Zhao-Qing Zhang

Illusion Optics: The Optical Transformation of an Object into Another Object

We propose to use transformation optics to generate a general illusion such that an arbitrary object appears to be like some other object of our choice. This is achieved by using a remote device that can transform the scattered light outside a virtual boundary into that of the object chosen for the illusion, irrespective of the profile and direction of the incident light. This type of illusion device also enables people to see through walls. Our work extends the concept of cloaking as a special form of illusion to the wider realm of illusion optics.

Lasing in chiral photonic structures

This article presents a review of the lasing and photonic properties of periodic one-dimensional anisotropic structures with the symmetry of a double helix. Examples are self-organized cholesteric liquid crystals (CLCs) and sculptured thin films created by vapor deposition. A reflection band with sharp, closely spaced transmission peaks at its edges occurs for circularly polarized light with the same handedness as the helical structure. Within the reflection band, this wave is evanescent, corresponding to a vanishing density of states (DOS). Oppositely polarized light is uniformly transmitted. Since optical emission is proportional to the DOS, it is suppressed within the reflection band. However, it is enhanced at the band edge, where a series of narrow long-lived transmission modes are found. For this reason lasing in dye-doped CLCs occurs at the edge of the stop band rather than at its center, where reflection is highest. Introducing an additional rotation or an isotropic layer within a chiral structure creates a single circularly polarized localized mode with the same handedness as the structure. A resonance appears in the transmission of light of this polarization in thin samples. In thicker samples, the resonance appears instead in the reflection for oppositely polarized light. In contrast to strong modulation of the intensity within the sample on a wavelength scale, a characteristic of layered dielectric medium, the intensity within a chiral medium varies slowly when the sample is excited either at the band edge or at a localized mode. A transverse coherence is created in emission over a length scale proportional to the square root of the photon dwell time at resonance with long-lived modes. This makes possible spatially coherent lasing over a large area in thin films. The photonic properties of chiral thin films make them promising candidates for a variety of filter and laser applications.

Elastic Metamaterials with Simultaneously Negative Effective Shear Modulus and Mass Density

We propose a type of elastic metamaterial comprising fluid-solid composite inclusions which can possess a negative shear modulus and negative mass density over a large frequency region. Such a material has the unique property that only transverse waves can propagate with a negative dispersion while longitudinal waves are forbidden. This leads to many interesting phenomena such as negative refraction, which is demonstrated by using a wedge sample and a significant amount of mode conversion from transverse waves to longitudinal waves that cannot occur on the interface of two natural solids.

First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals

By using the \vec{k}\cdot\vec{p} method, we propose a first-principles theory to study the linear dispersions in phononic and photonic crystals. The theory reveals that only those linear dispersions created by doubly-degenerate states can be described by a reduced Hamiltonian that can be mapped into the Dirac Hamiltonian and possess a Berry phase of -\pi. Triply-degenerate states can also generate Dirac-like cone dispersions, but the wavefunctions transform like a spin-1 particle and the Berry phase is zero. Our theory is capable of predicting accurately the linear slopes of Dirac/Dirac-like cones at various symmetry points in a Brilliouin zone, independent of frequency and lattice structure.

Engineering acoustic band gaps

By using a perturbative approach, we propose a simple, systematic, and efficient method to engineer acoustic band gaps. A gap can be enlarged or reduced by altering the microstructure according to the field-energy distributions of the Bloch states at the band edges as well as their derivatives. Due to the structure of the acoustic wave equation, the engineering of acoustic band gaps is much more efficient than that of photonic band gaps. The validity of the proposed method is supported by multiple-scattering calculations. Our method makes the acoustic band gap “designable.”

Emergence, Coalescence, and Topological Properties of Multiple Exceptional Points and Their Experimental Realization

Non-Hermitian systems distinguish themselves from Hermitian systems by exhibiting a phase transition point called an exceptional point (EP), which is the point at which two eigenstates coalesce under a system parameter variation. Many interesting EP phenomena such as level crossings/repulsions in nuclear/molecular and condensed matter physics, and unusual phenomena in optics such as loss-induced lasing and unidirectional transmission can be understood by considering a simple 2x2 non-Hermitian matrix. At a higher dimension, more complex EP physics not found in two-state systems arises. We consider the emergence and interaction of multiple EPs in a four-state system theoretically and realize the system experimentally using four coupled acoustic cavities with asymmetric losses. We find that multiple EPs can emerge and as the system parameters vary, these EPs can collide and merge, leading to higher order singularities and topological characteristics much richer than those seen in two-state systems.

Breakdown of diffusion in dynamics of extended waves in mesoscopic media.

We report the observation of nonexponential decay of pulsed microwave transmission through quasi-one-dimensional random dielectric media signaling the breakdown of the diffusion model. The decay rate of transmission falls nearly linearly in time corresponding to a nearly Gaussian distribution of the coupling strengths of quasinormal electromagnetic modes to free space at the sample surfaces. The peak and width of this distribution scale as L(-2.05) and L(-1.81), respectively.

Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems

Surface impedance is an important concept in classical wave systems such as photonic crystals (PCs). For example, the condition of an interface state formation in the interfacial region of two different one-dimensional PCs is simply Z_SL +Z_SR=0, where Z_SL (Z_SR)is the surface impedance of the semi-infinite PC on the left- (right-) hand side of the interface. Here, we also show a rigorous relation between the surface impedance of a one-dimensional PC and its bulk properties through the geometrical (Zak) phases of the bulk bands, which can be used to determine the existence or non-existence of interface states at the interface of the two PCs in a particular band gap. Our results hold for any PCs with inversion symmetry, independent of the frequency of the gap and the symmetry point where the gap lies in the Brillouin Zone. Our results provide new insights on the relationship between surface scattering properties, the bulk band properties and the formation of interface states, which in turn can enable the design of systems with interface states in a rational manner.

Dirac Spectra and Edge States in Honeycomb Plasmonic Lattices

We study theoretically the dispersion of plasmonic honeycomb lattices and find Dirac spectra for both dipole and quadrupole modes. Zigzag edge states derived from Dirac points are found in ribbons of these honeycomb plasmonic lattices. The zigzag edge states for out-of-plane dipole modes are closely analogous to the electronic ones in graphene nanoribbons. The edge states for in-plane dipole modes and quadrupole modes, however, have rather unique characters due to the vector nature of the plasmonic excitations. The conditions for the existence of plasmonic edge states are derived analytically.

Large Coherence Area Thin-Film Photonic Stop-Band Lasers

We demonstrate that the shift of the stop-band position with increasing oblique angle in periodic structures results in a wide transverse exponential field distribution corresponding to strong angular confinement of the radiation. The beam expansion follows an effective diffusive equation depending only upon the spectral mode width. In the presence of gain, the beam cross section is limited only by the size of the gain area. As an example of an active periodic photonic medium, we calculate and measure laser emission from a dye-doped cholesteric liquid crystal film.