Hot Topics

2022-11-27
PIER
Vol. 176, 35-44, 2023
Highly Transparent Tunable Microwave Perfect Absorption for Broadband Microwave Shielding
Dongdong Li Xiaojun Hu Bingtao Gao Wen-Yan Yin Hongsheng Chen Haoliang Qian
To shield undesirable microwave radiation to protect electronic systems and human health, microwave perfect absorbers have attracted increasing interests in recent years. However, the opaque or semitransparent nature of most implemented microwave absorbers limit their applications in optics. Here, we demonstrate a high-performance microwave absorber based on an impedance-assisted Fabry-Pérot resonant cavity with an ITO-dielectric-ITO structure without complex nanofabrication. The device features near-unity absorption (99.5% at 14.4 GHz with a 4.5 GHz effective bandwidth), excellent electromagnetic interference shielding performance (24 dB) in the Ku-band, and high optical transparency (89.0% from 400 nm to 800 nm). The peak absorption frequency of the device can be tuned by changing the thickness of glass slab and sheet resistance of ITO films. Our work provides a low-cost and feasible solution for highperformance optically transparent microwave shielding and stealth, paving the way towards applications in areas of microwave and optics.
Highly Transparent Tunable Microwave Perfect Absorption for Broadband Microwave Shielding
2022-04-30
PIER
Vol. 174, 33-42, 2022
TDFA-Band Silicon Optical Variable Attenuator
Maoliang Wei Hui Ma Chunlei Sun Chuyu Zhong Yuting Ye Peng Zhang Ruonan Liu Junying Li Lan Li Bo Tang Hongtao Lin
TDFA-band (2-μm waveband) has been considered as a promising optical window for the next generation of optical communication and computing. Absorption modulation, one of the fundamental reconfigurable manipulations, is essential for large-scale photonic integrated circuits. However, few efforts have been involved in exploring absorption modulation at TDFA-band. In this work, variable optical attenuators (VOAs) for TDFA-band wavelengths were designed and fabricated based on a silicon-on-insulator (SOI) platform. By embedding a short PIN junction length of 200 μm into the waveguide, the fabricated VOA exhibits a high modulation depth of 40.49 dB at 2.2 V and has a fast response time (10 ns) induced by the plasma dispersion effect. Combining the Fabry-Perot cavity effect and plasma dispersion effect of silicon, the attenuator could achieve a maximum attenuation of more than 50 dB. These results promote the 2-μm waveband silicon photonic integration and are expected to the future use of photonic attenuators in crosstalk suppression, optical modulation, and optical channel equalization.
TDFA-BAND SILICON OPTICAL VARIABLE ATTENUATOR
2023-04-04
PIER
Vol. 177, 33-42, 2023
Systemically Delivered, Deep-Tissue Nanoscopic Light Sources
Xiang Wu Fan Yang Sa Cai Guosong Hong
Light is widely used in life science in both controlling and observing biological processes, yet a long-standing challenge of using light inside the tissue lies in the limited penetration depth of visible light. In the past decade, many in vivo light delivery methods using photonics and materials science tools have been developed, with recent demonstrations of non-invasive, deep-tissue light sources based on systemically delivered luminescent nanomaterials. In this perspective, we provide an overview for the principles of intravital nanoscopic light sources and discuss their advantages over existing methods for in vivo light delivery. We then highlight their recent applications in optogenetics neuromodulation and fluorescent imaging in live animals. We also present an outlook section about the feasibility of combining these non-invasive light sources with other modalities to expand the utilities of light in biology.
Systemically Delivered, Deep-tissue Nanoscopic Light Sources
2020-11-30
PIER
Vol. 169, 33-43, 2020
One-Way Topological States Along Vague Boundaries in Synthetic Frequency Dimensions Including Group Velocity Dispersion (Invited)
Qingrou Shan Danying Yu Guangzhen Li Luqi Yuan Xianfeng Chen
We recently proposed a two-dimensional synthetic space including one spatial axis and one synthetic frequency dimension in a one-dimensional ring resonator array [Opt. Lett. 41, 741 (2016)]. Nevertheless, the group velocity dispersion (GVD) of the waveguides that compose rings was ignored for simplicity. In this paper, we extend the previous work and study the topological one-way edge states in such a synthetic space involving GVD. We show that the GVD brings a natural vague boundary in the frequency dimension, so the topological edge state still propagates at several frequency modes unidirectionally along the spatial axis. Positions of such vague boundary can be controlled by changing the magnitude of the GVD. In particular, a relatively strong GVD can degrade this two-dimensional synthetic space to one-dimensional spatial lattice, but yet the one-way state is still preserved in simulations. Our work therefore exhibits the impact of the GVD on topological photonics in the synthetic space, which will be important for future practical experimental implementations.
ONE-WAY TOPOLOGICAL STATES ALONG VAGUE BOUNDARIES IN SYNTHETIC FREQUENCY DIMENSIONS INCLUDING GROUP VELOCITY DISPERSION (INVITED)
2021-12-24
PIER
Vol. 172, 33-40, 2021
Non-Hermitian Skin Effect and Delocalized Edge States in Photonic Crystals with Anomalous Parity-Time Symmetry
Qinghui Yan Hongsheng Chen Yihao Yang
Non-Hermitian skin effect denotes the exponential localization of a large number of eigen-states at boundaries in a non-Hermitian lattice under open boundary conditions. Such a non-Hermiticity-induced skin effect can offset the penetration depth of in-gap edge states, leading to counterintuitive delocalized edge modes, which have not been studied in a realistic photonic system such as photonic crystals. Here, we analytically reveal the non-Hermitian skin effect and the delocalized edge states in Maxwell's equations for non-Hermitian chiral photonic crystals with anomalous parity-time symmetry. Remarkably, we rigorously prove that the penetration depth of the edge states is inversely proportional to the frequency and the real part of the chirality. Our findings pave a way towards exploring novel non-Hermitian phenomena and applications in continuous Maxwell's equations.
NON-HERMITIAN SKIN EFFECT AND DELOCALIZED EDGE STATES IN PHOTONIC CRYSTALS WITH ANOMALOUS PARITY-TIME SYMMETRY
2020-10-02
PIER
Vol. 168, 31-38, 2020
A Novel Millimeter-Wave Backward to Forward Scanning Periodic Leaky-Wave Antenna Based on Two Different Radiator Types
Yiming Zhang Hui Liu Chenyang Meng Yuxin Lin Yuan Zhang Erik Forsberg Sailing He
A periodic millimeter wave leaky-wave antenna (LWA), which has two different types of radiator elements that enable backward to forward radiation, is proposed. The unit-cell of the LWA consists of two quarter-wavelength microstrip lines and two corrugated substrate integrated waveguide (CSIW) cells with S-shaped quarter-wavelength open-circuit stubs. In addition to two parallel edge radiators, a single etched transverse slot with a tilt angle acts as an ancillary radiator, which ensures impedance matching in a large frequency range and achieves the backward to forward scanning. We analyze the proposed design through simulations, characterize a fabricated prototype and find it to have good radiation properties including broad impedance bandwidth. The measurement results show a high peak gain from 11 to 15.8 dBi with a large scanning angle range from -34° to +22° in the K-band operating frequency range.
A NOVEL MILLIMETER-WAVE BACKWARD TO FORWARD SCANNING PERIODIC LEAKY-WAVE ANTENNA BASED ON TWO DIFFERENT RADIATOR TYPES
2022-07-27
PIER
Vol. 175, 29-43, 2022
Low Cost and High Performance 5-Bit Programmable Phased Array Antenna at Ku-Band
Xin Li Han Qing Yang Rui Wen Shao Feng Zhai Guo Biao Liu Zheng Xing Wang Hong Fei Gao Ge Fan Jun Wei Wu Qiang Cheng Tie-Jun Cui
We present a low-cost and high-performance 5-bit programmable phased array antenna at Ku-band, which consists of 1-bit reconfigurable radiation structures, digital phase shifters, and coplanar waveguide feeding network. The 1-bit reconfigurable radiation structure utilizes symmetric geometries and PIN diodes to form stable 180° phase difference. The digital phase shifter provides 168.75° phase difference and together with the radiation structure form a 348.75° phase coverage. The antenna operates between 14.4 and 15.4 GHz, and the overall array contains 24×2 elements with each of them being individually addressable. By changing the states of the diodes and thus adjusting the phase coding sequences of the array, the antenna achieves 0°-60° precise beam scanning at 14.8 GHz, with the sidelobe level, cross-polarization, and gain fluctuation being less than -16 dB, -26 dB, and 2.4 dB, respectively. A prototype was fabricated to verify the design, and the measurement results agree well with simulations. Compared with traditional phased arrays composed of numerous phase shifters and T/R components, the proposed antenna features high performance, high flexibility, low profile, and low cost. The antenna provides a new and feasible solution of wavefront steering and will benefit the various application scenarios.
LOW COST AND HIGH PERFORMANCE 5-BIT PROGRAMMABLE PHASED ARRAY ANTENNA AT KU-BAND
2020-11-25
PIER
Vol. 169, 25-32, 2020
Designer Surface Plasmons Enable Terahertz Cherenkov Radiation (Invited)
Jie Zhang Xiaofeng Hu Hongsheng Chen Fei Gao
Cherenkov radiation (CR) is a promising method to generate high-power terahertz (THz) electromagnetic (EM) waves, which are highly desired in numerous practical applications. For the purpose of economy energy, naturally occurred materials with flat surface (e.g. graphene), which can support highly-confined surface-plasmon-polariton (SPP) modes, have been proposed to construct high-efficiency terahertz CR source; however, these emerging materials cannot be easily fabricated nor flexibly designed. Here, we propose a designer-SPP metamaterial scheme to pursue terahertz CR. The metamaterial is a structure-decorated metal surface, which is compatible with planar fabrication, and can support SPP-like EM modes in terahertz frequencies, also named as designer SPP. Due to the structure dependence of designer SPP, its dispersions can be flexibly designed by changing the structure geometries as well as choosing proper dielectric medias. Numerical results clearly demonstrated this scheme. Our proposal may promise future high-efficiency and intense THz source with design flexibilities.
DESIGNER SURFACE PLASMONS ENABLE TERAHERTZ CHERENKOV RADIATION (INVITED)
2022-11-26
PIER
Vol. 176, 25-33, 2023
Optical Neural Networks for Holographic Image Recognition (Invited Paper)
Yiming Feng Junru Niu Yiyun Zhang Yixuan Li Hongsheng Chen Haoliang Qian
Inspired by neural networks based on traditional electronic circuits, optical neural networks (ONNs) show great potential in terms of computing speed and power consumption. Though some progress has been made in devices and schemes, ONNs are still a long way from replacing electronic neural networks in terms of generalizability. Here, we present a complex optical neural network (cONN) for holographic image recognition, within which a high-speed parallel operating unit for complex matrices is proposed, targeting the real-imaginary-splitting and column splitting. Based on the proposed cONN, we have numerically demonstrated the training-recognition process on our cONN for holographic images converted from handwritten digit datasets, achieving an accuracy of 90% based on the back-propagation algorithm. Our training verification integrated architecture will enrich the further development and applications of on-chip photonic matrix computing.
Optical Neural Networks for Holographic Image Recognition (Invited Paper)
2022-03-04
PIER
Vol. 173, 25-36, 2022
Portable 4D Snapshot Hyperspectral Imager for Fastspectral and Surface Morphology Measurements (Invited Paper)
Jing Luo Zijian Lin Yuxin Xing Erik Forsberg Chengdong Wu Xinhua Zhu Tingbiao Guo Gaoxuan Wang Beilei Bian Dun Wu Sailing He
A portable 4D snapshot hyperspectral imager (P4DS imager) with compact size, fast imaging time, low cost, and simple design is proposed and demonstrated. The key components of the system are a projector, a liquid crystal tunable filter (LCTF), and a camera. It has two operating modes dependent on the set state of the LCTF: a 3D light measurement mode that produces a 3D point cloud reconstruction of the object, and a hyperspectral imaging mode yielding spectral data. The camera imaging plane is the same for both operating modes allowing the collected spatial and spectral data to be directly fused into a 4D data set without post-processing. The P4DS imager has excellent performance with a spectral resolution of 10 nm, a spatial depth accuracy of 55.7 um, and total 4D imaging time of 0.8 s. 4D imaging experiments of three different samples, colored doll statue, green broccoli, and a human face, are presented to demonstrate the efficiency and applicability of the system. Due to being cost-effective, portable, and good imaging performance, the proposed system is suitable for commercialization and mass production.
PORTABLE 4D SNAPSHOT HYPERSPECTRAL IMAGER FOR FASTSPECTRAL AND SURFACE MORPHOLOGY MEASUREMENTS (INVITED PAPER)
2020-08-30
PIER
Vol. 168, 25-30, 2020
Second-Order Nonlinear Susceptibility Enhancement in Gallium Nitride Nanowires (Invited)
Kangwei Wang Haoliang Qian Zhaowei Liu Paul K. L. Yu
We report the second-harmonic generation (SHG) from single GaN nanowire. The diameter of the GaN nanowire varies from 150 to 400 nm. We present a model for the SHG process in the GaN nanowire; the analysis shows quantitatively that the SHG is dominated by its surface area. The effective second order nonlinear optical susceptibility (χ(2)eff) increases as the diameter of the GaN nanowire decreases. For 150-nm diameter GaN nanowire, χ(2)eff reaches 136 pm/V.
SECOND-ORDER NONLINEAR SUSCEPTIBILITY ENHANCEMENT IN GALLIUM NITRIDE NANOWIRES (INVITED)
2022-04-29
PIER
Vol. 174, 23-32, 2022
Squeezing of Hyperbolic Polaritonic Rays in Cylindrical Lamellar Structures
Lu Song Lian Shen Huaping Wang
We propose the squeezing of hyperbolic polaritonic rays in cylindrical lamellar structures with hyperbolic dispersion. This efficient design is presented through conformal mapping transformation by combining with circular effective-medium theory (CEMT) that is adopted to predict the optical response of concentric cylindrical binary metal-dielectric layers. The volume-confined hyperbolic polaritons supported in these cylindrical lamellar structures could be strongly squeezed when they propagate toward the origin since their wavelength shortens, and velocity decreases. To demonstrate the importance of using CEMT for engineering highly-squeezed hyperbolic polaritons, both CEMT and planar effective-medium theory (PEMT) are utilized to design the cylindrical lamellar structures. It is shown that the PEMT-based design is unable to achieve hyperbolic polaritons squeezing even with a sufficiently large number of metal-dielectric binary layers. Remarkably, this study opens new opportunities for hyperbolic polaritons squeezing, and the findings are promising for propelling nanophotonics technologies and research endeavours.
SQUEEZING OF HYPERBOLIC POLARITONIC RAYS IN CYLINDRICAL LAMELLAR STRUCTURES
2023-03-23
PIER
Vol. 177, 21-32, 2023
Highly Sensitive Temperature Sensing via Photonic Spin Hall Effect
Shuaijie Yuan Jin Yang Yong Wang Yu Chen Xinxing Zhou
In this work, we propose a highly sensitive temperature sensor based on photonic spin Hall effect (PSHE). We find that, by involving the liquid crystal (LC) material, the spin spatial and angular shifts in PSHE are very sensitive to the tiny perturbation of temperature when the incident angle of light beam is near the Brewster and critical angles. Importantly, the phase transition from liquid crystal state to liquid state across the clearing point (CP) will lead to the transition of strong spin-orbit interaction to the weak one. During this process, we reveal that the sensitivity of our designed temperature sensor can reach a giant value with 8.27 cm/K which is one order of magnitude improvement compared with the previous Goos-Hänchen effect-based temperature sensor. This work provides an effective method for precisely determining the position of CP and actively manipulating the spin-orbit interaction.
Highly Sensitive Temperature Sensing via Photonic Spin Hall Effect
2020-11-25
PIER
Vol. 169, 17-23, 2020
Multi-Laser Scanning Confocal Fluorescent Endoscopy Scheme for Subcellular Imaging (Invited)
Xiaomin Zheng Xiang Li Qiao Lin Jiajie Chen Yueqing Gu Yonghong Shao
Fluorescence confocal laser scanning endomicroscopy is a novel tool combining confocal microscopy and endoscopy for in-vivo subcellular structure imaging with comparable resolution as the traditional microscope. In this paper, we propose a three-channel fluorescence confocal microscopy system based on fiber bundle and two excitation laser lines of 488nm and 650nm. Three fluorescent photomultiplier detecting channels of red, green and blue can record multi-color fluorescence signals from single sample site simultaneously. And its ability for in-vivo multi-channel fluorescence detection at subcellular level is verified. Moreover, the system has achieved an effective field of view of 154μm in diameter with high resolution. With its multi-laser scanning, multi-channel detection, flexible probing, and in-vivo imaging abilities it will become a powerful tool in bio-chemical research and diagnostics, such as the investigation of the transport mechanism of nano-drugs in small animals.
MULTI-LASER SCANNING CONFOCAL FLUORESCENT ENDOSCOPY SCHEME FOR SUBCELLULAR IMAGING (INVITED)
2020-08-22
PIER
Vol. 168, 15-23, 2020
Superscattering of Light in Refractive-Index Near-Zero Environments
Chan Wang Chao Qian Hao Hu Lian Shen Zuo Jia Wang Huaping Wang Zhiwei Xu Baile Zhang Hongsheng Chen Xiao Lin
Enhancing the scattering of light from subwavelength structures is of both fundamental and practical significance. While the scattering cross section from each channel cannot exceed the single-channel limit, it is recently reported that the total cross section can far exceed this limit if one overlaps the contribution from many channels. Such a phenomenon about enhancing the scattering from subwavelength structures in free space is denoted as the superscattering in some literature. However, the scatterer in practical scenarios is not always in free space but may be embedded in environments with non-unity refractive index n. The influence of environments on the superscattering remains elusive. Here the superscattering from subwavelength structures in the isotropic environment with near-zero index are theoretically investigated. Importantly, a smaller n can lead to a larger total cross section for superscattering. The underlying mechanism is that a smaller n can give rise to a larger single-channel limit. Our work thus indicates that the scattering from subwavelength structures can be further enhanced if one simultaneously maximizes the single-channel limit and the contribution from many channels.
SUPERSCATTERING OF LIGHT IN REFRACTIVE-INDEX NEAR-ZERO ENVIRONMENTS
2022-07-21
PIER
Vol. 175, 13-27, 2022
An Elliptically Polarized Wave Injection Technique via TF/SF Boundary in Subdomain Level DGTD Method
Xiaobing Han Hang Li Yuanguo Zhou Lin Wang Shangqing Liang Fawad Javaid
This study presents an effective solution on the basis of Discontinuous-Galerkin Time-Domain (DGTD) scheme for the injection of elliptically polarized plane wave through total-field/scattered-field (TF/SF) boundary. Generally, the elliptically polarized wave can be resolved into two linearly polarized waves in phase quadrature with the polarization planes at right angles to each other, but the proposed methodology is focused to utilize the principle of wave field formation to induce left-handed or right-handed elliptically polarized waves by regulating the phase and amplitude of the incident waves. The outcome of the proposed technique is achieved by deriving the EB-scheme equations and employing the explicit fourth order Runge-Kutta (RK4) time integration scheme in the DGTD methodology. An anisotropic Riemann solver and non-conformal mesh schemes are introduced for domain decomposition to allow efficient spatial discretization. Additionally, the proposed work is extended from single frequency to broadband elliptical polarized plane wave injection in the DGTD method, and the significance of this study is observed in the results. The experimental outcomes reveal that the proposed method is consistent with the analytical solution in free space and expected to provide efficient numerical solutions for analyzing scattering characteristics generated by various elliptically polarized waves.
AN ELLIPTICALLY POLARIZED WAVE INJECTION TECHNIQUE VIA TF/SF BOUNDARY IN SUBDOMAIN LEVEL DGTD METHOD
2021-12-20
PIER
Vol. 172, 13-22, 2021
Tunable Topological Refractions in Valley Sonic Crystals with Triple Valley Hall Phase Transitions (Invited Paper)
Ding Jia Yin Wang Yong Ge Shou-Qi Yuan Hong-Xiang Sun
Topological refractions created by valley sonic crystals (VSCs) have attracted great attentions in the communities of physics and engineering owing to the advantage of zero reflection of sound and the potential for designing advanced acoustic devices. In previous works, topological refractions of valley edge states are demonstrated to be determined by the projections of the valleys K and K′, and two types of topological refractions generally exist at opposite terminals or different frequency bands. However, the realization of tunable topological refractions at the fixed frequency band and terminal still poses great challenge. To overcome this, we report the realization of tunable topological refractions by VSCs with triple valley Hall phase transitions. By simply rotating rods, we realize 3 types of topological waveguides (T1, T2 and T3) composed of two VSCs, in which the projections of the observed valley edge states can be modulated between K and K′. Additionally, based on the measured transmittance spectra, we experimentally demonstrate that these valleyedge states are almost immune to backscattering against sharp bends. More importantly, we realize tunable topological refractions at the fixed frequency band and terminal, and experimentally observe the coexistence of positive and negative refractions for T1 and T3, and negative refractions for T2. The proposed tunable topological refractions have potential applications in designing multi-functional sound antennas and advanced communication devices.
TUNABLE TOPOLOGICAL REFRACTIONS IN VALLEY SONIC CRYSTALS WITH TRIPLE VALLEY HALL PHASE TRANSITIONS (INVITED PAPER)
2022-10-31
PIER
Vol. 176, 11-23, 2023
Optically Transparent and Mechanically Flexible Coplanar Waveguide-Fed Wideband Antenna Based on Sub-Micron Thick Micro-Metallic Meshes
Jing Pan Yuanqing Yao Liu Yang Hui Li Sailing He
An optically transparent and flexible coplanar waveguide (CPW)-fed wideband antenna is proposed and demonstrated experimentally based on sub-micron thick micro-metallic meshes (μ-MMs). Due to the high visible transmittance (83.1%) and low sheet resistance (1.75 Ω/sq) of the silver μ-MM with thickness of only 190 nm, the transparent CPW has very low insertion loss and provides a good feed to the high-performance transparent antenna. The measured S11 spectrum of our antenna matches well with that of the opaque counterpart. The measured fractional bandwidth is 22% from 3.4 to 4.25 GHz. Based on numerical modeling, whose accuracy is experimentally verified, the radiation efficiency and the peak gain of our transparent antenna at 3.45 GHz are calculated to be 89.7% and 3.03 dBi, respectively. Besides the good optical and electromagnetic properties, our transparent antenna is also highly flexible. Despite the sub-micron thick μ-MMs, the transparency, radiation efficiency and mechanical properties of our transparent antenna are obviously superior to those of the transparent antennas reported previously, and the overall size and radiation gain are also comparable. Therefore, our transparent antenna has an excellent comprehensive performance, showing great potential for practical applications as well as the emerging applications in the field of flexible and wearable electronics.
Optically Transparent and Mechanically Flexible Coplanar Waveguide-fed Wideband Antenna Based on Sub-micron Thick Micro-metallic Meshes
2022-02-28
PIER
Vol. 173, 9-23, 2022
Recent Progress on Achromatic Metalenses (Invited Review)
Qikai Chen Yitian Liu Yaoyuan Lei Sijie Pian Zhuning Wang Yaoguang Ma
As a potential alternative to conventional lenses, metalenses have the advantage of ultrathin volume and light weight. Such miniaturization is expected to apply to compact, nanoscale optical devices such as micro-cameras and high-resolution display. However, chromatic aberration is an important problem in the application of metalenses, which will damage the imaging resolution and color reality for multi-wavelength incident light. Here, we briefly discuss recent development of design methods for achromatic metalenses, containing one or more pieces, and experimental evaluation of their performances.
RECENT PROGRESS ON ACHROMATIC METALENSES (INVITED REVIEW)
2020-08-20
PIER
Vol. 168, 1-13, 2020
Classical and Quantum Electromagnetic Interferences: What Is the Difference?
Dong-Yeop Na Weng Cho Chew
The zeroing of second order correlation functions between output fields after interferences in a 50/50 beam splitter has been accepted decades-long in the quantum optics community as an indicator of the quantum nature of lights. But, a recent work [1] presented some notable discussions and experiments that classical electromagnetic fields can still exhibit the zero correlation under specific conditions. Here, we examine analytically classical and quantum electromagnetic field interferences in a 50/50 beam splitter in the context of the second order correlation function for various input conditions. Adopting the Heisenberg picture in quantum electromagnetics, we examine components of four-term interference terms in the numerator of second order correlation functions and elucidate their physical significance. As such, we reveal the fundamental difference between the classical and quantum interference as illustrated by the Hong-Ou-Mandel (HOM) effect. The quantum HOM effect is strongly associated with: (1) the commutator relation that does not have a classical analogue; (2) the property of Fock states needed to stipulate the one-photon quantum state of the system; and (3) a destructive wave interference effect. Here, (1) and (2) imply the indivisibility of a photon. On the contrary, the classical HOM effect requires the presence of two destructive wave interferences without the need to stipulate a quantum state.
CLASSICAL AND QUANTUM ELECTROMAGNETIC INTERFERENCES: WHAT IS THE DIFFERENCE?