TY - JOUR
T1 - A New Approach of Eigenmodes for Varying Refractive-Index Profile's Waveguides
AU - Zhu, Jianxin
AU - Li, Yutian
N1 - This work was supported in part by the Natural Science Foundation of China (NSFC) under Grant 11371319, in part by the Key Project of the Major Research Plan of NSFC under Grant 91130004, in part by the General Research Funds from the Hong Kong Research Grants Council under Grant 201513 and Grant 12303515, and in part by the HKBU Strategic Development Fund.
PY - 2016/10
Y1 - 2016/10
N2 - For the modal computation of an open optical waveguide with a varying refractive-index profile, two perfectly matched layers are used to terminate the waveguide, and the refractive-index profile is approximated by a piecewise polynomial of degree two. Then, the corresponding Sturm-Liouville problem (eigenvalue problem) of the Helmholtz operator in each layer can be solved analytically by the Whittaker functions, and the analytical approximate dispersion equations are established for both TE and TM cases. The approximate solutions converge fast to the exact ones for the continuous refractive-index function as the maximum value of the subinterval sizes tends to zero. Numerical simulations show that high-precision modes may be obtained by Muller's method with suitable initial values. The validation of the proposed method is also verified by use of the finite difference method with a fine grid.
AB - For the modal computation of an open optical waveguide with a varying refractive-index profile, two perfectly matched layers are used to terminate the waveguide, and the refractive-index profile is approximated by a piecewise polynomial of degree two. Then, the corresponding Sturm-Liouville problem (eigenvalue problem) of the Helmholtz operator in each layer can be solved analytically by the Whittaker functions, and the analytical approximate dispersion equations are established for both TE and TM cases. The approximate solutions converge fast to the exact ones for the continuous refractive-index function as the maximum value of the subinterval sizes tends to zero. Numerical simulations show that high-precision modes may be obtained by Muller's method with suitable initial values. The validation of the proposed method is also verified by use of the finite difference method with a fine grid.
KW - Dispersion equation
KW - eigenmodes
KW - open optical waveguide
KW - perfectly matched layer (PML)
KW - varying refractive-index profile
UR - http://www.scopus.com/inward/record.url?scp=85027445141&partnerID=8YFLogxK
U2 - 10.1109/TMTT.2016.2600325
DO - 10.1109/TMTT.2016.2600325
M3 - Journal article
AN - SCOPUS:85027445141
SN - 0018-9480
VL - 64
SP - 3131
EP - 3138
JO - IEEE Transactions on Microwave Theory and Techniques
JF - IEEE Transactions on Microwave Theory and Techniques
IS - 10
ER -