A method for solving the inverse problem of designing the structure of a one-dimensional photonic crystal is proposed and experimentally implemented. It is known that a one-dimensional photonic crystal with a spatial sinusoidal modulation of the refractive index, has a narrow photonic bandgap at a frequency related to the spatial frequency of this sinusoid. We propose a reverse engineering method for one-dimensional photonic crystals with an arbitrary given reflection spectrum by expanding this spectrum into elementary photonic band gaps and then summing them. This paper shows the application of this method to fabricate examples of photonic crystals with simple shapes of spectral reflection curves.
A method is presented for modelling the optical properties of a photonic crystal structure mounted on a substrate which is thick enough that the light reflected from the back is incoherent with reflections from the front. Transmission and reflection spectra are presented for the cases where the structure is a multilayer planar microcavity and an opal photonic crystal. The contributions from the incoherent reflections can be very large, and in the photonic crystal case, change the positions of the spectral peaks.
The time behaviour of microwaves undergoing partial reflection by photonic barriers was measured in the time and in the frequency domain. It was observed that unlike the duration of partial reflection by dielectric layers, the measured reflection duration of barriers is independent of their length. The experimental results point to a nonlocal behaviour of evanescent modes at least over a distance of some ten wavelengths. Evanescent modes correspond to photonic tunnelling in quantum mechanics.
Total internal reflection (TIR) is a ubiquitous phenomenon used in photonic devices ranging from waveguides and resonators to lasers and optical sensors. Controlling this phenomenon and light confinement are keys to the future integration of nanoelectronics and nanophotonics on the same silicon platform. We introduced the concept of relaxed total internal reflection in 2014 to control evanescent waves generated during TIR. These unchecked evanescent waves are the fundamental reason photonic devices are inevitably diffraction-limited and cannot be miniaturized. Our key design concept is the eng…
The physical origin of subwavelength photonic nanojet in retrograde-reflection mode (retro-PNJ) is theoretically considered. This specific type of photonic nanojet emerges upon sequential double focusing of a plane optical wave by a transparent dielectric microparticle located near a flat reflecting mirror. For the first time to the best of our knowledge, we report a unique property of retro-PNJ for increasing its focal length and intensity using microparticles with the optical contrast exceeding limiting value (n > 2) that fundamentally distinguishes retro-PNJ from regular PNJ behavior. This …
We investigate numerically optical properties of novel two-dimensional photonic materials where parallel dielectric rods are randomly placed with the restriction that the distance between rods is larger than a certain value. A large complete photonic gap (PG) is found when rods have sufficient density and dielectric contrast. Our result shows that neither long-range nor short-range order is an essential prerequisite to the formation of PGs. A universal principle is proposed for designing arbitrarily shaped waveguides, where waveguides are fenced with side walls of periodic rods and surrounded …
The possibility of overcoming the critical condition for localized photonic nanojet upon plane optical wave diffraction at mesoscale dielectric particle, which is commonly known as "the refractive index contrast is less than two", was recently reported in our works. To this end, the novel geometrical scheme of photonic nanojet generation in "reflection mode" was proposed based on a super-contrast microparticle (n~2) placed near a flat mirror. In this paper, through the numerical FDTD calculations of optical near-field structure of 2D and 3D dielectric microparticles (cylinder, sphere) we exten…
The time-dependence of the Bragg diffraction by one-dimensional photonic crystals and its influence on the short pulse reflection are studied in the framework of the coupled- wave theory. The indicial response of the photonic crystal is calculated and it appears that it presents a time-delay effect with a transient time conditioned by the extinction length. A numerical simulation is presented for a Bragg mirror in the x-ray domain and a pulse envelope modelled by a sine-squared shape. The potential consequences of the time-delay effect in time-dependent optics of short-pulses are emphasized.
We report the design of nonreciprocal resonant transmission/reflection using a one-dimensional photonic crystal (1DPC) adjacent to the magneto-optical (MO) metal film. The nonreciprocal surface modes are found at the interface between the PC and MO metal within the forbidden band of native PC structure. Breaking time-reversal symmetry using external magnetic field gives rise of such unique nonreciprocal properties. Quantitatively understanding of nonreciprocal resonant optical transmission/reflection behavior is performed using an effective admittance-matching theory. With excitation of the no…
Non-Hermitian photonic systems are known to exhibit unique phenomena, where non-Hermiticity is typically introduced by material loss or gain. Here, we propose and experimentally demonstrate unidirectional phenomena solely based on radiation. Our design is on the basis of a double-lattice photonic crystal that has a linear dispersion with a single exceptional point, where the magnitudes of Hermitian and non-Hermitian couplings are cancelled out in one direction. Based on this concept, we realize a unidirectional waveguide which shows perfect radiation when light is incident from one side, and s…
We develop and implement a new mathematical and computational framework for designing photonic elements with one or more high-$Q$ scattering resonances. The approach relies on solving for the poles of the scattering matrix, which mathematically amounts to minimizing the determinant of the Fredholm integral operator of the electric field with respect to the permittivity profile of the scattering element. We apply the method to design subwavelength gradient-permittivity structures with multiple scattering resonances and quality factors exceeding 500. We also find the spectral scattering cross se…
We construct a binary synthetic photonic lattice theoretically with an effective magnetic field by projecting two fiber loops' light intensity and adjusting the phase distribution precisely. By tuning the phase modulator, wave vector, and propagation constant of an effective waveguide, the interface's transmittance could be manipulated. Further light dynamics show that the light pulse can achieve total reflection without diffraction and exchanges the light energy in two optical fiber loops completely when phase distribution and wave vector meet certain conditions. Our study may provide a new w…
As a fundamental optical approach to interferometry, Sagnac interference has been widely used for reflection manipulation, precision measurements, and spectral engineering in optical systems. Compared to other interferometry configurations, it offers attractive advantages by yielding a reduced system complexity without the need for phase control between different pathways, thus offering a high degree of stability against external disturbance and a low wavelength dependence. The advance of integration fabrication techniques has enabled chip-scale Sagnac interferometers with greatly reduced foot…
A photonic jet (terajet at THz frequencies) commonly denotes a specific spatially localized region in the near-field at the front side of a dielectric particle with diameter comparable with wavelength illuminated with a plane wave from its backside (i.e., the jet emerges from the shadow surface of a dielectric particle). In this paper the formation of photonic is demonstrated using the recently proposed 3D dielectric cuboids working in reflection mode when the specific spatially localized region is localized towards the direction of incidence wavefront. The results of simulations based on Fini…
We theoretically study the interactions between plasmonic and photonic modes within a structure that is composed of two thin corrugated metallic plates, embedded in air. We show that the interactions depend upon the symmetry of the interacting modes. This observation is explained by the phase difference between the Fourier components of the two gratings. The phase can be controlled by laterally shifting one grating with respect to the other. Therefore, this relative shift provides an efficient "knob" that allows to control the interaction between the various modes, resulting in an efficient mo…
Based on the reciprocity theorem, we put forward a generalized parametric space for an arbitrary transfer matrix with parity time (PT) symmetry. Through this space, one can extract complete information involving PT phases, reflectances, transmittance and known extraordinary scattering phenomena. We demonstrate a PT heterostructure with coherent perfect absorption-lasing, anisotropic transmission resonance, and parity symmetry of reflection coefficients at the frequencies of interest. In addition, with the parametric space and the analytical formula, the corresponding complex dielectric permitt…
We study the resonant transmission of light in a coupled-resonator optical waveguide interacting with two nearly identical side cavities. We reveal and describe a novel effect of the coupled-resonator-induced reflection (CRIR) characterized by a very high and easily tunable quality factor of the reflection line, for the case of the inter-site coupling between the cavities and the waveguide. This effect differs sharply from the coupled-resonator-induced transparency (CRIT) -- an all-optical analogue of the electromagnetically-induced transparency -- which has recently been studied theoretically…
Electromagnetic (EM) waves propagating through an inhomogeneous medium inevitably scatter whenever electromagnetic properties of the medium change on the scale of a single wavelength. This fundamental phenomenon constrains how optical structures are designed and interfaced with each other. Recent theoretical work indicates that electromagnetic structures collectively known as photonic topological insulators (PTIs) can be employed to overcome this fundamental limitation, thereby paving the way for ultra-compact photonic structures that no longer have to be wavelength-scale smooth. Here we prese…
Ultrafast programmable Bragg reflection in photonic integrated circuits
John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Quantum Science and Engineering, Harvard University（哈佛大学量子科学与工程）
The optical properties of materials are strongly influenced by disorder. Control of disorder in photonic materials can unveil interesting optical properties. We have found an engineered photonic structure for which the average light reflection shows a linear behaviour with a slope change in a broad range of wavelengths. Such change in slope is due to a specific degree of disorder, which is quantified by the Shannon index.
We suggest a near deterministic compact model of a photonic CNOT gate based on a quantum dot trapped in a double sided optical microcavity and a universal cloner. Our design surpasses the cloner optimal limit of 5/6 and we show that it provides fidelity around 91 % in the weak coupling regime.
We determine the range of thicknesses and refractive indices for which omnidirectional reflection from quasiperiodic multilayers occurs. By resorting to the notion of area under the transmittance curve, we assess in a systematic way the performance of the different quasiperiodic Fibonacci multilayers.
Artificial gauge fields enable extending the control over dynamics of uncharged particles, by engineering the potential landscape such that the particles behave as if effective external fields are acting on them. Recent years have witnessed a growing interest in artificial gauge fields that are generated either by geometry or by time-dependent modulation, as they have been the enablers for topological phenomena and synthetic dimensions in many physical settings, e.g., photonics, cold atoms and acoustic waves. Here, we formulate and experimentally demonstrate the generalized laws of refraction …
In this article we have theoretically investigated the dispersion characteristics of dual-core PCF, based on square-lattice geometry by varying different parameters. The fiber exhibits a very large negative dispersion because of rapid slope change of the refractive indices at the coupling wavelength between the inner core and outer core. The dependence of different geometrical parameters namely hole-to-hole spacing (pitch) and different air-hole diameter (d) was investigated in detail. By proper adjustment of the available parameters, a high negative dispersion value of -47,500 ps/nm/km has be…
We introduce topological phases in Photonic Time-Crystals. Photonic Time-Crystals are materials in which the refractive index varies periodically and abruptly in time. When the refractive index changes abruptly, the light propagating in the material experiences time-refraction and time-reflection, analogous to refraction and reflection in photonic crystals. Interference between time-refracted and time-reflected waves gives rise to Floquet-Bloch states and dispersion bands, which are gapped in the momentum. We show that photonic time-crystals can be in a topologically non-trivial phase, and cal…
The physical origin of resonant Wood's anomalies in the reflection spectra of three-dimensional (3D) opaline photonic crystals covered with Ge$_2$Sb$_2$Te$_5$ (GST225) is discussed. For this purpose, the optical reflection spectra are studied for different incident angles of light both experimentally and theoretically. The performed eigenmode analysis reveals that the Wood's anomalies originate from the quasiguided modes which appear in the GST225 capping layer. This conclusion is supported by the simulated electromagnetic near-field distributions of incident light at resonant frequencies. The…
In this report we present an investigation of the optical properties and band structure calculations for the photonic structures based on the functional materials- ferroelectrics. A theoretical approach to the optical properties of the 2D and 3D photonic crystals which yields further insight in the phenomenon of the reflection from different families of lattice planes in relation to the presence of photonic gaps or photonic bands. We calculate the photonic bands and optical properties of LiNbO3 based photonic crystals. Calculations of reflection and transmission spectra show the features corre…
We develop and experimentally validate a novel neural network design framework for silicon photonics devices that is both practical and intuitive. The framework is applicable to nearly all known integrated photonics devices, but as case studies we consider simple waveguides and chirped Bragg Gratings. By using artificial neural networks, we decrease the computational cost relative to traditional design methodologies by more than 4 orders of magnitude. We also demonstrate the abstraction of the device models to a few simple input and output parameters relevant to designers. We then apply the re…
A thorough theoretical study of the optical properties of periodic Si nanosphere arrays is undertaken, placing particular emphasis on the synergy between electric and magnetic Mie resonances, which occur in high-refractive-index nanoparticles and can lead to a rich variety of phenomena ranging from perfect reflection to controlled diffraction. By means of systematic calculations using the layer-multiple-scattering method that we properly extended so as to describe periodic arrays with many scatterers per unit cell, in conjunction with finite-element simulations, we optimized surfaces of Si nan…
We describe a general recipe for designing high-quality factor (Q) photonic crystal cavities with small mode volumes. We first derive a simple expression for out-of-plane losses in terms of the k-space distribution of the cavity mode. Using this, we select a field that will result in a high Q. We then derive an analytical relation between the cavity field and the dielectric constant along a high symmetry direction, and use it to confine our desired mode. By employing this inverse problem approach, we are able to design photonic crystal cavities with Q > 4*10^6 and mode volumes V ~ (λ/n)^3. Our…
Designing photonic topological insulators is highly non-trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely different approach: we consider the design of photonic topological insulators as an inverse design problem and use topology optimization to maximize the transmission through an edge mode with a sharp bend. Two design domains composed of two different, but initially identical, C$_\text{6v}$-symmetric unit cells define the geometrical design problem. Remarkabl…
The Raman gain of a probe light in a three-state $Λ$-scheme placed into a defect of a one-dimensional photonic crystal is studied theoretically. We show that there exists a pump intensity range, where the transmission and reflection spectra of the probe field exhibit \textit{simultaneously} occurring narrow peaks (resonances) whose position is determined by the Raman resonance. Transmission and reflection coefficients can be larger than unity at pump intensities of order tens of $μ$W/cm$^{2}$. When the pump intensity is outside this region, the peak in the transmission spectrum turns into a na…
We propose a technique of compensating the spurious reflections implied by the multiple-scattering (MS) method, commonly used for analyzing finite photonic crystal (PC) systems, to obtain exact values of characteristic parameters, such as reflection and transmission coefficients, of PC functional elements. Rather than a modification of the MS computational algorithm, our approach involves postprocessing of results obtained by the MS method. We derive analytical formulas for the fields excited in a finite system, taking explicitly into account the spurious reflections occurring at the artificia…
Photonic topological insulators are an interesting class of materials whose photonic band structure can have a bandgap in the bulk while supporting topologically protected unidirectional edge modes. Recent studies [1-6] on bianisotropic metamaterials that emulate the electronic quantum spin Hall effect using its electromagnetic analog are examples of such systems with relatively simple and elegant design. In this paper, we present a rotating magnetic dipole antenna, composed of two perpendicularly oriented coils, that can efficiently excite the unidirectional topologically protected surface wa…
A previous work [1] experimentally confirmed that the special polarization characteristic features of a three-dimensional terahertz (THz) photonic crystal with a silicon inverse diamond structure whose lattice point shape was vacant regular octahedrons, did not apply to general physical and optical basic rules in appearance. One of the basic rules is that, according to Maxwell's equations, the electric-field direction of the reflected wave rotates by 180 degrees from that of the incident wave in the case of complete reflection (Bragg reflection) and normal incidence. It is said that three-dime…
We study experimentally the Goos-Hanchen effect observed at the reflection of a self-collimated beam from the surface of a two-dimensional photonic crystal and describe a method for controlling the beam reflection through surface engineering. The microwave photonic crystal, fabricated from alumina rods, allows control of the output position of a reflected beam undergoing an internal Goos-Hanchen shift by changing the rod diameter at the reflection surface. The experimental data is in good agreement with the results of the finite-difference time-domain numerical calculations.
We outline a recently developed theory of impedance-matching, or reflectionless excitation of arbitrary finite photonic structures in any dimension. It describes the necessary and sufficient conditions for perfectly reflectionless excitation to be possible, and specifies how many physical parameters must be tuned to achieve this. In the absence of geometric symmetries the tuning of at least one structural parameter will be necessary to achieve reflectionless excitation. The theory employs a recently identified set of complex-frequency solutions of the Maxwell equations as a starting point, whi…
Resonant periodic nanostructures provide perfect reflection across small or large spectral bandwidths depending on the choice of materials and design parameters. This effect has been known for decades, observed theoretically and experimentally via one-dimensional and two-dimensional structures commonly known as resonant gratings, metamaterials, and metasurfaces. The physical cause of this extraordinary phenomenon is guided-mode resonance mediated by lateral Bloch modes excited by evanescent diffraction orders in the subwavelength regime. In recent years, hundreds of papers have declared Fabry-…
We derive and validate a set of coupled Bloch wave equations for analyzing the reflection and transmission properties of active semiconductor photonic crystal waveguides. In such devices, slow-light propagation can be used to enhance the material gain per unit length, enabling, for example, the realization of short optical amplifiers compatible with photonic integration. The coupled wave analysis is compared to numerical approaches based on the Fourier modal method and a frequency domain finite element technique. The presence of material gain leads to the build-up of a backscattered field, whi…
In this paper we proposed a novel overlay alignment method using two sets of identical photonic crystals (PhCs). In this method the reflection or transmission spectrum of the two overlaid photonic crystals is measured to help wafer tilt, yaw rotation, and translation aligning. The initial testing results with two 1D photonic crystals and analysis of the alignment accuracy are presented. This method is particularly useful in building photonic crystal stacks with nanoimprint lithography (NIL).
Photonic crystals (PCs) offer unique ways to control light-matter interactions. The measurement of dispersion relations is a fundamental prerequisite if we are to create novel functionalities in PC devices. Angle-resolved spectroscopic techniques are commonly used for characterizing PCs that work in the visible and near-infrared regions. However, the techniques cannot be applied to the mid- and long-wavelength infrared regions due to the limited sensitivity of infrared detectors. Here, we propose an alternative approach to measuring infrared dispersion relations. We construct a high-precision …
We study the backward scatterings of plane waves by reciprocal scatterers and reveal that $n$-fold ($n\geq3$) rotation symmetry is sufficient to secure invariant backscattering for arbitrarily-polarized incident plane waves. It is further demonstrated that the same principle is also applicable for infinite periodic structures in terms of reflection, which simultaneously guarantees the transmission invariance if there are neither Ohmic losses nor extra diffraction channels. At the presence of losses, extra reflection symmetries (with reflection planes either parallel or perpendicular to the inc…
Wavelength division multiplexing (WDM) devices are key elements of Photonic integrated circuits (PICs). Conventional WDM devices based on silicon waveguides and photonic crystals have limited transmittance due to high loss introduced by the strong backward scattering from defects. In addition, it is challenging to reduce the footprint of those devices. Here we theoretically demonstrate a WDM device in the telecommunication range based on all-dielectric silicon topological valley photonic crystal (VPC) structures. We tune its effective refractive index by tuning the physical parameters of the l…
We point out that electromagnetic one-way edge modes analogous to quantum Hall edge states, originally predicted by Raghu and Haldane in 2D gyroelectric photonic crystals possessing Dirac point-derived bandgaps, can appear in more general settings. In particular, we show that the TM modes in a gyromagnetic photonic crystal can be formally mapped to electronic wavefunctions in a periodic electromagnetic field, so that the only requirement for the existence of one-way edge modes is that the Chern number for all bands below a gap is non-zero. In a square-lattice gyromagnetic Yttrium-Iron-Garnet p…
Semiconductor lasers in use today rely on mirrors based on the reflection at a cleaved facet or Bragg reflection from a periodic stack of layers. Here, we demonstrate an ultra-small laser with a mirror based on the Fano resonance between a continuum of waveguide modes and the discrete resonance of a nanocavity. The Fano resonance leads to unique laser characteristics. Since the Fano mirror is very narrow-band compared to conventional lasers, the laser is single-mode and in particular, it can be modulated via the mirror. We show, experimentally and theoretically, that nonlinearities in the mirr…
Buildings or vehicles with transparent envelope can be heated up by sunlight, causing energy consumption for cooling and in extreme cases leading to vehicular heatstroke in a hot climate. Because only visible light for illumination is essential for these applications, the NIR solar radiation should be reflected to reduce heat gain and the infrared radiation emission should be enhanced for further cooling by using the sky as a heat sink. With a high NIR reflection, a transparent radiative cooling photonic structure consisting of 2D silica gratings atop ZnO/Ag/ZnO is demonstrated for energy-savi…
We have discovered and studied the effect of the asymmetric deformation of a photonic crystal in the form of a change in the slope of the crystal planes as it is filled with a gaseous analyte. We have demonstrated that the use of a new effect leading to the displacement of the stop band against the unchanged spectrum of diffracted white light at the (glass-thin opal film) interface can be used as fast, compact, high sensitive and reproducible optical chemical sensor for ammonia. Low cost and simplicity of sensor fabrication, the response of which can be easily observed without resorting to spe…
We address soliton transmission and reflection in nonlinear photonic lattices embedded into uniform Kerr nonlinear media. We show that by introducing disorder into the guiding lattice channels, one may achieve soliton transmission even under conditions where regular lattices reflect the input beam completely. In contrast, in the parameter range where the lattice is almost transparent for incoming solitons, disorder may induce a significant reflection.
Through periodic index modulation, we create two different types of photonic structures in a heated rubidium vapor for controlled reflection, transmission and diffraction of light. The modulation is achieved through the use of the AC Stark effect resulting from a standing-wave control field. The periodic intensity structures create translationally invariant index profiles analogous to photonic crystals in spectral regions of steep dispersion. Experimental results are consistent with modeling.
Here, the frequency degree of freedom is introduced into valley photonic crystals with dual band gaps. Based on the high-order plane wave expansion model, we derive an effective Hamiltonian which characterizes dual band gaps. Metallic valley photonic crystals are demonstrated as examples in which all four topological phases are found. At the domain walls between topologically distinct valley photonic crystals, frequency-dependent edge states are demonstrated and a broadband photonic detouring is proposed. Our findings provide the guidance for designing the frequency-dependent property of topol…
We propose a method of measuring topological invariants of a photonic crystal through phase spectroscopy. We show how the Chern numbers can be deduced from the winding numbers of the reflection coefficient phase. An explicit proof of existence of edge states in system with nonzero reflection phase winding number is given. The method is illustrated for one- and two-dimensional photonic crystals of nontrivial topology.
