Symmetric Gratings Research Articles

Numerical investigation of an anti-symmetric nanophotonic structure for accelerating sub-relativistic electron beams

This study investigates an anti-symmetrically positioned nanophotonic dual-pillar structure, in which the dielectric and vacuum components are evenly distributed along the direction of electron propagation, with each dielectric pillar facing a vacuum region. Our numerical simulation results show that the previously proposed symmetric dielectric grating structure, where dielectric pillars facing each other are alternated with vacuum gaps, is accompanied by a deceleration region, preventing the achievement of high gradients during the acceleration process. By contrast, the anti-symmetric grating structure eliminates the deceleration field and generates a uniformly distributed acceleration field. This requires that the two oppositely directed laser beams crossing the structure in the transverse region must have a phase shift of π in the anti-symmetric case. This structure has significant potential for accelerating sub-relativistic electron beams. In this numerical simulation, the initial energy of the sub-relativistic electron beams is selected as 79 keV. The acceleration gradient provided by the symmetric design for sub-relativistic electrons is approximately 70 MeV/m; however, the anti-symmetric structure can provide a maximum acceleration gradient of up to ∼430 MeV/m.

Broken phase of parity-time symmetry enables efficient superluminal pulse transmission

Parity-time (PT) symmetric Bragg gratings (PTBGs) exhibit unique band characteristics compared to their traditional counterparts. Notably, when the PT symmetry is broken, the initial bandgap closes, and the upper and lower branches coalesce. We demonstrate that this believed to be novel band dispersion supports fast light, also known as the optical superluminality. A light pulse can propagate through a fiber PTBG with broken PT symmetry, achieving high transmission efficiency (comparable to, and even exceeding, unity) while maintaining its Gaussian shape. This effect offers a significant advantage over superluminal tunneling, where the transmission coefficient is typically very small. We also analyze the transmission of optical precursors and show that they cannot be superluminal, consistent with the principle of causality. This work presents a mechanism for realizing superluminality with some possible applications and underscores the vast potential of non-Hermitian optics.

Spacing mode multi-wavelength erbium doped fiber laser based on a symmetrical long-period fiber grating

We present a multiwavelength erbium-doped fiber laser based on a symmetrical long-period fiber grating (LPFG) with tunable spacing mode between single lasing mode and multiwavelength spectra. The LPFG was manufactured using a thermal expansion technique using an LZM-100 glass processing system equipped with a CO2 laser, and it was used as a wavelength-selective filter (WSF) in the laser ring cavity. The laser can emit single, double, triple, quadruple, quintuple, or sextuple lines in the range from 1546 to 1563 nm, which can be tunable by controlling the radius of curvature of the LPFG in the range 0–0.2662 m −1. A minimal spacing mode of 1.92 nm was observed in the multiwavelength region; meanwhile, the fiber laser offers an average spacing mode of 6.945 nm between the multiwavelength region and the single emission. This laser has a 3 dB linewidth of 0.11 nm and a side mode suppression ratio (SMSR) of 55.56 dB. Finally, according to experimental results, the laser has high wavelength stability at room temperature for 88 min.

On obtaining the coupled-mode theory using a model of coupled plane waves for symmetric resonant diffraction gratings

We consider two analytical models describing resonant scattering of light by resonant diffraction gratings possessing a horizontal symmetry plane. For the case of oblique incidence, a multiple interference model is formulated, on the basis of which, a new approach for deriving the coupled-mode theory for the considered structures is proposed. Both considered models describe resonances in the reflectance and transmittance spectra of the studied diffraction gratings arising due to the excitation of quasiguided modes and Fabry–Pérot modes. Interaction of these modes leads to the appearance of bound states in the continuum, which are also described by the proposed models.

Superluminality in parity-time symmetric Bragg gratings

Parity-time ( PT ) symmetric Bragg gratings (PTBGs) possess unique features compared to traditional ones. For example, the photonic bandgap of a PTBG can be modified and even closed when the PT symmetry evolves from an exact phase to a broken one, and the complex reflection coefficient of a PTBG is sensitive to the direction of incidence. In this article, we reveal how the superluminal effects of transmission behave following the modified band structure of PTBGs. The superluminality of the directionally sensitive reflection is also discussed. We then investigate the Hartman effect and argue that, to account for the superluminal effects in PTBGs, a directionally sensitive dwell time should be applied. This study offers unique insights into the mechanisms of superluminality and group delay of light in non-Hermitian open systems and contributes to the advancement of PTBGs, which can eventually become an indispensable platform for probing some of the exotic properties of optical wave phenomena and light–matter interactions.

Improved optical contrast of plasmonic phase change memory using a Fabry-Perot cavity

As a promising technology to realize multilevel, non-volatile data storage and information processing, optical phase change technologies have attracted extensive attention in recent years. However, existing phase-change photonic devices face significant challenges such as limited switching contrast and high switching energy. This study introduces an innovative approach to tackle these issues by leveraging Fabry-Perot (F-P) cavity resonance and plasmon resonance techniques to enhance the modulation effect of phase change materials (PCMs) on the light. To the best of our knowledge, a novel device structure is proposed, featuring an elliptic nano-antenna placed on an F-P cavity waveguide composed of symmetric Bragg grating. This design exploits the enhanced electric field to achieve low power consumption and high contrast. The device enables crucial functions, including read, write, and erase operations, under all light conditions. Through the synergistic utilization of plasma and F-P cavity effects, an ultra-high switching contrast of around 70.6% is achieved. By varying the pulse power or duration, the proportion between the crystalline and amorphous states of the PCMs is altered, consequently modifying its refractive index. With its wide range of applications in optical storage and computing, the device holds significant potential for advancing these fields.

Ultra low-power multistability in [formula omitted]-symmetric periodic structures with saturable coupling, gain and loss

The present work investigates the switching dynamics of conventional fiber Bragg gratings (FBGs) with saturable coupling and parity-time (PT)-symmetric fiber Bragg gratings (PTFBGs) with saturable coupling (SC) and saturable gain-loss (SGL) in the presence of Kerr nonlinearity (KNL) [model - I] and saturable nonlinearity (SNL) [model - II]. Both system models can generate distinct optical multistability (OM) and bistability (OB) curves, including S-shaped, ramp-like, and mixed OM curves in both unbroken and broken PT-symmetric regimes. The impact of each control parameter on controlling switching intensities, hysteresis width, and the number of stable states is thoroughly examined for both of these system models. The direction of right light incidence enables a significant reduction in the switching intensities to below 100 W/cm2, the lowest critical power ever reported in the literature of PTFBGs, thanks to the concept of both saturable coupling, gain and loss.

The study on application of high-order tilted asymmetric Bragg gratings in quantum cascade lasers

High-order gratings eliminate the need for high-resolution lithography in the definition process. However, they are not widely adopted due to inability to provide sufficient coupling coefficients in long-wave mid-infrared quantum cascade lasers (QCLs). Fifth order tilted asymmetric gratings (TAS-gratings) distributed feedback (DFB) QCLs with stable single longitudinal mode are firstly reported in this paper. TAS-gratings exhibit longitudinal mode selection capability across a broad range of asymmetric distances around 1.18 μm and duty cycles around 0.5, which is attributed to their larger effective duty cycles and phase differences caused by an 18° tilt angle of the grating in the middle and two asymmetrical distributions of gratings on both sides. Further experimental results indicate that DFB QCLs with TAS-gratings exhibit stable excitation of single longitudinal modes within the duty cycle range of 0.48–0.54 due to the large coupling coefficients, the temperature drift coefficient of 0.29 nm/K of TAS-grating device is reduced by 64% compared with symmetric gratings (S-gratings) devices, the maximum side-mode suppression ratio (SMSR) of the devices exceeds 25 dB. TAS-gratings offer greater process tolerance, design flexibility and lower preparation difficulty. This study provides a solution to achieve sufficiently large coupling coefficients for high-order gratings applied to long-wave mid-infrared QCLs.

Rigorous coupled-wave analysis of unilateral Smith-Purcell radiation from asymmetric resonators.

The Smith-Purcell radiation produced by electrons moving closely to a grating can be enhanced by resonances. Here, we show a method to manipulate the directionality of the resonance-enhanced radiation. Using the rigorous coupled-wave analysis method, we compare the radiation from symmetric and asymmetric gratings, showing that the enhanced Smith-Purcell radiation can become unilateral with a perturbation that breaks the structural symmetry. Our work provides an effective method for frequency-domain calculation of Smith-Purcell radiation and also an approach to realize more efficient use of the radiation.

Reflection performance of the Au/Cr asymmetrical grating under electric and magnetic fields

Symmetric grating is difficult to meet the requirements of optical communication, optical sensing, and solar cells, as the strictly integrating performance of the transmission or reflection efficiency, polarization, incident angle, and bandwidth. The asymmetrical grating is introduced to improve the performance of the optical devices. Here, the polarization properties, and spatial displacement of the P- and S- laser beams reflected from the Au/Cr asymmetrical grating under electric and magnetic fields are studied. The Goos-Hänchen (GH) shifts of the P-laser beam show dumbbell distribution. The GH shifts of the S-laser beam can be affected by the external direct current and magnetic field. The maximum GH and Imbert-Fedorov (IF) shifts of the P-laser beam are 15.75 µm and 35.10 µm, respectively. The maximum GH and IF shifts of the S-laser beam are 88.40 µm and 121.00 µm, respectively. The Au/Cr asymmetrical grating can be applied in polarization optics, magnetic sensors, electric sensors, and light manipulation.

High‐Contrast Switching of Light Enabled by Zero Diffraction

Diffraction allows to change the direction of light. Therefore, controlling the diffraction efficiency with high contrast enables controlling the pathway of light within optical systems. However, a high contrast requires that the diffraction efficiency is tunable close to zero. Probably the most prominent example for zero diffraction in a waveguide grating is a bound state in the continuum (BIC). Herein, zero diffraction of two plane waves under symmetric incidence to a leaky symmetric waveguide grating is found. The phenomenon not only occurs at singular spectral positions but on continuous curves in the energy–momentum space. The relative phase of the two waves enables large contrast control over diffraction in a wide spectral range. The practical meaning of this finding for local switching is demonstrated. Light is trapped into a nonlinear optical waveguide and detrapped at a desired position with electric control. A switching contrast exceeding 1000 is experimentally shown.

A method to achieve spectral beam combining based on a novel symmetric grating

A symmetric grating is proposed to obtain higher output power in spectral beam combination by increasing the number of lasers and spectral utilization. The grating allows laser beams to be incident from both sides of the grating normal to achieve coaxial beam combining, so the number of beams and the combined output power are doubled compared with the traditional grating under the same spectral line-width. The grating is designed with the central wavelength of 4.65 μm, and the calculation results show that this grating is very advantageous for spectral beam combining, especially for the light waves in the range 4.55–4.71 μm, where their diffraction efficiencies are high (over 80%) and correspond to a wide and linear range of incidence angles. Meanwhile, based on the symmetric gratings we further propose a circular grating to achieve the same frequency spectral beam combining. This beam combining design will not increase the laser spectral line width while enhancing the laser power, reducing the requirements for the unit laser spectral line width, which is very meaningful in some application fields and will further enrich the research of spectral beam combining.

Enhanced higher-order modulational instability in a parity–time-symmetric fiber Bragg grating system with modified saturable nonlinearity

With the use of cubic, quintic, and septic nonlinearities, we demonstrate the influence of modified nonlinear saturation on modulational instability (MI) in a nonlinear complex parity–time (PT)-symmetric fiber Bragg grating (FBG) structure. Using a modified coupled nonlinear Schrodinger equation and linear stability analysis, we derive a dispersion relation for instability gain spectra in a complicated PT-symmetric system. Our main aim is to examine the MI in non-Kerr nonlinearities with nonlinear saturation in three PT-symmetric regimes: below threshold point, at threshold point (breaking point), and above threshold point. The occurrence of MI is known to be problematic at the PT-symmetry threshold point in a standard FBG structure (A.K. Sharma, 2014). At the same time, MI can exist in the normal group velocity dispersion domain when the modified nonlinear saturation effect is used. With the help of a modified form of saturable nonlinearity, we discovered that MI could exist in all three regimes in a complex PT-symmetric FBG structure. In anomalous group velocity dispersion alone, we found bistability behavior in a PT-symmetric FBG structure with higher-order saturable nonlinearity. In the presence of a modified nonlinear saturation effect and higher-order non-Kerr nonlinearities, we found a novel type of dynamics in the PT-symmetric FBG structure. All alterations in the photonic device bandgap directly result from changes in the refractive index of the medium caused by the interaction of PT-symmetric potential with the cubic–quintic–septic and modified form of nonlinear saturation. As a result, we provide approaches for generating and managing the MI in a complex PT-symmetric FBG structure under the influence of the modified nonlinear saturation effect.

Double-layer symmetric gratings with bound states in the continuum for dual-band high-Q optical sensing.

Herein, we theoretically demonstrate that a double-layer symmetric gratings (DLSG) resonator consisting of a low-refractive-index layer sandwiched between two high-contrast gratings (HCG) layers, can host dual-band high-quality (Q) factor resonance. We find that the artificial bound states in the continuum (BIC) and Fabry-Pérot BIC (FP-BIC) can be induced by optimizing structural parameters of DLSG. Interestingly, the artificial BIC is governed by the spacing between the two rectangular dielectric gratings, while the FP-BIC is achieved by controlling the cavity length of the structure. Further, the two types of BIC can be converted into quasi-BIC (QBIC) by either changing the spacing between adjacent gratings or changing the distance between the upper and lower gratings. The simulation results show that the dual-band high-performance sensor is achieved with the highest sensitivity of 453 nm/RIU and a maximum figure of merit (FOM) of 9808. Such dual-band high-Q resonator is expected to have promising applications in multi-wavelength sensing and nonlinear optics.

Plasmonic Surface Lattice Resonances in Suspended Symmetric Double-Layer Gratings

Surface lattice resonances (SLRs) with high-quality factors supported by metal nanoparticle arrays are useful for plasmonic nanolasers, biochemical sensors, and surface-enhanced Raman spectroscopy. Most nanoparticle arrays are fabricated on a substrate, and the refractive index mismatch between the substrate and superstrate suppresses the performance of SLRs. In this work, we propose unique SLRs excited in suspended, self-aligned symmetric double-layer gratings with index-matched environment. The self-aligned double-layer gratings are fabricated using a single-step electron beam lithography and exhibit a Fano-like spectra resulting from interference between out-of-plane plasmonic resonances and diffraction modes. By changing the incident angle and refractive index of the surrounding medium, the SLRs can be tuned from visible to near-infrared regions with a high-quality factor of 120.

Inhomogeneous nonlinearity meets parity–time-symmetric Bragg structures: route to ultralow power steering and peculiar stable states

In the context of parity–time ( P T )-symmetric fiber Bragg gratings, tailoring the nonlinear profile along the propagation coordinate serves as a new direction for realizing low-power all-optical switches. The scheme is fruitful only when the nonlinearity profile will be either linearly decreasing or increasing form. If the rate of variation of the nonlinearity profile is high, the critical intensities fall below the input power of value 0.01 in the unbroken regime provided that the light launching direction is right. Nowadays, every new theoretical inception into the parity–time fiber Bragg grating (PTFBG) has started making sense of switching in the broken P T -symmetric regime, which was once believed to be the instability regime. When the inhomogeneous nonlinearity acts together with the broken P T symmetry and right light incidence, it leads to two peculiar settings. First, the switch-up intensities are ultralow. Second, the switch-down action takes place at zero critical intensities. Such optical bistability curves are unprecedented in the context of conventional gratings and found only in plasmonic devices and anti-directional couplers. Even though the nonlinearity is inhomogeneous, the ramp-like first stable states persist in the broken P T -symmetric regime, giving an additional indication that the broken PTFBG is closely associated with the plasmonic structures. In the existing PTFBG systems, the switching intensities are relatively higher in the broken regime. However, the proposed system records the lowest switching intensities in the broken regime. The reported intensities ( < 0.005 ) are also the lowest-ever switching intensities recorded in the perspective of PTFBGs to date.

Linear and nonlinear Bragg diffraction by electromagnetically induced gratings with PT symmetry and their active control in a Rydberg atomic gas

Due to its myriad applications in many fields of science and technology, novel light diffraction from specially designed optical gratings is a subject of great interest. Here, we propose a scheme to realize the linear and nonlinear Bragg diffractions from an electromagnetically induced grating (EIG) with parity-time $(\mathcal{PT})$ symmetry in a cold Rydberg atomic gas, where the Rydberg-Rydberg interaction between atoms are mapped to strong and long-range interaction between photons, characterized by a giant nonlocal Kerr nonlinearity. We show that a probe laser beam with very low light intensity incident upon the $\mathcal{PT}$-symmetric EIG can display distinctive asymmetric diffraction patterns, which can be actively manipulated through tuning the gain-absorption coefficient of the EIG and the input power of the laser beam. We also show that the intensity distribution among different diffraction orders depends significantly on the $\mathcal{PT}$-symmetry property of the EIG and on the magnitude and nonlocality degree of the Kerr nonlinearity. In addition, we demonstrate that such Bragg diffraction patterns can be controlled by an external gradient magnetic field, which provides a different way of diffraction control. The research results reported here are not only useful for understanding the unique properties of linear and nonlinear Bragg diffractions by $\mathcal{PT}$-symmetric gratings but may also be promising for designing optical devices applicable in optical information processing and transmission.

Flat-top filter using slanted guided-mode resonance gratings with bound states in the continuum

The attribute of bound states in the continuum (BICs) for highly efficient flat-top filter by using a slanted guided-mode resonance (GMR) grating is developed in this work. By introducing a slanted angle θ, the fully symmetric grating is broken to transform the dark BICs into bright quasi-BICs mode. Theoretical analysis based on the finite-different time-domain method is applied to evaluate the filtering performances. It is found that the GMR and quasi-BICs peaks combine at θ=31.4°, and the flat-top filtering response is realized at the central wavelength of 1550 nm under normal incidence. Moreover, the linewidth-tunable and central wavelength-tunable spectral response can be varied according to the change in the coupling strength of the GMR grating by changing the structural parameters such as period, fill factor and refractive index of the grating. It is the first report of a flat-top filter designed by combining GMR and quasi-BICs. The proposed structure shows promise for application in high-performance optical communication systems.

High- Q Surface Light Emission from Active Parity-Time-Symmetric Gratings

This work presents a theoretical investigation of an active photonic grating of the parity-time- ($PT$) symmetric architecture. The analytical study of the free-space mode propagation from the grating structure indicates the unique bifurcation property due to the $PT$-symmetry modulation. It is shown that both the gain-loss contrast and the lattice constant parameters are critical factors to modulate the active photonic system in between the $PT$-symmetry to the symmetry-broken phases. Furthermore, numerical simulations via the rigorous coupled-wave analysis (RCWA) method discover the existence of a unique spectral singularity phenomenon in this $PT$ grating structure, which corresponds to a nontrivial single mode and near-zero bandwidth photonic resonant emission. Also, the guiding procedure for fulfilling spectral singularity modes is found to be related to the unique formation of the scattering matrix applied in the $PT$-symmetric photonic gratings. This theoretical work takes a fresh look into the active $PT$-symmetric photonic gratings focusing on the discovery of nontrivial free-space emission modes, which could contribute to the development of high-performance surface-emitting semiconductor devices.

Two-dimensional electromagnetically induced phase grating via composite vortex light

We investigate the performance of a symmetrical two-dimensional electromagnetically induced grating produced in a four-level $N$-type atomic scheme, which interacts with a weak probe field and two simultaneous coupling fields: a two-dimensional standing wave and a composite optical vortex beam. Based on the Maxwell wave equation, we study numerically the behavior of the amplitude, the phase modulations, as well as the probe field diffraction intensities of different order under various conditions for the coupling field detunings and the orbital angular momentum of the Laguerre-Gaussian field. The different orders of diffraction are altered when the azimuthal angle of the composite vortex light changes, thus producing a two-dimensional symmetric grating which transfers the probe energy to higher orders of diffraction. A detailed analysis of the probe field energy transfer to these different orders proves the possibility for direct control over the performance of the grating.