tailieunhanh - Recent Optical and Photonic Technologies Part 2

Tham khảo tài liệu 'recent optical and photonic technologies part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 20 Recent Optical and Photonic Technologies Cross talk between modes of different symmetries The coupling between the waveguiding mode which is as seen in the above Sec. predominantly even and the odd modes leads to propagation loss. This is because the energy transfered to an odd mode is no longer spatially confined to the region of the waveguide and is irreversibly lost. To assess the efficacy of the waveguiding in PhCS with the trench one needs to quantify the extent of the cross-talk. In order to address this question we compared magnetic field profiles of the waveguiding mode even-like with the odd bulk mode for the frequencies close to the anti-crossing Fig. 9. We examined the overlap between two modes s j Hz 1 r H 2 r dv . Here we assumed the H fields to be already normalized. Fig. 10 a b plots the band structure for A ựj a 2 h d and the values of Ỗ for different branches of the dispersion curve. The frequency scales are aligned along the y-axis so the value of the overlap is plotted along the x-axis in Fig. 10b. The calculations indicate that the overlap between the bulk mode and the mode from a waveguiding branch is indeed small no greater than 2 . As expected the degree of the overlap within the other branch gradually increases away from the anticrossing. We argue that making the trench deeper smaller d and narrowing the width of the trench smaller A decreases the even- and odd- like character of the modes. The reasoning is the following by decreasing the depth of the waveguiding region one is introducing larger perturbations to the ideal symmetric slab about z 0. Thus the odd-like and even-like modes interact to a greater extent and the odd-even symmetry is lost. Further this should be seen in the overlap between the once even-like mode and the odd bulk mode. If odd-even symmetry has decreased then one expects the overlap to be greater. Indeed the calculations performed for a structure with A v 3 a 2 h d yield the