## Improved near-field calculations using vectorial diffraction integrals in the finite-difference time-domain method |

JOSA A, Vol. 28, Issue 8, pp. 1776-1783 (2011)

http://dx.doi.org/10.1364/JOSAA.28.001776

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### Abstract

We present an alternative mixed-surface implementation of the Stratton–Chu vectorial diffraction integrals as a means to improve near-field calculations outside the computational domain of the finite-difference time-domain method. This approach, originally derived for far-field calculations, reduces the effect of phase errors and reduces storage costs compared to standard single-surface implementations performed using arithmetic and geometric means. All three methods are applied to a strongly forward-scattering sphere, which is the gold standard for similar simulations with a corresponding analytical Mie series solution. Additionally, the mixed surface is applied to an ensemble of theoretical flow cytometry calibration standards in optical gel. The near-field electromagnetic scattering produced by these or any arbitrary object, such as a cell, could be used to simulate images in a high-numerical-aperture microscope. The results show the mixed-surface implementation outperforms the standard techniques for calculating the near-field electromagnetic fields.

© 2011 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(000.6800) General : Theoretical physics

(170.0180) Medical optics and biotechnology : Microscopy

(290.0290) Scattering : Scattering

(290.4020) Scattering : Mie theory

(050.1755) Diffraction and gratings : Computational electromagnetic methods

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: June 10, 2011

Manuscript Accepted: July 6, 2011

Published: August 1, 2011

**Virtual Issues**

Vol. 6, Iss. 9 *Virtual Journal for Biomedical Optics*

**Citation**

Ryan L. Coe and Eric J. Seibel, "Improved near-field calculations using vectorial diffraction integrals in the finite-difference time-domain method," J. Opt. Soc. Am. A **28**, 1776-1783 (2011)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-28-8-1776

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### References

- P. Török, P. R. T. Munro, and E. E. Kriezis, “Rigorous near- to far-field transformation for vectorial diffraction calculations and its numerical implementation,” J. Opt. Soc. Am. A 23, 713-722(2006). [CrossRef]
- K. Umashankar and A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. EMC-24, 397-405 (1982). [CrossRef]
- A. Taflove and K. Umashankar, “Radar cross section of general three-dimensional scatterers,” IEEE Trans. Electromagn. Compat. EMC-25, 433-440 (1983). [CrossRef]
- A. Taflove, K. R. Umashankar, and T. G. Jurgens, “Validation of FD-TD modeling of the radar cross-section of three-dimensional structures spanning up to nine wavelengths,” IEEE Trans. Antennas Propag. 33, 662-666 (1985). [CrossRef]
- T. Martin, “An improved near- to far-zone transformation for the finite-difference time-domain method,” IEEE Trans. Antennas Propag. 46, 1263-1271 (1998). [CrossRef]
- D. J. Robinson and J. B. Schneider, “On the use of the geometric mean in FDTD near-to-far-field transformations,” IEEE Trans. Antennas Propag. 55, 3204-3211 (2007). [CrossRef]
- J. Y. Fang and D. W. Xeu, “Numerical errors in the computation of impedances by FDTD method and ways to eliminate them,” IEEE Microw. Guid. Wave Lett. 5, 6-8 (1995). [CrossRef]
- T. Martin, “On the FDTD near-to-far-field transformations for weakly scattering objects,” IEEE Trans. Antennas Propag. 58, 2794-2795 (2010). [CrossRef]
- C. W. Penney and R. J. Luebbers, “Input impedance, radiation-pattern, and radar cross-section of spiral antennas using FDTD,” IEEE Trans. Antennas Propag. 42, 1328-1332(1994). [CrossRef]
- H. R. Chuang and L. C. Kuo, “3D FDTD design analysis of a 2.4 GHz polarization-diversity printed dipole antenna with integrated balun and polarization-switching circuit for WLAN and wireless communication applications,” IEEE Trans. Microw. Theory Tech. 51, 374-381 (2003). [CrossRef]
- I. R. Capoglu, C. A. White, J. D. Rogers, H. Subramanian, A. Taflove, and V. Backman, “Numerical simulation of partially coherent broadband optical imaging using the finite-difference time-domain method,” Opt. Express 36, 1596-1598(2011). [CrossRef]
- P. Török, P. R. T. Munro, and E. E. Kriezis, “High numerical aperture vectorial imaging in coherent optical microscopes,” Opt. Express 16, 507-523 (2008). [CrossRef] [PubMed]
- R. Drezek, A. Dunn, and R. Richards-Kortum, “Light scattering from cells: finite-difference time-domain simulations and goniometric measurements,” Appl. Opt. 38, 3651-3661(1999). [CrossRef]
- Y. L. Kim, Y. Liu, R. K. Wali, H. K. Roy, M. J. Goldberg, A. K. Kromin, K. Chen, and V. Backman, “Simultaneous measurement of angular and spectral properties of light scattering for characterization of tissue microarchitecture and its alteration in early precancer,” IEEE J. Sel. Top. Quantum Electron. 9, 243-256(2003). [CrossRef]
- G. Mie, “Articles on the optical characteristics of turbid tubes, especially colloidal metal solutions,” Ann. Phys. 330, 377-445(1908). [CrossRef]
- A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed., Artech House Antennas and Propagation Library (Artech House, 2005), pp. xxii, 1006.
- R. J. Luebbers, K. S. Kunz, M. Schneider, and F. Hunsberger, “A finite-difference time-domain near zone to far zone transformation [electromagnetic scattering],” IEEE Trans. Antennas Propag. 39, 429-433 (1991). [CrossRef]
- O. M. Ramahi, “Near- and far-field calculations in FDTD simulations using Kirchhoff surface integral representation,” IEEE Trans. Antennas Propag. 45, 753-759 (1997). [CrossRef]
- A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice Hall, 1991), pp. xviii, 637.
- T. Martin and L. Pettersson, “Dispersion compensation for Huygens' sources and far-zone transformation in FDTD,” IEEE Trans. Antennas Propag. 48, 494-501 (2000). [CrossRef]
- X. Li, A. Taflove, and V. Backman, “Modified FDTD near-to-far-field transformation for improved backscattering calculation of strongly forward-scattering objects,” IEEE Antennas Wirel. Propag. Lett. 4, 35-38 (2005). [CrossRef]
- F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, “Near-field Lorenz-Mie theory and its application to microholography,” Appl. Opt. 23, 4140-4148 (1984). [CrossRef] [PubMed]
- F. Slimani, G. Grehan, G. Gouesbet, and D. Allano, “Near-field Lorenz-Mie theory and its application to microholography,” Appl. Opt. 23, 4140-4148 (1984). [CrossRef] [PubMed]
- J. B. Schneider and K. Abdijalilov, “Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: PECs, TE, and TM,” IEEE Trans. Antennas Propag. 54, 2531-2542 (2006). [CrossRef]
- M. Fauver, E. Seibel, J. R. Rahn, M. G. Meyer, and F. W. Patten, “Three-dimensional imaging of single isolated cell nuclei using optical projection tomography,” Opt. Express 13, 4210-4223(2005). [CrossRef] [PubMed]

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