Publication
Coupling length of silicon-on-insulator directional couplers probed by Fourier-space imaging
Abstract
We use a Fourier-space imaging technique relying on outcoupling grating probes to study the coupled mode interaction and dispersion properties of guided modes in silicon-on-insulator codirectional couplers. Our approach allows us to measure the mode splitting inherent to coupled systems, determine the mode symmetry, and locally probe the coupling length with an accuracy of +/- 50 nm. A systematic study of directional couplers with different waveguide widths, coupling gaps, and e-beam exposure doses is reported in order to verify the results across a wider parameter space. (C) 2008 American Institute of Physics.
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Fourier transform
In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.
Fourier series
A Fourier series (ˈfʊrieɪ,_-iər) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series, but not all trigonometric series are Fourier series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation.
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In mathematics, Fourier analysis (ˈfʊrieɪ,_-iər) is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics.
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