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...

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...

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...

Coherent control has enabled various novel phenomena in wave scattering. We introduce an effect called coherent orthogonal scattering, where the output wave becomes orthogonal to the reference output state without scatterers. This effect leads to a unity extinction coefficient and complete mode conversion. We examine the conditions for this effect...

We investigate the majorization order for comparing wave coherence and reveal its fundamental consequences in transport measurements, including power distribution, absorption, transmission, and reflection. We prove that all these measurements preserve the majorization order under unitary control, enabling direct experimental characterization of the...

We numerically demonstrate the creation of Weyl points in a twisted multilayer photonic system. In our system, each layer is anisotropic with plasmonic response along a direction perpendicular to the layer and with anisotropic dielectric response within the layer. We show that Weyl points can be created by controlling the twist angles between the l...

The interaction of circularly polarized light with chiral matter and functional devices enables novel phenomena and applications. Recently, wafer-scale solid-state single-enantiomer carbon nanotube (CNT) films have become feasible and are emerging as a chiral photonic material platform thanks to their quantum-confinement-induced optical properties...

We investigate the passivity constraints on the relations between transmission, reflection, and absorption eigenvalues in linear time-invariant systems. Using techniques from matrix analysis, we derive necessary and sufficient conditions for the permissible combinations of these eigenvalues. Our analysis reveals that the set of allowable eigenvalue...

Space-time wavepackets (STWPs) have received significant attention since they can propagate in free space at arbitrary group velocity without dispersion and diffraction. However, at present, the generation of STWPs has been limited to the paraxial regime. Here we show that conventional optical elements can be used to extend STWPs beyond the paraxia...

Controlling wave transmission is crucial for various applications. In this work, we apply the concept of unitary control to manipulate multiport wave transmission. Unitary control aims to control the behaviors of a set of orthogonal waves simultaneously. The approach fully harnesses the capability of wavefront shaping techniques, with promising app...

The coherent control of wave absorption has important applications in areas such as energy harvesting, imaging, and sensing. However, most practical scenarios involve the absorption of partially coherent rather than fully coherent waves. Here we present a systematic theory of unitary control over the absorption of partially coherent waves by linear...

Coherent control of wave transmission and reflection is crucial for applications in communication, imaging, and sensing. However, many practical scenarios involve partially coherent waves rather than fully coherent ones. We present a systematic theory for the unitary control of partially coherent wave transmission and reflection. For a linear time-...

Non-Hermitian systems and their topological singularities, such as exceptional points (EPs), lines, and surfaces, have recently attracted intense interest. The investigation of these exceptional constituents has led to fruitful applications. The responsivity of the eigenvalue diverges at EPs, and chiral state transfer occurs when encircling an EP....

The coherent control of wave absorption has important applications in areas such as energy harvesting, imaging, and sensing. However, most practical scenarios involve the absorption of partially coherent rather than fully coherent waves. Here we present a systematic theory of unitary control over the absorption of partially coherent waves by linear...

Coherent control of wave transmission and reflection is crucial for applications in communication, imaging, and sensing. However, many practical scenarios involve partially coherent waves rather than fully coherent ones. We present a systematic theory for the unitary control of partially coherent wave transmission and reflection. For a linear time-...

Coherent control has enabled various novel phenomena in wave scattering. We introduce an effect called coherent orthogonal scattering, where the output wave becomes orthogonal to the reference output state without scatterers. This effect leads to a unity extinction coefficient and complete mode conversion. We examine the conditions for this effect...

We propose an all-optical approach to generating space–time wave packets in a multimode slab waveguide via the multilevel interband stimulated Brillouin scattering process. Two pump sources and a single-mode signal are fed into the waveguide. The pumps generate a single-mode acoustic wave through the electrostrictive process. The acoustic wave then...

Degeneracy points in non-Hermitian systems are of great interest. While a homotopic framework exists for understanding their behavior in the absence of symmetry, it does not apply to symmetry-protected degeneracy points with reduced codimension. In this work, utilizing algebraic topology, we provide a systematic classification of these symmetry-pro...

We achieve complex band degeneracy in a photonic crystal structure over a region of momentum space, which gives rise to polarization-independent transmission. The degeneracy manifests as a topological singularity in the structural parameter space.

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...

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].

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...

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...

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...

Lorentz reciprocity, energy conservation, and time-reversal symmetry are three important global constraints of Maxwell's equations. Unlike time-reversal symmetry, Lorentz reciprocity and energy conservation usually are not considered as symmetries, i.e., they are not associated with operators. In this paper, we provide a unified treatment of these...

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...

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...

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...

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...