Negative Index Materials Reverse the Optical Doppler Effect

(Top L to R) Jiabi Chen, Yan Wang, Baohua Jia, Tao Geng; (Bottom L to R) Xiangping Li, Bingming Liang, Min Gu, and Songlin Zhuang

Authors: Jiabi Chen¹, Yan Wang^1,2, Baohua Jia³, Tao Geng¹, Xiangping Li³, Lie Feng¹, Wei Qian¹, Bingming Liang¹, Xuanxiong Zhang¹, Min Gu³, and Songlin Zhuang¹

Affiliation:
¹Shanghai Key Lab of Contemporary Optical System, Optical Electronic Information and Computer Engineering College, University of Shanghai for Science and Technology, China，
²College of physics and communication electronics, Jiangxi Normal University, China，
³Center for Micro-Photonics and CUDOS, Swinburne University of Technology, Australia

In the past couple of decades, we have witnessed a dramatic boost of the nanofabrication technology. As a result, man-made nanostructures and nanomaterials showing optical properties -- that have never been available naturally before -- came forth. Among these artificial materials, negative index materials have been intensively researched. The driving force for this is, on one hand, due to the potential fascinating applications of negative index materials in super-resolution perfect lens imaging, invisible cloaking and optical communications. On the other hand, it also originates from the curiosity to see the possibility to completely subvert the fundamental physics rules that we learned at school.

In the recent Nature Photonics paper published on March 7 [1], our team at University of Shanghai for Science and Technology in China together with collaborators from Swinburne University in Australia reported the first demonstration of the reversal of the well-known Doppler effect in the optical region with a negative index photonic crystal.

Fig. 1 (a) Normal Doppler effect in normal materials (n>0). (b) Inverse Doppler effect in negative index materials (n<0)

Our common knowledge of a Doppler effect comes from the increasing tone (frequency increase) of a whistling train approaching us and the falling tone (frequency decrease) when it recedes. The same thing happens to light waves. When a light source and an observer approach each other, blue-shifted (frequency increase) light will be observed, as illustrated in Fig.1a. The intriguing inverse Doppler effect is that red-shifted (frequency decrease) light is observed when the light source and an observer are approaching each other, as shown in Fig.1b, or vice versa. The Doppler effect is proportional to the refractive index of the medium that it passes. All naturally existing materials have a refractive index ≥ 1, therefore the normal Doppler effect is expected.

Fig 2: Measured transmission power as a function of the refraction angle θ for a normally incident beam respect to the first interface of the PC (the incident angle at the exit interface is 60°). Inset: Schematic diagram of the experimental setup.

We were able to reverse the Doppler effect for the first time in the optical region by constructing a two-dimensional silicon photonic crystal with a negative index property. In order to have the negative index property, the photonic crystal was tailored to have periodic pillars with nanometric sizes, in which a photonic bandgap can be generated. When shining a beam of CO₂ laser ( λ=10.6 μm corresponding to the 2nd band of the photonic crystal along the ΓM direction), the beam experiences a refraction with a negative index. The experimental result is presented in Fig. 2. At a refraction angle of approximately θ=-26º (incident angle is 60º as indicated in the inset of Fig. 2) high intensity signal could be measured clearly revealing that the photonic crystal prism is operating in the negative refraction region, with a measured n_p=-0.5062.

We employed a highly sensitive two-channel heterodyne interferometric experimental setup to measure the inverse Doppler effect, and at the same time used a positive-index ZnSe prism (n_p=2.403) to conduct the controlled experiment. The results shown in Fig. 3a clearly indicates the measured beat frequency Δf < f^'₂ - f₀k (where f₀ is the original frequency of the CO₂ laser, f^’₂ the reference Doppler frequency shift at the detector surface and k is defined as

Note that the Doppler shift can and can only be positive, i.e. , which indicates that the Doppler frequency is blue-shifted and larger than the original frequency of the CO₂ laser when the optical path becomes larger in the negative index materials.

In contrast the measured frequency differences Δf for four velocities are all less than f^'₂ - f₀k as shown in Fig. 3b (note that here f^'₂ - f₀k < 0), which clearly demonstrates that the Doppler effect measured in the ZnSe prism is normal.

Fig. 3 (a) Measured frequency shifts ∆f in the NIM PC prism compared with the value of f^'₂ - f₀k. (b) Measured frequency shifts ∆f in the positive index ZnSe prism compared with the value of f^'₂ - f₀k.

Our results indicate that reversed Doppler effect at the optical frequency has been observed for the first time by refracting the beam in a negative index photonic crystal. The fascinating negative index materials will lead to more counterintuitive phenomena such as the perfect lens imaging and invisible cloaking.

Reference:
[1] Jiabi Chen, Yan Wang, Baohua Jia, Tao Geng, Xiangping Li, Lie Feng, Wei Qian, Bingming Liang, Xuanxiong Zhang, Min Gu and Songlin Zhuang, “Observation of the inverse Doppler effect in negative-index materials at optical frequencies,” Nat. Photonics 2011 IN PRESS; Published online March 6th 2011; doi: 10.1038/nphoton.2011.17. Abstract.