Shun-Der Wu

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.

Characteristics of DuPont photopolymers for slanted holographic grating formations

The characteristic parameters of DuPont OmniDex613 photopolymers including the shrinkage factor, diffusion coefficient, and nonlocal response length are studied for slanted holographic gratings recorded at the UV wavelength of 363.8 nm by application of the rigorous coupled-wave analysis in conjunction with an angular-selectivity measurement, a real-time diffraction-monitoring technique, and a nonlocal diffusion model. Both small ( 40 deg) slant-angle gratings are presented. Depending on the exposure intensity, the recording shrinkage factor of the photopolymer varies from ~2.75% to ~4.20%. Furthermore, the effects of postbaking conditions on the refractive-index modulations and the shifts of Bragg angles for slanted holographic gratings are also investigated systematically. It is found that the postbaking processing can not only increase the refractive-index modulations from Δn1~0.013 to ~0.028 for a small slant-angle grating and from Δn1~0.011 to ~0.022 for a large slant-angle grating, but can also compensate the recording shrinkage.

Volume holographic grating couplers: rigorous analysis by use of the finite-difference frequency-domain method

Two configurations of volume holographic grating couplers are rigorously analyzed by means of the finite-difference frequency-domain method (FDFD) for both TE and TM polarizations and for 0- and 45-deg output coupling. The two configurations depend on the position of the grating coupler, which can be placed either in the film or in the cover waveguide region. The FDFD results are compared with those obtained by the rigorous coupled-wave analysis in conjunction with the leaky-mode approach (RCWA-LM). Because the FDFD method is a rigorous solution of the Maxwell equations, it simulates the VHGC configuration and takes into account the waveguide-coupler discontinuity effects as well as the multimode excitation and interference effects, all of which are neglected by the traditional RCWA-LM.

Substrate-embedded and flip-chip-bonded photodetector polymer-based optical interconnects: analysis, design, and performance

The performance of three optoelectronic structures incorporating substrate-embedded InP-based inverted metal-semiconductor-metal photodetectors and/or volume holographic gratings are analyzed and compared at the primary optical communication wavelengths. These structures, in conjunction with optical-quality polymer layers, can be easily integrated into silicon microelectronic substrates for the purpose of implementing potentially low-cost high-data-rate chip-level or substrate-level optical interconnects. The structures are as follows: a) an evanescent-coupling architecture with a substrate-embedded photodetector, b) a volume-holographic-grating coupler architecture with a substrate-embedded photodetector, and c) a volume-holographic-grating coupler architecture with a flip-chip-bonded photodetector. It is found that the primary characteristic of the evanescent coupling architectures is the efficient performance for both TE and TM polarizations with the disadvantage of exponentially decreasing efficiency with increasing separation between the waveguide film layer and the photodetector layer. On the other hand, the primary characteristic of the volume holographic grating architectures is the possibility of wavelength and polarization selectivity and their independence on the separation between the photodetector layer and the waveguide. Comparison of the analysis with experimental results is also included in the case of the evanescent coupling into a substrate-embedded photodetector.

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.

Optimization of finite-length input volume holographic grating couplers illuminated by finite-width incident beams

A finite volume holographic grating coupler (VHGC) normally illuminated with various incident-beam profiles (such as a Gaussian beam, a flat cosine-squared beam, and an exponential-decay beam) with finite beam widths for input coupling is rigorously analyzed by use of the finite-difference frequency-domain method. The effects of the incident-beam width, the incident-beam position, the incident-beam profile, and the incident-beam angle of incidence on the input coupling efficiency are investigated. The optimum conditions for input coupling are determined. Both a VHGC embedded in the waveguide film region and a VHGC placed in the waveguide cover region are investigated. For a given finite VHGC, the input coupling efficiencies are strongly dependent on incident-beam widths, incident-beam positions, and incident-beam angles of incidence, but are only weakly dependent on incident-beam profiles.

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.

Angular sensitivities of volume gratings for substrate-mode optical interconnects

The angular sensitivities of slanted volume gratings (VGs) illuminated by three-dimensional (3-D) converging-diverging spherical Gaussian beams for substrate-mode optical interconnects in microelectronics are analyzed by application of 3-D finite-beam rigorous coupled-wave analysis. Angular misalignments about the z, y, and x axes that correspond to yaw, pitch, and roll misalignments resulting from manufacturing tolerances of chips are investigated. Two cases of linear polarization of the central beam of the Gaussian are considered: E perpendicular K and H perpendicular K, where K is the grating vector. From worst-case manufacturing tolerances, the ranges of yaw, pitch, and roll misalignment angles are alpha = +/-1.17 degrees, beta= +/-3.04 degrees, and gamma = +/-3.04 degrees, respectively. Based on these ranges of misalignment angles, the decreases of diffraction efficiencies for slanted VGs that are due to both the yaw and the roll misalignments are relatively small. However, the efficiency of substrate-mode optical interconnects achieved by slanted VGs could be reduced by 61.04% for E perpendicular K polarization and by 58.63% for H perpendicular K polarization because of the pitch misalignment. Thus the performance of a VG optical interconnect is most sensitive to pitch misalignment.

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).

Optimization of Anisotropically Etched Silicon Surface-Relief Gratings for Substrate-Mode Optical Interconnects

A simulated annealing algorithm in conjunction with the rigorous coupled-wave analysis (RCWA) is applied to determine the optimum profiles of right-angle-face anisotropically etched silicon (Si) gratings. The sensitivities of the optimized profiles are presented.