2004 Fiscal Year Final Research Report Summary
High Accuracy Numerical simulation of Light Propagation in Photonic Crystals
| Project/Area Number |
14550034
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Applied optics/Quantum optical engineering
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| Research Institution | University of Tsukuba |
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Principal Investigator |
COLE James B. Univ. of Tsukuba, Graduate School of Systems and Information Engineering, Associate Professor, 大学院・システム情報工学研究科, 助教授 (20280901)
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| Co-Investigator(Kenkyū-buntansha) |
CAI Dongsheng Univ. of Tsukuba, Graduate School of Systems and Information Engineering, Associate Professor, 大学院・システム情報工学研究科, 助教授 (70202075)
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| Project Period (FY) |
2002 – 2004
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| Keywords | photonic crystal / Maxwell's equation / optical switch / FDTD algorithm / Mie scattering / GNSFD calculation / optical circuit / optical memory |
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| Research Abstract |
Although the technology to fabricate photonic crystals in the optical to near-infrared region is essentially the same as that used for semiconductor fabrication, it is not cheap to build test devices. Rather we need to calculate what the expected characteristics of a device will be before it is fabricated. The propagation of light is governed by Maxwell's equations, but except for very simple structures with a high degree of symmetry, Maxwell's equations cannot be solved analytically. Numerical methods are thus needed to design realistic photonic crystal devices.
The finite-difference time-domain(FDTD) algorithm is a popular method, but the conventional algorithm is not very accurate. On a numerical grid of spacing ^h, the error is ^<ε〜(h/λ)^2>, where ^λ is the wavelength. Halving ^h(^<h→(h/2)>) yields ^<ε→ε/4>. The computational cost, ^C, is proportional to the number of space-time grid points, so in three dimensions ^<C→16C>, because the time step, ^<Δt>, is proportional to the space step ^h. The price of a 4-fold increase in accuracy is thus a 16-fold increase in computational cost. High accuracy design calculations of realistic devices will thus overtax even the best supercomputers.
We have developed a new high accuracy version of the FDTD algorithm, based on what are called nonstandard finite-differences (NS-FDTD), for which the error is ^<ε〜(h/λ)^6>. In this research project we have used our NS-FDTD algorithm to model various kinds of optical systems with subwavelength features.
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