Vector Electromagnetic Theory Research Articles

Transmittance analysis of diffraction phase grating

In order to accurately analyze and design the transmittance characteristic of a diffraction phase grating, the validity of both the scalar diffraction theory and the effective medium theory is quantitatively evaluated by the comparison of diffraction efficiencies predicted from both simplified theories to exact results calculated by the rigorous vector electromagnetic theory. The effect of surface profile parameters, including the normalized period, the normalized depth, and the fill factor for the precision of the simplified methods is determined at normal incidence. It is found that, in general, when the normalized period is more than four wavelengths of the incident light, the scalar diffraction theory is useful to estimate the transmittance of the phase grating. When the fill factor approaches 0.5, the error of the scalar method is minimized, and the scalar theory is accurate even at the grating period of two wavelengths. The transmittance characteristic as a function of the normalized period is strongly influenced by the grating duty cycle, but the diffraction performance on the normalized depth is independent of the fill factor of the grating. Additionally, the effective medium theory is accurate for evaluating the diffraction efficiency within an error of less than around 1% when no higher-order diffraction waves appear and only the zero-order waves exist. The precision of the effective medium theory for calculating transmittance properties as a function of the normalized period, the normalized groove depth, and the polarization state of incident light is insensitive to the fill factor of the phase grating.

VECTOR HOPKINS MODEL RESEARCH BASED ON OFF-AXIS ILLUMINATION IN NANOSCALE LITHOGRAPHY

Based on vector electromagnetic theory and the Waveguide Model, the vector Hopkins model is deduced. The model contains the vector Hopkins formula and the resist profile model of fast Optical Proximity Correction. The vector Hopkins formula considers incidence angles and azimuth angles of off-axis illumination, which differs from the traditional scalar Hopkins formula. The resist profile model is employed to analyze the effect of the photoresist diffusion under off-axis illumination by using self-adaptive Gaussian filter with scale adjustable, and a new transmission cross coefficient is obtained. The projection system parameters are introduced simultaneously, such as incidence angles, azimuth angles of off-axis illumination and diffusion parameters of photoresist. By simulating the aerial image of 3D mask in the actual lithography process, the optimal angular range of oblique incidence is studied; the image quality by impact with the oblique incidence angle is discussed as well.

Vector electromagnetic theory of transition and diffraction radiation with application to the measurement of longitudinal bunch size

We have developed a novel method based on vector electromagnetic theory and Schellkunoff's principles to calculate the spectral and angular distributions of transtion radiation (TR) and diffraction radiation (DR) produced by a charged particle interacting with an arbitrary target. The vector method predicts the polarization and spectral angular distributions of the radiation at an arbitrary distance form the source, i.e. in both the near and far fields, and in any direction of observation. The radiation fields of TR and DR calculated with the commonly used scalar Huygens model are shown to be limiting forms of those predicted by the vector theory and the regime of validity of the scalar theory is explicitly shown. Calculations of TR and DR done using the vector model are compared to results available in the literature for various limiting cases and for cases of more general interest. Our theory has important applications in the design of TR and DR diagnostics particularly those that utilize coherent TR or DR to infer the longitudinal bunch size and shape. A new technique to determine the bunch length using the angular distribution of coherent TR or DR is proposed.

Vectorial Hopkins formulation depending on angles of off-axis illumination

Basing on vector electromagnetic theory and the waveguide model, the vectorial Hopkins formula is deduced. It containes incidence angle and azimuth angle of off-axis illumination, which is different from the traditional scalar Hopkins formula. By simulating the aerial image of the three dimensional mask in actual lithography process, the optimal angular range of oblique incidence is analyzed, and the impact of oblique incidence angle on imaging quality is also discussed.

Numerical calculation of a converging vector electromagnetic wave diffracted by an aperture by using Borgnis potentials I General theory

A method is proposed, on the basis of the vector electromagnetic theory, for the numerical calculation of the diffraction of a converging electromagnetic wave by a circular aperture by using Borgnis potentials as auxiliary functions. The diffraction problem of vector electromagnetic fields is simplified greatly by solving the scalar Borgnis potentials. The diffractive field is calculated on the basis of the boundary integral equation, taking into consideration the contribution of the field variables on the diffraction screen surface, which is ignored in the Kirchhoff assumption. An example is given to show the effectiveness and suitability of this method and the distinctiveness of the diffractive fields caused by the vector characteristics of the electromagnetic fields.

Simulation of topographic images and artifacts in illumination-mode scanning-near-field optical microscopy

Scanning images in illumination-mode, scanning-near-field optical microscopy (SNOM) are numerically studied by the boundary element method based on rigorous vector electromagnetic theory. Computation results of constant-height and constant-distance images for samples with different topographic features are presented. Effects of the polarization of the input light and the optical parameters of samples on the resolution of SNOM are discussed. The artifacts in constant-distance images are also investigated. Numerical results indicate that the constant-height images for TM input light and constant-distance images for both TE and TM input light give only the local changes of the sample topography because of the loss of the low-frequency component of the topography.

Polarization of holographic grating diffraction. II. Experiment.

The transmittance, ellipsometric parameters, and depolarization of transmission, diffraction, and reflection of two volume holographic gratings (VHGs) are measured at a wavelength of 632.8 nm. The measured data are in good agreement with the theoretical simulated results, which demonstrated the correlation between the diffraction strength and the polarization properties of a VHG. Vector electromagnetic theory and polarization characterization are necessary for complete interpretation of the diffraction property of a VHG. The diffraction efficiency is measured at 532 nm in a polarization-sensing experiment. The measured data and theoretical simulation have demonstrated the potential application of the holographic beam splitter for polarization-sensor technology.

Optical Tunneling Effect of Solid Immersion Lens for High Density Optical Recording

A solid immersion lens has the advantage of decreasing the spot size and high optical coupling efficiency for high density data in optical recording. To accurately analyze the optical tunneling effect of the evanescent wave, the optical tunneling beam characteristics using the vector electro-magnetic theory are analyzed. The polarization dependence of the tunneling beam spot size, the energy transfer efficiency, and the coating layer effect are also clarified.