is the key to understand basic discharge mechanisms. Specific problems arise in the case of RF-excited plasmas, since the properties of electrons are subject to changes on a nanosecond time scale and show pronounced spatial anisotropy. We report on a novel spectroscopic method for phase- and space-resolved measurements of the electron energy distribution function of energetic (> 12 eV) electrons in RF discharges. These electrons dominate excitation and ionization processes and are therefore of particular interest. The technique is based on time-dependent measurements during the RF cycle of excited-state populations of rare gases admixed in small fractions. These measurements yield � in combination with an analytical model � detailed information on the excitation processes. Phase-resolved optical emission spectroscopy allows us to overcome the difficulties connected with the very low densities (107�109 cm�3) and the transient character of the electrons in the sheath region. The EEDF of electrons accelerated in the sheath region can be described by a shifted Maxwellian with a drift velocity component in direction of the electric field. The method yields the high-energy tail of the EEDF on an absolute scale. The applicability of the method is demonstrated at a capacitively coupled RF discharge in hydrogen.

Signal-to-Noise Ratio Analysis for Nonlinear N-ary Phase Filters

The problem of recognising targets in non-overlapping clutter using nonlinear N-ary phase filters is addressed. Using mathematical analysis, expressions were derived for an N-ary phase filter and the intensity variance of an optical correlator output. The N-ary phase filter was shown to consist of an infinite sum of harmonic terms whose periodicity was determined by N. For the intensity variance, it was found that under certain conditions the variance was minimised due to a hitherto undiscovered phase quadrature effect. Comparison showed that optimal real filters produced greater SNR values than the continuous phase versions as a consequence of this effect.

Optical diagnostics of micro discharge jets

Micro plasmas operated at ambient pressure with dimensions of the confining geometry in the order of a few ten micrometers to a millimeter are actually in the focus of interest due to the broad regime of applicability they offer and due to a similarly broad range of open physical questions. Here we present optical measurements within the discharge core and the effluent region of an especially developed micro discharge jet. To get an understanding of the complex system of this discharge it is important to analyse transport phenomena of energy and particles within both parts of the discharge by various highly sophisticated diagnostics. As a consequence of the limited access and the dimensions of the micro discharge most of these diagnostics are optical. Here we present diagnostics applied to determine spatially resolved absolute atomic oxygen densities as the most reactive constituent of the effluent, density maps of ozone as final reaction product of the gas chemical chain induced by the discharge and phase resolved optical emission spectroscopy yielding insight into the excitation dynamics of the discharge. (C) 2007 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim.

Space and phase resolved plasma parameters in an industrial dual-frequency capacitively coupled radio-frequency discharge

The dynamics of high energetic electrons (>= 11.7 eV) in a modified industrial confined dual-frequency capacitively coupled RF discharge (Exelan, Lam Research Inc.), operated at 1.937 MHz and 27.118 MHz, is investigated by means of phase resolved optical emission spectroscopy. Operating in a He-O-2. plasma with small rare gas admixtures the emission is measured, with one-dimensional spatial resolution along the discharge axis. Both the low and high frequency RF cycle are resolved. The diagnostic is based on time dependent measurements of the population densities of specifically chosen excited rare gas states. A time dependent model, based on rate equations, describes the dynamics of the population densities of these levels. Based on this model and the comparison of the excitation of various rare gas states, with different excitation thresholds, time and space resolved electron temperature, propagation velocity and qualitative electron density as well as electron energy distribution functions are determined. This information leads to a better understanding of the dual-frequency sheath dynamics and shows, that separate control of ion energy and electron density is limited.

Determination of the degree of dissociation in an inductively coupled hydrogen plasma using optical emission spectroscopy and laser diagnostics

Gas temperature is of major importance in plasma based surface treatment, since the surface processes are strongly temperature sensitive. The spatial distribution of reactive species responsible for surface modification is also influenced by the gas temperature. Industrial applications of RF plasma reactors require a high degree of homogeneity of the plasma in contact with the substrate. Reliable measurements of spatially resolved gas temperatures are, therefore, of great importance. The gas temperature can be obtained, e.g. by optical emission spectroscopy (OES). Common methods of OES to obtain gas temperatures from analysis of rotational distributions in excited states do not include the population dynamics influenced by cascading processes from higher electronic states. A model was developed to evaluate this effect on the apparent rotational temperature that is observed. Phase resolved OES confirmed the validity of this model. It was found that cascading leads to higher apparent temperatures, but the deviation (~25 K) is relatively small and can be ignored in most cases. This analysis is applied to investigate axially and radially resolved temperature profiles in an inductively coupled hydrogen RF discharge.

Determination of quenching coefficients in a hydrogen RF discharge by time-resolved optical emission spectroscopy

In gas discharges at elevated pressure, radiation-less collisional de-excitation (quenching) has a strong influence on the population of excited states. The knowledge of quenching coefficients is therefore important for plasma diagnostics and simulations. A novel time-resolved optical emission spectroscopic (OES) technique allows the measurement of quenching coefficients for emission lines of various species, particularly of noble gases, with molecular hydrogen as collision partner. The technique exploits the short electron impact excitation during the field reversal phase within the sheath region of a hydrogen capacitively coupled RF discharge at 13.56 MHz. Quenching coefficients can be determined subsequent to this excitation from the effective lifetime of the fluorescence decay at various hydrogen pressures. The measured quenching coefficients agree very well with results obtained by means of laser excitation. The time-resolved OES technique based on electron impact excitation is not limited - in contrast to laser techniques - by optical selection rules and the energy gap between the ground state and the observed excited level.

Plasma Ionization in Low-Pressure Radio-Frequency Discharges. Part I: Optical Measurements

The electron dynamics in the low-pressure operation regime ($«$ 5 Pa) of a neon capacitively coupled plasma is investigated using phase-resolved optical emission spectroscopy. Plasma ionization and sustainment mechanisms are governed by the expanding and contracting sheath and complex wave–particle interactions. Electrons are energized through the advancing and retreating electric field of the RF sheath. The associated interaction of energetic sheath electrons with thermal bulk plasma electrons drives a two-stream instability also dissipating power in the plasma.