Graded-index Waveguide Research Articles

Resonant-light diffusion in a disordered atomic layer

Light scattering in dense media is a fundamental problem of many-body physics, which is also relevant for the development of optical devices. In this work we investigate experimentally light propagation in a dense sample of randomly positioned resonant scatterers confined in a layer of sub-wavelength thickness. We locally illuminate the atomic cloud and monitor spatially-resolved fluorescence away from the excitation region. We show that light spreading is well described by a diffusion process, involving many scattering events in the dense regime. For light detuned from resonance we find evidence that the atomic layer behaves as a graded-index planar waveguide. These features are reproduced by a simple geometrical model and numerical simulations of coupled dipoles.

Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential.

We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time ([Formula: see text])-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave propagation in graded-index optical waveguides with balanced gain and loss. We find both fundamental and multipole solitons for both focusing and defocusing signs of the saturable nonlinearity in such [Formula: see text]-symmetric waveguides. The dependence of the propagation constant on the soliton's power is presented for different strengths of the nonlinearity saturation, S The stability of fundamental, dipole, tripole and quadrupole solitons is investigated by means of the linear-stability analysis and direct numerical simulations of the corresponding (1+1)-dimensional nonlinear Schrödinger-type equation. The results show that the instability of the stationary solutions can be mitigated or completely suppressed, increasing the value of SThis article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Rogue Waves for a (2+1)-Dimensional Coupled Nonlinear Schrödinger System with Variable Coefficients in a Graded-Index Waveguide**Supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023, and 11471050, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05) and by the Fundamental Research Funds for

Studied in this paper is a (2+1)-dimensional coupled nonlinear Schrödinger system with variable coefficients, which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifier with the polarization effects. According to the similarity transformation, we derive the type-I and type-II rogue-wave solutions. We graphically present two types of the rouge wave and discuss the influence of the diffraction parameter on the rogue waves. When the diffraction parameters are exponentially-growing-periodic, exponential, linear and quadratic parameters, we obtain the periodic rogue wave and composite rogue waves respectively.

Spin-wave beam propagation in ferromagnetic thin films with graded refractive index: Mirage effect and prospective applications

Using analysis of iso-frequency contours of the spin-wave dispersion relation, supported by micromagnetic simulations, we study the propagation of spin-wave (SW) beams in thin ferromagnetic films through the areas of the inhomogeneous refractive index. We compare the transmission and reflection of SWs in areas with gradual and step variation of the SW refractive index. In particular, we show the mirage effect for SWs with narrowing SW beam width, and an application of the gradual modulation of the SWs refractive index as a diverging lens. Furthermore, we study the propagation of SWs in ferromagnetic stripe with modulated refractive index. We demonstrate that the system can be considered as the graded-index waveguide, which preserves the width of the SW beam for a long distance-the property essential for prospective applications of magnonics.

Planar polymer waveguides with a graded-index profile resulting from intermixing of methacrylates in closed microchannels

Graded-index waveguides are known to exhibit lower losses and considerably larger bandwidths compared to step-index waveguides. The present work reports on a new concept for realizing such waveguides on a planar substrate by capillary filling microchannels (cladding) with monomer solution (core). A graded-index profile is obtained by intermixing between the core and cladding material at the microchannel interface. To this end, various ratios of methyl methacrylate (MMA) and octafluoropentyl methacrylate (OFPMA) were evaluated as starting monomers and the results showed that the polymers P50:50 (50:50 MMA:OFPMA) and P0:100 (100% OFPMA) were suitable to be applied as waveguide core and cladding material respectively. Light guiding in the resulting P50:50/P0:100 waveguides was demonstrated and the refractive-index profile was quantified and compared with that of conventional step-index waveguides. The results for both cases were clearly different and a gradual refractive index transition between the core and cladding was found for the newly developed waveguides. Although the concept has been demonstrated in a research environment, it also has potential for upscaling by employing drop-on-demand dispensing of polymer waveguide material in pre-patterned microchannels, for example in a roll-to-roll environment.

An efficient method based on FIR filtering and fourier transform for solving the eigen-problems in optoelectronic devices

This paper presents a highly efficient method based on finite impulse response filtering and Fourier transform techniques to solve the eigen-problems, especially with smoothly varying inhomogeneous-core, such as solving optical eigen modes in graded-index optical waveguides and electronic eigen states in intermixed quantum wells. This type of structure is normally less efficient to be dealt with in space domain directly, but bears with a narrow spectrum in spatial frequency domain. Simulation examples show that the computation cost of the proposed method is approximately at least one order of magnitude smaller than that of the conventional finite difference method solved by the most efficient multiple relatively robust representations method.

Chirped self-similar waves for quadratic–cubic nonlinear Schrödinger equation

We have constructed analytical self-similar wave solutions for quadratic–cubic Nonlinear Schrödinger equation (QC-NLSE) by means of similarity transformation method. Then, we have investigated the role of chirping on these self-similar waves as they propagate through the tapered graded index waveguide. We have revealed that the chirping leads to interesting features and allows us to control the propagation of self-similar waves. This has been demonstrated for two cases (i) periodically distributed system and (ii) constant choice of system parameters. We expect our results to be useful in designing high performance optical devices.

Competitive Evaluation of Planar Embedded Glass and Polymer Waveguides in Data Center Environments

Optical printed circuit board (OPCB) waveguide materials and fabrication methods have advanced considerably over the past 15 years, giving rise to two classes of embedded planar graded index waveguide based on polymer and glass. We consider the performance of these two emerging waveguide classes in view of the anticipated deployment in data center environments of optical transceivers based on directly modulated multimode short wavelength VCSELs against those based on longer wavelength single-mode photonic integrated circuits. We describe the fabrication of graded index polymer waveguides, using the Mosquito and photo-addressing methods, and graded index glass waveguides, using ion diffusion on thin glass foils. A comparative characterization was carried out on the waveguide classes to show a clear reciprocal dependence of the performance of different waveguide classes on wavelength. Furthermore, the different waveguide types were connected into an optically disaggregated data switch and storage system to evaluate and validate their suitability for deployment in future data center environments.

On multi-soliton solutions for the [formula omitted]-dimensional breaking soliton equation with variable coefficients in a graded-index waveguide

In this work, we construct multi-soliton solutions of the (2+1)-dimensional breaking soliton equation with variable coefficients by using the generalized unified method. We employ this method to obtain double- and triple-soliton solutions. Furthermore, we study the nonlinear interactions between these solutions in a graded-index waveguide. The physical insight and the movement role of the waves are discussed and analyzed graphically for different choices of the arbitrary functions in the obtained solutions. The interactions between the solitons are elastic whether the coefficients of the equation are constants or variables.

Propagation of p-polarized waves in a linearly graded index film surrounded by negative index materials

The theory of step-index waveguides is well-established. Most practical slab waveguide structures have a graded-index profile. The basic properties of graded-index planar waveguide structures are similar to those of step-index waveguides with subtle differences. The most common types of graded-index slab waveguides are linearly and exponentially graded-index profiles. We here treat linearly graded-index slab waveguide. In this work, a three-layer waveguide structure with linearly graded-index film is considered. We assume three structures: the first structure comprises a left-handed material (LHM) cladding, the second structure contains a LHM substrate layer and the third has a LHM cladding and substrate. Closed-form expressions for electric and magnetic fields and the characteristic equation are derived. The three normalized parameters: the asymmetry coefficient (a), the normalized film thickness (V) and the normalized guide index (b) are used to study the dispersion properties of the proposed slab waveguide structure.

Bright–dark soliton solutions for the (2+1)-dimensional variable-coefficient coupled nonlinear Schrödinger system in a graded-index waveguide

Under investigation in this paper is the (2[Formula: see text]+[Formula: see text]1)-dimensional coupled nonlinear Schrödinger (NLS) system with variable coefficients, which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifier with the polarization effects. Through a similarity transformation, we convert that system into a set of the integrable defocusing (1[Formula: see text]+[Formula: see text]1)-dimensional coupled NLS equations, and subsequently construct the bright–dark soliton solutions for the original system which are converted from the ones of the latter set. With the graphic analysis, we discuss the soliton propagation and collision with r(t), which is related to the nonlinear, profile and gain/loss coefficients. When r(t) is a constant, one soliton propagates with the amplitude, width and velocity unvaried, while velocity and width of the one soliton can be affected, and two solitons possess the elastic collision; When r(t) is a linear function, velocity and width of the one soliton varies with t increasing, and collision of the two solitons is altered. Besides, bound-state solitons are seen.

Ge-rich graded-index Si1-xGex waveguides with broadband tight mode confinement and flat anomalous dispersion for nonlinear mid-infrared photonics.

This work explores the use of Ge-rich graded-index Si1-xGex rib waveguides as building blocks to develop integrated nonlinear optical devices for broadband operation in the mid-IR. The vertical Ge gradient concentration in the waveguide core renders unique properties to the guided optical mode, providing tight mode confinement over a broadband mid-IR wavelength range from λ = 3 µm to 8 µm. Additionally, the gradual vertical confinement pulls the optical mode upwards in the waveguide core, overlapping with the Ge-rich area where the nonlinear refractive index is larger. Moreover, the Ge-rich graded-index Si1-xGex waveguides allow efficient tailoring of the chromatic dispersion curves, achieving flat anomalous dispersion for the quasi-TM optical mode with D ≤ 14 ps/nm/km over a ~1.4 octave span while retaining an optimum third-order nonlinear parameter, γeff. These results confirm the potential of Ge-rich graded-index Si1-xGex waveguides as an attractive platform to develop mid-IR nonlinear approaches requiring broadband dispersion engineering.

Dark solitons and Bäcklund transformation for the (2+1)-dimensional coupled nonlinear Schrödinger equation with the variable coefficients in a graded-index waveguide

Under investigation in this paper is a set of the (2 + 1)-dimensional coupled nonlinear Schrödinger equations, which describes the propagation of an optical beam inside a (2 + 1)-dimensional graded-index waveguide with the polarization effects. Employing the Hirota method and symbolic computation, we obtain the dark one-, two- and N-soliton solutions under the variable-coefficient constraints. Bäcklund transformation and the corresponding soliton solutions are derived. We graphically study the dark solitons with the influence of the profile function and nonlinearity coefficient. Parallel and period solitons are observed. Amplitudes of the dark solitons increase with the profile function increasing; When the profile function is a periodic function, amplitudes of the dark solitons change periodically. Decrease of the nonlinearity coefficient leads to the larger solitons' velocities, but does not affect the solitons' amplitudes.

Butterfly-shaped and dromion-like optical waves in a tapered graded-index waveguide with variable group-velocity dispersion

Butterfly-shaped and dromion-like optical waves in a tapered graded-index waveguide (GRIN) are reported for the first time. The generalized nonlinear Schrödinger equation, which describes wave propagation in GRIN with variable group-velocity dispersion (GVD), nonlinearity, PT symmetric optical potentials, is investigated and analytical solutions for this dynamical system are obtained. The physical effects affecting these waves are explicated in detail. The stability of dromion-like structures is analyzed when the GVD parameter is perturbed. We have observed oscillation structure exhibiting strong interference due to this applied perturbation. For a particular value of the modulation of the GVD parameter, the oscillation structure is transformed into two dromion-like structures. It indicates that the dromion-like structure is unstable, and the coherence intensity is affected by the modified perturbation parameter. We further demonstrate the phenomenon of unbreakable PT symmetry of these novel nonlinear waves for three explicit examples.

Compression of optical similaritons induced by cubic-quintic nonlinear media in a graded-index waveguide

We employ the similarity reductions in two steps to obtain a family of bright and dark similaritons for the variable coefficient cubic–quintic nonlinear Schrödinger equation. Also, parameter domains are delineated in which kink and double-kink similaritons exist for this model. This methodology introduces a free parameter through cubic nonlinearity coefficient which gives us freedom to tune the amplitude and the propagation distance of similaritons in a tapered graded-index waveguide. Furthermore, we observe rapid beam compression of these similaritons for varying detuning parameter and the coefficient of cubic nonlinearity.

Vector Laguerre-Gauss beams with polarization-orbital angular momentum entanglement in a graded-index medium.

It is shown that the vector-vortex Laguerre-Gauss modes with polarization-orbital angular momentum (OAM) entanglement are the vector solutions of the Maxwell equations in a graded-index medium. Focusing of linearly and circularly polarized vortex light beams with nonzero azimuthal and radial indices in a cylindrical graded-index waveguide is investigated. The wave shape variation with distance taking into account the spin-orbit and nonparaxial effects is analyzed. The effect of long-term periodic revival of wave packets due to mode interference in a graded-index cylindrical optical waveguide is demonstrated. High efficiency transfer of a strongly focused spot through an optical waveguide over large distances takes place with a period of revival.

Spin-dependent transverse force on a vortex light beam in an inhomogeneous medium

Spin-dependent effects on vortex light beams propagating in an inhomogeneous medium are demonstrated by solving the full three-component field Maxwell equations using the perturbation analysis. It is found that the hybrid Laguerre–Gauss modes with polarization-orbital angular momentum (OAM) entanglement are the vector solutions of the Maxwell equations in a graded-index medium. Focusing of linearly and circularly polarized vortex light beams in a cylindrical graded-index medium is investigated. It is shown that the vortex light beam undergoes an additional transverse force acting differently on circular polarized beams with opposite handedness. The wave shape variation with distance taking into account the spin–orbit and nonparaxial effects is analyzed. Effect of long-term periodical revival of wave packets due to mode interference in a graded-index cylindrical optical waveguide is demonstrated.

Low-loss light coupling with graded-index core polymer optical waveguides via 45-degree mirrors.

We experimentally investigate the optical loss of graded-index (GI) core polymer optical waveguides with a 45-degree mirror on their one end fabricated using the photo-addressing method. In addition, we also theoretically analyze the loss of GI square-core waveguides with mirrors using a ray-trace simulation tool. Then, in the waveguide based optical link including the optical path conversions via 45-degree mirrors, we show that GI waveguides realize lower total optical loss than conventional step-index (SI) core waveguides. The lower loss in the GI waveguide link is attributed to the tight optical confinement at the core center even after reflection at the mirrors.

Analytical stabilization of modulated optical similaritons in a tapered graded-index waveguide

We note that the self-similar waves recently reported, in a tapered graded-index waveguide, severely suffer from extreme increase in the amplitude, after traversing a finite distance. In this work, we theoretically described that by adding a suitable homogeneous background in the expression for widths of the self-similar solutions which is achievable through the modulation of tapering profile, we could avert this situation. We further find that the self-similar waves propagate in the nonlinear waveguide, quite a distance stably, albeit they undergo self-compression.

Semirational and symbiotic self-similar rogue waves in a (2+1)-dimensional graded-index waveguide

We have investigated the ()-dimensional variable coefficient-coupled nonlinear Schrödinger equation (vc-CNLSE) in a graded-index waveguide. Similarity transformations are used to convert the vc-CNLSE into constant coefficient CNLSE. Under certain functional constraints we could extract semirational, multi-parametric solution of the associated Manakov system. This family of solutions include known Peregrine soliton, mixture of either bright soliton and rogue wave or dark soliton and rogue wave or breather and rogue wave. Under a distinct set of self-phase modulation and cross-phase modulation coefficients we could establish symbiotic existence of different soliton pairs as solutions. These soliton pairs may constitute of one bright and a dark soliton, two bright solitons or two dark solitons. Finally, when two wave components are directly proportional, we find bright and dark similaritons, self-similar breathers, and rogue waves as different solutions.