关于光波导模拟的一点
学习总结
A simulation of a waveguide
Study summary
Theoretical Physics
Liu Baojie
References
[1].John Wiley&Sons ,Introduction to Optical Waveguide Analysis ,2001 [2].S.Longhi,M.Lobino etal,.Physical Review B 74 ,155116(2006) [3].S.Longhi.M.Marangoni etal ,Physical Review Lett 96.243901(2006) [4].Stefan Longhi,Physical Review Lett 96,023902(2008) [5].T.A.B Kennedy,E.M.Wright,Physical Review A 38,212(1988) [6].Non-Abelian geometric phase in four-waveguide arrays, Bao-Long Weng, Dong-Mei Lai, and X-D Zhang, Phys. Rev. A, 85, 053801 (2012). [7].S.Longhi,,1.Optical realization of the two site BHM in waveguide lattice ,Optics Letter (2009)
[8].].Stefano.Longhi,3.Quantum simulation of decoherence in optical waveguide lattices,Optics Letter (2013) [9].Stefano.Longhi,Quantum-optical structures,Laser & Photon. Rev.3(2008)
[10].Many-body physics with ultracold gases,Review of Modern Physics 80.885
[11].Cold Bosonic Atoms in Optical Lattices,Physical Review Lett 81,3108(1998)
[12].B.DeMarco,C.Lannert,etal,Physical Review A 71,063601(2005) [13].Bose Hubbard model in the presence of Ohmic dissipation, Physical Review A 79,053611(2009)
analogies
using
photonic
一. 光波导模拟的基本原理
1.波动方程：
1）假设电磁场振荡以单一的频率
E?r，t??Re?E?r?exp?jwt???振荡，其对应的电磁矢量可以表示为：
H?r，t??Re?H?r?exp?jwt??D?r，t??Re?D?r?exp?jwt??B?r，t??Re?B?r?exp?jwt??对应的Maxwell方程为：
（1）
??E?-j?B?-j??0H??H?j?D?j??E??H?0????rE??0???r?2?E??????rk0???0?0? （2）
根据（1）和(2)可以求得关于电场的波动方程：
?2??kE?0???c0 （3）
k?k0n?k0?r???0?0?r????0当?r为常数时，关于电场的波动方程可以写为：?E?kE?0
222.Beam Propagation Wave Equation:
标量的Helmholtz方程：
?2?T??x,y,z??2??x,y,z??k02n2?x,y,z??0?z （4） 22???2?T??x2?y22考虑slowly varying envelope approximation（SVEA）[1]在这个近似下传波函数，快速振荡相因子exp??j?z?和缓慢变化的部分??x,y,z?分开了：
??x,y,z????x,y,z?exp??j?z? （5） n2???nsk0?ns?s?0?其中ns为substrate或者cladding折射率，对（5）式两边对z求二阶导数可以得到：
光波导模拟waveguidesimulation
