Front Cover Picture: Laser & Photon. Rev. 7(2)/2013

Nonlinear propagation of light in a graphene monolayer is studied theoretically. In this article, it is shown how the large intrinsic nonlinearity of graphene at optical frequencies enables the formation of quasi one‐dimensional self‐guided beams (spatial solitons) featuring subwavelength widths at moderate electric‐field peak intensities. A novel class of nonlinear self‐confined modes resulting from the hybridization of surface plasmon polaritons with graphene optical solitons is also demonstrated. (Picture:M. L. Nesterov et al. dx.doi.org/10.1002/lpor.201200079 , pp. L7–L11, in this issue)     

Gap Solitons in Fractional Dimensions With a Quasi‐Periodic Lattice

The existence and stability of gap solitons in the nonlinear fractional Schrödinger equation are investigated with a quasi‐periodic lattice. In the absence of nonlinearity, the exact band‐gap spectrum of the proposed system is obtained, and it is found that the spectrum gap size can be adjusted by the sublattice depth and the Lévy index. Under self‐defocusing nonlinearity, both in‐phase and out‐of‐phase gap solitons have been searched in the first four gaps. It is revealed that in‐phase gap solitons are generally stable in wide regions of their existence, whereas stable out‐of‐phase gap solitons can only exist in the fourth spectrum gap. Linear stability analysis of gap solitons is in good agreement with their corresponding nonlinear evolutions in fractional dimensions. The presented numerical findings may lead to interesting applications, such as transporting of light beams through the optical medium, and other areas connected with the Kerr effect and fractional effect.     

Dissipative plasmon‐solitons in multilayer graphene

Nonlinear properties of a multi‐layer stack of graphene sheets are studied. It is predicted that such a structure may support dissipative plasmon‐solitons generated and supported by an external laser radiation. Novel nonlinear equations describing spatial dynamics of the nonlinear plasmons driven by a plane wave in the Otto configuration are derived and the existence of single and multi‐hump dissipative solitons in the graphene structure is predicted.     

Spatial optical (2+1)‐dimensional scalar‐ and vector‐solitons in saturable nonlinear media

(2+1)‐dimensional optical spatial solitons have become a major field of research in nonlinear physics throughout the last decade due to their potential in adaptive optical communication technologies. With the help of photorefractive crystals that supply the required type of nonlinearity for soliton generation, we are able to demonstrate experimentally the formation, the dynamic properties, and especially the interaction of solitary waves, which were so far only known from general soliton theory. Among the complex interaction scenarios of scalar solitons, we reveal a distinct behavior denoted as anomalous interaction, which is unique in soliton‐supporting systems. Further on, we realize highly parallel, light‐induced waveguide configurations based on photorefractive screening solitons that give rise to technical applications towards waveguide couplers and dividers as well as all‐optical information processing devices where light is controlled by light itself. Finally, we demonstrate the generation, stability and propagation dynamics of multi‐component or vector solitons, multipole transverse optical structures bearing a complex geometry. In analogy to the particle‐light dualism of scalar solitons, various types of vector solitons can ‐ in a broader sense ‐ be interpreted as molecules of light.     

BaTiO3晶体中光束自陷的理论研究

对聚焦光束通过有一定外加电场ＢａＴｉＯ３晶体时的自陷现象进行了理论分析，发现在正切割晶体中观察空间孤子是不合适的，因仅利用了很微小的电光系数γ３３。对异型切割情况进行了讨论，给出了维持光束自陷的外加电场范围和实际观察的最佳角度。     

Ultra‐short and ultra‐intense X‐ray free‐electron laser single pulse in one‐dimensional photonic crystals

The propagation within a one‐dimensional photonic crystal of a single ultra‐short and ultra‐intense pulse delivered by an X‐ray free‐electron laser is analysed with the framework of the time‐dependent coupled‐wave theory in non‐linear media. It is shown that the reflection and the transmission of an ultra‐short pulse present a transient period conditioned by the extinction length and also the thickness of the structure for transmission. For ultra‐intense pulses, non‐linear effects are expected: they could give rise to numerous phenomena, bi‐stability, self‐induced transparency, gap solitons, switching, etc., which have been previously shown in the optical domain.     

一维标量光折变大光强、饱和光强空间灰孤子

推导出了光折变空间灰孤子在大光强和饱和光强条件下所满足的非线性波方程,并进行了数值求解,给出了大光强和饱和光强一维标量光折变灰孤子的复振幅空间分布。     

Solitons in a system of coupled graphene waveguides

Propagation of extremely-short optical pulses that can be considered as discrete solitons in a system of graphene waveguides has been studied. The effective equation having the form of an analog of the classical sin-Gordon equation has been derived. The effects observed with varying the initial pulse width have been investigated     

Broadband 10 Gb/s operation of graphene electro‐absorption modulator on silicon

High performance integrated optical modulators are highly desired for future optical interconnects. The ultra‐high bandwidth and broadband operation potentially offered by graphene based electro‐absorption modulators has attracted a lot of attention in the photonics community recently. In this work, we theoretically evaluate the true potential of such modulators and illustrate this with experimental results for a silicon integrated graphene optical electro‐absorption modulator capable of broadband 10 Gb/s modulation speed. The measured results agree very well with theoretical predictions. A low insertion loss of 3.8 dB at 1580 nm and a low drive voltage of 2.5 V combined with broadband and athermal operation were obtained for a 50 μm‐length hybrid graphene‐Si device. The peak modulation efficiency of the device is 1.5 dB/V. This robust device is challenging best‐in‐class Si (Ge) modulators for future chip‐level optical interconnects.     

Efficient Integrated Graphene Photonics in the Visible and Near‐IR

Graphene photonics has emerged as a promising platform for providing desirable optical functionality. However, graphene's monolayer‐scale thickness fundamentally restricts the available light matter interaction, posing a critical design challenge for integrated devices, particularly in wavelength regimes where graphene plasmonics is untenable. While several plasmonic designs have been proposed to enhance graphene light interaction in these regimes, they suffer from substantial insertion loss due to metal absorption. Here we report a non‐resonant metamaterial‐based waveguide platform to overcome the design bottleneck associated with graphene device. Such metamaterial structure enables low insertion loss even though metal is being utilized. By examining waveguide dispersion characteristics via closed‐form analysis, it is demonstrated that the metamaterial approach can provide optimized optical field that overlaps with the graphene monolayer. This enables graphene‐based integrated components with superior optical performance. Specifically, the metamaterial‐assisted graphene modulator can provide 5‐fold improvement in extinction ratio compared to Si nanowire, while reducing insertion loss by one order magnitude compared to plasmonic structures. Such a waveguide configuration thus allows one to maximize the optical potential that graphene holds in the telecom and visible regimes.     

Reduction of Soliton Interaction in Distributed Erbium-Doped Fiber Amplifiers

Methods of reducing the soliton interaction in distributed erbium-doped fiber amplifiers have been studied. The results show: if the optical phase conjugation is applied in proper periodic length, input relative phase between two solitons, and non-equal amplitude input is chosen, the soliton-soliton interaction and soliton self frequency shift can be deleted effectively.     

Polarization‐independent absorption enhancement in a graphene square array with a cascaded grating structure

The polarization‐independent enhanced absorption effect of graphene in the near‐infrared range is investigated. This is achieved by placing a graphene square array on top of a dielectric square array backed by a two‐dimensional multilayer grating. Total optical absorption in graphene can be attributed to critical coupling, which is achieved through the combined effect of guided‐mode resonance with the dielectric square array and the photonic band gap with the two‐dimensional multilayer grating. To reveal the physical origin of such a phenomenon, the electromagnetic field distributions for both polarizations are illustrated. The designed graphene absorber exhibits near‐unity polarization‐independent absorption at resonance with an ultra‐narrow spectrum. Moreover, the polarization‐independent absorption can be tuned simply by changing the geometric parameters. The results may have promising potential for the design of graphene‐based optoelectronic devices.     

Dissipative soliton operation of an ytterbium-doped fiber laser mode locked with atomic multilayer graphene

Mode locking of an ytterbium-doped fiber laser with atomic multilayer graphene is, to the best of our knowledge, experimentally demonstrated for the first time. Dissipative solitons with duration of 580 ps at 1069.8 nm were generated. Since graphene can also be used to mode lock erbium-doped fiber lasers, our result shows that graphene indeed has wavelength-independent saturable absorption, which could be exploited to mode lock fiber lasers with various operating wavelengths.     

Temporal behaviour of open-circuit photovoltaic solitons

Based on the time-dependent band-transport model in a photorefractive medium, dark open-circuit photovoltaic (PV) solitons are investigated both theoretically and experimentally. Compared with those of the time-independent models, our theoretical results revealed that quasi-steady-state and steady-state PV solitons can both be obtained. Our results also revealed that when r < 1 (r is the normalized intensity at infinity), the full width at half maximum (FWHM) of solitons decreases monotonically to a constant value; when r > 1, however, the FWHM of solitons first decreases to a minimum before it increases to a constant value. Moreover, the FWHM of steady solitons decreases with increasing intensity ratio for r < 1, and increases with increasing intensity ratio for r > 1. We further observed dark PV solitons in experiments, and recorded their evolution. These results indicated that steady solitons can be observed at low optical power, while quasi-steady-state solitons can only be generated at higher optical power. Good agreement is found between theory and experiment.     

Tunable n‐ and p‐type doping of single‐layer graphene by engineering its interaction with the SiO2 support

We report a technique to tune the excess charge concentration in single‐layer graphene from p‐ to n‐type up to densities of |n | ～ 1.2 × 10¹³ cm^–2, corresponding to a displacement electric field of ～2.5 V/nm. The tuning is achieved by engineering the interaction between graphene and the underlying Si/SiO₂ substrate with an amino group‐terminated self‐assembled monolayer, and subsequent rinsing in aqueous solutions at controlled pH. Raman spectroscopy and electrical measurements on treated graphene devices confirm the occurrence of doping. Interestingly, we found the field‐effect mobility not to be significantly affected by the procedure. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Large‐Scale Modulation of Left‐Handed Passband in Hybrid Graphene/Dielectric Metasurface

Large‐scale modulation of the left‐handed transmission with a high quality factor is greatly desired by high‐performance optical devices, but the requirements are hard to be satisfied simultaneously. This paper presents a hybrid graphene/dielectric metasurface to realize a large transmission modulation for the left‐handed passband at near‐infrared frequencies via tuning the Fermi energy of graphene. By splitting the nanoblocks, i.e. introducing an additional symmetry breaking in the unit cell, the metasurface demonstrates an ultrahigh quality factor (Q ≈ 550) of Fano resonance with near‐unity transmission and full 2π phase coverage due to the interference between Mie‐type magnetic and electric resonances, which induces the negative refraction property. Besides, the split in the nanoblock greatly enhances the local field by increasing the critical coupling area, so the light‐graphene interaction is promoted intensively. When the surface conductivity of graphene is electrically tuned, the hybrid graphene/dielectric metasurface exhibits a deep modulation of 85% for the left‐handed passband, which is robust even for the highest loss of graphene. Moreover, the simple configuration remarkably reduces the fabrication requirements to facilitate the widespread applications.     

Substrate‐Induced Synthesis of Nitrogen‐Doped Holey Graphene Nanocapsules for Advanced Metal‐Free Bifunctional Electrocatalysts

The development of efficient metal‐free electrocatalysts for oxygen electrocatalysis is of great significance for various energy conversion devices. Herein, novel nitrogen‐doped holey graphene nanocapsules (NHGNs) are reported prepared by self‐assembly of graphene oxide nanosheets on the surface of amino‐functionalized silica template and NH₃ activation with simultaneously enhanced nitrogen doping and etching of nanopores in graphene, followed by template etching. The silica template is demonstrated to show a substrate‐enhanced effect on nitrogen doping and etching of nanopores in graphene based on density functional theory calculations. Benefiting from the large surface area, unique pore distribution, and high surface functionality of nitrogen doping, the resulting NHGNs exhibit superior bifunctional electrocatalytic activity and durability for both oxygen reduction reaction and oxygen evolution reaction, which is similar to that of the commercial Pt/C and RuO₂ electrocatalysts, respectively. This work presents an advance in developing new nitrogen‐doped graphene species for highly efficient metal‐free electrocatalysis.     

Spatial solitons in an optical lattice with varying diffraction and spatially inhomogeneous nonlinearity

In this paper, we present the (1+1)-dimensional inhomogeneous nonlinear Schrödinger (NLS) equation that describes the propagation of optical waves in nonlinear optical systems exhibiting optical lattice, inhomogeneous nonlinearity and varying diffraction at the same time. A series of interesting properties of spatial solitons are found from the numerical calculations, such as the stable propagation in the a nonperiodic optical lattice induced by periodic diffraction variations and periodic nonlinearity variations. Finally, the interaction of neighboring spatial solitons in a nonperiodic optical lattice is discussed, and the results reveal that two spatial solitons can propagate periodically and separately in the optical lattice without interaction.     

Wavelet based spectral analysis of optical solitons

The propagation of solitons or a pulse or a signal through optical fibers has been a major area of research given its potential applicability in all optical communication systems. In a modern optical communication system, the transmission link is composed of optical fibers and amplifiers. This manifests in noise, clutters and distortion when the signal propagates through optical fibers, consequently affecting the capacity and performance of the optical system. The dynamics of solitons has therefore become an active field of research in nonlinear optics for couple of decades. The nonlinear Schrodinger's equation (NLSE) with log law nonlinearity governs the propagation of optical solitons through optical fibers and its dynamics. Most of the studies reveal that the optical solitons have Gaussian wave profile called Gaussons. This entails the use of wavelet techniques for the processing of optical solitons.