New type of ellipsometry in infrared spectroscopy: The double-reference method

We have developed a conceptually new type of ellipsometry which allows the determination of the complex refractive index by simultaneously measuring the unpolarized normal-incidence reflectivity relative to the vacuum and to another reference media. From these two quantities the complex optical response can be directly obtained without Kramers-Kronig transformation. Due to its transparency and large refractive index over a broad range of the spectrum, from the far-infrared to the soft ultraviolet region, diamond can be ideally used as a second reference. The experimental arrangement is rather simple compared to other ellipsometric techniques.Comment: submitted to Appl. Phys. Let

Constructing Fresnel reflection coefficients by ruler and compass

A simple and intuitive geometical method to analyze Fresnel formulas is presented. It applies to transparent media and is valid for perpendicular and parallel polarizations. The approach gives a graphical characterization particularly simple of the critical and Brewster angles. It also provides an interpretation of the relation between the reflection coefficients for both basic polarizations as a symmetry in the plane

Line tension and structure of smectic liquid crystal multilayers at the air-water interface

At the air/water interface, 4,-8-alkyl[1,1,-biphenyl]-4-carbonitrile (8CB) domains with different thicknesses coexist in the same Langmuir film, as multiple bilayers on a monolayer. The edge dislocation at the domain boundary leads to line tension, which determines the domain shape and dynamics. By observing the domain relaxation process starting from small distortions, we find that the line tension is linearly dependent on the thickness difference between the coexisting phases in the film. Comparisons with theoretical treatments in the literature suggest that the edge dislocation at the boundary locates near the center of the film, which means that the 8CB multilayers are almost symmetric with respect to the air/water interface.Comment: 21 pages, 6 figure

Optical Study of the Free Carrier Response of LaTiO3/SrTiO3 Superlattices

We used infrared spectroscopic ellipsometry to investigate the electronic properties of LaTiO3/SrTiO3 superlattices (SLs). Our results indicated that, independent of the SL periodicity and individual layer-thickness, the SLs exhibited a Drude metallic response with sheet carrier density per interface ~3x10^14 cm^-2. This is probably due to the leakage of d-electrons at interfaces from the Mott insulator LaTiO3 to the band insulator SrTiO3. We observed a carrier relaxation time ~ 35 fs and mobility ~ 35 cm^2V^-1s^-1 at 10 K, and an unusual temperature dependence of carrier density that was attributed to the dielectric screening of quantum paraelectric SrTiO3.Comment: 4 pages, 4 figure

Fresnel coefficients as hyperbolic rotations

We describe the action of a plane interface between two semi-infinite media in terms of a transfer matrix. We find a remarkably simple factorization of this matrix, which enables us to express the Fresnel coefficients as a hyperbolic rotation.Comment: 6 pages, 3 figure

The language of Einstein spoken by optical instruments

Einstein had to learn the mathematics of Lorentz transformations in order to complete his covariant formulation of Maxwell's equations. The mathematics of Lorentz transformations, called the Lorentz group, continues playing its important role in optical sciences. It is the basic mathematical language for coherent and squeezed states. It is noted that the six-parameter Lorentz group can be represented by two-by-two matrices. Since the beam transfer matrices in ray optics is largely based on two-by-two matrices or $ABCD$ matrices, the Lorentz group is bound to be the basic language for ray optics, including polarization optics, interferometers, lens optics, multilayer optics, and the Poincar\'e sphere. Because the group of Lorentz transformations and ray optics are based on the same two-by-two matrix formalism, ray optics can perform mathematical operations which correspond to transformations in special relativity. It is shown, in particular, that one-lens optics provides a mathematical basis for unifying the internal space-time symmetries of massive and massless particles in the Lorentz-covariant world.Comment: LaTex 8 pages, presented at the 10th International Conference on Quantum Optics (Minsk, Belarus, May-June 2004), to be published in the proceeding

Electron effective mass in Sn-doped monoclinic single crystal β\beta-gallium oxide determined by mid-infrared optical Hall effect

The isotropic average conduction band minimum electron effective mass in Sn-doped monoclinic single crystal $\beta$-Ga$_2$O$_3$ is experimentally determined by mid-infrared optical Hall effect to be $(0.284\pm0.013)m_{0}$ combining investigations on ($010$) and ($\bar{2}01$) surface cuts. This result falls within the broad range of values predicted by theoretical calculations for undoped $\beta$-Ga$_2$O$_3$. The result is also comparable to recent density functional calculations using the Gaussian-attenuation-Perdue-Burke-Ernzerhof hybrid density functional, which predict an average effective mass of $0.267m_{0}$ (arXiv:1704.06711 [cond-mat.mtrl-sci]). Within our uncertainty limits we detect no anisotropy for the electron effective mass, which is consistent with most previous theoretical calculations. We discuss upper limits for possible anisotropy of the electron effective mass parameter from our experimental uncertainty limits, and we compare our findings with recent theoretical results

Iwasawa Effects in Multi-layer Optics

There are many two-by-two matrices in layer optics. It is shown that they can be formulated in terms of a three-parameter group whose algebraic property is the same as the group of Lorentz transformations in a space with two space-like and one time-like dimensions, or the $Sp(2)$ group which is a standard theoretical tool in optics. Among the interesting mathematical properties of this group, the Iwasawa decomposition drastically simplifies the matrix algebra under certain conditions, and leads to a concise expression for the S-matrix for transmitted and reflected rays. It is shown that the Iwasawa effect can be observed in multi-layer optics, and a sample calculation of the S-matrix is given.Comment: RevTex 10 pages including 1 psfi

Surface roughness in XeF2 etching of a-Si/c-Si(100)

Single wavelength ellipsometry and at. force microscopy (AFM) were applied in a well-calibrated beam-etching expt. to characterize the dynamics of surface roughening induced by chem. etching of a .apprx.12 nm amorphous Si (a-Si) top layer and the underlying cryst. Si (c-Si) bulk. In both the initial and final phase of etching, where either only a-Si or only c-Si is exposed to the XeF2 flux, we observe a similar evolution of the surface roughness as a function of the XeF2 dose proportional to D(XeF2)b with b~0.2. In the transition region from the pure amorphous to the pure cryst. silicon layer, we observe a strong anomalous increase of the surface roughness proportional to D(XeF2)b with b~1.5. Not only the growth rate of the roughness increases sharply in this phase, also the surface morphol. temporarily changes to a structure that suggests a cusp-like shape. The remaining a-Si patches on the surface act effectively as a capping layer which causes the growth of deep trenches in the c-Si. The ellipsometry data on the roughness are corroborated by the AFM results, by equating the thickness of the rough layer to 6 s, with s the root-mean-square variation of the AFM's distribution function of height differences. In the AFM data, the anomalous behavior is reflected in a too small value of s which again suggests narrow and deep surface features that cannot be tracked by the AFM tip. The final phase morphol. is characterized by an effective increase in surface area by a factor of two, as derived from a simple bilayer model of the reaction layer, using the exptl. etch rate as input. We obtain a local reaction layer thickness of 1.5 monolayer consistent with the 1.7 ML value of Lo et al. [Lo et al., Phys. Rev. B 47, 648 (1993)] that is also independent of surface roughness. [on SciFinder (R)

Nematic liquid crystal alignment on chemical patterns

Patterned Self-Assembled Monolayers (SAMs) promoting both homeotropic and planar degenerate alignment of 6CB and 9CB in their nematic phase, were created using microcontact printing of functionalised organothiols on gold films. The effects of a range of different pattern geometries and sizes were investigated, including stripes, circles and checkerboards. EvanescentWave Ellipsometry was used to study the orientation of the liquid crystal (LC) on these patterned surfaces during the isotropic-nematic phase transition. Pretransitional growth of a homeotropic layer was observed on 1 ¹m homeotropic aligning stripes, followed by a homeotropic mono-domain state prior to the bulk phase transition. Accompanying Monte-Carlo simulations of LCs aligned on nano-patterned surfaces were also performed. These simulations also showed the presence of the homeotropic mono-domain state prior to the transition.</p