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The classical reciprocity theorem of electromagnetic field proposed by Lorentz H.A. in 1896 is one of the important theories of electromagnetics. The Lorentz reciprocity theorem is widely used in many fields such as communication, antenna signal transmission, and electromagnetic imaging. The Lorentz reciprocity theorem is an “energy-based” reciprocity theorem. Over the past hundred years, some new reciprocity theorems of electromagnetic field have been discovered, including reciprocity theorems in frequency domain and time domain. In 2020, Lindell et al. extended the concept of the 'Rumsey reaction' in a differential form to include both the Lorentz force density reaction term and the power density reaction term. In the same year, Liu et al. derived the momentum reciprocity theorem from the Maxwell's equations. The momentum reciprocity theorem, like the Lorentz reciprocity theorem, can be used for both theoretical analysis and practical applications. Huygens’ principle is usually derived by the Lorentz reciprocity theorem. In this paper, the momentum reciprocity theorem is employed to derive the Huygens’ principle.
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Keywords:
- Lorentz reciprocity /
- omentum eciprocity /
- Huygens’ principle
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[2] 陈云天, 王经纬, 陈伟锦, 徐竞 2020 69 154206
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Chen Y T, Wang J W, Chen W J, Xu J 2020 Acta Phys. Sin. 69 154206
Google Scholar
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Fu G X 1991 Engineering Electromagnetic Theory and Methods (Beijing: People’s Post and Telecommunications Press) pp58, 59 (in Chinese)
[4] 陈传升, 王秉中, 王任 2021 70 070201
Google Scholar
Chen C S, Wang B Z, Wang R 2021 Acta Phys. Sin. 70 070201
Google Scholar
[5] Zhao Q, Li J, Liu S, Liu G Q, Liu J 2021 IEEE Trans. Instrum. Meas. 70 1
Google Scholar
[6] Feld Y N, Miller D G 1992 Soviet Phys. Doklady. 37 235
[7] Tai C T. 1992 IEEE Trans. Antennas. Prop. 40 675
Google Scholar
[8] Rumsey V H 1954 Phys. Rev. 94 1483
Google Scholar
[9] 赵双任 1987 电子学报 15 88
Google Scholar
Zhao S R 1987 Acta Electron. Sin. 15 88
Google Scholar
[10] Lindell I V, Sihvola A 2020 Prog. Electromagn. Res. Lett. 89 1
Google Scholar
[11] Liu G Q, Li Y Y, Liu J 2020 IEEE Antennas Wirel. Propag. Lett. 19 2159
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[12] 刘国强, 刘婧, 李元园 2020 电磁场广义互易定理 (北京: 科学出版社) 第38, 53, 95—101页
Liu G Q, Liu J, Li Y Y 2020 Generalized Reciprocity Theorem for Electromagnetic Fields (Beijing: Science Press) pp38, 53, 95–101 (in Chinese)
[13] 全绍辉 2013 高等工程电磁场理论(北京: 北京航空航天大学出版社) 第149—151页
Quan S H 2013 Advanced Engineering Electromagnetic Field Theory (Beijing: Beijing University of Aeronautics and Astronautics Press) pp149–151 (in Chinese)
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图 1 实际的电流源、磁流源、电荷源和磁荷源产生的场
Figure 1. Fields generated by the actual current, magnetic current, charge sources and magnetic charge sources.
图 2 惠更斯面电流源、面磁流源、面电荷源和磁荷源产生的场
Figure 2. Fields generated by the Huygens surface current, magnetic current, charge sources and magnetic charge sources.
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[1] Lorentz H A 1896 Amsterdammer Akademie der Wetenschappen 4 176
[2] 陈云天, 王经纬, 陈伟锦, 徐竞 2020 69 154206
Google Scholar
Chen Y T, Wang J W, Chen W J, Xu J 2020 Acta Phys. Sin. 69 154206
Google Scholar
[3] 符果行 1991 工程电磁理论方法 (北京: 人民邮电出版社) 第58, 59页
Fu G X 1991 Engineering Electromagnetic Theory and Methods (Beijing: People’s Post and Telecommunications Press) pp58, 59 (in Chinese)
[4] 陈传升, 王秉中, 王任 2021 70 070201
Google Scholar
Chen C S, Wang B Z, Wang R 2021 Acta Phys. Sin. 70 070201
Google Scholar
[5] Zhao Q, Li J, Liu S, Liu G Q, Liu J 2021 IEEE Trans. Instrum. Meas. 70 1
Google Scholar
[6] Feld Y N, Miller D G 1992 Soviet Phys. Doklady. 37 235
[7] Tai C T. 1992 IEEE Trans. Antennas. Prop. 40 675
Google Scholar
[8] Rumsey V H 1954 Phys. Rev. 94 1483
Google Scholar
[9] 赵双任 1987 电子学报 15 88
Google Scholar
Zhao S R 1987 Acta Electron. Sin. 15 88
Google Scholar
[10] Lindell I V, Sihvola A 2020 Prog. Electromagn. Res. Lett. 89 1
Google Scholar
[11] Liu G Q, Li Y Y, Liu J 2020 IEEE Antennas Wirel. Propag. Lett. 19 2159
Google Scholar
[12] 刘国强, 刘婧, 李元园 2020 电磁场广义互易定理 (北京: 科学出版社) 第38, 53, 95—101页
Liu G Q, Liu J, Li Y Y 2020 Generalized Reciprocity Theorem for Electromagnetic Fields (Beijing: Science Press) pp38, 53, 95–101 (in Chinese)
[13] 全绍辉 2013 高等工程电磁场理论(北京: 北京航空航天大学出版社) 第149—151页
Quan S H 2013 Advanced Engineering Electromagnetic Field Theory (Beijing: Beijing University of Aeronautics and Astronautics Press) pp149–151 (in Chinese)
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