Optimum parallel-face slanted surface-relief gratings

Using a combination of rigorous coupled-wave analysis and simulated annealing, parallel-face slanted surface-relief gratings (PFSSRGs) are optimized. For substrate-mode optical interconnects, profiles are presented for both polymer and silicon PFSSRGs for both TE and TM polarizations at normal incidence with grating periods designed to give a 45 degrees output angle in the negative-first forward-diffracted order. The resulting diffraction efficiencies range from 70% to 99%, with a majority of the optimized profiles yielding over 90%. Optimized polymer profiles for TE and TM polarizations exhibit similar high diffraction efficiencies, but the TM profiles generally require greater groove depths. Silicon profiles optimized for TM polarization have greater diffraction efficiencies than those for TE polarization. Profiles that can feasibly be fabricated are identified, and sensitivities to groove depth, filling factor, slant angle, and incident angle are shown to be modest.     

Design and fabrication of binary slanted surface-relief gratings for a planar optical interconnection

We propose the use of binary slanted surface-relief gratings with parallel-groove walls as input and output couplers in a planar optical interconnect. Parametric optimization of cascaded output couplers is employed to design an interconnect consisting of N output couplers producing a uniform intensity distribution with a high efficiency that may be realized in one lithographic etching step. The sensitivity of a N = 4 interconnect to various fabrication errors is analyzed. We demonstrate the operation of a slanted surface-relief grating manufactured with electron-beam lithography and reactive-ion etching for an operating wavelength of lambda = 0.633 mum.     

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.     

Subwavelength surface-relief gratings for stellar coronagraphy

We present a new design of a phase mask coronagraph implemented with subwavelength diffractive optical elements consisting of optimized surface-relief gratings. Phase mask coronagraphy is a recent technique that seeks to accommodate both high dynamic and high angular resolution imaging of faint sources around bright astrophysical objects such as exoplanets orbiting their host stars. The original design we propose is a new, integrated, and flexible solution to the pi phase-shift chromaticity of the phase mask coronagraphs. It will allow broadband observations, i.e., shorter integration times and object characterizations, by means of spectroscopic analysis. The feasibility of the component manufacturing is also considered through a tolerance study.     

Study of broadband polarization conversion with metallic surface-relief gratings by rigorous coupled-wave analysis

The conical rigorous coupled-wave analysis (RCWA) is employed to calculate the polarization conversion through the excitation of surface plasmons on metallic gratings. Various examples are examined with this numerical scheme. Our calculated results are consistent with those obtained from experiment and from other numerical methods. Three types of subwavelength surface-relief gratings are studied for the capability of broadband polarization conversion in the visible region. For wide-angle applications, various incident angles are studied and high polarization conversion efficiency is achieved.     

Systematic design process for slanted grating couplers

We have developed a systematic design process for recently proposed slanted grating couplers (SGCs) that operates in the strong coupling regime. Based on rigorous analysis of SGC properties, this design process utilizes the k-vector diagram and a rigorous grating leaky-mode solver to intentionally enforce the phase-match and Bragg conditions. We demonstrate that the resultant SGC designs have performance similar to those obtained by parallel micro-genetic algorithm (muGA) optimization with the two-dimensional finite-difference time-domain (2D FDTD) method. Only two 2D FDTD simulations are necessary in the later stages of our systematic design process. Therefore the time saving is tremendous compared to a muGA 2D FDTD design tool, which can require thousands of individual 2D FDTD simulation runs. We illustrate the utility of our new systematic design process with an embedded slanted grating coupler example.     

White LED light coupling into light guides with diffraction gratings

Radial diffractive gratings are used to couple light of a white LED into a light guide. Theoretical coupling efficiencies are evaluated with rigorous diffraction theory in a pure conical mounting. It is shown that when the refractive index of the grating increases from 1.46 to 2.05 the incoupling efficiency increases from 42% to 63%. Also, with the increasing refractive index the incoupling efficiency is shown to become more nearly uniform over the visible spectrum. Experimental results for the incoupled efficiencies and the color coordinates of the incoupled spectra are introduced for refractive indices n=1.46 and n=1.56.     

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).     

Scattering analysis of slanted fiber gratings

The diffraction efficiency of a tilted in-core fiber grating is analyzed with the scattering formalism and the first Born approximation. Without any prior physical assumptions about the shape or direction of the scattered wave, it is shown that diffraction occurs when the so-called Bragg conditions are nearly satisfied and the interaction process can be described by a pair of coupled first-order differential equations that are exactly the same as those obtained through the coupled-mode analysis.     

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.     

Finite-difference-time-domain analysis of finite-number-of-periods holographic and surface-relief gratings

The total-field-scattered-field formulation of the finite-difference time-domain method (FDTD) is used to analyze the diffraction of finite incident beams by finite-number-of-periods holographic and surface-relief gratings. Both second-order and fourth-order FDTD formulations are used with various averaging schemes to treat permittivity discontinuities and a comparative study is made with alternative numerical methods. The diffraction efficiencies for gratings of several periods and various beam sizes, for both TE and TM polarization cases, are calculated and the FDTD results are compared with the finite-difference frequency-domain (FDFD) method results in the case of holographic gratings, and with the boundary element method results in the case of surface-relief gratings. Furthermore, the convergence of the FDTD results to the rigorous coupled-wave analysis results is investigated as the number of grating periods and the incident beam size increase.     

Strip gratings on dielectric substrates as output couplers for submillimeter lasers

This paper describes the use and advantages of metallic strip gratings on dielectric substrates as output couplers for both optically pumped and discharge-excited submillimeter lasers. Formulas are presented for the calculation of transmittance and loss of such couplers, taking account of loss in the strip grating as well as loss and multiple reflections in the substrate. Included are expressions for the phase shifts on reflection and transmission by an arbitrary lossy grid on a plane boundary between two dielectrics according to a transmission-line model that is applicable for wavelengths in both dielectrics longer than the grid period. In relation to these phase shifts attention is drawn to an important sign convention. The theory is shown to agree well with measured transmittance of a typical device between 500 and 1600 GHz as well as spot measurements at 891 (337-microm HCN laser), 1540, and 1578 GHz (195- and 190-microm DCN laser). Finally, the theory is used to design a low-loss coupler for the low-gain 119-microm line of discharge excited H2O.     

Polarization analysis of surface-relief D-fiber Bragg gratings

Surface-relief fiber Bragg gratings exhibit substantially more polarization dependence than standard fiber Bragg gratings. Using D-fiber with different core orientations, surface-relief gratings are analyzed and fabricated to determine the polarization dependence. We show that the largest Bragg reflection occurs for the polarization state with a dominant TE field component parallel to the flat surface of the fiber. The polarization dependence is adjusted by changing the index of refraction of the surrounding media and by fabricating the surface relief grating using rotated core D-fiber.     

Modal method for classical diffraction by slanted lamellar gratings

We consider lamellar gratings made of dielectric or lossy materials used in classical diffraction mounts. We show how the modal diffraction formulation may be generalized to deal with slanted lamellar gratings and illustrate the accuracy and versatility of the new method through study of highly slanted gratings in a homogenization limit. We also comment on the completeness of the eigenmode basis and present tests enabling this completeness to be verified numerically.     

Rectangular surface-relief transmission gratings with a very large first-order diffraction efficiency (~95%) for unpolarized light

Computer optimization shows that the first-order diffraction efficiency of a lossless-transmission surface-relief grating with a rectangular surface profile can be made very large (~95%) simultaneously for light of TE and TM polarizations incident near the Bragg angle by the proper choice of the fill factor. The case for visible light incident close to the Bragg angle on unslanted gratings with periodicities corresponding to Bragg angles of 30 degrees , 37.5 degrees , and 45 degrees is presented. The refractive index of the grating material was chosen in the range between 1.2 and 2.     

Subwavelength surface-relief gratings fabricated by microcontact printing of self-assembled monolayers

We have designed and tested subwavelength diffractive optical elements consisting of surface-relief gratings made by microcontact printing of self-assembled monolayers. The first device is a beam deflector for 1.55-mum operation consisting of a surface-relief grating made up of eight pillars over one period (9.3 mum) of the grating. The widths of the pillars vary to approximate a linear phase profile within each grating period. The second device is a quarter-wave plate for 632.8-nm operation consisting of a subwavelength surface-relief grating with a 300-nm period and 58% duty cycle.     

Reformulation of the fourier modal method for surface-relief gratings made with anisotropic materials

Abstract

By the use of the correct Fourier factorization rules presented in an earlier paper by Li the Fourier modal method (FMM) for anisotropic surface-relief gratings is reformulated. The newly formulated FMM converges much faster than the old formulation when the permittivity contrast in the grating groove region is large. Highly conducting lamellar gratings coated with anisotropic materials can now be analysed easily. In addition, a simple set of criteria are given for determining the energy propagation directions of the plane waves associated with the real solutions of the Booker quartic.     

Modeling and design of planar slanted volume holographic gratings for wavelength-division-multiplexing applications

Holographic gratings are modeled and designed for path-reversed substrate-guided-wave wavelength-division demultiplexing (WDDM) as a continuation of earlier research [Appl. Opt. 38, 3046 (1999)]. An efficient and practical method is developed to simulate the slanted volume holographic gratings. The trade-off between dispersion and the bandwidth of the holograms is analyzed. A 60 degrees (incident angle of the grating)/60 degrees (diffraction angle of the grating in air) grating structure is selected to demultiplex optical signals in the 1555-nm spectral region, and a 45 degrees /45 degrees grating structure is chosen for the spectral region near 800 nm. Experimental results are consistent with the simulation results for these two WDDM devices. A four-channel WDDM is also demonstrated at a center wavelength of 1555 nm and with a channel spacing of 2 nm.     

Numerical study on spectral properties of tungsten one-dimensional surface-relief gratings for spectrally selective devices

Spectral properties of one-dimensional tungsten gratings with various depths and widths of grooves were investigated by means of finite-difference time-domain simulation with a multi-Lorentz model. Shallow gratings showed a strong absorption peak due to surface plasmon polaritons when the oscillation of the electric field was parallel to the grating vector. On the other hand, deep gratings with wide grooves showed a different absorption attributed to the microcavity effect when the oscillation of the electric field was perpendicular to the grating vector. With narrowed grooves, another absorption with d-dependence occurred, which was probably due to vertically oscillating surface plasmons to the grooves.