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Liu Qing Cao Zhuang Qi Shen Qishun Dou Xiaoming Chen Yingli 《Optical and Quantum Electronics》2001,33(6):675-683
In this paper, we propose a novel analytic transfer matrix method (ATMM) to the analysis of planar waveguides with index discontinuity or index slope discontinuity, for the cases when the conventional WKB method is no longer valid. We also analyze the physical insight of the approximations in WKB theory, and according to our research, the phase shift at the turning point is not /2, but exactly . Test calculations are done for an index profile with a known solution and the comparison shows that our method gives extremely accurate propagation constant. 相似文献
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本文利用转移矩阵方法对两种简单的具有吸引尾的势进行了研究.我们发现反射系数在波矢k→0时R=1,反射率与波矢k在k→0时呈线性关系.这说明在发生阱内量子反射时有利于超冷原子生存,因为超冷原子是低速低能原子.此外,我们可以用一个反射时间变化量Δt来判断量子反射的延迟或者超前. 相似文献
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The analytical transfer matrix method (ATMM) is applied to
calculating the critical radius $r_{\rm c}$ and the dipole
polarizability $\alpha_{\rm d}$ in two confined systems: the hydrogen
atom and the Hulth\'{e}n potential. We find that there exists a
linear relation between $r_{\rm c}^{1/2}$ and the quantum number $n_{r}$
for a fixed angular quantum number $l$, moreover, the three bounds
of $\alpha_{\rm d}$ ($\alpha_{\rm d}^{K}$, $\alpha_{\rm d}^{B}$,
$\alpha_{\rm d}^{U}$) satisfy an inequality:
$\alpha_{\rm d}^{K}\leq\alpha_{\rm d}^{B}\leq\alpha_{\rm d}^{U}$. A comparison
between the ATMM, the exact numerical analysis, and the variational
wavefunctions shows that our method works very well in the systems. 相似文献
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