Optimization of anisotropically etched silicon surface-relief gratings for substrate-mode optical interconnects

The optimum profiles of right-angle-face anisotropically etched silicon surface-relief gratings illuminated at normal incidence for substrate-mode optical interconnects are determined for TE, TM, and random linear (RL) polarizations. A simulated annealing algorithm in conjunction with the rigorous coupled-wave analysis is used. The optimum diffraction efficiencies of the -1 forward-diffracted order are 37.3%, 67.1%, and 51.2% for TE-, TM-, and RL-polarization-optimized profiles, respectively. Also, the sensitivities to grating thickness, slant angle, and incident angle of the optimized profiles are presented.     

Optimization of sawtooth surface-relief gratings: effects of substrate refractive index and polarization

The effect of the refractive index of the substrate together with the incident polarization on the optimization of sawtooth surface-relief gratings (SRGs) is investigated. The global optimum diffraction efficiencies of the -1st forward-diffracted order of sawtooth SRGs are 63.3% occurring at n2=1.47 for TE polarization and 73.8% occurring at n2=2.88 for TM polarization. Incident TE polarization has higher optimum diffraction efficiency than TM polarization for all n2<1.85. In contrast, TM polarization has higher optimum diffraction efficiency than TE polarization for all n2>1.85. A polymer (n2=1.5) optimum sawtooth SRG exhibits 62.6% efficiency for TE polarization. A silicon (n2=3.475) optimum sawtooth SRG exhibits 68.6% efficiency for TM polarization. These sawtooth SRGs are compared to right-angle-face trapezoidal SRGs. It is found that the optimum profiles of right-angle-face trapezoidal SRGs have only very slightly increased efficiencies over sawtooth SRGs (0.04% for TE and 0.55% for TM).     

Design of transmission blazed binary gratings for optical limiting with the form-birefringence theory

The structure of transmission blazed binary gratings for optical limiting is designed with the form-birefringence theory. This kind of grating has subwavelength features, can imitate the transmission blazed grating effectively, and has higher efficiencies than a transmission blazed grating with a subwavelength structure. The diffraction efficiencies are calculated and analyzed. For the normal incident light with 10.6 microm wavelength, the transmissivities for the designed grating at 0 degrees deviation angle for TE and TM polarizations are 0.05% and 5.09%, respectively, which are basically identical to the results of the finite-difference time-domain method. The diffraction efficiencies of the first transmitted order for TE and TM polarizations are 93.95% and 83.88%, respectively.     

Optical measurement of depth and duty cycle for binary diffraction gratings with subwavelength features

We describe a new and unique method for simultaneous determination of the groove depth and duty cycle of binary diffraction gratings. For a near-normal angle of incidence, the +1 and -1 diffracted orders will behave nearly the same as the duty cycle is varied for a fixed grating depth. The difference in their behavior, quantified as the ratio of their respective diffraction efficiencies, is compared to a look-up table generated by rigorous coupled-wave theory, and the duty cycle of the grating is thus obtained as a function of grating depth. Performing the same analysis for the orthogonal probe-light polarization results in a different functional dependence of the duty cycle on the grating depth. By use of both TE and TM polarizations, the depth and duty cycle for the grating are obtained by the intersection of the functions generated by the individual polarizations. These measurements can also be used to assess qualitatively both the uniformity of the grating and the symmetry of the grating profile. Comparison with scanning electron microscope images shows excellent agreement. This method is advantageous since it can be carried out rapidly, is accurate and repeatable, does not damage the sample, and uses low-cost, commonly available equipment. Since this method consists of only four fixed simple measurements, it is highly suitable for quality control in a manufacturing environment.     

Color separation of high-density dielectric rectangular grating in the Fresnel diffraction region

A high-density dielectric rectangular grating is designed for color separation in a Fresnel diffraction field. The Fresnel field distribution is analyzed and the optimization conditions for color separation are given. The process of the modes propagating and energy exchanging with the diffraction orders are expressed by modal method. The color separation for different polarizations can be realized. The energy efficiency is 96.3% at the 633 nm wavelength and 86.9% at the 488 mm wavelength for both TE polarizations, while the energy efficiency is theoretically 96.3% at the 633 nm wavelength for TE polarization and 90.6% at the 488 nm wavelength for TM polarization. The field distributions are scanned by the near-field scanning optical microscopy, and the efficiency is 71.2% for the 633 nm wavelength and 67.3% for the 488 nm wavelength for both TE polarizations experimentally.     

Polarization-independent wideband mixed metal dielectric reflective gratings

A polarization-independent wideband mixed metal dielectric grating with high efficiency of the -1st order is analyzed and designed in Littrow mounting. The mixed metal dielectric grating consists of a rectangular-groove transmission dielectric grating on the top layer and a highly reflective mirror composed of a connecting layer and a metal film. Simplified modal analysis is carried out, and it shows that when the phase difference accumulated by the two propagating modes is odd multiples of π/2, the diffraction efficiency of the -1st order will be high. Selecting grating depth and duty cycle for satisfying the phase difference condition for both TE (electric field parallel to grooves) and TM (magnetic field parallel to grooves) polarizations, a polarization-independent high-efficiency grating can be designed. Using rigorous coupled-wave analysis and a simulated annealing algorithm, geometric parameters of the reflective grating are exactly obtained. The optimized grating for operation around a wavelength of 800 nm exhibits diffraction efficiencies higher than 90% for both TE and TM polarizations over a 120 nm wavelength bandwidth. The simplified modal analysis can be applied in other types of reflective gratings if the top layer is a dielectric transmission grating.     

Polarization dependence of diffraction gratings that have total internal reflection facets

The total internal reflection (TIR) grating is an integrated optical diffraction grating designed to achieve high efficiency for the retrodiffracted order by use of total internal reflection twice within a groove of the grating rather than by use of metalized grooves. Numerical calculations are presented for both TE and TM polarizations of incident light. When the TIR grating was used in the -mth-order Littrow mount with m > 13, the diffraction efficiency was found to decrease linearly with 1/m. The polarization dependence of the retrodiffraction efficiency exceeds 3 dB for TIR gratings formed in silica glass (n = 1.5) but is very small for gratings with InP-based technology (n = 3.2).     

Design of retrodiffraction gratings for polarization-insensitive and polarization-sensitive characteristics by using the Taguchi method

We present the design of retrodiffraction gratings that utilize total internal reflection (TIR) in a lamellar configuration to achieve high performance for both TE and TM polarized light and polarization-sensitive performance for gratings behaving as polarizer filters; the design was based on rigorous coupled wave analysis (RCWA) and the Taguchi method. The components can thus be fabricated from a single dielectric material and do not have to be coated with a metallic or dielectric film layer to enhance the reflectance. The effects of the structural and optical parameters of lamellar gratings were investigated, and the TIR gratings in a lamellar configuration were structurally and optically optimized in terms of the signal-to-noise ratio (S/N) and a statistical analysis of variance (ANOVA) of the refractive index, grating period, filling factor, and grating depth as control factors and the estimated efficiency by RCWA as a noise factor. For more accurate robustness, a two-step optimization process was used for each purpose. For TIR gratings designed to perform similarly for TE and TM incident polarization, the -1st-order efficiencies were estimated to be up to 92.0% and 88.5% for TE and TM polarization, respectively. Also, for the TIR gratings designed to achieve polarization-sensitive performance when behaving as a polarizer filters, the -1st-order diffraction efficiencies for TE and TM polarization were estimated to be up to 95.5% and 2.7%, respectively. From these analysis results, it was confirmed that the Taguchi method shows feasibility for an optimization approach to a technique for designing optical devices.     

Efficiency of a grazing-incidence off-plane grating in the soft-x-ray region

Efficiency measurements of a grazing-incidence diffraction grating in the off-plane mount were performed using polarized synchrotron radiation. The grating had 5000 grooves/mm, an effective blaze angle of 14 degrees, and was gold coated. The efficiencies in the two polarization orientations (TM and TE) were measured in the 1.5-5.0 nm wavelength range and were compared with the efficiencies calculated using the PCGrate-SX code. The TM and TE efficiencies differ, offering the possibility of performing unique science studies of astrophysical, solar, and laboratory sources by exploiting the polarization sensitivity of the off-plane grating.     

Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method

The effects of finite number of periods (FNP) and finite incident beams on the diffraction efficiencies of holographic gratings are investigated by the finite-difference frequency-domain (FDFD) method. Gratings comprising 20, 15, 10, 5, and 3 periods illuminated by TE and TM incident light with various beam sizes are analyzed with the FDFD method and compared with the rigorous coupled-wave analysis (RCWA). Both unslanted and slanted gratings are treated in transmission as well as in reflection configurations. In general, the effect of the FNP is a decrease in the diffraction efficiency with a decrease in the number of periods of the grating. Similarly, a decrease in incident-beam width causes a decrease in the diffraction efficiency. Exceptions appear in off-Bragg incidence in which a smaller beam width could result in higher diffraction efficiency. For beam widths greater than 10 grating periods and for gratings with more than 20 periods in width, the diffraction efficiencies slowly converge to the values predicted by the RCWA (infinite incident beam and infinite-number-of-periods grating) for both TE and TM polarizations. Furthermore, the effects of FNP holographic gratings on their diffraction performance are found to be comparable to their counterparts of FNP surface-relief gratings.     

Three-port binary reflective grating with high efficiency under second Bragg angle incidence

Abstract

A binary three-port reflective grating under second Bragg angle incidence is designed in this paper. Under second Bragg angle incidence, the grating can separate nearly 33% light wave energy into the 2nd order, the 1st order and the 0th diffractive orders, respectively. Rigorous coupled-wave analysis can give numerical calculation to optimize the three-port grating depths and periods. For the optimized reflective three-port grating, TE polarization and TM polarization can have different values of grating depth and period. Compared with the reported three-port binary grating under Bragg angle incidence, the diffraction efficiencies can be improved. Moreover, the modal method is applied to explain the propagating mechanism. The highly efficient three-port binary reflective grating under second Bragg angle incidence would be manufactured in the emerging industry for its novel performance.     

A Broadband Microwave Metamaterial Absorber with Octave Bandwidth

In this paper, a broadband metamaterial absorber has been presented for practical applications. The unit cell of the proposed structure comprises metallic patch of single circular split-ring imprinted on top surface of a metal-backed dielectric substrate. The geometrical dimensions of the structure have been optimized in such a way that the structure exhibits broadband absorptivity response of 9.12 GHz from 6.70 to 15.82 GHz with more than 90 % absorptivity. Three distinct absorption peaks are observed at 7.16, 10.74 and 14.96 GHz. The absorption phenomena at these three frequencies have been analyzed and the roles of several geometrical parameters involved in the design are investigated. The proposed structure has been studied under oblique incidence, both for TE and TM polarizations where it shows wideband absorption characteristics up to 30° incident angle for TE polarization and 45° incident angle for TM polarization. The proposed structure is very thin (~λ/8.4 with respect to the centre frequency of absorption bandwidth) compared to the commercially available microwave absorbers.     

Analysis of diffraction gratings by using an edge element method

Typically the grating problem is formulated for TE and TM polarizations by using, respectively, the electric and magnetic fields aligned with the grating wall and perpendicular to the plane of incidence, and this leads to a one-field-component problem. For some grating profiles such as metallic gratings with a triangular profile, the prediction of TM polarization by using a standard finite-element method experiences a slower convergence rate, and this reduces the accuracy of the computed results and also introduces a numerical polarization effect. This discrepancy cannot be seen as a simple numerical issue, since it has been observed for different types of numerical methods based on the classical formulation. Hence an alternative formulation is proposed, where the grating problem is modeled by taking the electric field as unknown for TM polarization. The application of this idea to both TE and TM polarizations leads to a two-field-component problem. The purpose of the paper is to propose an edge finite-element method to solve this wave problem. A comparison of the results of the proposed formulation and the classical formulation shows improvement and robustness in the new approach.     

Three-dimensional converging-diverging Gaussian beam diffraction by a volume grating

The diffraction characteristics of a volume grating (VG) illuminated by a three-dimensional (3-D) converging-diverging Gaussian beam at conical incidence are investigated by applying 3-D finite-beam (FB) rigorous coupled-wave analysis (RCWA) based on the conventional 3-D RCWA in conjunction with two-dimensional plane-wave decomposition. The Gaussian beam is assumed to have an arbitrary incidence angle, an arbitrary azimuthal angle, and any linear polarization. The two cases with linear polarizations of the central beam of the Gaussian (E perpendicular K and H perpendicular K) are investigated. The diffraction efficiencies and the diffracted beam profiles for both unslanted VGs and slanted VGs (designed for substrate-mode optical interconnects) are presented. In general, the diffraction efficiencies of a converging-diverging spherical Gaussian beam diffracted by both unslanted VGs and slanted VGs increase and approach the central-beam results as the refractive-index modulation increases.     

Periodic defects in 2D-PBG materials: full-wave analysis and design

In this paper, an accurate and efficient characterization of two-dimensional photonic bandgap structures with periodic defects is performed, which exploits a full-wave diffraction theory developed for one-dimensional gratings. The high convergence rate of the proposed technique is demonstrated. Results are presented for both TE and TM polarizations, showing the efficiencies as a function of wavelength, incidence angle, geometrical and physical parameters. A comparison with other theoretical results reported in the literature is shown with a good agreement. The transmission properties of photonic crystals with periodic defects are studied, investigating the effects of the variation of geometrical and physical parameters; design efficiency maps and formulas are given; moreover, the application of the analyzed structures as filters is discussed.     

Transmitted scattered light from a thin film with shallow random rough interfaces

The transmitted scattered energy of plane electromagnetic waves from a thin metallic film with shallow rough interfaces bounded by two semi-infinite media is calculated. Both interfaces are modeled as independent stationary random processes with a Gaussian roughness spectrum. Scattering of light is calculated for both TM (p) or TE (s) polarizations for normal and oblique angles of incidence. An integral equation is obtained for the transmitted field based on the Rayleigh method and their solution involves Fourier coefficients, depending on the roughness profiles. We present some results for the case of a single thin metallic film in the attenuated total reflection configuration for s and p polarization around the angle of the excitation of surface-plasma waves θ(sp). The transmitted scattered intensity shows a maximum at the resonant angle θ(sp) in the case of p polarization.     

Analysis of the focal characteristics of cylindrical lenses made of anisotropically dielectric material based on rigorous electromagnetic theory

Abstract

The focal characteristics of refractive cylindrical lenses made of anisotropically dielectric material (uniaxial crystal) are analysed based on rigorous electromagnetic theory and the boundary element method. The performances of the lenses with different f numbers are appraised for both incident waves of the TE (transverse electric) and TM (transverse magnetic) polarizations. Numerical results show that the focal performance of this kind of lens for the TE polarization and the TM polarization of incident light wave is a difference, in particular, different focal lengths, owing to the anisotropy of the material. However, for the conventional isotropic lens, the focal features for both the TE and TM polarizations are the same. It is anticipated that this new kind of lens proposed for the first time may serve as a light switching device with high speed used in the micro-optical communication.     

Numerical investigation on the filtering behavior of 2-D PBGs with multiple periodic defects

In this study, the transmission properties of photonic crystals with multiple periodic defects are studied by using a full-wave approach. The high convergence rate of the employed technique has allowed us to accurately and efficiently predict the filtering behavior of the considered structures. Results are presented for both TE and TM polarizations, showing the transmission efficiencies as a function of the involved parameters. In order to give more physical insight, a comparison with a simpler one-dimensional model has been provided. From our numerical investigation, it turns out that, by suitably configuring the photonic bandgap, it is possible to shape the filtering properties in TE polarization in a simple and versatile way.     

Effective grating theory for resonance domain surface-relief diffraction gratings

An effective grating model, which generalizes effective-medium theory to the case of resonance domain surface-relief gratings, is presented. In addition to the zero order, it takes into account the first diffraction order, which obeys the Bragg condition. Modeling the surface-relief grating as an effective grating with two diffraction orders provides closed-form analytical relationships between efficiency and grating parameters. The aspect ratio, the grating period, and the required incidence angle that would lead to high diffraction efficiencies are predicted for TE and TM polarization and verified by rigorous numerical calculations.     

TM and TE propagating modes of photonic crystal waveguide based on honeycomb lattices

The waveguide based on the honeycomb photonic crystal has propagating modes for both the TE and TM polarizations. The group index-normalized frequency curves are U-shaped for the two polarizations. The average group index of the TE mode is approximately 3, while the average group index of the TM mode is over 10, which implies that the TM mode is a slow light mode. With the shift value 0 ≤ δx ≤ 0.025a, the group index is over 10 and the normalized delay-bandwidth product is from 0.316 to 0.349, which is ideal for the slow light mode of the TM polarization. In the group velocity dispersion of the waveguide, there is a very large "zero" dispersion region for both the TM and TE modes, which is far larger than that of other photonic crystal waveguides. The TM mode of this kind of waveguide structure is a slow light mode with wide bandwidth and a large "zero" dispersion region.