Research on the transmission coefficient of plasma photonic crystals based on the ICCG–SFDTD method

2015 ◽  
Vol 29 (12) ◽  
pp. 1550052 ◽  
Author(s):  
Ying-Jie Gao ◽  
Hong-Wei Yang ◽  
Rui Weng ◽  
Qing-Xia Niu ◽  
Yu-Jie Liu ◽  
...  
Keyword(s):  
Finite Difference ◽  
Photonic Crystals ◽  
Transmission Coefficient ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Sparse Matrix ◽  
Fdtd Method ◽  
Computational Time ◽  
Plasma Photonic Crystals ◽  
Difference Time

Compared with the traditional finite-difference time-domain (FDTD) method, the symplectic finite-difference time-domain (SFDTD) method has the characteristics of high precision and low dispersion. However, because the higher-order difference is necessary for the calculation, a large sparse matrix is generated. It causes that the computational time is relatively long and the memory is more. To solve this problem, the incomplete Cholesky conjugate gradient (ICCG) method for solving the large sparse matrix needs to be taken into the SFDTD differential equations. The ICCG method can accelerate the iterations of the numerical calculation and reduce the memory with fast and stable convergence speed. The new ICCG–SFDTD method, which has both the advantages of the ICCG method and SFDTD method, is proposed. In this paper, the ICCG–SFDTD method is used for research on the characteristic parameters of the plasma photonic crystals (PPCs) under different conditions, such as the reflection electric field and the transmission coefficient, to verify the feasibility and accuracy of this method. The results prove that the ICCG–SFDTD method is accurate and has some advantages.

scholarly journals From Time-Collocated to Leapfrog Fundamental Schemes for ADI and CDI FDTD Methods

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 23
Author(s):  
Eng Leong Tan
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Fdtd Method ◽  
Unconditionally Stable ◽  
Alternating Direction Implicit ◽  
One Dimensional ◽  
Alternating Direction ◽  
Fdtd Methods ◽  
Difference Time

The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes are presented for ADI and CDI FDTD methods. For the ADI FDTD method, the time-collocated fundamental schemes are implemented using implicit E-E and E-H update procedures, which comprise simple and concise right-hand sides (RHS) in their update equations. From the fundamental implicit E-H scheme, the leapfrog ADI FDTD method is formulated in conventional form, whose RHS are simplified into the leapfrog fundamental scheme with reduced operations and improved efficiency. For the CDI FDTD method, the time-collocated fundamental scheme is presented based on locally one-dimensional (LOD) FDTD method with complying divergence. The formulations from time-collocated to leapfrog schemes are provided, which result in the leapfrog fundamental scheme for CDI FDTD method. Based on their fundamental forms, further insights are given into the relations of leapfrog fundamental schemes for ADI and CDI FDTD methods. The time-collocated fundamental schemes require considerably fewer operations than all conventional ADI, LOD and leapfrog ADI FDTD methods, while the leapfrog fundamental schemes for ADI and CDI FDTD methods constitute the most efficient implicit FDTD schemes to date.

scholarly journals Butterfly-Inspired 2D Periodic Tapered-Staggered Subwavelength Gratings Designed Based on Finite Difference Time Domain Method

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Houxiao Wang ◽  
Wei Zhou ◽  
Er Ping Li ◽  
Rakesh Ganpat Mote
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Focused Ion Beam ◽  
Ion Beam ◽  
Fdtd Method ◽  
Subwavelength Structures ◽  
Surface Reflection ◽  
Subwavelength Gratings ◽  
Difference Time

The butterfly-inspired 2D periodic tapered-staggered subwavelength gratings were developed mainly using finite difference time domain (FDTD) method, assisted by using focused ion beam (FIB) nanoscale machining or fabrication. The periodic subwavelength structures along the ridges of the designed gratings may change the electric field intensity distribution and weaken the surface reflection. The performance of the designed SiO2gratings is similar to that of the corresponding Si gratings (the predicted reflectance can be less than around 5% for the bandwidth ranging from 0.15 μm to 1 μm). Further, the antireflection performance of the designedx-unspaced gratings is better than that of the correspondingx-spaced gratings. Based on the FDTD designs and simulated results, the butterfly-inspired grating structure was fabricated on the silicon wafer using FIB milling, reporting the possibility to fabricate these FDTD-designed subwavelength grating structures.

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