We report the observation of imaging beyond the diffraction limit due to bound surface states in negative refraction photonic crystals. We achieve an effective negative index figure-of-merit [-Re(n)/Im(n)] of at least 380, ~125x improvement over recent efforts in the near-infrared, with a 0.4 THz bandwidth. Supported by numerical and theoretical analyses, the observed near-field resolution is 0.47 lambda, clearly smaller than the diffraction limit of 0.61 lambda. Importantly, we show this sub-diffraction imaging is due to the resonant excitation of surface slab modes, allowing refocusing of non-propagating evanescent waves.
Refraction represents one of the most fundamental operations that may be performed by a metasurface. However, simple phasegradient metasurface designs suffer from restricted angular deflection due to spurious diffraction orders. It has been recently shown, using a circuit-based approach, that refraction without spurious diffraction, or diffraction-free, can fortunately be achieved by a transverse metasurface exhibiting either loss-gain or bianisotropy. Here, we rederive these conditions using a medium-based - and hence more insightfull - approach based on Generalized Sheet Transition Condition…
Phase reversal occurs in the propagation of an electromagnetic wave in a negatively refracting medium or a phase-conjugate interface. Here we report the experimental observation of phase reversal diffraction without the above devices. Our experimental results and theoretical analysis demonstrate that phase reversal diffraction can be formed through the first-order field correlation of chaotic light. The experimental realization is similar to phase reversal behavior in negatively refracting media.
Considering the diffraction of a plane wave by a periodically corrugated half-space, we show that the transformation of the refracting medium from positive/negative phase-velocity to negative/positive phase-velocity type has an influence on the diffraction efficiencies. This effect increases with increasing corrugation depth, owing to the presence of evanescent waves in the troughs of the corrugated interface.
We describe propagation of light in a gas with periodic density modulation, demonstrating photonic-crystal-like refraction with negative refraction angles. We address the role of poorly defined boundaries and damping, and derive an optical analog of the quantum adiabatic theorem. For Cs atoms in an optical lattice, we show that relying on semi-adiabatic propagation one can excite and spatially split positively and negatively refracting modes at experimentally available gas densities.
Diffraction of electromagnetic plane waves by the gratings made by periodically corrugating the exposed planar boundaries of homogeneous, isotropic, linear dielectric--magnetic half--spaces is examined. The phase velocity vector in the diffracting material can be either co-parallel or anti-parallel to the time-averaged Poynting vector, thereby allowing for the material to be classified as of either the positive or the negative negative phase-velocity (PPV or NPV) type. Three methods used for analyzing dielectric gratings - the Rayleigh-hypothesis method, a perturbative approach, and the C form…
Kossel diffraction under standing-wave excitation in a one-dimensional photonic crystal is investigated. It is shown that by combining the reciprocity theorem, the Fermi golden rule and the concept of density of photonic modes, it is possible to predict the behaviour of the Kossel diffraction in such a system.
In this paper, we show the photonic nanojet is the central bright maxima in focused near-field diffraction pattern. Using a simplified Huygens-Fresnel model, and using numerical simulations, we generate photonic nanojets from curved interfaces between media of different refractive indices and study the length, width, and peak intensity of the resultant photonic nanojet. We confirm that photonic nanojets are not sub-diffraction optical modes and are adequately described using diffraction theory. We also show how modifying the optogeometric environment can be used to tailor relevant features of …
We extend results of [Liu et al. Proc. Roy. Soc. Lond. A 469, 20130240, 2013] on artificial magneto-electric coupling and magnetism in moderate contrast dielectric layered media via high-order homogenization to the three-dimensional setting. For this, we consider asymptotic expansions in the vector Maxwell system. We then illustrate effect of magneto-electric coupling with numerical simulations for a layered system alternating positively and negatively refracting index. We unveil hyperbolic behaviour and magneto-electric coupling and derive a sharper estimate for the anisotropic effective medi…
We extend a modal theory of diffraction by a set of parallel fibers to deal with the case of a hard boundary: that is a structure made for instance of air-holes inside a dielectric matrix. Numerical examples are given concerning some resonant phenomena.
Despite the steady advancements in nanofabrication made over the past decade that had prompted a plethora of intriguing applications across various fields, achieving compatibility between miniaturized photonic devices and electronic dimensions remains unachievable due to the inherent diffraction limit of photonic devices. Several approaches have emerged to overcome the diffraction restriction and leverage the spatial information carried by the evanescent waves. Negative dielectric permittivity materials can be utilized to build photonic crystals (PhCs) based on surface plasmon-polaritons. This…
We suggest a novel type of photonic structures where the strength of diffraction can be managed in a very broad frequency range. We introduce optimized arrays of curved waveguides where light beams experience wavelength-independent normal, anomalous, or zero diffraction. Our results suggest novel opportunities for efficient self-collimation, focusing, and reshaping of beams produced by white-light and super-continuum sources. We also show how to manipulate light patterns through multicolor Talbot effect, which is possible neither in free space nor in conventional photonic lattices.
Metamaterials are artificial composite materials that, by virtue of their microstructure, exhibit properties not exhibited by their component materials. Much excitement has been generated by negatively refracting metamaterials, typically consisting of coupled, metallic, subwavelength elements that simulate electric and magnetic dipoles, because of their unusual ability to manipulate visible light, infrared waves and microwaves. In such a metamaterial, an electromagnetic wave propagates so that the direction of its energy flow is opposed to its phase velocity, a condition captured by the real p…
We experimentally demonstrate how to solve the phase problem of diffraction using multi-wave interference with standard diffraction experimental setups without the need for taking any auxiliary data. In particular, we show that the phases of the Fourier components of a periodic structure can be fully recovered by deliberately choosing a probe wavelength of the diffracting radiation much smaller than the lattice constant. In the course of the demonstration, we accurately determine the refractive index profile of nanocomposite phase gratings by light and neutron diffraction measurements.
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.
The results of spectroscopic studies of the diffraction anomalies (the so-called resonant Wood anomalies) in spatially-periodic hybrid structures based on halcogenide (GST225)-coated opal films of various thickness are presented. A theoretical analysis of spectral-angular dependencies of the Wood anomalies has been made by means of a phenomenological approach using the concept of the effective refractive index of waveguiding surface layer.
We investigate propagation of light pulses in photonic crystals in the vicinity of the zero-diffraction point. We show that Gaussian pulses due to nonzero width of their spectrum spread weakly in space and time during the propagation. We also find the family of nonspreading pulses, propagating invariantly in the vicinity of the zero diffraction point of photonic crystals.
The Lieb lattice and the kagome lattice, which are both well known for their Dirac cones and flat bands, can be continuously converted into each other by a shearing transformation. During this transformation, the flat band is destroyed, but the Dirac cones remain and become tilted, with types I, II, and III occurring for different parameters. In this work, we first study these tilted Dirac cones using a tight-binding model, revealing how they can be engineered into the different types. We then demonstrate conical diffraction in a photonic lattice realization of the Lieb-kagome lattice using sp…
We present waveguides with photonic crystal cores, supporting energy propagation in subwavelength regions with a mode structure similar to that in telecom fibers. We design meta-materials for near-, mid-, and far-IR frequencies, and demonstrate efficient energy transfer to and from regions smaller than 1/25-th of the wavelength. Both positive- and negative-refractive index light transmissions are shown. Our approach, although demonstrated here in circular waveguides for some specific frequencies, is easily scalable from optical to IR to THz frequency ranges, and can be realized in a variety of…
A finite element-based modal formulation of diffraction of a plane wave by an absorbing photonic crystal slab of arbitrary geometry is developed for photovoltaic applications. The semi-analytic approach allows efficient and accurate calculation of the absorption of an array with a complex unit cell. This approach gives direct physical insight into the absorption mechanism in such structures, which can be used to enhance the absorption. The verification and validation of this approach is applied to a silicon nanowire array and the efficiency and accuracy of the method is demonstrated. The metho…
The equations providing to describe generation process in FEL with varied parameters of diffraction grating (photonic crystal) are obtained. It is shown that applying diffraction gratings (photonic crystal) with the variable period one can significantly increase radiation output. It is mentioned that diffraction gratings (photonic crystal) can be used for creation of the dynamical wiggler with variable period in the system. This makes possible to develop double-cascaded FEL with variable parameters changing, which efficiency can be significantly higher that of conventional system.
We generate experimentally different types of two-dimensional Bloch waves of a square photonic lattice by employing the phase imprinting technique. We probe the local dispersion of the Bloch modes in the photonic lattice by analyzing the linear diffraction of beams associated with the high-symmetry points of the Brillouin zone, and also distinguish the regimes of normal, anomalous, and anisotropic diffraction through observations of nonlinear self-action effects.
We report a general description of quasi-phase-matched parametric process in nonlinear photonic crystals (NLPC) by extending the conventional X-ray diffraction theory in solids. Under the virtual wave approximation, phase-matching resonance is equivalent to the diffraction of the scattered virtual wave. Hence a modified NLPC Ewald construction can be built up, which illustrates the nature of the accident for the diffraction of the virtual wave in NLPC and further reveals the complete set of diffractions of the virtual wave for both of the air-dielectric and dielectric-dielectric contacts. We s…
This paper considers the refraction and diffraction of waves in three-dimensional crystals formed by anisotropically scattering centers. The partial wave expansion method is used to consider the effect of multiple rescattering of waves by centers composing a crystal. The expression for the refractive index of a crystal is derived. It is shown that instead of the diagonal elements of the scattering matrix $\mathbf{T}$, appearing in the expression for the refractive index of a chaotic medium, the derived expression includes the diagonal elements of the reaction matrix $\mathbf{K}$. This fact is …
We demonstrate that the tuning of the optical properties of a photonic crystal infiltrated with liquid crystal can be calculate using the Von-Laue diffraction condition. We present a simple formula to predict the shift of the stop band for all the diffraction orders using an effective index of the composite structure. We consider that our formula is useful to determine in a simple manner the shift of the optical properties of tunable photonic crystals. We compare the accuracy of our method with calculations obtained with the Plane Wave Method.
We introduce a grating assisted tunneling scheme for tunable synthetic magnetic fields in photonic lattices, which can be implemented at optical frequencies in optically induced one- and two-dimensional dielectric photonic lattices. We demonstrate a conical diffraction pattern in particular realization of these lattices which possess Dirac points in $k$-space, as a signature of the synthetic magnetic fields. The two-dimensional photonic lattice with grating assisted tunneling constitutes the realization of the Harper-Hofstadter Hamiltonian.
The model of nonlinear interaction of proper waves of photonic crystal with plane acoustic wave was developed. The formulation of the model is reduced to the eigenvalue problem, which can be solved by computer simulations. By means of the formulae given in present paper one can predict which polarizations of acoustic wave can result in Bragg diffraction of optical waves of TE or TM polarizations. Computer simulation allows obtaining amplitudes of interaction waves in the case of Bragg diffraction when phase-matching conditions are fulfilled.
Recently we proposed a paradigm shift in light confinement strategy showing how relaxed total internal reflection and photonic skin-depth engineering can lead to sub-diffraction waveguides without metal (S. Jahani and Z. Jacob, "Transparent sub-diffraction optics: nanoscale light confinement without metal," Optica 1, 96-100 (2014)). Here, we show that such extreme-skin-depth (e-skid) waveguides can counter-intuitively confine light better than the best-case all-dielectric design of high index silicon waveguides surrounded by vacuum. We also analytically establish that figures of merit related …
By applying the properties of Fabry-Perot resonance and Rayleigh anomaly, we have shown that a photonic crystal slab can scatter the light from an incident plane wave into a diffracted light with a very large reflection or transmission coefficient. The enhanced field is either a propagating diffraction order (with a grazing angle of diffraction) or a weakly evanescent order, so it can be particularly useful for applications requiring an enhanced propagating field (or an enhanced field with a low attenuation). An efficient effective medium technique is developed for the design of the resonant p…
We discuss the propagation of an electromagnetic field in an inhomogeneously anisotropic material where the optic axis is rotated in the transverse plane but is invariant along the propagation direction. In such a configuration, the evolution of an electromagnetic wavepacket is governed by the Pancharatnam-Berry phase (PBP), responsible for the appearance of an effective photonic potential. In a recent paper [A. Alberucci et al., "Electromagnetic confinement via spin-orbit interaction in anisotropic dielectrics", ACS Photonics \textbf{3}, 2249 (2016)] we demonstrated that the effective potenti…
We show that diffraction of electromagnetic radiation (in particular of a visible light) can disappear in propagation through materials with periodically in space modulated refraction index, i.e. photonic crystals. In this way the light beams of arbitrary width can propagate without diffractive broadening and, equivalently, arbitrary light patterns can propagate without diffractive smearing.
Ultrawide-angle diffraction-limited 2D beam steering via hybrid integrated metasurface-photonic circuit
Massachusetts Institute of Technology（麻省理工学院）；Pi Inc.（2Pi公司）；Singapore-MIT Alliance for Research and Technology (SMART)（新加坡-麻省理工学院研究与技术联盟）；University of Maryland, College Park（马里兰大学帕克分校）；NASA Langley Research Center（美国国家航空航天局兰利研究中心）；Korea Advanced Institute of Science and Technology（韩国科学技术院）
We uncover a strong coupling between nonlinearity and diffraction in a photonic crystal at the supercollimation point. We show this is modeled by a nonlinear diffraction term in a nonlinear schroedinger 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.
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.
We demonstrate a mesoscopic self-collimation effect in photonic crystal superlattices consisting of a periodic set of all-positive index 2D photonic crystal and homogeneous layers. We develop an electromagnetic theory showing that diffraction-free beams are observed when the curvature of the optical dispersion relation is properly compensated for. This approach allows to combine slow light regime together with self-collimation in photonic crystal superlattices presenting an extremely low filling ratio in air.
Refraction and diffraction of waves in natural crystals and artificial crystals formed by anisotropically scattering centers are considered. A detailed study of the electromagnetic wave refraction in a two-dimensional photonic crystal formed by parallel threads is given by way of example. The expression is derived for the effective amplitude of wave scattering by a thread (in a crystal) for the case when scattering by a single thread in a vacuum is anisotropic. It is established that for a wave with orthogonal polarization, unlike a wave with parallel polarization, the index of refraction in c…
Emerging technology based on artificial materials containing metallic structures has raised the prospect for unprecedented control of terahertz waves through components like filters, absorbers and polarizers. The functionality of these devices is static by the very nature of their metallic or polaritonic composition, although some degree of tunability can be achieved by incorporating electrically biased semiconductors. Here, we demonstrate a photonic structure by projecting the optical image of a metal mask onto a thin GaAs substrate using a femtosecond pulsed laser source. We show that the re…
Small manufacturing-tolerant photonic crystal cavities are systematically designed using topology optimization to enhance the ratio between quality factor and mode volume, Q/V. For relaxed manufacturing tolerance, a cavity with bow-tie shape is obtained which confines light beyond the diffraction limit into a deep-subwavelength volume. Imposition of a small manufacturing tolerance still results in efficient designs, however, with diffraction-limited confinement. Inspired by numerical results, an elliptic ring grating cavity concept is extracted via geometric fitting. Numerical evaluations demo…
A theoretical study of photonic bands for one-dimensional (1D) lattices embedded in planar waveguides with strong refractive index contrast is presented. The approach relies on expanding the electromagnetic field on the basis of guided modes of an effective waveguide, and on treating the coupling to radiative modes by perturbation theory. Photonic mode dispersion, gap maps, and intrinsic diffraction losses of quasi-guided modes are calculated for the case of self-standing membranes as well as for Silicon-on-Insulator structures. Photonic band gaps in a waveguide are found to depend strongly on…
Surface scattering of neutral helium beams created by supersonic expansion is an established technique for measuring structural and dynamical properties of surfaces on the atomic scale. Helium beams have also been used in Fraunhofer and Fresnel diffraction experiments. Due to the short wavelength of the atom beams of typically 0.1nm or less, Fraunhofer diffraction experiments in transmission have so far been limited to grating structures with a period (pitch) of up to 200nm. However, larger periods are of interest for several applications, for example for the characterization of photonic cryst…
We present a proof of concept compact diffraction limited high-resolution fiber-fed spectrograph by using a 2D multicore array input. This high resolution spectrograph is fed by a 2D pseudo-slit, the Photonic TIGER, a hexagonal array of near-diffraction limited single-mode cores. We study the feasibility of this new platform related to the core array separation and rotation with respect to the dispersion axis. A 7 core compact Photonic TIGER fiber-fed spectrograph with a resolving power of around R~31000 and 8 nm bandwidth in the IR centered on 1550 nm is demonstrated. We also describe possibl…
A solid-state active beamformer based on the annular-ring diffraction pattern is proposed for an integrated photonic platform. Such a circularly symmetric annular-ring aperture achieves radiating element limited FOV. Furthermore, it is demonstrated that a multi-annular-ring aperture with a fixed linear density of elements maintains the beam efficiency for larger apertures while reducing the beamwidth and side-lobe-level (SLL). A 255-element multi-annular-ring OPA with active beamforming is implemented in a standard photonics process. 510 phase and amplitude modulators enable beamforming and be…
We study the configuration of efficient nonlinear Cerenkov diffraction generated from a one-dimensional nonlinear photonic crystal surface, which underlies the incorporation of both quasi-phase-matching and total internal reflection by the crystal surface. Multidirectional radiation spots with different Cerenkov angles are demonstrated experimentally, which results from different orders of reciprocal vectors. At specific angles, the incident light and total internal reflect light associating with quasi-phase-matching format completely phase-matching scheme, leading to great enhancement of harm…
We study dynamical reshaping of polychromatic beams due to collective nonlinear self-action of multiple-frequency components in periodic photonic lattices and predict the formation of polychromatic discrete solitons facilitated by localization of light in spectral gaps. We show that the self-trapping efficiency and structure of emerging polychromatic gap solitons depends on the spectrum of input beams due to the lattice-enhanced dispersion, including the effect of crossover from localization to diffraction in media with defocusing nonlinearity.
The great interest to the two and three dimensionally periodic structures, called photonic crystals (PCs), has begun with the pioneer works of Yablonovitch and John as one can efficiently control the propagation of the electromagnetic (EM) waves in the same manner with semiconductors that affect the electron conduction. One of the main peculiar properties of PCs is that they have photonic band gap in the transmission spectrum similar to electronic band gap and hence, they are able to prevent the light to propagate in certain frequency regions irrespective of the propagation direction in space.…
We address the propagation of light beams in longitudinally modulated PT-symmetric lattices, built as arrays of couplers with periodically varying separation between their channels, and show a number of possibilities for efficient diffraction control available in such non-conservative structures. The dynamics of light in such lattices crucially depends on the ratio of the switching length for the straight segments of each coupler and the longitudinal lattice period. Depending on the longitudinal period, one can achieve either beam rectification, when the input light propagates at a fixed angle…
We investigate the diffraction conditions and associated formation of stopgaps for waves in crystals with different Bravais lattices. We identify a prominent stopgap in high-symmetry directions that occurs at a frequency below the ubiquitous first-order Bragg condition. This sub-Bragg diffraction condition is demonstrated by reflectance spectroscopy on two-dimensional photonic crystals with a centred rectangular lattice, revealing prominent diffraction peaks for both the sub-Bragg and first-order Bragg condition. These results have implications for wave propagation in 2 of the 5 two-dimensiona…
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…
Tunable optical material properties enable novel applications in both versatile metamaterials and photonic components including optical sources and modulators. Transparent conductive oxides (TCOs) are able to highly tune their optical properties with applied bias via altering their free carrier concentration and hence plasma dispersion. The TCO material indium tin oxide (ITO) exhibits unity-strong index changes, and epsilon-near-zero behavior. However, with such tuning the corresponding high optical losses, originating from the fundamental Kramers-Kronig relations, result in low cavity finesse…
We use numerical modeling to study the features of parametric (quasi-Cherenkov) cooperative radiation arising when an electron bunch passes through a crystal (natural or artificial) under the conditions of dynamical diffraction of electromagnetic waves in the presence of shot noise. It is shown that in both Laue and Bragg diffraction cases, parametric radiation consists of two strong pulses: one emitted at small angles with respect to the particle velocity direction and the other emitted at large angles to it. Under Bragg diffraction conditions, the intensity of parametric radiation emitted at…
In several areas of optics and photonics like wave propagation, digital holography, holographic microscopy, diffraction imaging, biomedical imaging and diffractive optics, the behavior of the electromagnetic waves has to be calculated with the scalar theory of diffraction by computational methods. Many of these high speed diffraction algorithms based on a fast Fourier transformation are in principle approximations of the Rayleigh-Sommerfeld Diffraction (RSD) theory. However, to investigate their numerical accuracy, they should be compared with and verified by RSD. All numerical simulations are…
Celestially, Positronium (Ps), has only been observed through gamma-ray emission produced by its annihilation. However, in its triplet state, a Ps atom has a mean lifetime long enough for electronic transitions to occur between quantum states. This produces a recombination spectrum observable in principle at near IR wavelengths, where angular resolution greatly exceeding that of the gamma-ray observations is possible. However, the background in the NIR is dominated by extremely bright atmospheric hydroxyl (OH) emission lines. In this paper we present the design of a diffraction-limited spectro…
