波矢方向对二维光子晶体能带及应用的影响

利用平面波法分析了由介电常数为13和1的两种介质分别构成圆形柱和背景组成的三角晶格、蜂巢状晶格和正方晶格,波矢偏离周期性平面对它们能带分布及应用的影响。波矢偏离周期性平面分量增加,对色散曲线的影响表现在:波矢在周期性平面内形成的带隙逐渐减小,甚至消失;低频端出现不存在模式区域,并且该区域逐渐变宽;出现新的简并能级,原有的简并能级简并解除或消失;能带趋于平坦化;易于在低阶能带间形成绝对带隙等。波矢偏离周期性平面时,对三种晶格形成带隙情况分析得到:三角晶格和蜂巢状晶格形成的绝对带隙比正方晶格形成的绝对带隙宽,能更有效地减小发生自发发射的概率;三角晶格绝对带隙的宽度在泄漏模区域比蜂巢状晶格要宽,所以三角晶格比蜂巢状晶格更适合用作反射镜等。

Influences of Wave Vector Direction on Energy Bands and Applications of Two-Dimensional Photonic Crystals

The influences of the wave vectors off the periodic plane on the distribution of energy bands of triangular,honeycomb and square lattices are analyzed by plane wave method.The rods and background of these lattices are all composed of two mediums with dielectric constants equal to 13 and 1.With the increase of wave vectors off periodic plane,many changes will take place in the dispersion relation of these lattices: the band gaps of wave vectors in the periodic plane will decrease gradually and even disappear;a region,which does not exist modes,will appear in the low frequency range and it will be broaden with the increase of wave vectors off periodic plane;new degenerated energy levels appear and primarily degenerated levels will disappear;the energy bands tend to become flat;the absolute band gaps can easily form among the lowest energy bands.By the analyses of the band gaps of three lattices,some conclusions can be obtained: the width of absolute band gaps in triangular and honeycomb lattices are larger than those of square lattices,which make triangular and honeycomb lattices lower the rate of spontaneous radiation more effectively than square lattices;the width of band gaps of triangular lattices in the leaky region is larger than that of honeycomb lattices,which made triangular lattices be more appropriate to be used as reflect mirror than honeycomb lattices.