Title :
Improved coupled-mode formulation based on composite modes for parallel grating-assisted co-directional couplers
Author :
Huang, W.-P. ; Hong, J. ; Mao, Z.M.
Author_Institution :
Dept. of Electr. & Comput. Eng., Waterloo Univ., Ont., Canada
fDate :
11/1/1993 12:00:00 AM
Abstract :
An improved coupled-mode formulation based on the ideal modes of the coupled waveguides (ideal composite modes) is presented. In comparison with the formulation based on the ideal modes of the individual waveguides (ideal waveguide modes), the formulation in terms of composite modes is more rigorous and yields a more accurate grating period and coupling lengths. In addition, the radiation loss due to input and output junctions can in the composite-mode formulation. A new to the coupled-mode equations is derived in which all the spatial harmonics generated by the periodic grating are taken into account. The power exchange between the waveguides is examined by considering the input and the output conditions. The phase-matching conditions and the coupling lengths are calculated and compared with the analysis in terms of the waveguide modes. The grating period predicted by the waveguide-mode formulation agrees very well with that by the composite-mode formulation; however, dramatically different coupling lengths are predicted by the two formulations
Keywords :
diffraction gratings; directional couplers; optical couplers; optical losses; optical waveguide theory; composite modes; composite-mode formulation; coupled-mode formulation; coupling lengths; grating period; ideal modes; input junctions; output junctions; parallel grating-assisted co-directional couplers; periodic grating; phase-matching conditions; power exchange; radiation loss; spatial harmonics; Coupled mode analysis; Couplers; Equations; Frequency conversion; Gratings; Harmonic analysis; Mathematics; Power markets; Refractive index; Waveguide theory;
Journal_Title :
Quantum Electronics, IEEE Journal of