Recent research in topological photonics has not only proposed and realized novel topological phenomena such as one‐way broadband propagation and robust transport of light, but also designed and fabricated photonic devices with high‐performance indexes, which are immune to fabrication errors such as defects or disorders. Photonic crystals, which are periodic optical structures with the advantages of good light field confinement and multiple adjusting degrees of freedom, provide a powerful platform to control the flow of light. With the topology defined in the reciprocal space, photonic crystals have been widely used to reveal different topological phases of light and demonstrate topological photonic functionalities. This review presents the physics of topological photonic crystals with different dimensions, models, and topological phases. The design methods of topological photonic crystals are introduced. Furthermore, the applications of topological photonic crystals in passive and active photonics are reviewed. These studies pave the way for applying topological photonic crystals in practical photonic devices.

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Topological Photonic Crystals: Physics, Designs, and Applications

Geometric phases that characterize the topological properties of Bloch bands play a fundamental role in the band theory of solids. Here we report on the measurement of the geometric phase acquired by cold atoms moving in one-dimensional optical lattices. Using a combination of Bloch oscillations and Ramsey interferometry, we extract the Zak phase—the Berry phase gained during the adiabatic motion of a particle across the Brillouin zone—which can be viewed as an invariant characterizing the topological properties of the band. For a dimerized lattice, which models polyacetylene, we measure a difference of the Zak phase’ Zak D 0:97(2) for the two possible polyacetylene phases with different dimerization. The two dimerized phases therefore belong to different topological classes, such that for a filled band, domain walls have fractional quantum numbers. Our work establishes a new general approach for probing the topological structure of Bloch bands in optical lattices.

http://absimage.aps.org/image/DAMOP13/MWS_DAMOP13-2013-000470.pdf

Direct Measurement of the Zak phase in Topological Bloch Bands

Dynamical encirclement of an Exceptional Point (EP) and corresponding time-asymmetric mode evolution properties due to breakdown in adiabatic theorem have been a key to range of exotic physical effects in various open atomic, molecular and optical systems. Here, exploiting a gain-loss assisted dual-mode optical waveguide that hosts a dynamical EP-encirclement scheme, we have explored enhanced nonreciprocal effect in the dynamics of light with onset of saturable nonlinearity in the optical medium. We propose a prototype waveguide-based isolation scheme with judicious tuning of nonlinearity level where one can pass only a chosen mode in any of the desired directions as per device requirement. The deliberate presence of EP enormously enhances the nonreciprocal transmission contrast even up to 40 dB over the proposed device length with a scope of further scalability. This exclusive topologically robust mode selective all-optical isolation scheme will certainly offer opportunities in integrated photonic circuits for efficient coupling operation from external sources and improve device performances.

Exceptional Point and Toward Mode Selective Optical Isolation

Abstract Opening a new door to tailoring electromagnetic (EM) waves, temporal boundaries have attracted the attention of researchers in recent years, which have led to many intriguing applications. However, the current theoretical approaches are far from enough to handle the complicated temporal systems. In this paper, we develop universal matrix formalism, paired with a unique coordinate transformation technique. The approach can effectively deal with temporally stratified structures with complicated material anisotropy and arbitrary incidence angles. This formulation is applied to various practical systems, enabling the solution of these temporal boundary related problems in a simple and elegant fashion, and also facilitating a deep insight into the fundamental physics.

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Generalized temporal transfer matrix method: a systematic approach to solving electromagnetic wave scattering in temporally stratified structures

We propose a framework to study the topological properties of an optical bound state in the continuum (BIC). Here, the formation of a BIC has been shown using the interaction between proximity resonances undergoing avoided resonance crossing in a simple fabrication, feasible gain-loss assisted microcavity. Similar to a Friedrich-Wingten (FW)-type BIC, the formation of an ultrahigh-quality ($Q$) mode due to the precise destructive interference between resonances has been reported. The enhancement in the $Q$ factor was found to be more than four orders of magnitude greater than the other participating resonances. Furthermore, multiple such FW-type high-$Q$ operating points from the same set of proximity resonances have been identified. Upon further inspection, we report the formation of a special-BIC line in the system parameter space connecting the locations of these operating points. Further, we closely investigate the light dynamics of systems near single and multiple quasi-BICs. Aiming to develop a scheme to enhance the performance of optical sensing in a microcavity, we study the sensitivity of transmission coefficients and quality factor to sense even ultrasmall perturbations in the system configuration. Our proposed scheme would open up a vast potential for an enhanced desired optical response in enhanced nonlinear applications, low-threshold nano- and microlasers, and device-level sensors.

Ultrasensitive light confinement: Driven by multiple bound states in the continuum

Light propagating through periodic photonic lattice supporting Bloch modes are leaky in nature. Recently it has been established that such 1-D photonic lattices can provide robust loss-less guidance of light by appropriate structural modulation following special models. However, these special models compel the structure to be quasi-periodic, which makes their fabrication less feasible. Thus, we propose a fabrication feasible 1-D periodic lattice having topological features which are established by Zak phase analysis. We demonstrate the existence of an edge state in this specialty photonic lattice as well as its robustness against lattice dislocations. By numerical simulation, we have also illustrated that these states can be amplified without any distortion by introducing homogeneous gain to the lattice substrate. This is a strikingly different phenomenon from the conventionally known fact that with the introduction of gain to periodic lattices, the propagating state of light spreads in the transverse direction due to enhanced complex coupling. Therefore, we present a study of the interplay between topology and non-Hermiticity from the standpoint of device application in this report. The findings suffice to propose the utility of such systems as on-chip optical interconnects and have the potential for topological amplifiers within the regime of optical communication.

Identifying topological signature of 1-D photonic lattice by Zak phase analysis and towards robust amplification of edgestate

We study optical pulse propagation through a linear, dispersive, gain-loss-assisted bulk medium whose refractive index is time-varying. To analyze the dynamics, we have used a novel technique of time transformation that provides universal formulas of pulse propagation. Our analytical and numerical investigations reveal that optical pulses show asymmetric behavior while propagating in opposite direction through such a medium, in both the temporal and spectral domains. Moreover, the wavelength shift during this process is the most interesting outcome which is limited in range, but could be tuned by varying the refractive index with time. Phenomena that are observed in this Letter are novel and realizable in practical devices such as coupled waveguides where the refractive index is a function of time.

Asymmetric propagation and limited wavelength translation of optical pulses through a linear dispersive time-dynamic system.

Topological photonics provides a new platform to control and manipulate the flow of light in photonic devices that exhibit topological phase transitions. One way to introduce such transition of geometric phases in photonic waveguides is to modulate the structure of the photonic crystals, array waveguides, or the metamaterials in such a way that it eventually changes the bulk topology. Such topological waveguides localize the light at the boundary of the two distinct bulk systems with different topological invariant. Based on this fundamental physics, we demonstrate a robust and controlled propagation of light in a class of specialty optical fiber which exhibits the topological phase transition between a nontrivial one-dimensional (1D) periodic cylinder and its topologically trivial counterpart. The key idea is to explore the possibility of topological phase transition of 1D photonic bands over the momentum space by tuning the unit-cell dimension and its individual thicknesses. We have systematically computed the trivial and the nontrivial topological invariants, the Zak phase, of designed cylindrical 1D lattices with inversion symmetry over the first Brillouin zone. To establish the presence and the robustness of the localized edge mode, we have studied the reflectance of the geometry in the presence of disorder. Also, the simulated field profile and the back-reflectionless propagation of the edge mode through the fiber have been shown. Besides conventional fibers, such topological optical fibers are definitely a waveguide geometry for robust delivery of light and thus would be very significant to open up a new paradigm in guided wave photonics.

Specialty topological fiber using periodic lattice geometries

We present a novel fiber design concept based on the formation of concentric effective optical cores in a photonic bandgap geometry supporting ultra-large bandwidth for stable propagation of short optical pulses over longer distances.

Piyali Biswas

Papers

Identifying topological signature of 1-D photonic lattice by Zak phase analysis and towards robust amplification of edgestate

Asymmetric propagation and limited wavelength translation of optical pulses through a linear dispersive time-dynamic system.

Specialty topological fiber using periodic lattice geometries

A Specialty Endless-Core Photonic Bandgap Fiber with Ultra-wide Bandwidth for Short Pulse Propagation