Negative refraction mediated by bound states in the continuum
Fig 1. Coupling of a Gaussian beam with a stereo incident angle to the planar negative refraction mode mediated by the quasi-BICs.
Developing new ways to manipulate the transportation of light is very important from both the fundamental science and the technological points of view in photonics. In general, the incident and the refracted beams are on either side of the interface normal. Envisioned by Veselago in the 1960s, negative refraction has received intense research efforts from the photonics community with long-term quests for new scopes and functionality.
In particular, the experimental demonstration of negative refraction in the photonic crystal (PhC) slab provides on-chip solutions for molding the flow of light for various applications, such as couplers and micro-spectrometer, just to name a few. Total internal reflection (TIR) represents a fundamental guiding mechanism to channel lightwave in an optical chip which is generally considered as a cornerstone for guide wave optics. Such mechanism is essentially below the light cone of the cladding and substrate media.
To data, the canonical way to realize on-chip negative refraction strictly relies on total internal refraction, which inevitably imposes a fundamental limitation that negative refraction can only be achieved below the light cone of surrounding media.
To overcome this limitation, Dr. Yi Xu now in Prof. Yuwen Qin's group from the Advanced Institute of Photonics Technology, School of Information Engineering at Guangdong University of Technology, together with his Master student Zhanyuan Zhang and colleagues, propose and experimentally demonstrate a new mechanism which achieves planar negative refraction beyond total internal refraction. Related research results are published in Photonics Research, Vol. 9, Issue 8, 2021 (Zhanyuan Zhang, Feifei Qin, Yi Xu, Songnian Fu, Yuncai Wang, Yuwen Qin. Negative refraction mediated by bound states in the continuum[J]. Photonics Research, 2021, 9(8): 08001592).
They apply the concept of Bound state in the continuum (BIC) in which electromagnetic modes possess theoretical unbound quality factors to realize negative refraction within the radiative continuum. The proposed mechanism relies on the synchronous engineering of the spatial dispersion and radiative lifetime of the Bloch modes in momentum space for a PhC slab.
Therefore, the out-of-plane guiding is enabled by the quasi-BIC while the in-plane propagation direction is tailored by the elaborated spatial dispersion of PhC slab, simultaneously. The physical mechanism of negative refraction mediated by quasi-BIC is general, and it can be applied over a wide spectral range of electromagnetic waves.
To further verify the theoretical results, microwave experiments are conducted to characterize the negative refraction phenomenon mediated by quasi-BIC. Their experimental measured near-field profiles confirm that the refracted beam in the PhC slab is on the same side of the interface normal as the incident beam, and the acquired phase fronts of the incident and outgoing beam are parallel to each other.
By taking Fourier transform of the measured near-field results, it is validated that the observed negative refraction is indeed beyond the light cone. Compared with the traditional negative refraction phenomenon based on total internal reflection, the proposed mechanism breaks the limitation that the negative refraction can only be achieved in the two-dimensional plane for a PhC slab and provides the possibility to realize stereo-coupling between free-space and the quasi-BIC mode featured with negative refraction (Fig. 1).
Although the bandwidth of negative refraction mediated by BIC is limited, which would hamper subsequent applications of the demonstrated concept, merging multiple BICs in momentum space proposed recently can be used to expand the bandwidth. More promisingly, the proposed mechanism is fully compatible with the guiding mechanisms below the light cone, manifested itself as a promising platform for multiplexing of dense optical signals.
The team members think that this work provides an example that the physical concept of BIC can harness new functionalities and possibility for manipulating the flow of light in photonics, which might open up an avenue for exploring anormal refraction within the radiative continuum and find applications in optical couplers, multiplexers, and mode sorting.
Prof. Cheng-Wei Qiu, Editor of Photonics Research from Department of Electrical and Computer Engineering in National University of Singapore, believes that this highly innovative work provides a distinct BIC perspective revisiting the physics of negative refraction and guided wave optics beyond the light line. It thus paves the way toward advanced multiplexing of optical signal beyond and below the light cone simultaneously. Though their proof-of-concept experiment is performed in microwave region, the optical demonstration in silicon platform is readily expected to accomplish in the near future because of the scalability of PhCs.
基于连续谱束缚态的负折射现象
图1、倾斜入射高斯光束与基于准BIC的负折射模式间的耦合
从光子学基础理论与技术应用发展的角度来看，开发新的光传输操控方式至关重要。通常情况下，入射光束与折射光束分别位于界面法线的两侧。20世纪60年代Veselago提出了光的负折射这一猜想，从此负折射现象得到了光子学界的广泛关注，并且面向基于负折射的新功能和新应用进行了长期的探索。
光子晶体平板中的负折射现象为各种应用（如耦合器、微光谱仪等）提供了片上解决方案。一般来说，全内反射是在光学芯片中引导光的基本机制，被认为是导波光学的基本理论，其工作范围位于包层与基底材料的光锥下方。截至目前，实现片上负折射的方法严格依赖于全内反射，这将不可避免地限制了片上负折射现象在光锥上方的应用。
为了克服上述限制，广东工业大学信息工程学院先进光子技术研究院秦玉文教授课题组的徐毅博士、硕士研究生张展源及其他成员，提出并通过实验验证了一种不依赖于全内反射在光子晶体平板中实现负折射的机制。相关结果发表于Photonics Research 2021年第8期(Zhanyuan Zhang, Feifei Qin, Yi Xu, Songnian Fu, Yuncai Wang, Yuwen Qin. Negative refraction mediated by bound states in the continuum[J]. Photonics Research, 2021, 9(8): 08001592)。
该团队通过连续谱束缚态（BIC）理论中品质因子无限大的机制代替了全内反射效应实现导光。此机制依赖于在光子晶体平板动量空间中同时调控布洛赫模式的空间色散和品质因子，使得负折射光束在的导波机制由准BIC提供，而面内传播方向由光子晶体平板的空间色散决定。
为了进一步验证理论结果，该团队还开展了微波验证实验。实验中测量得到的近场场图证实，光子晶体平板中的折射光束与入射光束位于界面法线的同侧，并且入射与出射光束的波前彼此平行。他们通过对测量得到的近场结果进行傅里叶变换，验证了观察到的负折射现象确实位于光锥之上。
相比较基于全内反射调控的负折射现象，该机制打破了平板光子晶体只能在二维平面内实现负折射的限制，为实现自由空间与片上负折射模式之间的耦合提供了可能性 (图1)。
虽然基于准BIC的负折射频率范围有限，但其带宽可以通过近期提出的在动量空间中合并多个BIC的机制进行扩展。更重要的是，此项工作所提出的导光机制与光锥之下的导光机制可以完全兼容，有望用于实现密集光信号的片上复用。
该团队认为，这项工作提供了一种利用BIC来操纵光传输性质的例子，这可能会为探索连续谱内的异常折射开辟一条新的道路，并在光学耦合器、多路复用器和模式分类中得到广泛应用。
Photonics Research期刊编委、新加坡国立大学仇成伟教授表示，这项工作以独特的视角将BIC与负折射结合起来，重新审视了光锥之上的负折射与导波光学的物理特性，从而为同时实现光锥上下光信号的多路复用铺平了道路。尽管该验证性实验是基于微波波段完成，但相信在不久的将来也有望在硅平台上的光学实验中实现。