Rotating polarizer, compensator, and analyzer ellipsometry

In this paper we propose theoretically a set of ellipsometric configurations using a rotating polarizer, compensator, and analyzer at a speed ratio of N 1 ω: N 2 ω: N 3 ω. Different ellipsometric configurations can be obtained by giving different integral values to N 1, N 2, and N 3. All configurations are applied to bulk c-Si and GaAs to calculate the real and imaginary parts of the refractive index of the samples. The accuracies of all ellipsometric configurations are investigated in the presence of a hypothetical noise and with small misalignments of the optical elements. Moreover, the uncertainties in the ellipsometric parameters as functions of the uncertainties of the Fourier coefficients are studied. The comparison among different configurations reveals that the rotating compensator—analyzer configuration corresponds to the minimum error in the calculated optical parameters

Thermoelectricity Based on Cuo as a Semiconducting Material

In this paper, thermoelectricity based on copper(II) oxide CuO as semiconducting material is explored. The electrical properties of the samples were studied under different temperature gradients and pressures. Moreover, the effect of baking temperature was also investigated. CuO prepared using decomposition of Cu(NO3)2 as well as CuO nanopowder prepared using microwave-assisted synthesis technique were investigated and their results were compared. It was found that the current density can be enhanced with increasing the pressing pressure of the sample and when the sample undergoes a baking process. Moreover, it was found that the current density can be considerably enhanced with increasing the temperature gradient between the two ends of the sample. The CuO prepared using microwave-assisted synthesis technique was found to exhibit much better results over those of the CuO prepared using decomposition of Cu(NO3)2

Theoretical investigation of five-layer waveguide structure including two left-handed material layers for refractometric applications

A slab waveguide structure consisting of five layers is studied for optical sensing applications. The five-layer waveguide structure has a guiding dielectric film, two left-handed material (LHM) layers and two dielectric layers as a substrate and a cladding. The dispersion relation and the sensitivity to any change in the index of the analyte layer are derived. The sensitivity is explored with different parameters of the structure. It is found that the sensitivity of the proposed structure can be significantly improved with the increase of the index of the guiding layer and the decrease of the permittivity of the LHM layers. Moreover, it can be also improved with the increase of the thickness of the LHM layers

Photonic crystal as a refractometric sensor operated in reflection mode

In this work, one dimensional ternary photonic crystal is investigated as refractometric sensor. Using Chebyshev polynomials of the second kind, the transmission of an incident wave from a ternary photonic crystal is studied in details. The variation of the transmissivity with the angle of incidence and wavelength of incident light for different values of number of periods is investigated. Water and air are assumed to be analyte layers. It is found that for water as an analyte, the peak angular shift is Δθ = 1.6° and the peak wavelength shift is Δλ = 2.6 nm for a change in the index of refraction Δn = 0.02. Moreover, the peak angular shift can reach up to Δθ = 7.05° for specific values of the layer thicknesses

Propagation of p-polarized waves in a linearly graded index film surrounded by negative index materials

The theory of step-index waveguides is well-established. Most practical slab waveguide structures have a graded-index profile. The basic properties of graded-index planar waveguide structures are similar to those of step-index waveguides with subtle differences. The most common types of graded-index slab waveguides are linearly and exponentially graded-index profiles. We here treat linearly graded-index slab waveguide. In this work, a three-layer waveguide structure with linearly graded-index film is considered. We assume three structures: the first structure comprises a left-handed material (LHM) cladding, the second structure contains a LHM substrate layer and the third has a LHM cladding and substrate. Closed-form expressions for electric and magnetic fields and the characteristic equation are derived. The three normalized parameters: the asymmetry coefficient (a), the normalized film thickness

A spectroscopic ellipsometer using rotating polarizer and analyzer at a speed ratio 1: 1 and a compensator

Ellipsometers have been widely used in thin film characterization. They have shown a high degree of accuracy. We here propose theoretically a rotating polarizer and analyzer ellipsometer at a speed ratio 1:1 with a fixed compensator placed just after the rotating polarizer. Our calculations of the optical properties of c-Si and SiO reveal a substantial decrease in the percent error due to the fixed compensator. The uncertainties in the ellipsometric parameters as functions of the uncertainties of the Fourier coefficients are presented in details

Effect of the orientation of the fixed analyzer on the ellipsometric parameters in rotating polarizer and compensator ellipsometer with speed ratio 1: 1

In a recent work, rotating polarizer compensator ellipsometer (RPCE) with a fixed analyzer was proposed. Three different ellipsometric configurations were presented by considering different speed ratios of the rotating elements. It was shown the speed ratio 1:1 corresponds the minimum error in the calculated optical parameters of c-Si and GaAs samples. In this paper, we investigate the effect of the fixed analyzer alignment on the ellipsometric parameters and in RPCE structure with speed ratio 1:1 to find out the optimal angle at which the analyzer must be oriented to minimize the uncertainty in the calculated ellipsometric parameters. The uncertainties in the two ellipsometric parameters due to the uncertainties in Fourier coefficients are studied in details and it is found that an analyzer angle in the range – corresponds to the minimum uncertainty in and and therefore this range is recommended

Ellipsometric configurations using a phase retarder and a rotating polarizer and analyzer at any speed ratio

In this paper, we propose an ellipsometer using a phase retarder and rotating polarizer and analyzer at a speed ratio 1: N. Different ellipsometric configurations are presented by assuming N= 1, 2, and 3. Moreover, two values of the offset angle of the retarder are considered for each ellipsometric configuration. The Mueller formalism is employed to extract the Stokes parameters, from which the intensity received by the detector is obtained. The optical properties of c-Si are calculated using all configurations. A comparison between different configurations is carried out considering the effect of the noise on the results and the uncertainties in the ellipsometric parameters as functions of the uncertainties of the Fourier coefficients. It is found that the alignment of the phase retarder has a crucial impact on the results and the ellipsometric configuration with speed ratio 1: 1 is preferred over the other configurations

Thin film characterization using rotating polarizer analyzer ellipsometer with a speed ratio 1: 3

In a recent previous work, we proposed a rotating polarizer-analyzer ellipsometer (RPAE) in which the two elements are rotating synchronously in the same direction with a speed ratio 1: 3. We applied this technique to bulk samples. In this work, we present theoretically the characterization of 100 nm SiO2 thin film using this spectroscopic RPAE. We assume a structure consisting of air (ambient)/SiO2 (thin film)/c-Si (substrate). The ellipsometric parameters ψ and Δ are calculated when a clean signal is received by the detector and when a hypothetical noise is imposed on this signal. The film thickness and the optical constants of the film are calculated for the noisy signal in the spectrum range 200-800 nm. The results are compared with the proposed thickness and with the accepted values for SiO2 optical constants