一维和二维系统中电子禁带与光子禁带的数学等价特性(英文)

THE MATHEMATICAL EQUIVALENCE OF PHOTONIC BANDGAPS AND ELECTRONIC BANDGAPS FOR 1D AND 2D SYSTEMS

论证了在不针对特殊的结构和未做任何近似的情况下 ,一维和二维系统中的电子的Schrodinger方程和沿垂直方向传播的 S极化光子的 Maxwell方程具有完全相同的数学形式 ,即二者在数学上是完全等价的 ,这自然解释了到目前为止发现的存在于电子晶体的电子禁带和光子晶体的光子禁带之间的许多相似性 .这种等价性还表明 ,在电子晶体中出现的许多现象可以推广到光子晶体中 ;

From the quantum theory of electrons and the electromagnetic theory of photons,authors find that the Schrdinger equation of electron waves and the Maxell′s wave equation of s polarized photons traveled in normal directions in photonic crystals take exactly the same form for 1D and 2D systems without concerning any specific structure and taking any approximation,i.e,the two equations are mathematically equivalent.This naturally explains the similarity existed in the photonic bandgap properties of photonic crystals and the electronic bandgap properties in electronic crystals.And this means that many useful concepts,research methods and results relating to 1D and 2D electronic crystals can be transplanted for investigating 1D and 2D photonic crystals for s polarized photoms.