Designing coupled-resonator optical waveguides based on high-Q tapered grating-defect resonators

We present a systematic design of coupled-resonator optical waveguides (CROWs) based on high-Q tapered grating-defect resonators. The formalism is based on coupled-mode theory where forward and backward waveguide modes are coupled by the grating. Although applied to strong gratings (periodic air holes in single-mode silicon-on-insulator waveguides), coupled-mode theory is shown to be valid, since the spatial Fourier transform of the resonant mode is engineered to minimize the coupling to radiation modes and thus the propagation loss. We demonstrate the numerical characterization of strong gratings, the design of high-Q tapered grating-defect resonators (Q>2 × 10^6, modal volume = 0.38•(λ/n)^3), and the control of inter-resonator coupling for CROWs. Furthermore, we design Butterworth and Bessel filters by tailoring the numbers of holes between adjacent defects. We show with numerical simulation that Butterworth CROWs are more tolerant against fabrication disorder than CROWs with uniform coupling coefficient

Synthesis of high-order bandpass filters based on coupled-resonator optical waveguides (CROWs)

We present a filter design formalism for the synthesis of coupled-resonator optical waveguide (CROW) filters. This formalism leads to expressions and a methodology for deriving the coupling coefficients of CROWs for the desired filter responses and is based on coupled-mode theory as well as the recursive properties of the coupling matrix. The coupling coefficients are universal and can be applied to various types of resonators. We describe a method for the conversion of the coupling coefficients to the parameters based on ring resonators and grating defect resonators. The designs of Butterworth and Bessel CROW filters are demonstrated as examples

Substantial gain enhancement for optical parametric amplification and oscillation in two-dimensional χ(2) nonlinear photonic crystals

We have analyzed optical parametric interaction in a 2D NPC. While in general the nonlinear coefficient is small compared to a 1D NPC, we show that at numerous orientations a multitude of reciprocal vectors contribute additively to enhance the gain in optical parametric amplification and oscillation in a 2D patterned crystal. In particular, we have derived the effective nonlinear coefficients for common-signal amplification and common-idler amplification for a tetragonal inverted domain pattern. We show that in the specific case of signal amplification with QPM by both G10 and G11, symmetry of the crystal results in coupled interaction with the corresponding signal amplification by G10 and G1,-1. As a consequence, this coupled utilization of all three reciprocal vectors leads to a substantial increase in parametric gain. Using PPLN we demonstrate numerically that a gain that comes close to that of a 1D QPM crystal could be realized in a 2D NPC with an inverted tetragonal domain pattern. This special mechanism produces two pairs of identical signal and idler beams propagating in mirror-imaged forward directions. In conjunction with this gain enhancement and multiple beams output we predict that there is a large pulling effect on the output wavelength due to dynamic signal build-up in the intrinsic noncollinear geometry of a 2D NPC OPO

Motion-sensitive optical correlator using a VanderLugt correlator

A new type of optical correlator is presented. The correlator performs motion detection or background clutter suppression and correlation simultaneously in a single photorefractive crystal. Additionally, the device is useful for moving target identification and tracking and for stationary clutter rejection. The correlation is of the VanderLugt type, and the motion detection or background clutter suppression is based on the erasing property of photorefractive crystals

Upgrading school efficiencies and learning interests through innovative teaching of digital mobile e-learning

Abstract. Assessing the digital mobile e-learning whether to affect school efficiency is an important yet complex issue. Consequently, this study goal of this research is to evaluate the innovative teaching to affect school efficiency (total efficiency (TE), pure technical efficiency (PTE) and scale efficiency (SE) estimated by the data envelopment analysis (DEA) through using digital mobile e-learning of high school in Taiwan. Additionally, the Tobit regression model (TRM) is employed to discuss whether the other determinants affect using digital mobile e-learning of school efficiency. The findings can briefly be concluded as follows. The empirical results of this research indicate the following results: (1) Importing digital mobile e-learning can really enhance the efficiency of school management. (2) technical Efficiency (TE), pure technical efficiency (PTE) and scale efficiency (SE) in the TRM analysis, it also indicates that school size, teacher-student ratio, school high-vocational attribute, especially the numbers of technical teachers in teaching or consulting about digital mobile e-learning knowledge and numbers of Tablet PC (the proxy for digital mobile e-learning) an important role in affecting these three efficiency of school management. Besides, the results show of total equipment expenses associated with tablet PC has a small negative influence on school management efficiency. Due to increasing costs for network equipment small effects on teaching and learning among teachers and students. The results of this research can also be the reference for educational authorities when formulating policies and regulations for promoting digital mobile e-learning.Keywords. Technical efficiency, Pure technical efficiency, Scale efficiency, Digital mobile e-Learning, Data envelopment analysis (DEA), Tobit regression model (TRM),Vocational and senior high school.JEL. I21, I25, I28

The Effect of Anelasticity on Periods of the Earth's Free Oscillations (Toroidal Modes)

It is known that the anelastic properties of the Earth characterized by a ‘Q’ structure will affect the periods of free oscillation. It is generally considered that the effect is negligible compared to the other perturbing effects due to rotation, ellipticity, and lateral inhomogeneities. Nevertheless, it is of some interest to investigate the precise magnitude of this effect for the observed free oscillation modes since it could provide us with another constraint in the determination of the Q structure of the Earth. An application of perturbation theory provides us with a good estimate of the magnitude of the changes in the periods of an elastic model due to inclusion of anelastic effects. Calculations based on currently accepted mean elastic and anelastic models for the Earth show that the shift in period due to anelasticity is at most 0·023 per cent for the toroidal modes from _0T_2 to _0T_(99), the maximum occurring near _0T_(60). For more extreme Q models, which may be locally applicable, period shifts of the order 0·1 per cent occur, with the maximum again near _0T_(60), corresponding to a period of approximately 150 s. Observational accuracy for the toroidal oscillations is around 0·1 per cent so that anelastic shifts in toroidal oscillation periods are at the present limit of observational accuracy. Viewed in terms of propagating surface waves, the dispersion due to anelasticity results in at most 0·005-0·01 km s^(−1) variations in the phase and group velocities. Such shifts are within the observational resolution of surface dispersion measurements using narrow band filtering techniques. Compared to other perturbing effects, anelasticity is significant for the toroidal oscillation only in the 50- to 300-s period range. In this range, lateral variations in structure generally cause larger perturbations. However, when viewed in terms of propagating surface waves in selected homogeneous regions, anelasticity becomes the dominating effect. Further, the frequency shift due to anelasticity is scaled by (1/Q)^2, so that the anelastic effect can be well within observational accuracy and comparable to any perturbing effect for more extreme, yet acceptable, Q models. In particular, when applied to surface waves propagating across a tectonic region with a strong low velocity zone in the upper mantle, the anelasticity induced dispersion on frequency shift can be significant and measurable. In such cases a joint inversion of elastic and anelastic properties is appropriate