Dual photonic and phononic band gaps in Silicon dielectric waveguide

LI ChangSheng, HUANG Dan, NIE JianJun, GUO JieRong



Dual photonic and phononic band gaps in Silicon dielectric waveguide

LI ChangSheng, HUANG Dan, NIE JianJun, GUO JieRong

(Department of Physics and Electronics Science, Hunan University of Arts and Science, Changde 415000, China)

Phononic and photonic band structures were theoretically investigated in a special silicon dielectric waveguides by plane wave extended method. Periodic stubs were designed along the usual waveguides in favor of creating phononic and photonic band gaps. At appropriate geometrical parameters, a complete phononic gap was obtained together with a photonic gap at given symmetries.

band structure; phononic crystal; photonic crystal; waveguide

Periodic structures that exhibit band gaps with a certain range of acoustic or optical waves inhibited to propagate are the so-called phononic or photonic crystals. They have attracted attentions since decades ago[1—4]. Phononic and photonic band gaps were found separately in highly periodic bulk materials, multilayer materials, and slabs[5—6]. With recent advances in nanoscale fabrication techniques, the control of phonons and photons in the same structure becomes possible. The simultaneous existence of photonic and phononic band gaps has been widely investigated in two dimensional structures like Silicon slabs drilled with periodic holes[7—10]. One dimensional structure like dielectric waveguide was usually used in photonics, recognized for its ability to manipulate light. Recent studies found that the elastic properties of such wire structures can greatly influence the optical behavior because of the so-called phonon-photon interaction or acousto-optical interaction. There has been an emerging research field of the so called opto-mechanical or nanomechanical materials[11—12]. On the other hand, the commonly used photonic dielectric waveguides usually don’t have a phononic band gap. Only those periodic stubbed structures could be in favor of creating a phononic band gap. The study of dielectric waveguide with periodic stubbed structures for dual band gaps becomes increasingly important. In this paper, we theoretically investigate the phononic and photonic band structures of stubbed dielectric waveguides, and search the optimal parameters to achieve dual band gap. The practical parameter to work at telecom range is also discussed.

1 Model and calculating details

The stubbed Silicon dielectric waveguide model is shown in Fig. 1. It is cut from the usual silicon PC plates in air. We choose silicon dielectric waveguides because of the fact that silicon dielectric waveguides are able to guide optical and acoustic waves and widely used in electronics and telecommunications. In simulation, Silicon is considered as a cubic material with elastic constants11=165.7 GPa,12=63.9 GPa,44=79.62 GPa, and mass density 2331 kg/m3. It is optically isotropic with a refractive index of 3.47.

The phononic or photonic band structures can be calculated by various methods, such as plane wave extended method (PWE), finite-difference time-domain (FDTD) method, or finite-element (FE) method. The PWE method is efficient in simulating band structures of highly periodic structures, while the FDTD method has advantage in simulating some structures with open boundaries. The FE method can be used in many structures and efficient in displacement analysis. Results calculated from PWE, FDTD and FE are coincided with each other in previous work[13-14].

Fig.1 Schematic view of the stubbed Silicon dielectric waveguide

In this work, we employed PWE method in phononic and photonic band structure calculations. For all the simulations, we have compared our PWE results with FE calculation results. For the photonic calculations, we have used up to 4 641 basis in the PWE calculation to achieve convergence.

2 Results and discussion

In the following we would like to show the band structure about the stubbed silicon waveguide. As seen in Fig.2, the simulation of the band structures has been performed in both phononic and photonic waveguides. The phononic band structure presents a large absolute band gap (with parameters/= 0.75;/= 0.25;w/= 0.75;w/= 1). In the same geometry, we have also calculated the photonic dispersion curves and observed clearly three absolute photonic band gaps for the odd modes and two for the even one. The lower and the upper gaps of the odd modes correspond to complete photonic band gaps of the structure (see black dashed lines in Fig.2).

Fig.2 Phononic and photonic dispersion curves of the stubbed nanowire structure (with parameters h/a = 0.75; w/a = 0.25; wi/a=0.75; We/a = 1).

Then we test the possibility to work experimentally in the first photonic band gap regime. For a wavelength located around 1 550 nm working with frequencies in the windows of optical communications, the following parameters can be estimated: For the photonic low frequency gap (at reduced frequency 0.258 1 in Fig. 2),=w= 400 nm,=w= 300 nm,= 100 nm; The corresponding phononic middle gap frequency is 6.4 GHz. For the photonic high frequency gap (at reduced frequency 0.40 in Fig. 2),=w= 617 nm,=w= 463 nm,= 154 nm; The corresponding phononic middle gap frequency is 4.1 GHz.

3 Summary

We have theoretically investigated the phononic and photonic band structures of stubbed silicon dielectric waveguides. Phononic and photonic band gaps were identified simultaneously within the same waveguide at appropriate geometrical ratios. The practical parameter to work experimentally at telecom range is also obtained.

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硅介电波导管的光子与声子双重带隙

李长生*, 黄 丹, 聂建军, 郭杰荣

(湖南文理学院 物理与电子科学学院, 湖南 常德, 415000)

通过平面波展开法, 我们对一种特殊的硅介电波导管的声子能带结构与光子能带结构进行了理论研究. 为了同时产生光子带隙和声子带隙, 在通常的波导管结构中设计了一种周期性的桩型结构. 研究发现: 在适当的结构参数条件下, 一个完整的声子带隙和特定极化对称性的光子带隙可以同时得到.

能带结构; 声子晶体; 光子晶体; 波导管

P 15

1672-6146(2014)02-0026-03

10.3969/j.issn.1672-6146.2014.02.006

通讯作者email: lcs135@163.com.

2014-05-06

国家自然科学基金(NSFC 11104069, NSFC 61204104); 湖南文理学院重点建设项目(光学);光电信息集成与光学制造技术湖南省重点实验室项目.

(责任编校:刘刚毅)