Continuous Refractive Index Profile Research Articles

Graded index all-dielectric lens antenna designed by phase manipulation and optical path rescaling

A rotationally symmetric all-dielectric lens antenna is designed by defining the phase function inside the dielectric directly via a closed-form series formula. The refractive index of the lens is modified using state-of-the-art optical path rescaling to keep the refractive index within practical values. The lens optimization is done using the genetic algorithm in MATLAB, where each case is evaluated by conducting linked ray tracing and full-wave electromagnetic simulation in COMSOL. A lens prototype is shown to provide a directivity enhancement of 5.1 dB compared to the optimal conical horn antenna, an improvement of 2 dB compared to the Luneburg lens, and an improvement of 3.8 dB compared to a reference graded index lens. All the examined cases shared a similar length of 5λ for the center frequency of 10 GHz. The prototype lens antenna has a maximum refractive index of 2.1, a reflection coefficient of −22 dB, and a side-lobe level of −25 dB at the center frequency of 10 GHz. The lens’ performance is consistent in the 9–11 GHz band supported by the standard circular waveguide. The results from a prototype with a discretized refractive index simulated in CST Studio Suite are in excellent agreement with the ones with a continuous refractive index profile simulated in COMSOL.

Terahertz oscillatory radiation torque at the microscale

We propose and demonstrate numerically, through time-domain simulations of Maxwell’s equations, a method to generate an oscillatory radiation torque of pN ⋅ μm strength and sub-picosecond period of oscillation. The approach is based on the change of light’s instantaneous angular momentum as it resonantly excites a micro-cylindrical rod possessing an azimuthally varying continuous refractive index profile. The torque amplitude and its oscillation period can be controlled by a proper change in the rod’s size and in light’s frequency and electric field amplitude.

Conformal optical devices based on geodesic lenses.

Conformal transformation optics provides a simple scheme for manipulating light rays with inhomogeneous isotropic dielectrics. However, there is usually discontinuity for refractive index profile at branch cuts of different virtual Riemann sheets, hence compromising the functionalities. To deal with that, we present a special method for conformal transformation optics based on geodesic lenses with special closed surfaces. The requirement is a continuous refractive index profile of dielectrics, which shows the almost perfect performance of designed devices. We demonstrate such a proposal by achieving conformal transparency (invisibility without cloaking region) and reflection. We can further achieve conformal invisible cloaks by two methods with perfect conductors. The conformal transformation optics method based on geodesic lenses may also find applications in other waves that obey the Helmholtz wave equation in two dimensions.

Reflection coefficient due to a discontinuity in the nth order derivative of the refractive index

Surfaces within a dielectric material, where the derivatives of a continuous and real refractive index profile are discontinuous, are shown to enhance reflection. To this end, the amplitude and phase representation of electromagnetic waves is used to model light propagating normally through a transparent medium with a continuous refractive index profile that varies only in one spatial direction. The amplitude equation is solved under the slowly varying refractive index approximation (SVRI). To isolate the effect of a single surface where the refractive index derivatives are discontinuous, an n(z) profile is proposed that is analytical, smooth and slowly varying except for a single piecewise junction. At this junction, n(z) is continuous but some of the mth order derivatives are not. Two different SVRI approximated solutions are joined at the discontinuity plane and, by demanding that boundary conditions are satisfied, a general complex reflection coefficient is obtained. By categorizing profiles according to the lowest order discontinuous derivative at the junction, a simple expression for the reflection coefficient can be written. Results are compared favorably with previous numerical solutions. Furthermore, a conjecture by the authors in a previous paper, ‘for a Cm−1 refractive index profile type, where m stands as the order of the lowest order discontinuous derivative, phase change upon reflection at the discontinuity plane is for an increasing lowest order discontinuous derivative and for the decreasing case’, is proved here.

Phase change of light reflected by a discontinuity in the derivatives of the refractive index

The amplitude and phase representation of classic plane electromagnetic waves is used to model light propagating through transparent stratified media, with a continuous refractive index profile. Numeric solutions for the nonlinear amplitude equation at normal incidence are obtained. Discontinuities of the refractive index derivatives exhibit reflection enhancement. Depending on the order of the discontinuity, the phase change upon reflection obtained from the numerical results can be ±π/2 in addition to the usual 0, or ±π.

Study of the feasibility of optical coatings with a continuous refractive index profile

The effect of the instability of deposition rates on the spectral characteristics of optical coatings with a continuous refractive index profile was studied. A correlation between the error level in the experimental data and the accuracy of the reproducibility of spectral characteristics of these coatings was found.

Towards a more accurate refractive index profile of ion-exchanged waveguides

We evaluated the accuracy of the standard m-line method in the description of the refractive index profile of ion-exchanged waveguides by comparing its results with those from energy dispersion spectroscopy and direct near-surface/extended Brewster–Pfund (DNS-B) Method. Looking at a few single and double-exchange processes, the comparison shows three major situations: (i) the m-line accuracy is validated by the other two methods; (ii) discontinuity of ion-concentration does not allow the assumption of a continuous refractive index profile; or (iii) although the overall m-line profile is compatible with results from the other two methods, these significantly depart by a near-surface inflection-in which case, the DNS-B can be used together with the m-line experimental data to produce a more accurate index profile.

Analysis of inhomogeneous thin films of ZrO2 by the combined optical method and atomic force microscopy

AbstractIn this paper results concerning the complete optical analysis of inhomogeneous ZrO2 films are introduced. The optical analysis of these films is carried out using the combined optical method based on interpreting experimental data corresponding to variable angle of incidence spectroscopic ellipsometry (VASE) and near‐normal incidence spectroscopic reflectometry (NNSR). The model of the ZrO2 films used for interpretation of the experimental data achieved using the combined method exhibits a continuous refractive index profile. It is shown that this model is satisfactory for treating the experimental data. Further, it is shown that all the parameters characterizing the model mentioned can be determined with high accuracy. By means of atomic force microscopy (AFM) it is found that the upper boundaries of the inhomogeneous ZrO2 films are slightly rough. The values of the basic statistical quantities characterizing this boundary roughness are evaluated using the AFM data. The optical inhomogeneity of the ZrO2 films studied is explained by the columnar structure of these films. Copyright © 2001 John Wiley & Sons, Ltd.

Antireflection coating on germanium for dual channel (3–5 and 7.5–10.6 μm) thermal imagers

The dual channel thermal imager, operating in the 3–5 and 7.5–10.6 μm wavelength bands, is one of the latest achievements in instrumentation for target recognition and acquisition. While the 3–5 μm band is utilised for detecting hot objects such as engine exhausts of vehicles and fighter planes, the 7.5–10.6 μm band is employed for human bodies and objects at ambient temperatures. Many substrates are available which transmit in both these wavelength bands and their transmission can be enhanced by providing a suitable antireflection coating. In this paper, a broad band antireflection coating on germanium substrate is reported. The design approach involves achieving a continuously varying refractive index from that of the incident medium to the substrate. The continuously varying refractive index profile may be generated by using a sequence of thin layers of high and low refractive index materials. In this design a continuous refractive index profile is approximated by using a 13-layer stack of thorium fluoride and germanium as low and high index coating materials respectively. This coating conforms to environmental stability standards and shows an average transmission of 91% in 3–5 μm band and 94.5% in 7.5–10.6 μm band with a peak of 97% at 9 μm on 10 mm thick germanium substrate. Polycrystalline germanium has 2.5% absorption for a 10 mm thick substrate.