Following this approach, it is reasonable to vary the layer-to-layer distances of the PhC structure from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.35\ast \frac{\sqrt{2}}{4}a$$\end{document}1.35∗24a to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.15\ast \frac{\sqrt{2}}{4}a$$\end{document}1.15∗24a. However, one must take into account that the direct coupling into the slow light mode from the air region is problematic due to the mode mismatch at the air- PhC interface40, 41. Furthermore, in order to avoid photon tunneling into the air cladding, one needs additional layers at the end of the structure. These two requirements can be both satisfied by increasing the layer-to-layer distance interval further including \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{1.00,1.50\}\ast \frac{\sqrt{2}}{4}a$$\end{document}{1.00,1.50}∗24a. In this way, the wave enters the structure with a wave vector away from the slow light region and the leakage due to the large penetration depth of the slow light modes is suppressed. On the other hand, since the operational frequency region is at the upper cut-off region, the layer-to-layer distance should decrease along the propagation direction, as discussed previously. Moreover, the number of rods in each layer is chosen to be 7, as it is restricted by the length of the Al2O3 rods (h = 8.463a). The number of layers, on the other hand, is chosen to be 30, to create a smoothly varying chirp function. In this case, the local layer-to-layer distance between the nth and (n + 1)th layer is equal to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${a}_{z}(n)=[(42.5-0.5n)\ast \frac{\sqrt{2}}{4}a]/28$$\end{document}az(n)=[(42.5−0.5n)∗24a]/28. Here, we note that an important criterion that should be satisfied in adiabatic structures (to reduce the back-reflections) is the Wentzel-Kramers-Brillouin approximation18, which requires1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\delta }_{n}=\frac{{k}^{-1}(n+1)-{k}^{-1}(n)}{{a}_{z}(n)}\ll 1$$\end{document}δn=k−1(n+1)−k−1(n)az(n)≪1where δ n is the adiabatic parameter between the nth and (n + 1)th layer and k(n) is the local wave vector at the nth layer. To reveal whether the adiabaticity condition is satisfied for the proposed PhC structure, the local wave vector distribution was obtained numerically for the frequency 7.91 GHz (which is predicted numerically to localize at the 24th layer), by calculating the dispersion curve for all intermediate periods. By inserting the obtained wave vector variation and the a z(n) variation into equation (1), the adiabatic parameter has been evaluated to be in the range of 0.005 and 0.009, which already satisfies equation (1). Possible solutions to further decrease the adiabatic parameter (and, thus, to decrease the back-reflections) could be increasing the number of layers or decreasing the chirping interval. However, the mode coupling mismatch at the slow light regime40, 41 should be further taken into account when tailoring the latter one, as was discussed above.