本文利用座標之間的轉換關係設計任意形狀的轉換材料(如隱形斗篷、集中器)，並模擬電磁波在任意形狀轉換材料中的傳播情形。由於理想隱形斗篷的材料在內圈邊界上會有奇異性的情形，因此本文利用保持色散關係的不變性將隱形斗篷材料係數簡化，一階座標轉換簡化下的隱形斗篷在外邊界會有阻抗不連續的情況，故以二階座標轉換設計隱形斗篷再將其材料係數簡化，使得簡化後的隱形斗篷外邊界阻抗能連續，二階座標轉換簡化後的隱形斗篷不僅能夠消除材料的奇異性，其散射情形也比一階轉換簡化後的隱形斗篷小。圓柱集中器可以將入射光往中心集中使得能量進入內圈部份甚至提高進入內圈的能量。運用座標轉換函數設計任意多邊形的集中器，如此即可依照不同形狀的要求製造集中器。數值模擬亦證實任意形狀集中器能使入射光經過材料後能回到原來路徑如同將內圈材料隱形，本文亦探討集中裝置的其他應用。

In this work we design invisibility cloaks for electromagnetic waves and light concentrators of arbitrary shapes based on coordinate transformations. Simplified material parameters are proposed using quadratic transformation functions which, in contrast to linear transformation, will enable us to eliminate the singularity at inner boundary and also diminish the scattering field outside the cloaking layer. By selecting appropriate transformation functions cylindrical and other profiles of concentrators are studied as well. Our results are confirmed by numerical simulations based on finite element calculations. Some potential application are also envisaged based on the concept of transformation optics.

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