Investigation of 1-D photonic crystal waveguide based on Hermite-Gaussian function method

HE Ting; SU Xiaoxing; ZHANG Bo; LI Xiaoshuang

doi:10.7510/jgjs.issn.1001-3806.2016.01.012

Volume 40 Issue 1

Nov. 2015

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Citation:

Investigation of 1-D photonic crystal waveguide based on Hermite-Gaussian function method

1.
School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing 100044, China;
2.
Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, China

Corresponding author: SU Xiaoxing, xxsu@bjtu.edu.cn ;
Received Date: 2014-11-03
Accepted Date: 2014-12-11

Abstract

In order to simulate the light propagation in 1-D refractive-index-typed photonic crystal (PC) defect waveguide effectively, Hermite-Gaussian function expansion method was adopted. At first, the detailed theoretical derivations of the calculation method were presented. And then, dispersion relation, mode field patterns, energy control factor and equivalent refractive index of 1-D PC waveguides with different polarizations and different structural parameters were calculated. The results show that there are significant differences in the high-ordered modes between 1-D PC defect waveguides and step planar waveguides. The transmission of high-order modes can be controlled effectively by adjusting the structural parameters of 1-D PC.
- optical devices,
- propagation property,
- Hermite-Gaussian function method,
- photonic crystal waveguide

References

[1]	JOANNOPOULOS J D, JOHNSON S G, WINN J N, et al. Photonic crystals: molding the flow of light[M]. 2nd ed.Princeton,USA: Princeton University Press, 2008: 2-5, 44-65.
[2]	LEE B, ROH S,PARK J. Current status of micro-and nano-structured optical fiber sensors[J].Optical Fiber Technology, 2009, 15(3):209-221.
[3]	DUDLEY J M, GENTY G, COEN S. Supercontinuum generation in photonic crystal fiber[J]. Reviews of Modern Physics, 2006, 78(4):1135-1184.
[4]	ATKIN D M. Photonic crystals in planar waveguides[D]. Southampton, Britain: University of Southampton, 1998:17-19.
[5]	JIANG W. Study of photonic crystal based waveguide and channel drop filter and localization of light on photonic crystal[D]. Austin,USA: University of Texas at Austin, 2000:8-10.
[6]	STOUT B, STOUT S, NEVIERE M.Photonic crystal waveguides:a one-dimensional model theory[J]. Journal of Electromagnetic Waves and Applications, 2001, 15(7): 961-988.
[7]	PARK Y, JEON H. One-dimensional photonic crystal waveguide: a frame for photonic integrated circuits[J]. Journal of the Korean Physical Society, 2001, 39(6):994-997.
[8]	TANIYAMA H. Waveguide structures using one-dimensional photonic crystal[J]. Journal of Applied Physics, 2002, 91(6): 3511-3515.
[9]	PARK Y, JEON H. Optimal design for one-dimensional photonic crystal waveguide[J]. Journal of Lightwave Technology, 2004, 22(2):509-513.
[10]	SEVIM K. One dimensional photonic crystal waveguide[D]. Izmir,Turkey: Izmir Institute of Technology, 2004:30-35.
[11]	HUNG C L, MEENEHAN S M, CHANG D E, et al. Trapped atoms in one-dimensional photonic crystals[J]. New Journal of Physics, 2013, 15(8): 083026.
[12]	TANIYAMA H, NOTOMI M, YOSHIKUNI Y. Propagation characteristics of one-dimensional photonic crystal slab waveguides and radiation loss[J]. Physical Review, 2005,B71(15): 153103.
[13]	GERACE D, GALLI M, BAJONI D, et al.Wide-band transmittance of one-dimensional photonic crystals carved Si3N4 /SiO2 channel waveguides[J].Applied Physics Letters,2005, 87(21): 211116.
[14]	CHEN B, HUANG L, LIU C, et al. A waveguide reflector based on hybrid one-dimensional photonic crystal waveguides with a semi-cylinder defect[J].Optics Express,2010,18(25): 25567-25572.
[15]	DUBEY R S, SANKAR N S. Near field computation in 1-D photonic crystal waveguides for TE polarization [J]. Digest Journal of Nanomaterials and Biostructures, 2012, 7(3): 893-898.
[16]	MIRLOHI S. Exact solutions of planar photonic crystal waveguides with infinite claddings[D].Virginia, USA: Virginia Polytechnic Institute and State University, 2003:17-22.
[17]	MOGILEVTSEV D, BIRKS T A, RUSSELL P S J. Localized function method for modeling defect modes in 2-D photonic crystals[J]. Journal of Lightwave Technology, 1999, 17(11): 2078-2081.
[18]	WANG Z, REN G B, LOU S Q, et al. Supercell lattice method for photonic crystal fibers[J]. Optics Express, 2003, 11(9): 980-991.
[19]	KNUDSEN E, BJARKLEV A. Modelling photonic crystal fibres with Hermite-Gaussian functions[J]. Optics Communications, 2003, 222(1): 155-160.
[20]	SARRAFI P, NAQAVI A, MEHRANY K, et al. An efficient approach toward guided mode extraction in two-dimensional photonic crystals[J]. Optics Communications, 2008, 281(10): 2826-2833.
[21]	SARRAFI P, MEHRANY K. Fast convergent and unconditionally stable Galerkin's method with adaptive Hermite-Gauss expansion for guided-mode extraction in two-dimensional photonic crystal based waveguides[J]. Journal of the Optical Society of America, 2009,B26(1): 169-175.
[22]	KUO F Y, WO?NIAKOWSKI H. Gaussian-Hermite quadratures for functions from Hilbert spaces with Gaussian reproducing kernels[J]. BIT Numerical Mathematics, 2012, 52(2):425-436.
[23]	ARFKEN G B, WEBER H J, RUBY L. Mathematical methods for physicists[M]. 3rd ed. New York,USA: Academic Press, 1985:712-717.
[24]	WU C Q.Waveguide theory [M]. 2nd ed. Beijing: Tsinghua University Press, 2005:24, 26-27(in Chinese).

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通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

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Investigation of 1-D photonic crystal waveguide based on Hermite-Gaussian function method

Corresponding author: SU Xiaoxing, xxsu@bjtu.edu.cn;

1. School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing 100044, China;

2. Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, China

Received Date: 2014-11-03

Accepted Date: 2014-12-11

Available Online: 2016-01-25

Abstract: In order to simulate the light propagation in 1-D refractive-index-typed photonic crystal (PC) defect waveguide effectively, Hermite-Gaussian function expansion method was adopted. At first, the detailed theoretical derivations of the calculation method were presented. And then, dispersion relation, mode field patterns, energy control factor and equivalent refractive index of 1-D PC waveguides with different polarizations and different structural parameters were calculated. The results show that there are significant differences in the high-ordered modes between 1-D PC defect waveguides and step planar waveguides. The transmission of high-order modes can be controlled effectively by adjusting the structural parameters of 1-D PC.

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Reference (24)

[1]	JOANNOPOULOS J D, JOHNSON S G, WINN J N, et al. Photonic crystals: molding the flow of light[M]. 2nd ed.Princeton,USA: Princeton University Press, 2008: 2-5, 44-65.
[2]	LEE B, ROH S,PARK J. Current status of micro-and nano-structured optical fiber sensors[J].Optical Fiber Technology, 2009, 15(3):209-221.
[3]	DUDLEY J M, GENTY G, COEN S. Supercontinuum generation in photonic crystal fiber[J]. Reviews of Modern Physics, 2006, 78(4):1135-1184.
[4]	ATKIN D M. Photonic crystals in planar waveguides[D]. Southampton, Britain: University of Southampton, 1998:17-19.
[5]	JIANG W. Study of photonic crystal based waveguide and channel drop filter and localization of light on photonic crystal[D]. Austin,USA: University of Texas at Austin, 2000:8-10.
[6]	STOUT B, STOUT S, NEVIERE M.Photonic crystal waveguides:a one-dimensional model theory[J]. Journal of Electromagnetic Waves and Applications, 2001, 15(7): 961-988.
[7]	PARK Y, JEON H. One-dimensional photonic crystal waveguide: a frame for photonic integrated circuits[J]. Journal of the Korean Physical Society, 2001, 39(6):994-997.
[8]	TANIYAMA H. Waveguide structures using one-dimensional photonic crystal[J]. Journal of Applied Physics, 2002, 91(6): 3511-3515.
[9]	PARK Y, JEON H. Optimal design for one-dimensional photonic crystal waveguide[J]. Journal of Lightwave Technology, 2004, 22(2):509-513.
[10]	SEVIM K. One dimensional photonic crystal waveguide[D]. Izmir,Turkey: Izmir Institute of Technology, 2004:30-35.
[11]	HUNG C L, MEENEHAN S M, CHANG D E, et al. Trapped atoms in one-dimensional photonic crystals[J]. New Journal of Physics, 2013, 15(8): 083026.
[12]	TANIYAMA H, NOTOMI M, YOSHIKUNI Y. Propagation characteristics of one-dimensional photonic crystal slab waveguides and radiation loss[J]. Physical Review, 2005,B71(15): 153103.
[13]	GERACE D, GALLI M, BAJONI D, et al.Wide-band transmittance of one-dimensional photonic crystals carved Si3N4 /SiO2 channel waveguides[J].Applied Physics Letters,2005, 87(21): 211116.
[14]	CHEN B, HUANG L, LIU C, et al. A waveguide reflector based on hybrid one-dimensional photonic crystal waveguides with a semi-cylinder defect[J].Optics Express,2010,18(25): 25567-25572.
[15]	DUBEY R S, SANKAR N S. Near field computation in 1-D photonic crystal waveguides for TE polarization [J]. Digest Journal of Nanomaterials and Biostructures, 2012, 7(3): 893-898.
[16]	MIRLOHI S. Exact solutions of planar photonic crystal waveguides with infinite claddings[D].Virginia, USA: Virginia Polytechnic Institute and State University, 2003:17-22.
[17]	MOGILEVTSEV D, BIRKS T A, RUSSELL P S J. Localized function method for modeling defect modes in 2-D photonic crystals[J]. Journal of Lightwave Technology, 1999, 17(11): 2078-2081.
[18]	WANG Z, REN G B, LOU S Q, et al. Supercell lattice method for photonic crystal fibers[J]. Optics Express, 2003, 11(9): 980-991.
[19]	KNUDSEN E, BJARKLEV A. Modelling photonic crystal fibres with Hermite-Gaussian functions[J]. Optics Communications, 2003, 222(1): 155-160.
[20]	SARRAFI P, NAQAVI A, MEHRANY K, et al. An efficient approach toward guided mode extraction in two-dimensional photonic crystals[J]. Optics Communications, 2008, 281(10): 2826-2833.
[21]	SARRAFI P, MEHRANY K. Fast convergent and unconditionally stable Galerkin's method with adaptive Hermite-Gauss expansion for guided-mode extraction in two-dimensional photonic crystal based waveguides[J]. Journal of the Optical Society of America, 2009,B26(1): 169-175.
[22]	KUO F Y, WO?NIAKOWSKI H. Gaussian-Hermite quadratures for functions from Hilbert spaces with Gaussian reproducing kernels[J]. BIT Numerical Mathematics, 2012, 52(2):425-436.
[23]	ARFKEN G B, WEBER H J, RUBY L. Mathematical methods for physicists[M]. 3rd ed. New York,USA: Academic Press, 1985:712-717.
[24]	WU C Q.Waveguide theory [M]. 2nd ed. Beijing: Tsinghua University Press, 2005:24, 26-27(in Chinese).

Investigation of 1-D photonic crystal waveguide based on Hermite-Gaussian function method

Abstract

References

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通讯作者: 陈斌, bchen63@163.com

Proportional views