Supersymmetric Chern-Simons Theory in Presence of a Boundary in the Light-Like Direction

In this paper, we will analyze a three dimensional supersymmetric Chern-Simons theory on a manifold with a boundary. The boundary we will consider in this paper will be defined by $n\cdot x=0$, where $n$ is a light-like vector. It will be demonstrated that this boundary is preserved under the action of the $SIM(1)$ subgroup of the Lorentz group. Furthermore, the presence of this boundary will break half of the supersymmetry of the original theory. As the original Chern-Simons theory had $\mathcal{N} =1$ supersymmetry in absence of a boundary, it will only have $\mathcal{N}=1/2$ supersymmetry in presence of this boundary. We will also observe that the Chern-Simons theory can be made gauge invariant by introducing new degrees of freedom on the boundary. The gauge transformation of these new degrees of freedom will exactly cancel the boundary term obtained from the gauge transformation of the Chern-Simons theory.Comment: 24 pages, Accepted in Nucl. Phys.

Chern-Simons Theory in SIM(1) Superspace

In this paper, we will analyse a three dimensional supersymmetric Chern-Simons theory in SIM(1) superspace formalism. The breaking of the Lorentz symmetry down to the SIM(1) symmetry, breaks half the supersymmetry of the Lorentz invariant theory. So, the supersymmetry of the Lorentz invariant Chern-Simons theory with N=1 supersymmetry will break down to N=1/2 supersymmetry, when the Lorentz symmetry is broken down to the SIM(1) symmetry. First, we will write the Chern-Simons action using SIM(1) projections of N=1 superfields. However, as the SIM(1) transformations of these projections are very complicated, we will define SIM(1) superfields which transform simply under SIM(1) transformations. We will then express the Chern-Simons action using these SIM(1) superfields. Furthermore, we will analyse the gauge symmetry of this Chern-Simons theory. This is the first time that a Chern-Simons theory with N=1/2 supersymmetry will be constructed on a manifold without a boundary.Comment: 26 page

SIM(2) and supergraphs

We construct Feynman rules and Supergraphs in SIM(2) superspace. To test our methods we perform a one-loop calculation of the effective action of the SIM(2) supersymmetric Wess-Zumino model including a term which explicitly breaks Lorentz invariance. The renormalization of the model is also discussed.Comment: 28 page

Optics of Inhomogeneous Thin Films with Defects: Application to Optical Characterization

This review paper is devoted to optics of inhomogeneous thin films exhibiting defects consisting in transition layers, overlayers, thickness nonuniformity, boundary roughness and uniaxial anisotropy. The theoretical approaches enabling the inclusion of these defects into formulae expressing the optical quantities of these inhomogeneous thin films are summarized. These approaches are based on the recursive and matrix formalisms for the transition layers and overlayers, averaging of the elements of the Mueller matrix using local thickness distribution or polynomial formulation for the thickness nonuniformity, scalar diffraction theory and Rayleigh-Rice theory or their combination for boundary roughness and Yeh matrix formalism for uniaxial anisotropy. The theoretical results are illustrated using selected examples of the optical characterization of the inhomogeneous polymer-like thin films exhibiting the combination of the transition layers and thickness nonuniformity and inhomogeneous thin films of nonstoichiometric silicon nitride with the combination of boundary roughness and uniaxial anisotropy. This characterization is realized by variable angle spectroscopic ellipsometry and spectroscopic reflectometry. It is shown that using these optical techniques, the complete optical characterization of the mentioned thin films can be performed. Thus, it is presented that the values of all the parameters characterizing these films can be determined

Optical characterization of inhomogeneity of polymer-like thin films arising in the initial phase of plasma-enhanced chemical vapor deposition

In this study, an optical investigation in a wide spectral range of polymer-like (SiOxCyHz) thin films deposited by plasma-enhanced chemical vapor deposition (PECVD) is presented. The primary focus is on assessing the homogeneity of the grown films. Within the PECVD, it is possible to alter the properties of the deposited material by continually adjusting deposition process parameters and hence allow for the growth of inhomogeneous layers. However, as shown in this study, the growth of homogeneous layers could be similarly challenging. This challenge is especially pronounced at the beginning of the deposition process, where it is necessary to consider the influence of the substrate among other factors, as even slight variations in the deposition conditions can lead to the formation of inhomogeneous layers. Several series of polymer-like thin films were deposited onto silicon substrates with the goal of producing homogeneous layers, i.e. all deposition parameters were held constant. These samples were optically characterized with a special interest in homogeneity, especially at the beginning of the growth. It was found that initial inhomogeneous growth is always present. The thickness of the initial inhomogeneous part was found to be surprisingly large

Optical Characterization of Gadolinium Fluoride Films Using Universal Dispersion Model

The optical characterization of gadolinium fluoride (GdF3) films is performed in a wide spectral range using heterogeneous data-processing methods (the ellipsometric and spectrophotometric measurements for five samples with thicknesses ranging from 20 to 600 nm are processed simultaneously). The main result of the characterization is the optical constants of GdF3 in the range from far infrared to vacuum ultraviolet, both in the form of a table and in the form of dispersion parameters of the universal dispersion model (UDM). Such reliable data in such a broad spectral range have not been published so far. The GdF3 films exhibit several defects related to the porous polycrystalline structure, namely, surface roughness and a refractive index profile, which complicate the optical characterization. The main complication arises from the volatile adsorbed components, which can partially fill the pores. The presented optical method is based on the application of the UDM for the description of the optical response of GdF3 films with partially filled pores. Using this dispersion model, it is possible to effectively separate the optical response of the host material from the response of the adsorbed components. Several recently published structural and dispersion models are used for optical characterization for the first time. For example, a model of inhomogeneous rough films based on Rayleigh–Rice theory or asymmetric peak approximation with a Voigt profile for the phonon spectra of polycrystalline materials

Optical Characterization of Gadolinium Fluoride Films Using Universal Dispersion Model

The optical characterization of gadolinium fluoride (GdF3) films is performed in a wide spectral range using heterogeneous data-processing methods (the ellipsometric and spectrophotometric measurements for five samples with thicknesses ranging from 20 to 600 nm are processed simultaneously). The main result of the characterization is the optical constants of GdF3 in the range from far infrared to vacuum ultraviolet, both in the form of a table and in the form of dispersion parameters of the universal dispersion model (UDM). Such reliable data in such a broad spectral range have not been published so far. The GdF3 films exhibit several defects related to the porous polycrystalline structure, namely, surface roughness and a refractive index profile, which complicate the optical characterization. The main complication arises from the volatile adsorbed components, which can partially fill the pores. The presented optical method is based on the application of the UDM for the description of the optical response of GdF3 films with partially filled pores. Using this dispersion model, it is possible to effectively separate the optical response of the host material from the response of the adsorbed components. Several recently published structural and dispersion models are used for optical characterization for the first time. For example, a model of inhomogeneous rough films based on Rayleigh–Rice theory or asymmetric peak approximation with a Voigt profile for the phonon spectra of polycrystalline materials