## UTD solution for the diffraction by an anisotropic impedance wedge at arbitrary skew incidence: numerical matching method |

Optics Express, Vol. 19, Issue 24, pp. 23751-23769 (2011)

http://dx.doi.org/10.1364/OE.19.023751

Acrobat PDF (1348 KB)

### Abstract

a numerical matching method (NMM) based on the framework of the uniform geometrical theory of diffraction (UTD) is proposed to build the spectral functions for computing the diffraction field by anisotropic impedance wedge at an arbitrary skew incidence. The NMM starts from the coupled integral equations before they are converted into the coupled difference equations as the classic Maliuzhinets methods. Then, the spectral function in the Sommerfeld integral representation of the longitudinal components of the EM field is expanded by a series about the spectrum and the skew incident angle with unknown coefficients. With respect to the oblique incident angle based on normal to the edge incidence or grazing to the edge incidence, the spectral function is derived numerically by solving a system of algebraic equations constructed from the coupled integral equations, after choosing the numerical matching regions on the wedge faces and setting a Sommerfeld numerical integration path. On the basis of the sampled incidences, the asymptotic waveform evaluation (AWE) technique is employed to deduce the spectral function at any other skew incidence in the whole angle space (0°-90°) rapidly. Finally, the UTD solutions are provided far beyond the applicability of the perturbation approach and the numerical examples provide a uniform behavior of the field with respect to the observation angle.

© 2011 OSA

## 1. Introduction

1. N. Y. Zhu and F. M. Landstofer, “Numerical study of diffraction and slope-diffraction at anisotropic impedance wedges by the method of parabolic equation: space waves,” IEEE Trans. Antenn. Propag. **45**(5), 822–828 (1997). [CrossRef]

3. B. V. Budaev and D. B. Bogy, “Diffraction of a plane skew electromagnetic wave by a wedge with general anisotropic impedance boundary conditions,” IEEE Trans. Antenn. Propag. **54**(5), 1559–1567 (2006). [CrossRef]

4. F. Yuan and G. Q. Zhu, “Electromagnetic diffraction of a very obliquely incident plane wave field by a wedge with anisotropic impedance faces,” J. Electromagn. Waves Appl. **19**(12), 1671–1685 (2005). [CrossRef]

14. G. Manara, P. Nepa, and G. Pelosi, “A UTD solution for plane wave diffraction at an edge in an artificially hard surface: oblique incidence case,” Electron. Lett. **31**(19), 1649–1650 (1995). [CrossRef]

5. G. Manara, P. Nepa, and G. Pelosi, “Electromagnetic scattering by a right angled anisotropic impedance wedge,” Electron. Lett. **32**(13), 1179–1180 (1996). [CrossRef]

8. F. Yuan and G. Q. Zhu, “Electromagnetic diffraction at skew incidence by a wedge with anisotropic impedance faces,” Radio Sci. **40**(6), RS6014 (2005). [CrossRef]

9. G. Pelosi, G. Manara, and P. Nepa, “A UTD solution for the scattering by a wedge with anisotropic impedance faces: skew incidence case,” IEEE Trans. Antenn. Propag. **46**(4), 579–588 (1998). [CrossRef]

8. F. Yuan and G. Q. Zhu, “Electromagnetic diffraction at skew incidence by a wedge with anisotropic impedance faces,” Radio Sci. **40**(6), RS6014 (2005). [CrossRef]

9. G. Pelosi, G. Manara, and P. Nepa, “A UTD solution for the scattering by a wedge with anisotropic impedance faces: skew incidence case,” IEEE Trans. Antenn. Propag. **46**(4), 579–588 (1998). [CrossRef]

15. Z. Q. Gong, B. X. Xiao, G. Zhu, and H. Y. Ke, ““Improvements to the hybrid MM-PO technique for scattering of plane wave by an infinite wedge,” IEEE Trans. Antenn. Propag. **54**(1), 251–255 (2006). [CrossRef]

8. F. Yuan and G. Q. Zhu, “Electromagnetic diffraction at skew incidence by a wedge with anisotropic impedance faces,” Radio Sci. **40**(6), RS6014 (2005). [CrossRef]

9. G. Pelosi, G. Manara, and P. Nepa, “A UTD solution for the scattering by a wedge with anisotropic impedance faces: skew incidence case,” IEEE Trans. Antenn. Propag. **46**(4), 579–588 (1998). [CrossRef]

## 2. Outline of the solution

*k*and

**40**(6), RS6014 (2005). [CrossRef]

**46**(4), 579–588 (1998). [CrossRef]

**40**(6), RS6014 (2005). [CrossRef]

**46**(4), 579–588 (1998). [CrossRef]

15. Z. Q. Gong, B. X. Xiao, G. Zhu, and H. Y. Ke, ““Improvements to the hybrid MM-PO technique for scattering of plane wave by an infinite wedge,” IEEE Trans. Antenn. Propag. **54**(1), 251–255 (2006). [CrossRef]

## 3. Spectral function for one arbitrary given incidence with NMM

### 3.1 Based on normal to the edge incidence case

**40**(6), RS6014 (2005). [CrossRef]

**46**(4), 579–588 (1998). [CrossRef]

**40**(6), RS6014 (2005). [CrossRef]

**40**(6), RS6014 (2005). [CrossRef]

**40**(6), RS6014 (2005). [CrossRef]

### 3.2 Based on grazing to the edge incidence case

**40**(6), RS6014 (2005). [CrossRef]

## 4. Spectral functions for arbitrary skew incidence with AWE technique

16. Y. E. Erdemli, J. Gong, C. J. Reddy, and J. L. Volakis, “Fast RCS pattern fill using AWE technique,” IEEE Trans. Antenn. Propag. **46**(11), 1752–1753 (1998). [CrossRef]

## 5. UTD solution and numerical results

**46**(4), 579–588 (1998). [CrossRef]

15. Z. Q. Gong, B. X. Xiao, G. Zhu, and H. Y. Ke, ““Improvements to the hybrid MM-PO technique for scattering of plane wave by an infinite wedge,” IEEE Trans. Antenn. Propag. **54**(1), 251–255 (2006). [CrossRef]

### 5.1 Cases based on normal incidence 25 o ≤ β 0 ≤ 90 o

3. B. V. Budaev and D. B. Bogy, “Diffraction of a plane skew electromagnetic wave by a wedge with general anisotropic impedance boundary conditions,” IEEE Trans. Antenn. Propag. **54**(5), 1559–1567 (2006). [CrossRef]

2. G. Pelosi, S. Selleri, and R. D. Graglia, “Numerical analysis of the diffraction at an anisotropic impedance wedge,” IEEE Trans. Antenn. Propag. **45**(5), 767–771 (1997). [CrossRef]

**46**(4), 579–588 (1998). [CrossRef]

10. R. G. Rojas, “Electromagnetic diffraction of an obliquely incident plane wave field by a wedge with impedance face,” IEEE Trans. Antenn. Propag. **36**(7), 956–970 (1988). [CrossRef]

2. G. Pelosi, S. Selleri, and R. D. Graglia, “Numerical analysis of the diffraction at an anisotropic impedance wedge,” IEEE Trans. Antenn. Propag. **45**(5), 767–771 (1997). [CrossRef]

3. B. V. Budaev and D. B. Bogy, “Diffraction of a plane skew electromagnetic wave by a wedge with general anisotropic impedance boundary conditions,” IEEE Trans. Antenn. Propag. **54**(5), 1559–1567 (2006). [CrossRef]

10. R. G. Rojas, “Electromagnetic diffraction of an obliquely incident plane wave field by a wedge with impedance face,” IEEE Trans. Antenn. Propag. **36**(7), 956–970 (1988). [CrossRef]

**54**(1), 251–255 (2006). [CrossRef]

**46**(4), 579–588 (1998). [CrossRef]

### 5.2 Cases based on grazing to the edge incidence 0 o < β 0 ≤ 30 o

### 5.3 Examination for uniformity of the overlapped angle range (25 o ≤ β 0 ≤ 30 o )

### 5.4 Validation of the solution derived through AWE technique

## 6. Conclusion

## Acknowledgments

## References and links

1. | N. Y. Zhu and F. M. Landstofer, “Numerical study of diffraction and slope-diffraction at anisotropic impedance wedges by the method of parabolic equation: space waves,” IEEE Trans. Antenn. Propag. |

2. | G. Pelosi, S. Selleri, and R. D. Graglia, “Numerical analysis of the diffraction at an anisotropic impedance wedge,” IEEE Trans. Antenn. Propag. |

3. | B. V. Budaev and D. B. Bogy, “Diffraction of a plane skew electromagnetic wave by a wedge with general anisotropic impedance boundary conditions,” IEEE Trans. Antenn. Propag. |

4. | F. Yuan and G. Q. Zhu, “Electromagnetic diffraction of a very obliquely incident plane wave field by a wedge with anisotropic impedance faces,” J. Electromagn. Waves Appl. |

5. | G. Manara, P. Nepa, and G. Pelosi, “Electromagnetic scattering by a right angled anisotropic impedance wedge,” Electron. Lett. |

6. | M. A. Lyalinov, “Diffraction by a wedge with anisotropic face impedances,” Ann. Telecommun. |

7. | G. D. Maliuzhinets, “Excitation, reflection and emission of surface waves from a wedge with given face impedances,” Sov. Phys. Dokl. |

8. | F. Yuan and G. Q. Zhu, “Electromagnetic diffraction at skew incidence by a wedge with anisotropic impedance faces,” Radio Sci. |

9. | G. Pelosi, G. Manara, and P. Nepa, “A UTD solution for the scattering by a wedge with anisotropic impedance faces: skew incidence case,” IEEE Trans. Antenn. Propag. |

10. | R. G. Rojas, “Electromagnetic diffraction of an obliquely incident plane wave field by a wedge with impedance face,” IEEE Trans. Antenn. Propag. |

11. | G. Pelosi, G. Manara, and P. Nepa, “Electromagnetic scattering by a wedge with anisotropic impedance faces,” IEEE Antenn. Propag. Mag. |

12. | J. M. L. Bernard, “Diffraction at skew incidence by an anisotropic impedance wedge in electromagnetism theory: a new class of canonical cases,” J. Phys. Math. Gen. |

13. | M. A. Lyalinov and N. Y. Zhu, “Exact solution to diffraction problem by wedges with a class of anisotropic impedance faces: oblique incidence of a plane electromagnetic wave,” IEEE Trans. Antenn. Propag. |

14. | G. Manara, P. Nepa, and G. Pelosi, “A UTD solution for plane wave diffraction at an edge in an artificially hard surface: oblique incidence case,” Electron. Lett. |

15. | Z. Q. Gong, B. X. Xiao, G. Zhu, and H. Y. Ke, ““Improvements to the hybrid MM-PO technique for scattering of plane wave by an infinite wedge,” IEEE Trans. Antenn. Propag. |

16. | Y. E. Erdemli, J. Gong, C. J. Reddy, and J. L. Volakis, “Fast RCS pattern fill using AWE technique,” IEEE Trans. Antenn. Propag. |

**OCIS Codes**

(050.1940) Diffraction and gratings : Diffraction

(290.0290) Scattering : Scattering

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: August 8, 2011

Revised Manuscript: October 19, 2011

Manuscript Accepted: October 19, 2011

Published: November 8, 2011

**Citation**

Ji Li, Siyuan He, Dingfeng Yu, Fangshun Deng, Hongcheng Yin, and Guoqiang Zhu, "UTD solution for the diffraction by an anisotropic impedance wedge at arbitrary skew incidence: numerical matching method," Opt. Express **19**, 23751-23769 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-23751

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### References

- N. Y. Zhu and F. M. Landstofer, “Numerical study of diffraction and slope-diffraction at anisotropic impedance wedges by the method of parabolic equation: space waves,” IEEE Trans. Antenn. Propag.45(5), 822–828 (1997). [CrossRef]
- G. Pelosi, S. Selleri, and R. D. Graglia, “Numerical analysis of the diffraction at an anisotropic impedance wedge,” IEEE Trans. Antenn. Propag.45(5), 767–771 (1997). [CrossRef]
- B. V. Budaev and D. B. Bogy, “Diffraction of a plane skew electromagnetic wave by a wedge with general anisotropic impedance boundary conditions,” IEEE Trans. Antenn. Propag.54(5), 1559–1567 (2006). [CrossRef]
- F. Yuan and G. Q. Zhu, “Electromagnetic diffraction of a very obliquely incident plane wave field by a wedge with anisotropic impedance faces,” J. Electromagn. Waves Appl.19(12), 1671–1685 (2005). [CrossRef]
- G. Manara, P. Nepa, and G. Pelosi, “Electromagnetic scattering by a right angled anisotropic impedance wedge,” Electron. Lett.32(13), 1179–1180 (1996). [CrossRef]
- M. A. Lyalinov, “Diffraction by a wedge with anisotropic face impedances,” Ann. Telecommun.49, 667–672 (1994).
- G. D. Maliuzhinets, “Excitation, reflection and emission of surface waves from a wedge with given face impedances,” Sov. Phys. Dokl.3, 752–755 (1958).
- F. Yuan and G. Q. Zhu, “Electromagnetic diffraction at skew incidence by a wedge with anisotropic impedance faces,” Radio Sci.40(6), RS6014 (2005). [CrossRef]
- G. Pelosi, G. Manara, and P. Nepa, “A UTD solution for the scattering by a wedge with anisotropic impedance faces: skew incidence case,” IEEE Trans. Antenn. Propag.46(4), 579–588 (1998). [CrossRef]
- R. G. Rojas, “Electromagnetic diffraction of an obliquely incident plane wave field by a wedge with impedance face,” IEEE Trans. Antenn. Propag.36(7), 956–970 (1988). [CrossRef]
- G. Pelosi, G. Manara, and P. Nepa, “Electromagnetic scattering by a wedge with anisotropic impedance faces,” IEEE Antenn. Propag. Mag.40(6), 29–35 (1998). [CrossRef]
- J. M. L. Bernard, “Diffraction at skew incidence by an anisotropic impedance wedge in electromagnetism theory: a new class of canonical cases,” J. Phys. Math. Gen.31(2), 595–613 (1998). [CrossRef]
- M. A. Lyalinov and N. Y. Zhu, “Exact solution to diffraction problem by wedges with a class of anisotropic impedance faces: oblique incidence of a plane electromagnetic wave,” IEEE Trans. Antenn. Propag.51(6), 1216–1220 (2003). [CrossRef]
- G. Manara, P. Nepa, and G. Pelosi, “A UTD solution for plane wave diffraction at an edge in an artificially hard surface: oblique incidence case,” Electron. Lett.31(19), 1649–1650 (1995). [CrossRef]
- Z. Q. Gong, B. X. Xiao, G. Zhu, and H. Y. Ke, ““Improvements to the hybrid MM-PO technique for scattering of plane wave by an infinite wedge,” IEEE Trans. Antenn. Propag.54(1), 251–255 (2006). [CrossRef]
- Y. E. Erdemli, J. Gong, C. J. Reddy, and J. L. Volakis, “Fast RCS pattern fill using AWE technique,” IEEE Trans. Antenn. Propag.46(11), 1752–1753 (1998). [CrossRef]

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