Negative Refraction at a Lossy Interface and a Bold Hypothesis via Complex Frequency

doi:10.1007/s12204-019-2099-x

Abstract

Abstract: We investigate the negative refraction effect at a planar interface of a highly absorptive material, where the direct experimental verification is difficult because of the loss-induced skin depth effect. An apparent contradiction occurs when we try to determine the group velocity direction by the method of equifrequency contours (EFCs) in detail. This contradiction forbids any physical solution to be found for negative refraction. We conclude that this paradox is mainly caused by the definition of complex wavevector k which is conventionally adopted in the case of complex permittivity. The complex wavevector may result in ambiguously defined optical path, which limits the application of the classical Snell's law. We propose a bold suggestion that the complex wavevector k should be replaced by a complex frequency ω. Therefore, the optical path can always be defined as real. The proposed hypothesis is capable of resolving the contradiction about the loss-induced negative refraction, and the obtained theoretical prediction fits well with the reported experimental results.

Key words: Drude material| negative refraction| anomalous dispersion| complex frequency

摘要： We investigate the negative refraction effect at a planar interface of a highly absorptive material, where the direct experimental verification is difficult because of the loss-induced skin depth effect. An apparent contradiction occurs when we try to determine the group velocity direction by the method of equifrequency contours (EFCs) in detail. This contradiction forbids any physical solution to be found for negative refraction. We conclude that this paradox is mainly caused by the definition of complex wavevector k which is conventionally adopted in the case of complex permittivity. The complex wavevector may result in ambiguously defined optical path, which limits the application of the classical Snell's law. We propose a bold suggestion that the complex wavevector k should be replaced by a complex frequency ω. Therefore, the optical path can always be defined as real. The proposed hypothesis is capable of resolving the contradiction about the loss-induced negative refraction, and the obtained theoretical prediction fits well with the reported experimental results.

关键词: Drude material| negative refraction| anomalous dispersion| complex frequency

CLC Number:

O 435

YIN Cheng (殷澄), KAN Xuefen (阚雪芬), SHAN Minglei (单鸣雷), CAO Zhuangqi (曹庄琪), WANG Xianping (王贤平). Negative Refraction at a Lossy Interface and a Bold Hypothesis via Complex Frequency[J]. Journal of Shanghai Jiao Tong University (Science), 2019, 24(5): 545-550.

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