Compact high-resolution spectrometer based on super-prism and local-super-collimation effects of photonic crystal.

We propose a design of the compact high-resolution photonic crystal (PhC) spectrometer with a wide working bandwidth based on both super-prism and local-super-collimation (LSC) effects. The optimizing methods, finding the ideal incident angle and oblique angle of PhC for a wider working bandwidth and ideal incident beam width and PhC size for a certain resolution requirement, are developed. Besides the theoretical work, for the first time, the experiment of such a PhC spectrometer is conducted in the microwave frequency range, and the beam-splitting effects for different frequencies in a wide working bandwidth agree very well with the theoretical predictions. According to the scalability, with the condition to control the deviations in the fabrication processes the design could be extended to optical frequency ranges, e.g., infrared, visible-light, and ultraviolet ranges. The spectrometer in optical frequencies can be implemented on silicon-on-insulator (SOI) chips as a thin-slab structure so that the operating bandwidth can be expanded further through the multi-layer design. Theoretically, the size of the ultra-high-resolution PhC spectrometer in optical frequency ranges based on our design could be two orders smaller than the traditional design.

The generalized method to calculate the real-space winding number for one-dimensional systems with complex multi-band-gap structure.

The topological study of the complicated one-dimensional (1D) systems with multi-band-gap structures, including quasi-crystals (QCs), is very hard since the lack of effective topological invariants to describe the non-triviality of gaps. A generalized method, based on the contracted wave-function, is proposed in this work to calculate the real-space winding number for the complicated 1D systems with multi-band-gap structures. First, the effectiveness of the generalized method is demonstrated to obtain the quantized real-space winding number for the gaps and correctly predict the topological phase transition and the existing fractional charge on the edges for the periodic 4-atoms SSH model (4A-SSH model). Then, we apply the generalized method to more complicated 1D Thue-Morse (TM) systems, which is one kind of QCs. The quantized real-space winding number is obtained for two traditional gaps and two fractal gaps for the TM systems and can also correctly predict the existence of topological edge-states and fractional charge on the ends. Several new phenomena are observed, e.g. the topological phase transition and the edge-states for the gaps in multi-band-gap structures, the1/4fractional charge for the 4A-SSH model, the fluctuation of local charge and the asymmetric (but still with a quantized difference) fractional charge at the ends of TM system. The generalized method could be a powerful tool to study the topology of gaps in the complicated periodic systems or QCs.

Origin of the frequency-sensitive super-collimation phenomenon from the geometry of band dispersion surface for two-dimensional photonic crystals.

Frequency-sensitive super-collimation (FSSC) is a novel dispersion phenomenon of photonic crystals (PhCs) that can realize the beam collimating propagation with very high frequency sensitivity. In order to deeply investigate the origin and the stability of FSSC phenomenon in a wide parameter space, we study the geometry of dispersion surface in detail. Four features for the special geometry of dispersion surface with FSSC are found for rectangular PhCs. The special geometry supports the stability of FSSC in a wide range of parameter space. Two-parameter modulation (TPM) method, in which the aspect ratio ß and the dielectric constant of rods ɛr of rectangular lattice are chosen as the key parameters, is used to analyze the geometry of dispersion surface from the frequency changes at the high-symmetry points. Step by step, the origin of such geometry is revealed and the evolving process can be explained by the field distribution changes of Bloch modes at the high-symmetry points. Furthermore, we show that the geometry not only can be used to explain the origin and the stability of FSSC, but also can help us to find other FSSC phenomenons. Theoretically, we believe the geometry of dispersion surface and the TPM can be widely used on the studies of complex dispersion properties of PhCs. The FSSCs found in this work with higher sensitivity or higher stability can help us to design new on-chip PhC devices.

New dynamical nonlinear mechanism, a way to enhance nonlinear efficiency and detect ultrafast electronic processes in photonic crystals.

We quantitatively investigate the energy efficiency and the possibility of detecting the electronic ultrafast processes of a new dynamical nonlinear mechanism suitable for the nonlinear photonic crystal switching effect with femtosecond pumping. It is found that the energy efficiency of the new dynamical nonlinear mechanism is considerably higher than traditional band-gap shift mechanism, and the characteristics of the transmission curve are related to the parameters of the electronic ultrafast processes. Thus, the dynamical nonlinear mechanism is a new way to enhance the nonlinear efficiency and to indirectly detect the electronic femtosecond or even attosecond processes. Besides that, the totally new patterns of transmission and reflection spectra revealed in this work also imply the deep differences between two mechanisms. Wide potential usages could be expected for the properties found by this work.

Beam propagation in the photonic crystal of the local super-collimation regions.

We investigate the beam propagation behavior in the photonic crystal (PhC) of the local super-collimation (LSC) regions both theoretically and numerically. A theory based on the cubic dispersion model in the LSC regions is established, which is a powerful tool to predict the beam evolution after a long propagation distance. The numerical experiments are also implemented, whose results agree well with those from our theory. Both the theoretical and simulation results show the new phenomenon of the asymmetric beam broadening for beams in the LSC regions, which is quite different from the traditional symmetric broadening. Physical reasons of such asymmetric broadening are explained by the cubic dispersion model and the solution to suppress the asymmetric broadening is proposed. Since the LSC beams could be widely used in photonic devices, such as hypersensitive spectrometers and demultiplexers, the deep insights of the beam propagation behavior in the LSC regions can help us to optimize our designs, such as choosing the proper beam width and the proper working range in the phase space.

Hyper collimation ability of two-dimensional photonic crystals.

We theoretically investigate the collimation ability of photonic crystals (PhCs) and present a design of rectangular lattice PhC structure which has ultra-high collimation ability, referred to hyper collimation ability of PhC in this work. The competition between the range and the flatness of a "flat segment" on the PhC equi-frequency contour (EFC) is revealed, so that both should be considered simultaneously if we hope to evaluate the collimation ability of a PhC structure. We introduce a new dimensionless value, the normalized collimation length (NCL), to evaluate the collimation ability of a PhC structure. We find that the hyper collimation ability can be achieved by tuning the aspect ratio of a rectangular lattice PhC. It is also demonstrated that our theoretical predictions of the propagation behavior of beams agree very well with numerical experiments. We propose that the PhCs with hyper collimation ability could be widely used in the design of photonic circuits and other devices.

Two classes of singularities and novel topology in a specially designed synthetic photonic crystals.

Zak phase and topological protected edge state are usually studied in one-dimensional (1D) photonic systems with spatial inversion symmetry (SIS). In this work, we find that specific classes of 1D structure without SIS can be mapped to a system with SIS and also exhibit novel topology, which manifest as phase cut lines (PCLs) in our specially designed synthetic photonic crystals (SPCs). Zak phase defined in SIS is extended to depict the topology of PCLs after redefinition, and a topological protected edge state is also achieved in our 1D structure without SIS. In our SPCs, the relationship between Chern numbers in two dimensions (2D) and the extended Zak phases of 1D PCLs is given, which are bound by the first type singularities. Higher Chern numbers and multi-chiral edge states are achieved utilizing the concept of synthetic dimensions. The effective Hamiltonian is given, based on which we find that the band edges of each PCL play a role analogous to the valley pseudospin, and our SPC is actually a new type of valley photonic crystal that is usually studied in graphene-like honeycomb lattice. The chiral valley edge transport is also demonstrated. In higher dimensions, the shift of the first type singularity in expanded parameter space will lead to the Weyl point topological transition, which we proposed in our previous work. In this paper, we find a second type of singularity that manifests as a singular surface in our expanded parameter space. The shift of the singular surface will lead to the nodal line topological transition. We find the states on the singular surface possess extremely high robustness against certain randomness, based on which a topological wave filter is constructed.

Tunable photonic crystal lens with high sensitivity of refractive index.

We design a photonic crystal (PhC) lens whose focal length is highly tunable based on the frequency sensitive super-collimation (FSSC) phenomenon. Theoretically, an analytic expression of the focal length in PhCs is derived. The diffraction could be dramatically changed by modest change in refractive index of the dielectric rods in PhCs, because the sensitivity of the equi-frequency-contours around FSSC to refractive index is several orders larger than that in common bulk material. Numerically, we demonstrate that focal length can be nearly one order larger with only 0.2% refractive index change, from 28a (a is lattice constant) to 240a. With its micro-size, high sensitivity and feasibility by on-chip technology, such tunable lens has great potentials in modern optical systems.

Tunable control of electromagnetically induced transparency analogue in a compact graphene-based waveguide.

An easily-integrated compact graphene-based waveguide structure is proposed to achieve an analogue of electromagnetically induced transparency (EIT) effect at terahertz frequencies. The structure is composed of a graphene waveguide and two identical-shape graphene ribbons located parallel on the same side of the waveguide at different distances, in which the closer and the farther ribbons behave as the bright and the dark resonators, respectively. The EIT-like effect is caused by the destructive interference of the two resonators. By shifting the Fermi energy levels of ribbons, the transparency window can be dynamically tuned. The structure may offer another way for tunable integrated optical devices.

Enhanced wavelength sensitivity of the self-collimation superprism effect in photonic crystals via slow light.

We demonstrate that the wavelength sensitivity of a self-collimation superprism in photonic crystals (PhCs) can be greatly improved via slow light. With the help of a saddle point Van Hove singularity, we present an approach to obtain such a wavelength-sensitive self-collimation superprism. Our superprism not only has extremely high wavelength sensitivity, but also can suppress beam divergence, irregular beam generation, and wavelength channel dropout, overcoming the limitations of traditional PhC-based superprisms. Based on our superprism, a high-performance compact demultiplexer is also proposed.

High-efficiency nonlinear platform with usage of metallic nonlinear susceptibility.

A scheme with usage of metallic nonlinearity, especially in generating the surface plasmon polariton (SPP) time-reversal wave (TRW), is investigated. It is composed of a metal film and an attached photonic crystal, in which both a far-field-excitable tunneling mode and an SPP guided mode could exist. Two modes are degenerated, deeply penetrated into metal, well overlapped, and localized. Therefore, the tunneling mode acts as the pumping field, while the SPP mode acts as the signal field. Because of the large metallic nonlinear susceptibility, the TRW efficiency could increase thousand times. This scheme can be widely used as a high-efficiency platform for other nonlinear devices.

Characterization of short necklace states in the logarithmic transmission spectra of localized systems.

High transmission plateaus exist widely in the logarithmic transmission spectra of localized systems. Their physical origins are short chains of coupled localized states embedded inside the localized system, which are dubbed as 'short necklace states'. In this work, we define the essential quantities and then, based on these quantities, we investigate the properties of the short necklace states statistically and quantitatively. Two different approaches are utilized and their results agree very well. In the first approach, the typical plateau-width and the typical order of short necklace states are obtained from the correlation function of the logarithmic transmission. In the second approach, we investigate the statistical distribution of the peak/plateau-width measured in the logarithmic transmission spectra. A novel distribution is found, which can be exactly fitted by the summation of two Gaussian distributions. These two distributions are the results of sharp peaks of localized states and the high plateaus of short necklace states. The center of the second distribution also tells us the typical plateau-width of short necklace states. With increasing system length, the scaling property of the typical plateau-width is very special since it hardly decreases. The methods and quantities defined in this work can be widely used in Anderson localization studies.

Super-collimation with high frequency sensitivity in 2D photonic crystals induced by saddle-type van Hove singularities.

Using detailed numerical simulations, and theoretical modeling, we predict a new super-collimation operation regime which is very sensitive on frequency. This operation regime is predicted to exist in 2D photonic crystals of dielectric rods in low index media. We explain the physical origin of this operation regime, as well as discuss how it could be of interest for implementation of low-power non-linear devices, novel sensors, as well as low-threshold lasers.

Impurity-induced bound states in superconductors with topological order.

The study of classical spins in topological insulators (Liu and Ma 2009 Phys. Rev. B 80 115216) is generalized to topological superconductors. Based on the characteristic features of the so-called F-function, the Bogoliubov-de Gennes Hamiltonian for superconductors is classified to positive, negative, and zero 'gap' categories for topologically trivial and nontrivial phases of a topological superconductor as well as a BCS superconductor, respectively. It is found that the F-function determines directly the presence or absence of localized excited states, induced by bulk classical spins and nonmagnetic impurities, in the superconducting gap and their persistence with respect to impurity strength. Our results provide an alternative way to identify topologically insulating and superconducting phases in experiments without resorting to the surface properties.

Cancellation of reflection and transmission at metamaterial surfaces.

Based on analytical derivations and numerical simulations, we show that both reflection and transmission can be canceled at the surface of a metamaterial (MM) with a metal-dielectric stratified structure. Strong anisotropic absorption and the surface direction are found to play important roles in this phenomenon. For the angle between the surface and the layers of MMs above a critical value, only reflection is eliminated and transmission is permitted. Since they are not related to resonance, the phenomena can occur in a broad frequency range.

Surface plasmon coupling enhanced dielectric environment sensitivity in a quasi-three-dimensional metallic nanohole array.

An enhanced dielectric environment response is observed in a kind of metallic nanohole arrays which are prepared by metal deposition on a sacrificial two dimensional colloidal crystal template. The periodic metallic structures are composed of interlinked metallic half-shells supported on a planar dielectric substrate. When putting in dielectric matrix of different refractive index, the measured sensitivity of the quasi-three-dimensional metallic nanohole array can reach a value of 1192 nm per refractive index unit which shows a five-fold increase as compared with the metallic structures supported on the template. The observed boost in sensitivity is found to originate from a substantially reduced substrate effect, resulting in a pronounced surface plasmon coupling of which its strength is independent of the dielectric environment, a characteristics absent in conventional planar metallic subwavelength hole arrays. These findings are analyzed theoretically and confirmed by numerical simulations.

Remote control of light behavior by transformation optical devices.

Based on the transformation optics, a general method of light-behavior remote control is proposed. From this method, the important coefficients of a cavity, i.e. the quality factor Q and the resonant frequency ?0 could be tuned in a wide range by a transformation optical device in distance, so that the light behavior can be remotely controlled. To confirm this original idea, three schemes, such as, the remote modification of output energy current from an absorptive cavity, the remote control of lasing behaviors, and the remote tuning of the resonant frequency or photonic band-gap, are presented and confirmed by our numerical simulations based on finite-difference time-domain and finite-element methods. With some special advantages, e.g., without physical change or damage of original devices, large tuning range, and easily to hide the controller, this method could be widely used in optical/photonic or electromagnetic designs in the future.

Nonlinear photonic crystals near the supercollimation point.

We uncover a strong coupling between nonlinearity and diffraction in a photonic crystal at the supercollimation point. We show that this is modeled by a nonlinear diffraction term in a nonlinear-Schrödinger-type equation in which the properties of solitons are investigated. Linear stability analysis shows solitons are stable in an existence domain that obeys the Vakhitov-Kolokolov criterium. In addition, we investigate the influence of the nonlinear diffraction on soliton collision scenarios.

Vertical surface emitting open coupled-cavities based on photonic crystal surface modes.

Two types of vertical surface emitting photonic crystal cavities based on beaming mechanism and coupled surface modes are studied. It is shown that vertical emission with a zero divergence angle and a high quality factor can be easily achieved by the back-to-back cavity design. The periodic modulation to the cavity surface alters nonradiative surface modes into radiative surface modes, and the constructive interference of the radiative waves gives rise to vertical emission and improves the quality of the output beam. A high quality factor can be attributed to the nonradiative surface mode on the cavity back whose small part of energy can be transferred into the cavity surface by coupling. The resonant property and the coupling efficiency of the cavities are investigated and optimal cavity configurations are obtained. These open coupled-cavities are good candidates of highly directional light sources.

Effects induced by Mie resonance in two-dimensional photonic crystals.

The effects of Mie resonance on the photonic band-gap structure of two-dimensional photonic crystals are investigated in detail. Firstly, we demonstrate the correlation between the band-gap structure and Mie resonance, such as the midgap frequency and the changes in gap width with different cylinder radii. We find that the midgap frequency and the gap width increase linearly and then saturate, before and after the Mie resonance frequency crosses the midgap frequency. The radius value at the crossing point between the midgap frequency and the Mie resonance frequency becomes smaller with the increase in the refractive contrast. For large radius, all the Mie resonance frequencies fall into the corresponding bands. Secondly, the changes in the gap width are studied with increasing index of the cylinders. Changing rules of the gap width are found depending on the position of the Mie resonance frequency. For example, when the Mie resonance falls inside the gap the gap width increases most rapidly and reaches its maximum value when the Mie resonance is leaving the gap range (around the lower edge of the gap). After that the gap width decreases very steeply with increase in the refractive contrast. Thirdly, we investigate the effect of Mie resonance on the band width for the 'heavy-photon band', which is the third band of our system. We find that, quite different from other bands, the band widths of such bands are determined by the overlapping integral of the Mie resonance states. All these results can be explained by the Mie resonance based on two physical pictures, i.e. the scattering picture and the hopping picture. According to these analyses and results, we may understand more clearly how the Mie resonances influence the formation of the band-gap structure. The Mie resonance effects on photonic band-gap structure presented in this paper would be valuable in designing various kinds of photonic crystals.