橫向磁化磁光介質之光學特性研究

本論文主要討論由 TM 模態的電磁波在橫向磁化磁光介質所組成的光學元件內的光學性質，並討論此種介質的介質參數（介電張量與導磁張量）非對角線元素數值大小對光學性質的影響。橫向磁化磁光介質的介質參數為一赫米特矩陣（Hermitian matrix），利用馬克斯威爾方程組可以計算 TM 模態下的磁場、電場與波印亭向量在此種介質內的解析解，經分析發現電場向量運動軌跡是個橢圓形並且躺在與波向量平行的平面上。利用電磁場在界面上的連續條件，可解出光從均向性介質入射磁光介質或由磁光介質入射均向性介質的反射率與透射率，並且我們證明以上兩種情況下均不會有布魯斯特角產生。另外我們推導含橫向磁化磁光介質的一維傳遞矩陣法。再根據此傳遞矩陣法計算由橫向磁化磁光介質所組成的一維非互易性光子晶體的頻帶結構。分析介電張量非對角線元素的數值大小對光子晶頻帶結構的影響，發現其數值愈大非互易性愈為明顯，在合適條件下此類光子晶體除了有單向傳播的特性外還有負折射現象。借由場圖模擬以平面波、高斯波及點波源入射此種非互易性光子晶體，得以方便觀察及討論光在此種元件的行為。在討論負折射現象時發現以點光源入射後，在出射區會有成像的行為，進一步探討波源位置與成像位置的關係，結果顯示它初步符合幾何光學的關係，不會因為此元件的非互易性而不同。

關鍵字

磁光介質；一維光子晶體

並列摘要

We investigate the propagating properties of the electromagnetic waves in the trans- versely magnetized magneto-optical (MO) media and the devices composed of MO me- dia and isotropic medium. The permittivity tensor and permeability tensor of the MO me- dium is a Hermitian matrix, and the equation of magnetic field, electric field and Poyn- ting vector of the TM mode can be derive by using Maxwell equations. It is shown that the endpoint of the electric field vector sweeps out an ellipse lying on the plane of inci- dence. Furthermore, we derive the formulas for evaluating the reflection rate in the cases of MO-to- isotropic medium incidence or isotropic-to-MO medium incidence. We also prove that there is no Brewster’s angle corresponding to these situations. In addition, the transfer matrix for calculating the transmission rate and band struc- ture of the one dimensional transversely magnetized magneto-optical photonic crystal (MOPC) is derived. From these results, we find that the larger the values of the off-diagonal elements of the dielectric tensor, the stronger the spectral asymmetry (non- reciprocity) of the MOPCs. The strong spectral asymmetry leads to a number of interest- ing phenomena, including one-way transparency and negative refraction. To verify the predicted phenomena in MOPC based on band structure analysis, we implement a lot of numerical simulations on the steady state magnetic field distribution and time-averaged energy-flow density for the cases of plane wave, Gaussian beam and point source waves. All the phenomena have been confirmed numerically.

並列關鍵字

1D photonic crystal ； magneto-optical media

參考文獻

[1] I. L. Lyubchanskii et al., "Spectra of bigyrotropic magnetic photonic crystals" Physica Status Solidi A, 201 (2004).

[2] I. L. Lyubchanskii et al., "Bigyrotropic photonic crystals" Complex Mediums V: Light and Complexity, 5508 ( 2001).

[3] P.K. Choudhury,Onkar N. Singh, Frontiers in Optical Technology: Materials And Devices. Nova Science Pub Inc (2006).

[4] David M. Pozar, Microwave Engineering. Addison Wesley (1997).

[7] A. Figotin and I.Vitebsky, "Nonreciprocal magnetic photonic crystals" Phys. Rev. E 63, 066609 (2001).

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橫向磁化磁光介質之光學特性研究

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