Negative Propagation Effects in Two-Dimensional  Silicon Photonic Crystals

<table>Band curves of 2D PhC of hexagonal lattice for TM polarization. The lattices are made of air holes of radius <svg height="11.125" id="M20" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 55.512501 11.125" width="55.512501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M393 379q-9 -16 -28 -29q-15 -10 -23 -2q-19 19 -36 19q-21 0 -52 -38q-57 -72 -82 -126l-40 -197q-23 -3 -75 -18l-7 7q49 196 74 335q7 43 -2 43q-7 0 -30 -14.5t-47 -37.5l-16 23q37 42 82 73t67 31q41 0 15 -113l-11 -50h4q41 71 85 117t77 46q29 0 45 -26
q13 -21 0 -43z" id="x1D45F"></path></g><g transform="matrix(.017,-0,0,-.017,11.945,10.862)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,26.649,10.862)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,34.808,10.862)"><use xlink:href="#x2E"></use></g><g transform="matrix(.017,-0,0,-.017,38.684,10.862)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g><g transform="matrix(.017,-0,0,-.017,46.843,10.862)"><use xlink:href="#x1D44E"></use></g>
</svg> in a silicon host material with <svg height="11.125" id="M21" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 42.837502 11.125" width="42.837502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M387 375q0 -16 -17 -31t-29 -15q-9 0 -12 13q-13 74 -80 74q-36 0 -61 -24.5t-25 -56.5t24 -51.5t68 -19.5q33 0 47 2l2 -7l-32 -42q-20 2 -54 2q-45 0 -74 -21.5t-29 -60.5q0 -41 28 -65.5t73 -24.5q78 0 145 67l17 -23q-33 -47 -84.5 -75t-111.5 -28q-70 0 -114.5 35.5
t-44.5 92.5q0 46 38 78t95 45v2q-35 10 -54.5 33t-19.5 52q0 55 53 88.5t122 33.5q67 0 98.5 -23.5t31.5 -49.5z" id="x1D700"></path></g><g transform="matrix(.017,-0,0,-.017,11.741,10.862)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,26.445,10.862)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,34.604,10.862)"><use xlink:href="#x32"></use></g>
</svg>. The light line shifted to Γ point is shown in black. The red line indicates the frequency range of negative refraction.</table>

International Journal of Photoenergy

fig5

Figure 5

Figure 5: Negative Propagation Effects in Two-Dimensional  Silicon Photonic Crystals 