High efficient optical spot size converter (SSC) is one of the most important building blocks for dense optical interconnection network and high-speed optical fiber communications due to efficient optical power transfer between different optical modules. Using tapered optical direction coupler (TODC) as SSC can reduce the dimension with high efficiency because of resonant condition and tapered structure. However, the strong dependence of operation on wavelength leads to narrow band operation, reducing the usage of wavelength division multiplexer (WDM) technique for upgrading optical data capacity through optical spectrum. In this work, based on multi- resonant points of TODC, a broadband SSC integrated with optical electroabsorption modulator (EAM) is proposed, designed, and fabricated. By tapering quantum well of the top active waveguide (AW), the integration with bottom passive waveguide (PW) can form a TODC. With the tapered structure, the gradually varied effective index forms a resonant point along wave propagation, inducing strong coupling, collecting optical power after resonant point, and thus leading to high efficient coupling. With multi-section of resonant conditions and also tapered structure, broadband operation can be realized. Through 3 section of tapered AW of TODC, the calculated coupling efficiency from bottom PW with larger than 70% is found for the regime of 1530nm~1550nm wavelength. The EAM-integrated SSC is also fabricated. With counter direction of optical coupling, the measured photocurrent in EAM shows a broadband of flap coupling from 1570nm~1585nm is observed, suggesting the multi-section TODC can bring out broadband operation.

"Enhanced index fund" is an investment strategy, combining active and passive management elements, for index tracking and return enhancing through disciplined market timing, stock selection and leverage activities. Though enhanced index funds have been well developed globally, there is only one enhanced index fund in Taiwan - "Polaris/P-Shares Taiwan Dividend+ ETF". Taiwan's stock market falls between weak form and semi-strong form efficiency. With the growth of Taiwan's mutual fund industry size, the enhanced index funds have very good chance to become the main investment instruments of institutional investors, index investors, and pensions. This study attempts to build enhanced index funds, then analyzes the performance and checks the feasibility of launching such products in Taiwan. In this study, we select "TSEC Taiwan 50 index (TW50)" as the benchmark index. The innovative "Multi-section Adjustment Model" divides the original weights of constituent stocks into two sections. Each section is adjusted through parameters. The "multi-factor model section" is responsible for the delivery of enhanced return, while the "cash dividend yield section" is used to provide excess cash dividend yield. The investment target is set for less than 1.5 percent tracking error, at least 1 percent tracking difference, and higher cash dividend yield than the benchmark. Building methodology can be divided into "fixed parameter model" and "floating parameters model" according to its update frequency. Empirical studies show that: (1) The enhanced index fund built from the "fixed parameter model" not only exhibits risk slightly lower than the benchmark, but also enjoys higher return. (2) In the short-term, the performance of the enhanced index fund built from "floating parameters model" is difficult to predict; in the long-term, however, the risk is lower and the return is higher than TW50. The cumulative return from the "fixed parameter model" is higher than the "floating parameters model" by about 2 percent. (3) The effectiveness of the parameters used to control the optimal weight distribution is decreasing over time, so it is necessary to update parameters regularly. (4) Raising "enhancement multiplier" will cause higher tracking error, but also bring higher tracking difference. This result proves that "multi-factor model section" works nicely and has its contribution. (5) As the "section allotment" and/or "fixed rate" getting lower, there will be more and more weights distributed to the cash dividend yield level, resulting in higher cash dividend yield. It means the "cash dividend yield section" has its merit as well. (6) Regular parameter updates to the "floating parameters model" helps to reduce the tracking error and, at the same time, maintain positive tracking difference. Considering the perpetual life of real world funds, "floating parameters model" should be a better building methodology. "Multi-Section Adjustment Model" has following advantages: (1) Its concept is intuitive and easy to use. (2) Sections can be customized based on investment objectives. (3) It is easy to analyze the impacts and trade-off among the parameters.