Cheng Guo

Stanford University | SU · Department of Applied Physics

Reciprocity is a fundamental symmetry of Maxwell’s equations. It is known that reciprocity imposes constraints on transmission, absorption, and emission. Here, we reveal reciprocity constraints on reflection. We determine the sets of all attainable reflection coefficients of n-port scattering matrices with prescribed singular values, both with and...

Weyl semimetals are topological materials whose electron quasiparticles obey the Weyl equation. They possess many unusual properties that may lead to new applications. This is a tutorial review of the optical properties and applications of Weyl semimetals. We review the basic concepts and optical responses of Weyl semimetals, and survey their appli...

Unitary control changes the absorption and emission of an object by transforming the external light modes. It is widely used and underlies coherent perfect absorption. Yet two basic questions remain unanswered: For a given object under unitary control, what absorptivity α, emissivity e, and their contrast δ=e−α are attainable? How to obtain a given...

Let A : [0, 1] → GL(n, C) be continuous with A(0) = A(1), thus the winding number of det A is well-defined. If the winding number is not divisible by n, then the origin belongs to the numerical range of A(ϕ) for some ϕ ∈ [0, 1].

We present a systematic topological theory of the scattering matrix and its submatrices, focusing on the singular values and vectors. We study the topological properties of the scattering matrix in the parameter space and determine a set of topological characteristics for a general system, including the winding number, Berry phase, and skew polariz...

In photonics, band degeneracies at high-symmetry points in wavevector space have been shown to exhibit rich physical phenomena. However, obtaining degenerate bands away from such points is highly nontrivial. In this work, we achieve complex band degeneracy in a photonic crystal structure over a region of momentum space. We show that this band degen...

Spatiotemporal sculpturing of light pulse with ultimately sophisticated structures represents the holy grail of the human everlasting pursue of ultra-fast information transmission and processing as well as ultra-intense energy concentration and extraction. It also holds the key to unlock new extraordinary fundamental physical effects. Traditionally...

In photonics, band degeneracies at high-symmetry points in wavevector space have been shown to exhibit rich physical phenomena. However, obtaining degenerate bands away from such points is highly nontrivial. In this work, we achieve complex band degeneracy in a photonic crystal structure over a region of momentum space. We show that this band degen...

We present a non-reciprocal thermal emitter based on the dynamic space-time modulation of graphene. Compound symmetry in the system gives rise to a new dimension of tunable thermal emission in non-reciprocal systems.

We design a polarization-independent metasurface using guided resonances with degenerate band curvatures in a photonic crystal slab. Our device can perform both free-space compression and spatial differentiation when operated at different frequencies at normal incidence.

Nanophotonic engineering provides an effective platform to manipulate thermal emission on-demand, enabling unprecedented heat management superior to conventional bulk materials. Amongst a plethora of nanophotonic structures, symmetries play an important role in controlling radiative heat transfer in both near-field and far-field. In physics, broken...

Spatiotemporal sculpturing of light pulse with ultimately sophisticated structures represents the holy grail of the human everlasting pursue of ultrafast information transmission and processing as well as ultra-intense energy concentration and extraction. It also holds the key to unlock new extraordinary fundamental physical effects. Traditionally,...

Weyl semimetals are topological materials whose electron quasiparticles obey the Weyl equation. They possess many unusual properties that may lead to new applications. This is a tutorial review of the optical properties and applications of Weyl semimetals. We review the basic concepts and optical responses of Weyl semimetals, and survey their appli...

Space–time wave packets can propagate invariantly in free space with arbitrary group velocity thanks to the spatio‐temporal correlation. Here it is proved that the space–time wave packets are stable in dispersive media as well and free from the spread in time caused by material dispersion. Furthermore, the law of anomalous refraction for space–time...

Supplementary Materials for "Reciprocity Constraints on Reflection"

We study the relation between angular spectral absorptivity and emissivity for any thermal emitter, which consists of any linear media that can be dispersive, inhomogeneous, bianisotropic, or nonreciprocal. First, we establish an adjoint Kirchhoff's law for mutually adjoint emitters. This law is based on generalized reciprocity and is a natural gen...

Flat optics has demonstrated great advances in miniaturizing conventional bulky optical elements due to recent developments in metasurface design. Specific applications of such designs include spatial differentiation and the compression of free-space. However, metasurfaces designed for such applications are often polarization-dependent and are desi...

We design a nonreciprocal thermal emitter that features absorptivity-emissivity contrast in semitransparent setting, by using magneto-optical effect. Our emitter can overcome the restriction that Kirchhoff’s law of thermal radiation imposes on solar energy harvesting.

We propose the generation of 3D linear light bullets propagating in free space using a single passive optical surface. Our approach provides simultaneous control of various properties including group velocity, spin, and orbital angular momentum.

We design a topological differentiator that operates isotropically in transmission mode at normal incidence. The device an optical transfer function with a symmetry-protected, topological charge of ± 2 and performs second-order differentiation.

We investigated a family of spatiotemporal optical vortices with arbitrarily oriented orbital angular momentum, and introduce a compact metasurface device for its generation. This is achieved by engineering the transmission nodal line of the device.

We propose and design photonic meta-crystal slab for general implementation of optical convolution. Our device is compact, scalable, and operates directly on optical fields. Potential applications include imaging and energy efficient computing.

Flat optics has demonstrated great advances in miniaturizing conventional, bulky optical elements due to the recent developments in metasurface design. Specific applications of such designs include spatial differentiation and the compression of free space. However, metasurfaces designed for such applications are often polarization-dependent and are...

We propose the generation of 3D linear light bullets propagating in free space using a single passive nonlocal optical surface. The nonlocal nanophotonics can generate space–time coupling without any need for bulky pulse-shaping and spatial modulation techniques. Our approach provides simultaneous control of various properties of the light bullets,...

The emissivity and absorptivity of nonreciprocal thermal emitters are not constrained by the well-known Kirchhoff law of thermal radiation, which usually serves as the theoretical basis to characterize thermal properties. When thermal emitters are nondiffracting, which is the case in previous studies of nonreciprocal thermal emitters, the angular d...

Laser cooling of rare-earth doped solids has been demonstrated across a wide range of material platforms, inspiring the development of simple phenomenological models such as the four-level model to elucidate the universal properties of laser cooling under various operating conditions. However, these models usually require the input of full absorpti...

Laser cooling of rare-earth doped solids has been demonstrated across a wide range of material platforms, inspiring the development of simple phenomenological models such as the four-level model to elucidate the universal properties of laser cooling under various operating conditions. However, these models usually require the input of full absorpti...

Space-time wave packets can propagate invariantly in free space with arbitrary group velocity thanks to the spatio-temporal correlation. Here it is proved that the space-time wave packets are stable in dispersive media as well and free from the spread in time caused by material dispersion. Furthermore, the law of anomalous refraction for space-time...

We propose an integrated photonic approach to generating guided space-time wave packets in a conventional multimode waveguide using multilevel interband photonic transitions. It can generate broadband propagation-invariant space-time wave packets with arbitrary group velocity and tailored field profiles. Our work reveals an important connection bet...

Kirchhoff’s law of thermal radiation imposes a constraint on photon-based energy harvesting processes since part of the incident energy flux is inevitably emitted back to the source. By breaking the reciprocity of the system, it is possible to overcome this restriction and improve the efficiency of energy harvesting. Here, we design and analyze a s...

We show that by using a perturbed photonic Dirac-cone, one can realize an ultra-narrow and finite Q-factor peak in the wavevector space, with both the peak value and the width separately tunable. We also discuss a lower bound in the minimal viable width given a peak Q-value while maintaining sufficient Q differentiation among modes. The strong angu...

Differentiation has widespread applications, particularly in image processing for edge detection. Significant advances have been made in using nanophotonic structures and metamaterials to perform such operations. In particular, a recent work demonstrated a topological differentiator in which the transfer function exhibited a topological charge, mak...

It has been recently demonstrated that optical pulses can hold transverse orbital angular momentum (OAM). Generation of such vortices typically requires bulky optics, and only OAMs that are fully longitudinal or transverse have been demonstrated until now. Here we investigate a general family of spatiotemporal vortices with arbitrarily oriented OAM...

Kirchhoff's law of thermal radiation imposes a constraint on photon-based energy harvesting processes since part of the incident energy flux is inevitably emitted back to the source. By breaking the reciprocity of the system, it is possible to overcome this restriction and improve the efficiency of energy harvesting. Here, we design and analyze a s...

Differentiation has widespread applications, particularly in image processing for edge detection. Significant advances have been made in using nanophotonic structures and metamaterials to perform such operations. In particular, a recent work demonstrated a topological differentiator in which the transfer function exhibits a topological charge, maki...

We show that by using a perturbed photonic Dirac-cone, one can realize ultra-narrow and finite Q-factor peak in the wavevector space, with both the peak value and the width separately tunable. We also discuss a lower bound in the minimal viable width given a peak Q-value while maintaining sufficient Q differentiation among modes. The strong angular...

A Correction to this paper has been published: https://doi.org/10.1038/s41467-021-22493-6

We analyze scattering properties of twisted bilayer photonic crystal slabs through a high-dimensional plane wave expansion method. The method is applicable for arbitrary twist angles and does not suffer from the limitations of the commonly used supercell approximation. We show strongly tunable resonance properties of this system which can be accoun...

Wavelength-tunable narrow-band thermal emitters are highly desired for various applications including multigas sensing. However, current thermal emitters suffer from either too broad bandwidth or too narrow tuning range. Here, based on the moiré effect, we provide a scheme of wavelength-tunable narrow-band thermal emitters with tunability over a wi...

Optical computing holds significant promise of information processing with ultrahigh speed and low power consumption. Recent developments in nanophotonic structures have generated renewed interests due to the prospects of performing analog optical computing with compact devices. As one prominent example, spatial differentiation has been demonstrate...

We show that a momentum-space meron spin texture for electromagnetic fields in free space can be generated by controlling the interaction of light with a photonic crystal slab having a nonzero Berry curvature. Our work highlights the opportunities of using photonic structures for the exploration of topological spin textures.

We show that free space can be substituted with nonlocal flat optics with a wavevector-dependent transfer function. We provide a concrete photonic crystal slab de- vice, which can substitute free space of 144 times greater thickness.

We analyze scattering properties of twisted bilayer photonic crystal slabs through a high-dimensional plane wave expansion method, which does not involve super-cell approximation, and explain the spectrum with an intuitive correspondence relation.

We theoretically propose and numerically demonstrate a radiative thermal router based on magnetic Weyl semimetals. In designing the thermal router, we utilize two unique properties of optical gyrotropy in magnetic Weyl semimetals: great tunability and nanoscale inhomogeneity. The proposed thermal router consists of three spheres made of magnetic We...

Completely disordered systems are suitable for large‐scale fabrication and may host non‐trivial optical properties. In article number 2000151 by Victor S. Asadchy, Shanhui Fan, and co‐workers, the designed colloid metamaterial exhibits isotropic chirality three orders of magnitude larger than known natural and artificial materials. Such giant chira...

Motivated by the theoretical observation that isotropic chirality can exist even in completely random systems, a dielectric metamaterial consisting of a random colloid of meta‐atoms is designed, which exhibits unprecedentedly high isotropic optical activity. Each meta‐atom is composed of a helically arranged cluster of silicon nanospheres. Such clu...

We study the constraints on reciprocal and non-reciprocal many-body radiative heat transfer imposed by symmetry and the second law of thermodynamics. We show that the symmetry of such a many-body system in general forms a magnetic group, and the constraints of the magnetic group on the heat transfer can be derived using a generalized reciprocity th...

There has been substantial interest in miniaturizing optical systems by flat optics. However, one essential optical component, free space, fundamentally cannot be substituted with conventional local flat optics with space-dependent transfer functions, since the transfer function of free space is momentum-dependent instead. Overcoming this difficult...

We study the constraints on reciprocal and non-reciprocal many-body radiative heat transfer imposed by symmetry and the second law of thermodynamics. We show that the symmetry of such a many-body system in general forms a magnetic group, and the constraints of the magnetic group on the heat transfer can be derived using a generalized reciprocity th...

The paper presents the design of sub‐wavelength high‐performing nonreciprocal optical devices using recently discovered magnetic Weyl semimetals. These passive bulk topological materials exhibit anomalous Hall effect which results in magneto‐optical effects that are orders of magnitude higher than those in conventional materials, without the need o...

Motivated by the theoretical observation that isotropic chirality can exist even in completely random systems, we design a dielectric metamaterial consisting of a random colloid of meta-atoms, which exhibits unprecedentedly high isotropic optical activity. Each meta-atom is composed of a helically arranged cluster of silicon nanospheres. Such clust...

There has been substantial interest in miniaturizing optical systems by flat optics. However, one essential optical component, free space, fundamentally cannot be substituted with conventional local flat optics with space-dependent transfer functions, since the transfer function of free space is momentum-dependent instead. Overcoming this difficult...

We show that a momentum-space meron spin texture for electromagnetic fields in free space can be generated by controlling the interaction of light with a photonic crystal slab having a nonzero Berry curvature. These spin textures in momentum space have not been previously noted either in electronic or photonic systems. Breaking the inversion symmet...

Objects around us constantly emit and absorb thermal radiation. The emission and absorption processes are governed by two fundamental radiative properties: emissivity and absorptivity. For reciprocal systems, the emissivity and absorptivity are restricted to be equal by Kirchhoff's law of thermal radiation. This restriction limits the degree of fre...

There are significant recent interests in using nanophotonic structures to perform differentiation operation on images for edge detection purposes. All previous works using nanophotonic structures, however, can only operate with coherent light. Here we introduce a hybrid optoelectronic approach that enables one to use nanophotonic structures to per...

We design sub-wavelength high-performing non-reciprocal optical devices using recently discovered magnetic Weyl semimetals. These passive bulk topological materials exhibit anomalous Hall effect which results in magnetooptical effects that are orders of magnitude higher than those in conventional materials, without the need of any external magnetic...

We show that free space can be substituted with nonlocal flat o ptics with a wavevector-dependent transfer function. We provide a concrete photonic crystal slab device, which can substitute free space of 144 times greater thickness.

We study the photon thermal Hall effect and the persistent heat current in radiative heat transfer. We show that the photon thermal Hall effect is not a uniquely nonreciprocal effect; it can arise in some reciprocal systems with broken-mirror symmetry. This is in contrast with the persistent heat current, which is a uniquely nonreciprocal effect th...

Objects around us constantly emit and absorb thermal radiation. The emission and absorption processes are governed by two fundamental radiative properties: emissivity and absorptivity.For reciprocal systems, the emissivity and absorptivity are restricted to be equal by Kirchhoff's law of thermal radiation. This restriction limits the degree of free...

We study the photon thermal Hall effect and the persistent heat current in radiative heat transfer. We show that the photon thermal Hall effect is not a uniquely nonreciprocal effect; it can arise in some reciprocal systems with broken mirror symmetry. This is in contrast with the persistent heat current, which is a uniquely non-reciprocal effect t...

We reveal the meron and antimeron spin textures in momentum space in a photonic crystal slab. These spin textures in momentum space have not been previously noted either in electronic or photonic systems. Breaking the inversion symmetry of a honeycomb photonic crystal gaps out the Dirac cones at the corners of Brillouin zone. The spin textures of p...

Temporal coupled-mode theory has been widely used to describe the physics of resonant optical systems. In general, an optical system can be constrained by energy conservation, time-reversal symmetry, and reciprocity. Most previous developments of temporal coupled-mode theory made use of all three constraints. In this paper, we consider separately t...

We discuss the implementation of several isotropic image filters in the wavevector domain using a single photonic crystal slab device. Such a slab is designed so that the guided resonance near the Γ point exhibits an isotropic band structure. Depending on the light frequency and the choice of transmission or reflection mode, the device realizes iso...

The recent observation of high-harmonic generation from solids creates a new possibility for engineering fundamental strong-field processes by patterning the solid target with subwavelength nanostructures. All-dielectric metasurfaces exhibit high damage thresholds and strong enhancement of the driving field, making them attractive platforms to cont...

We show that several types of isotropic image filters in the wavevector domain can be implemented with a single photonic crystal slab device. Such a slab is designed so that the guided resonance near the Γ point exhibits an isotropic band structure. Depending on the light frequency and the choice of transmission or reflection mode, the device reali...

Spatial differentiation is important in image-processing applications such as image sharpening and edge-based segmentation. In these applications, of particular importance is the Laplacian, the simplest isotropic derivative operator in two dimensions. Spatial differentiation can be implemented electronically. However, in applications requiring real...

We propose an implementation of a Laplace differentiator based on a photonic crystal slab that operates at transmission mode. Such a device may facilitate nanophotonics-based optical analog computing for image processing.

We report resonantly enhanced non-perturbative high-harmonic emission by more than two orders of magnitude from a Si metasurface that possesses a Fano-like resonance resulting from a classical analog of electromagnetically induced transparency.

We introduce an implementation of a Laplace differentiator based on a photonic crystal slab that operates at transmission mode. We show that the Laplace differentiator can be implemented provided that the guided resonances near the $\Gamma$ point exhibit an isotropic band structure. Such a device may facilitate nanophotonics-based optical analog co...

The first Weyl semimetal was recently discovered in the NbP class of compounds. Although the topology of these novel materials has been identified, the surface properties are not yet fully understood. By means of scanning tunneling spectroscopy, we find that NbP’s (001) surface hosts a pair of Dirac cones protected by mirror symmetry. Through our h...

Weyl nodes are topological objects in three-dimensional metals. Whereas the energy of the lowest Landau band of a conventional Fermi pocket increases with magnetic field due to the zero-point energy (1/2ω), the lowest Landau band of Weyl cones stays at zero energy unless a strong magnetic field couples Weyl fermions of opposite chirality. In the We...

Heterojunctions, quantum wells, and superlattices with precise doping profiles are behind today's electronic and photonic devices based on III–V compound semiconductors such as GaAs. Currently, there is considerable interest in constructing similar artificial 3D architectures with tailored electrical and optical properties by using van der Waals ju...

One of the outstanding challenges in nanotechnology is how to assemble individual nano-objects into macroscopic architectures while preserving their extraordinary properties. For example, the one-dimensional character of electrons in individual carbon nanotubes leads to extremely anisotropic transport, optical, and magnetic phenomena, but their mac...

The recent discovery of the first Weyl semimetal in TaAs provides the first observation of a Weyl fermion in nature and demonstrates a novel type of anomalous surface state, the Fermi arc. Like topological insulators, the bulk topological invariants of a Weyl semimetal are uniquely fixed by the surface states of a bulk sample. Here, we present a se...

Weyl semimetals are expected to open up new horizons in physics and materials science because they provide the first realization of Weyl fermions and exhibit protected Fermi arc surface states. However, they had been found to be extremely rare in nature. Recently, a family of compounds, consisting of TaAs, TaP, NbAs and NbP was predicted as Weyl se...

Weyl semimetals may open a new era in condensed matter physics, materials science and nanotech after graphene and topological insulators. We report the first atomic scale view of the surface states of a Weyl semimetal (NbP) using scanning tunneling microscopy/spectroscopy. We observe coherent quantum interference patterns that arise from the scatte...