非线性光子晶体光传输特性的理论研究
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摘要
光子晶体(photonic crystals简称:PC)是折射率在空间周期性变化的介电结构,其变化周期和光的波长为同一个数量级。光子晶体也称为光子带隙材料(photonic band gap materials,也有人把它叫做电磁晶体(electromagnetic crystals)。它极大地修正了光子的色散关系,在其中可能存在着类似于半导体能带结构中的禁带,称之为光子带隙。频率落在光子带隙内的电磁波不能在光予晶体中传播,因此它具有许多特异的物理现象。如自发辐射的抑制,零点脉动的消失,能量转移,光子压缩态,光双稳和光开关等。由于这些独特的性质,它已吸引了越来越多的研究者的关注。
光子晶体的研究,近十年来一直十分活跃。有关光子晶体的带隙结构理论,其功能性质和技术应用已有许多的报道。对于光子晶体的非线性光学效应的研究也一直受到科学家的重视。S。John等人(1993年)研究了光子晶体中的带隙孤子,M。Scalora等人(1994年)研究了光子晶体中的光限制效应,V。Berger(1998)研究了光子晶体中光学谐波的产生,A。Hache等人(2000年)研究了光子晶体中双光子吸收和光克尔非线性。
以上所说的光子晶体,也有人称之为线性光子晶体。
非线性光子晶体(具有周期变化的电极化率结构)不同于线性光子晶体,也不是指能产生非线性光学效应的光子晶体。非线性光子晶体是近二、三年由Berger在他人研究的基础上提出的,可采用在材料中嵌入二阶或三阶非线性光学棒状介质来得到。由于非线性光子晶体具有强而快的非线性光学响应,且创造了产生和观察非线性局域光子模的理想条件而产生独特的非线性效应,并在许多领域具有广泛的应用,因此近两年来,对其相关机理的研究受到各国科学家的极大关注。在非线性光子晶体的基础上,有人提出了非线性光子晶体波导,这种非线性光子晶体波导可由在晶体中插入一排附加的具有三阶非线性极化率的棒状介质组成,而线性光子晶体波导则可由在光子晶体中去掉一排电介棒状介质而得到。
在以往研究的一维光子晶体(one-dimensional photonic crystal)中,有较大的
During the past decade, the photonic band gap structure has attracted considerable research attentiono In general, nonlinear photonic band gap structures are structures in which the nonlinear susceptibility is a periodic function in space. The nonlinear effects include steady state optical bistability and band gap solitary waves in nonlinear photonic band gap structure have been studied. The large omnidirectional band gaps in metallodielectric photonic band gap structures have been studied. And the two-dimensional photonic band gap optical limiter in the visible has been investigated.In the one-dimensional photonic band gap structure studied previously, a multilayer stack of dielectric material is arranged in such a way that alternating layers with a high index of refraction and a low index of refraction is alternated. And the thickness of each layer also alternates. The thicknesses are a and b which are constants.In this paper, the variation of the transmission and the dispersion relation with respect to the frequency in one-dimensional linear photonic band gap structure with variable period is demonstrated by numerical simulation, in which the thickness of the layers with high and low index of refraction is not constant that is different from the general one-dimensional photonic band gap structure. It is shown that the position of the photonic band gap will shift to the red side with the increase of the changing thickness of the layers. This effect becomes obvious with the increasing of frequency. And for the same structure, it can be shown that the photonic band gaps shift to the red side and the transmission with respect to the frequency becomes larger with the increasing of the applied intensity.And in this paper, the variation of the transmission and the dispersion relation with respect to the frequency of one-dimensional linear photonic band gap structure with variable period is demonstrated by numerical simulation.In this paper, the intense second harmonic field induces a nonlinear phase change
on a fundamental field simultaneously through cascaded second order processes is demonstrated by numerical simulation. It was shown that, the phase change dependson both the propagation length and input fundamental power density Ex.And the variations of the complex amplitude of the third wave at frequency 2>a> in one-dimensional photonic crystal are obtained through cascaded second order nonlinear processes by numerical simulation. Compared with a smaller amplitude of the second harmonic field, for a larger amplitude of the second harmonic field, in the procedure that the amplitude of the third field decreases quickly with the increase of the wavelength of the fundamental wave, there is a range of the refractive index in that the amplitude of the third field increases slowly. With the increase of the refractive index, the change of the amplitude of the third field exhibits special property.
光子晶体的研究,近十年来一直十分活跃。有关光子晶体的带隙结构理论,其功能性质和技术应用已有许多的报道。对于光子晶体的非线性光学效应的研究也一直受到科学家的重视。S。John等人(1993年)研究了光子晶体中的带隙孤子,M。Scalora等人(1994年)研究了光子晶体中的光限制效应,V。Berger(1998)研究了光子晶体中光学谐波的产生,A。Hache等人(2000年)研究了光子晶体中双光子吸收和光克尔非线性。
以上所说的光子晶体,也有人称之为线性光子晶体。
非线性光子晶体(具有周期变化的电极化率结构)不同于线性光子晶体,也不是指能产生非线性光学效应的光子晶体。非线性光子晶体是近二、三年由Berger在他人研究的基础上提出的,可采用在材料中嵌入二阶或三阶非线性光学棒状介质来得到。由于非线性光子晶体具有强而快的非线性光学响应,且创造了产生和观察非线性局域光子模的理想条件而产生独特的非线性效应,并在许多领域具有广泛的应用,因此近两年来,对其相关机理的研究受到各国科学家的极大关注。在非线性光子晶体的基础上,有人提出了非线性光子晶体波导,这种非线性光子晶体波导可由在晶体中插入一排附加的具有三阶非线性极化率的棒状介质组成,而线性光子晶体波导则可由在光子晶体中去掉一排电介棒状介质而得到。
在以往研究的一维光子晶体(one-dimensional photonic crystal)中,有较大的
During the past decade, the photonic band gap structure has attracted considerable research attentiono In general, nonlinear photonic band gap structures are structures in which the nonlinear susceptibility is a periodic function in space. The nonlinear effects include steady state optical bistability and band gap solitary waves in nonlinear photonic band gap structure have been studied. The large omnidirectional band gaps in metallodielectric photonic band gap structures have been studied. And the two-dimensional photonic band gap optical limiter in the visible has been investigated.In the one-dimensional photonic band gap structure studied previously, a multilayer stack of dielectric material is arranged in such a way that alternating layers with a high index of refraction and a low index of refraction is alternated. And the thickness of each layer also alternates. The thicknesses are a and b which are constants.In this paper, the variation of the transmission and the dispersion relation with respect to the frequency in one-dimensional linear photonic band gap structure with variable period is demonstrated by numerical simulation, in which the thickness of the layers with high and low index of refraction is not constant that is different from the general one-dimensional photonic band gap structure. It is shown that the position of the photonic band gap will shift to the red side with the increase of the changing thickness of the layers. This effect becomes obvious with the increasing of frequency. And for the same structure, it can be shown that the photonic band gaps shift to the red side and the transmission with respect to the frequency becomes larger with the increasing of the applied intensity.And in this paper, the variation of the transmission and the dispersion relation with respect to the frequency of one-dimensional linear photonic band gap structure with variable period is demonstrated by numerical simulation.In this paper, the intense second harmonic field induces a nonlinear phase change
on a fundamental field simultaneously through cascaded second order processes is demonstrated by numerical simulation. It was shown that, the phase change dependson both the propagation length and input fundamental power density Ex.And the variations of the complex amplitude of the third wave at frequency 2>a> in one-dimensional photonic crystal are obtained through cascaded second order nonlinear processes by numerical simulation. Compared with a smaller amplitude of the second harmonic field, for a larger amplitude of the second harmonic field, in the procedure that the amplitude of the third field decreases quickly with the increase of the wavelength of the fundamental wave, there is a range of the refractive index in that the amplitude of the third field increases slowly. With the increase of the refractive index, the change of the amplitude of the third field exhibits special property.
引文
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[3] 张友俊,姬波,王向前,等.光子晶体及其应用[J].红外与激光工程,2004,(3):320～322。
[4] Lijun Zhang , Romulo F, Jimenez Broas, et al. High-Impedance Electromagnetic Surfaces with a Forbidden Fre2 quency Band [J]. IEEE Transactions on Microwave Theory and Techniques, 1999, 47 (11): 2059～2074.
[5] Brown E R, Parker C D, Yabnolovitch E. Radiation proper2 ties of a planar antenna on a photonic crystal substrate [J]. Opt. Soc. Am. B, 1993, (10): 404～407.
[6] Yasushi Horri MakotoTsutsumi. Hamonic Control by Photonic Bandgap on Microstrip Patch Antenna [J]. IEEE Microwave and Guided Wave Letters, 1999, 9 (1): 13～15.
[7] Yongxi Qian, Sievenpiper D, Radisic V, et al. A novel ap2 proach for gain and bandwidth enhancement of patch antennas [A]. RAWCON' 98 Proceedings[C]. 1998.221～224.
[8] Yongxi Qian, Sievenpiper D, Radisic V, et al. A Mocrostrip patch antenna using novel photonic band - gap structure [J] . Microwave Journel, 1999 ,(1): 221~224.
[9] F Ryang , R Coccioli , Y Qian , et al. PBG- assisted gain enhancement of patch antennas on High - Dielectric Con2 stantsustrate [J] . IEEE Antenna and Progation Society , 1999 ,3 (8): 1920—1923.
[10] Coccioli R , Fei - Ran Yang , Kuang - Ping Ma , et al. Aperture - coupled patch antenna on UC - PBG substrate [J] . IEEE Trans. Microwave Theoryand Techniques , 1999 , 47(11): 2123-2130.
[11] E R Brown , C D Parker , E Yablonovitch. Radiation prop2 erties of a planar antenna on a photonic - crystal substrate [J ] . Opt. Soc. Am. B , 1993 , 10 (2): 404~407.
[12] Ramon Gonzalo Peter de Maagt Mario Sorolla. Enhanced patch antenna perfonnance by suppressing surface waves us2 ing photonic - bandgap substrates [J] . IEEE Trans. Mi2 crowave Theory and Techniques , 1999 , 47 (11) :213~12138.
[13] R Coccioli , W R Deal , T Itoh. Radiation characteristics of a patch antenna on a thin PBG substrate[J] . IEEE Antenna and Progation society , 1998 , 2 (2) : 656-659.
[14] K Taesun , S Chulhun. A Novel Photonic Bandgap Structure for Low - Pass Filter of Wide Stopband [J ] . IEEE Mi2 crowave and Guided Wave Letters , 2000 , 10(1): 13-15.
[15 ] Siou Teck Chew , Tatsuo Itoh. EBG- excited split - mode resonator bandpass filter[J] . IEEE Microwave and Wireless Components Letters , 2001 , 9 (11) : 364—366.
[16] Yun - Qi Fu , Guo - Hua Zhang , Nai - Chang Yuan. A novel EBG coplanar waveguide [J ] . IEEE Microwave and Wireless Components Letters , 2001 ,11(11): 447-449.
[17] Q Xue , K Shun , C H Chan. Novel 1 - D microstrip PBG cell [J] . IEEE Microwave and Guided Wave Letters , 2000 ,10(1): 403—405.
[18] V Radisic , YQian , R Coccioli , et al. Novel 2 - D photon2 ic bandgap structure for microstrip lines [J] . IEEE Mi2 crowave and Guided Wave Letters ,
1998, 2 (2): 69～71.
[19] TJ Ellis, GM Rebeiz. MM-wave tapered slot antennas on micromashined photonic bandgap dielectrics[J]. IEEE MTT-S Int. Microwave Syrup. Dig., 1996, (6): 1157～1160.
[20] Hu Ron, Zhang Xue Xia, Gao Bao Xin. 2-D PBG structure in microstrip line and symmetrical microstrip line [A]. Mi2 crowave Conference, 2000 Asia-Pacific [C]. 3～ Dec.2000. 1218"-~1221.
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