Photonic Crystal Modes Research Articles

Inverse design of broadband and lossless topological photonic crystal waveguide modes.

Topological photonic crystal waveguides can create edge states that may be more robust against fabrication disorder and can yield propagation modes below the light line. We present a fully three-dimensional method to modify state-of-the-art designs to achieve a significant bandwidth improvement for lossless propagation. Starting from an initial design with a normalized bandwidth of 7.5% (13.4 THz), the modification gives more than 100% bandwidth improvement to 16.2% (28.0 THz). This new design is obtained using an automatic differentiation enabled inverse design and a guided mode expansion technique to efficiently calculate the band structure and edge state modes.

Non-spin-mixing defect modes in the split-ring dielectric photonic crystals

Topological photonic crystals (PCs) with unique optical performances have tremendous potential application in the realm of integrated photonic circuits. In this paper, we propose split-ring topological PCs manufactured by conventional silicon material, which hosts both topological transition and helical edge states mimicking the quantum spin Hall effect. A large nontrivial bandgap from 224.85 THz to 235.03 THz can be achieved. Non-spin-mixing defect modes with the nature of topological protection are demonstrated when line defects are introduced by fabricating the sectional columns with Al2O3 at the interface of two different topologies. A guide path for the non-spin-mixing defect modes reveals that light can propagate unidirectionally with high efficiency, powerful optical localization, and strong stability. This work provides a versatile method to improve the performances of optical transmission and reveals a novel mechanism to guide light transmission, which has vast application prospects in the all-optical integrated circuits.

Fluorescence coupling to internal modes of 1D photonic crystals characterized by back focal plane imaging

The coupling of fluorescence with surface electromagnetic modes, such as surface plasmons on thin metal films or Bloch surface waves (BSWs) on truncated one-dimensional photonic crystals (1DPCs), are presently utilized for many fluorescence-based applications. In addition to the surface wave, 1DPCs also support other electromagnetic modes that are confined within the 1DPC structure. These internal modes (IMs) have not received much attention for fluorescence coupling due to lack of spatial overlap of their electric fields with the surface bound fluorophores. However, our recent studies have indicated that the fluorescence coupling with IMs occurs quite efficiently. This observed internal mode-coupled emission (IMCE) is (similar to BSW-coupled emission) indeed wavelength dependent, directional and S-polarized. In this paper, we have carried out back-focal plane imaging to reveal that the IMs of 1DPCs can couple with surface bound excited dye molecules, with or without a BSW mode presence. Depending on the emission wavelength, the coupling is observed with BSW and IMs or only IMs of the 1DPC structure. The experimental results are well matching with numerical simulations. The occurrence of IMCE regardless of the availability of BSWs removes the dependence on just the surface mode for obtaining coupled emission from 1DPCs. The observation of IMCE is expected to widen the scope of 1DPCs for surface-based fluorescence sensing and assays.

Quasi-D-Shaped Fiber Optic Plasmonic Biosensor for High-Index Analyte Detection

In this paper, we propose a highly sensitive quasi-D-shaped fiber optic biosensor for detection of high refractive index (RI) liquid analytes via surface plasmon resonance. The main mechanism of sensing is interplay between photonic crystal fiber fundamental mode and plasmonic mode which leads to formation of different resonance peaks depending on the analyte RI. We numerically analyze the structure sensitivity to design parameters and demonstrate the sensing performance of the proposed biosensor using both spectral sensitivity and amplitude sensitivity methods. The proposed biosensor has a RI detection range of 0.15 refractive index unit (RIU) from 1.45 to 1.6. The sensor exhibits linear sensing performance with a RI spectral sensitivity of 9300 nm/RIU for analyte RI ranging from 1.45 to 1.525, 1176 nm/RIU for analyte RI ranging from 1.525 to 1.6 and in particular, 11800 nm/RIU for analyte RI between 1.475 and 1.5. Furthermore, an average RI sensitivity of 4800 nm/RIU for analyte RI ranging from 1.45 to 1.6 is demonstrated. We also study the amplitude sensitivities of the proposed sensor which show promising maximum values of 183.6 RIU $^{-1}$ for 785 nm excitation and 820 RIU $^{-1}$ for 1050 nm excitation. Due to the simple structure of the proposed biosensor, large detection range, high sensitivity and promising linear sensing performance, the proposed biosensor can be a promising candidate for detecting various high RI chemical and biochemical samples.

Salinity and temperature detection for seawater based on a 1D-defective photonic crystal material

In this work, we demonstrate the sensing principle to simultaneously detect the salinity and temperature of seawater using a 1D-defective photonic crystal structure. We designed a one-dimensional defective mode photonic crystal based on the well-known transfer matrix method (TMM) for detecting the seawater salinity and temperature. Our proposed optical sensor is based on the following concept. Since the concentration of the salinity in the seawater changes the refractive index of the seawater, the sensitivity can be calculated by a peak wavelength shift happening in the output transmission spectrum for its variation of different concentration of samples. By adjusting the design parameters of our proposed structure such as the thickness of the defect layer, the temperature and the salinity, we investigated the corresponding optical properties response where the resulted transmittance peak can be turned over the considered range.

Robustness of topological corner modes in photonic crystals

We analyze the robustness of corner modes in topological photonic crystals, taking a $C_6$-symmetric breathing honeycomb photonic crystal as an example. First, we employ topological quantum chemistry and Wilson loop calculations to demonstrate that the topological properties of the bulk crystal stem from an obstructed atomic limit phase. We then characterize the topological corner modes emerging within the gapped edge modes employing a semi-analytical model, determining the appropriate real space topological invariants. For the first time, we provide a detailed account of the effect of long-range interactions on the topological modes in photonic crystals, and we quantify their robustness to perturbations. We conclude that, while photonic long-range interactions inevitably break chiral symmetry, the corner modes are protected by lattice symmetries.

Optical Frequency Comb Generation via Cascaded Intensity and Phase Photonic Crystal Modulators

Nanophotonics, driven by low processing power and high density integration, is appearing as the next logical step for microwave photonics. Optical frequency combs (OFCs), which play a vital role in integrated microwave photonics, have not yet generated using nano-structured devices. In this paper, we propose OFC generation based on all-optical modulation of nanophotonic structures. A theoretical model based on temporal coupled mode theory is developed to describe cascaded all-optical photonic crystal intensity and phase modulators. Using a modulation light with a sinusoidal waveform, a separate carrier light is modulated to generate an OFC. By manipulating the modulation power and device dimensions, a flat OFC that spans over a 600 GHz is delivered. The proposed system offers OFC generation with tunable comb line spacing using devices with high density integration capabilities.

Wannier-function expansion of localized modes in 1D photonic crystals without inversion symmetry

The localized modes of one-dimensional photonic crystals without inversion symmetry are calculated by using linear combinations of Wannier functions. A closed form is given for the phase of the Bloch function leading to maximally localized Wannier functions. The defect consists of changing the refractive index of one layer in a single unit cell. The results for the frequencies and magnetic-field profiles of the localized modes are found in good agreement with calculations based on the transfer-matrix method. The need for maximally localized Wannier functions is discussed.

Silicon Photonic Crystal Modulators for High-Speed Transmission and Wavelength Division Multiplexing

For next-era optical interconnects in data centers, development of compact, energy-efficient, low-cost, and high-speed optical transceivers are required, for which high-performance external modulators in silicon photonics will be key components. We present a silicon photonic crystal waveguide slow light Mach-Zehnder modulator suitable for this purpose. The enhancement in the modulation efficiency via the slow light effect reduces the halfwave voltage-length product VπL, maintaining a wide working spectrum over 15 nm. The frequency response of the slow light modulator is constricted by an electrooptic phase mismatch between slow light and RF signals. In this study, this was dramatically improved by matching the phase using meanderline electrodes that delay RF signals. The cutoff frequency was experimentally evaluated to be 32-38 GHz. Using this device, we demonstrated high-speed modulation, including 64-Gbps on-off keying, 100-Gbps pulse amplitude modulation, and 50-Gbps/ch wavelength division multiplexing in 170-200-μm- long devices.

Thermally tunable terahertz omnidirectional photonic bandgap and defect mode in 1D photonic crystals containing moderately doped semiconductor

A new one-dimensional photonic crystal (1DPC) containing moderately doped silicon (m-Si) semiconductor is proposed and its tunable properties are theoretically investigated. The tunable complex permittivity of m-Si with temperature is the central idea that makes the 1DPC thermally tunable. The 1DPC systems such as (m-Si/SiO2)12 and defective (m-Si/SiO2)6D(m-Si/SiO2)6 are examined in the spectral range of 0.4–0.8 THz with varying temperature from 40 to 100 K. Air and m-Si are considered as defect layer (D) in two different 1DPC systems. Our simulation shows that the photonic band gap (PBG) shifts to higher frequency and the omnidirectional PBG gets narrower with increasing temperature. The defect mode in both defective 1DPCs shifts to higher frequency with increasing temperature. The temperature sensitivity of peak transmission is found better in the air defective 1DPC, while that of defect frequency is better in the m-Si defective 1DPC. The angle of incidence and polarization dependency of the defect modes are studied in detail. The present work can be utilized for the development of tunable omnidirectional mirrors and narrow bandpass filters in the terahertz region as well as THz light based thermal sensors.

Kinetics of the Luminescence Response of Self-Assembled Ge(Si) Nanoislands Embedded in Two-Dimensional Photonic Crystals

The results of studies of the spectral and kinetic characteristics of the photoluminescence of photonic crystals formed on the basis of structures with self-assembled Ge(Si) nanoislands are reported. The experimentally observed enhancement of the photoluminescence-signal intensity of the nanoislands in the spectral range 1.1–1.6 μm due to interaction with the radiative modes of photonic crystals in the vicinity of the Γ point of the Brillouin zone and the effect of such interaction on the probability of radiative recombination in Ge(Si) nanoislands are considered.

Sensing improvement of 1D photonic crystal sensors by hybridization of defect and Bloch surface modes

There are enormous efforts to make new optical sensors based on photonic crystals with improved features. In this paper, we utilize the coupling behavior of two different localized modes of a one-dimensional photonic crystal to promote the sensing performance of sensors based on Bloch surface waves. Defect modes are appeared by embedding a periodic Dirac semimetal material-Dielectric layers into a one-dimensional photonic crystal. The dispersion relations of surface and the defect modes are obtained using the transfer matrix method. The hybridization of the defect and surface modes are examined and optimized by the period number and also the position of the defect layers, physical parameters of Dirac semimetal and the distance of defect layers from the prism. The sensing characteristics are studied under the Kretschmann configuration with the reflectance spectrum. The Bloch surface waves are excited in Kretschmann configuration and the sensing characteristics such as the angular sensitivity and the figure of merits are investigated by the reflection spectrum changes. The results reveal that foregoing parameters have great influences on the sensor performances. Besides, the results are compared with those of the structures with ordinary periodic dielectric- dielectric layers (no Dirac semimetal). Considerable improvement of sensor performance is achieved in these structures and consequently, our findings can be present promising applications of Bloch surface wave based sensors.

Photonic crystal surface mode imaging for multiplexed and high-throughput label-free biosensing

A photonic crystal surface mode imaging (PCSMi) technique is implemented for the simultaneous detection of antibody binding with specific antigens in arrays containing 96- and 384-spots. Like the surface plasmon resonance imaging (SPRi) technique, the presented approach is label-free and permits interrogating an analyte by hundreds of different ligands immobilized in small spots. The adsorption kinetics is recorded with a sub-picogram resolution at every spot simultaneously. Possible implementations of this technique for multiplexed and high-throughput biosensing are discussed.

Band characterization of topological photonic crystals using the broadband Green's function technique.

A novel method is developed in this paper to characterize the band diagram and band modal fields of gyromagnetic photonic crystals that support topological one-way edge states. The proposed method is based on an integral equation formulation that utilizes the broadband Green's function (BBGF). The BBGF is a hybrid representation of the periodic lattice Green's function with imaginary extractions that has accelerated convergence and is suitable for broadband evaluations. The effects of the tensor permeability of the gyromagnetic scatterers are incorporated in a new formulation of surface integral equations (SIEs) with BBGF as the kernel that can be solved by the method of moments. The results are compared against Comsol simulations for various cases to demonstrate the accuracy and efficiency of the proposed method. Simulations results are illustrated and discussed for the modes of topological photonic crystals in relation to the physics of degeneracy, applied magnetic fields, and bandgaps.

Controlling the band structures and electromagnetic density of modes in one-dimensional photonic crystals with Lamb wave

We have modeled and investigated band structures and the electromagnetic density of modes in one-dimensional photonic crystal whose refractive index is modulated by the excitation of the fundamental symmetric mode of Lamb wave using the Wigner phase time approach and transfer matrix method. The Rayleigh–Lamb dispersion curves are plotted to select the proper thickness of each sub-layer of considered photonic crystal structure which is comprised of silica (SiO2) and rutile (TiO2) layers as sub-layers of unit cell. The propagation of Lamb wave into the considered structures produced phononic band gaps in gigahertz frequency for acoustic waves. Also, the propagation of Lamb wave into the considered structures causes compression in SiO2 and dilation in TiO2 or vice versa, which can further increase or decrease the refractive index of both layers. Thus, there can be three combinations of change in refractive indices: case 1 (both layers have an unperturbed refractive index), case 2 (maximum change of the refractive index in SiO2 and minimum change in the refractive layer of TiO2), and case 3 (minimum change of the refractive index in SiO2 and maximum change in the refractive layer of TiO2). The band gap structures of considered structures are plotted for both polarized electromagnetic waves.

Enhancement of the Luminescence Signal from Self-Assembled Ge(Si) Nanoislands due to Interaction with the Modes of Two-Dimensional Photonic Crystals

The results of studies of the luminescence properties of two-dimensional photonic crystals formed on the basis of silicon structures with self-assembled Ge(Si) nanoislands are reported. The possibilities of substantially enhancing the luminescence response of the active medium (Ge(Si) nanoislands) in the wavelength range 1.2–1.6 μm are shown for such structures. The specific features of the luminescence response of a photonic crystal in the vicinity of the Γ point of its Brillouin zone are studied. It is shown that, along with the broadband response characteristic of the radiative modes of photonic crystals, high-Q resonances, for which the Q factor exceeds 103, can also be observed in such structures. The last-mentioned resonances are observed in a certain range of lattice parameters of photonic crystals.

Tuning the chiral edge states and unidirectional transmission by surface morphology of gyromagnetic photonic crystal

Though topologically protected one-way edge states are determined by the bulk mode of the magnetic photonic crystal (MPC), the edge profile can influence topological edge states and associated wave propagation since the waves at the states are localized at the edge of the photonic crystal. By truncating the honeycomb structured MPC at the same side but at different cuts, we show the MPC slab will present different topological edge band, and the associate transmission of a one-way surface wave will change a lot. We demonstrate the good transmission efficiency of the one-way surface wave needs a good field localization at the edge of MPC at the topological edge states, and bearded edge has better field localization ability than the zigzag one in a wider frequency range. In addition to the different cuts, one can modify the topological edge state by tuning the radius of outmost rods of the slab or the material parameters of the rods, which does not affect the topological state of the MPC. Our study provides an effective means to improve the performances of the devices based on topological edge states of the materials, such as one-way waveguide.

Polariton Modes in Two-Dimensional Dispersive and Absorptive Photonic Crystals

Two-dimensional photonic crystals play important role in practical photonic devices. In this study, Hamiltonian method is used to determine the evolution equations for the fields. This method allows us to determine the polariton modes inside a periodically structured medium. For a two-dimensional photonic crystal, the Hamiltonian for electromagnetic field interaction with structured medium is constructed and the evolution equations for fields are determined from Hamilton’s equations of motion. The polariton modes are found from the canonical form of the Hamiltonian.

Topological charge of finite-size photonic crystal modes

Topological charges are the winding numbers of polarization vectors around the vortex centers of far-field radiation. In this work, the topological charge of photonic crystal modes is theoretically analyzed using an envelope function approach. A group of modes is discovered with unique polarization properties dictated by their non-trivial envelope functions. Experimentally, lasing operation on such mode is demonstrated in an electrically pumped mid-infrared photonic crystal surface-emitting laser with high slope efficiency. The topological charge is directly observed from the polarization properties of single-mode laser emission.

Topologically protected defect modes in all-dielectric photonic crystals

Inspired by the studies of topological materials, topological edge states—striking examples that support robust energy transport in photonic systems—have enriched condensed matter physics. Here we propose all-dielectric photonic crystals manipulating topologically protected defect modes at the edge of the configuration, which is distinct from previous platforms where helical edge states were excited at the interface between trivial and nontrivial crystals. The localization of frequency dispersion of one-way propagating defect modes is measured. Topological protection gives rise to the pseudospin-dependent transport and robustness against perturbations. Our proposal that enables one-way defect modes is promising for benefitting the microminiaturization and application of photonic topological structures.