The phase-shifting mask consists of a normal transmission mask that has been coated with a transparent layer patterned to ensure that the optical phases of nearest apertures are opposite. Destructive interference between waves from adjacent apertures cancels some diffraction effects and increases the spatial resolution with which such patterns can be projected. A simple theory predicts a near doubling of resolution for illumination with partial incoherence σ < 0.3, and substantial improvements in resolution for σ < 0.7. Initial results obtained with a phase-shifting mask patterned with typical device structures by electron-beam lithography and exposed using a Mann 4800 10× tool reveals a 40-percent increase in usuable resolution with some structures printed at a resolution of 1000 lines/mm. Phase-shifting mask structures can be used to facilitate proximity printing with larger gaps between mask and wafer. Theory indicates that the increase in resolution is accompanied by a minimal decrease in depth of focus. Thus the phase-shifting mask may be the most desirable device for enhancing optical lithography resolution in the VLSI/VHSIC era.

Improving resolution in photolithography with a phase-shifting mask

Theoretical prediction of effective properties for multiphase material systems is very important not only to analysis and optimization of material performance, but also to new material designs. This review first examines the issues, difficulties and challenges in prediction of material behaviors by summarizing and critiquing the existing major analytical approaches dealing with material property modeling. The focus then shifts to some recent advances in numerical methodology that are able to predict more accurately and efficiently the effective physical properties of multiphase materials with complex internal microstructures. A random generation-growth algorithm is highlighted for reproducing multiphase microstructures, statistically equivalent to the actual systems, based on the geometrical and morphological information obtained from measurements and experimental estimations. Then a high-efficiency lattice Boltzmann solver for the corresponding governing equations is described which, while assuring energy conservation and the appropriate continuities at numerous interfaces in a complex system, has demonstrated its numerical power in yielding accurate solutions. Various applications are provided to validate the feasibility, effectiveness and robustness of this new methodology by comparing the predictions with existing experimental data from different transport processes, accounting for the effects due to component size, material anisotropy, internal morphology and multiphase interactions. The examples given also suggest even wider potential applicability of this methodology to other problems as long as they are governed by the similar partial differential equation(s). Thus, for given system composition and structure, this numerical methodology is in essence a model built on sound physics principles with prior validity, without resorting to ad hoc empirical treatment. Therefore, it is useful for design and optimization of new materials, beyond just predicting and analyzing the existing ones.

Predictions of effective physical properties of complex multiphase materials

Recently it has been shown that it is possible to achieve directional emission out of a subwavelength aperture in a periodically corrugated metallic thin film. We report on theoretical and experimental studies of a related phenomenon concerning light emitted from photonic crystal waveguides that are less than a wavelength wide. We find that the termination of the photonic crystal end facets and an appropriate choice of the wavelength are instrumental in achieving very low numerical apertures. Our results hold promise for the combination of photonic crystal waveguides with conventional optical systems such as fibers, waveguides, and freely propagating light beams.

Highly Directional Emission from Photonic Crystal Waveguides of Subwavelength Width

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We investigate the influence of array order in the optical transmission properties of subwavelength hole arrays, by comparing the experimental spectral transmittance of periodic and quasiperiodic hole arrays as a function of frequency. We find that periodicity and long-range order are not necessary requirements for obtaining enhanced and suppressed optical transmission, provided short-range order is maintained. Transmission maxima and minima are shown to result, respectively, from constructive and destructive interference at each hole, between the light incident upon and exiting from a given hole, and surface plasmon polaritons (SPPs) arriving from individual neighboring holes. These SPPs are launched along both illuminated and exit surfaces, by diffraction of the incident and emerging light at the neighboring individual subwavelength holes. By characterizing the optical transmission of a pair of subwavelength holes as a function of hole-hole distance, we demonstrate that a subwavelength hole can launch SPPs with an efficiency up to 35%, and with an experimentally determined launch phase φ = π/2, for both input-side and exit-side SPPs. This characteristic phase has a crucial influence on the shape of the transmission spectra, determining transmission minima in periodic arrays at those frequencies where grating coupling arguments would instead predict maxima.

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Universal optical transmission features in periodic and quasiperiodic hole arrays.

A graded index photonic crystal (GRIN PC) configuration was placed at the input side of a photonic crystal waveguide (PCW) in order to efficiently couple the light waves into the waveguide. We compared the transmission efficiencies of light in the absence and presence of the GRIN PC structure. We report a significant improvement in coupling when the GRIN PC is incorporated with the PCW. The intensity profiles were obtained by carrying out the experiments at microwave frequencies. Finite difference time domain based simulations were found to be in good agreement with our experimental results.

/pdf/high-efficiency-of-graded-index-photonic-crystal-as-an-input-4a3tnbp4dj.pdf

High efficiency of graded index photonic crystal as an input coupler

Spatial filtering is demonstrated at beam-type excitations by utilizing finite thickness slabs of two-dimensional dielectric photonic crystals (PCs) showing exotic Fabry–Perot resonances that are preserved over a wide range of variation of the incidence angle. Bandstop and dual-bandpass filtering effects are illustrated theoretically and the corresponding filters are validated in the microwave experiments by using square-lattice PCs. It is shown that the basic transmission features that were observed earlier for a plane-wave illumination are also recognizable at beam-type excitations. The proposed spatial filtering mechanism exhibits directional beaming. The desired widths and the locations of the passbands and stopbands are attainable in the angle domain with a proper choice of the operating frequency for the given excitation characteristics.

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Spatial filtering using dielectric photonic crystals at beam-type excitation

Unidirectional transmission is studied theoretically and experimentally for the gratings with one-side corrugations (non-symmetric gratings), which are based on two-dimensional photonic crystals composed of alumina rods. The unidirectional transmission appears at a fixed angle of incidence as a combined effect of the peculiar dispersion features of the photonic crystal and the properly designed corrugations. It is shown that the basic unidirectional transmission characteristics, which are observed at a plane-wave illumination, are preserved at Gaussian-beam and horn antenna illuminations. The main attention is paid to the single-beam unidirectional regime, which is associated with the strong directional selectivity arising due to the first negative diffraction order. An additional degree of freedom for controlling the transmission of the electromagnetic waves is obtained by making use of the asymmetric corrugations at the photonic crystal interface.

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Unidirectional transmission in photonic-crystal gratings at beam-type illumination

We report an enhanced transmission through a single circular subwavelength aperture that is incorporated with a split ring resonator (SRR) at the microwave regime. Transmission enhancement factors as high as 530 were observed in the experiments when the SRR was located in front of the aperture in order to efficiently couple the electric field component of the incident electromagnetic wave at SRR’s electrical resonance frequency. The experimental results were supported by numerical analyses. The physical origin of the transmission enhancement phenomenon was discussed by examining the induced surface currents on the structures.

/pdf/enhanced-transmission-through-a-subwavelength-aperture-using-4mbx4uay60.pdf

Enhanced transmission through a subwavelength aperture using metamaterials

We introduced fractal geometry to the conventional bowtie antennas. We experimentally and numerically showed that the resonance of the bowtie antennas goes to longer wavelengths, after each fractalization step, which is considered a tool to miniaturize the main bowtie structure. We also showed that the fractal geometry provides multiple hot spots on the surface, and it can be used as an efficient SERS substrate.

/pdf/validation-of-electromagnetic-field-enhancement-in-near-5dc1dxu8wd.pdf

Atilla Ozgur Cakmak

Papers

High efficiency of graded index photonic crystal as an input coupler

Spatial filtering using dielectric photonic crystals at beam-type excitation

Unidirectional transmission in photonic-crystal gratings at beam-type illumination

Enhanced transmission through a subwavelength aperture using metamaterials

Validation of electromagnetic field enhancement in near-infrared through Sierpinski fractal nanoantennas.