Graded-index Waveguide Research Articles

Light bullets under conditions of third harmonics generation

Abstract An analytical study of the possibility of a two-color light bullet forming during generation of the third harmonics in a graded index waveguide with the focusing Kerr nonlinearity is carried out. It is shown that under conditions of phase and group matching, as well as the absence of group velocity dispersion at the third harmonic frequency, a stable light bullet can be formed under certain restrictions. This applies to the lower limit on the temporal duration of the light bullet and to the upper limit on its power. The most stringent condition is the double restriction on the transverse radius of the light bullet.

Transverse Inscription of Silicon Waveguides by Picosecond Laser Pulses

AbstractIn this work, picosecond laser inscription of segmented waveguides in crystalline silicon based on a deterministic single‐pulse modification process is demonstrated. Pulses of 43 ps duration at 1.55 wavelength are used to transversely inscribe periodic structures with a pulse‐to‐pulse pitch of ≈2 . Infrared shadowgraphy images and Raman spectroscopy measurements indicate that the modifications exhibit a spherical shape. Characterization of waveguide performance at 1.55 for various pulse energies and periods is carried out. Direct comparison with numerical simulations confirms the presence of graded index waveguides, encompassing a micrometer core size and a maximum refractive index change of . This short‐pulse inscription approach can pave the way for 3D integrated photonic devices in the bulk of silicon.

Optimum core structural design of the polymer optical waveguides as edge couplers for co-packaging.

We simulate the optical properties of polymer optical waveguides with different refractive index profiles in their cores as coupling components (edge couplers) between single-mode fiber and SiOx waveguides. In this paper, we focus on the single-mode operation of graded-index (GI) core polymer waveguides, for which we previously demonstrated low propagation loss under multimode operation. We design the optimum core structure (size and index contrast) for different refractive index profiles, and then demonstrate the unique optical properties of GI waveguides contributing to the low optical loss compared to the step-index counterparts, in particular, mode field diameter variation and taper angle tolerance.

A hybrid variational method for beam propagation and interaction in a graded-index nonlinear waveguide

The hybrid variational method can be used to simplify multidimensional numerical simulations. We examine the applicability of this method to study the nonlinear propagation of a single beam and the interference of two spatial soliton beams in a graded-index optical waveguide governed by a two-dimensional nonlinear Schrodinger equation. We classified three distinct regimes of the dynamics that emerge during single Gaussian beam propagation, corresponding to beam decay, breather formation, and self-focusing. When two spatial soliton beams were set up to interfere in the waveguide, we identified the boundary where the nonlinear interaction during the interference led to excitation or self-focusing. These quite involved dynamics were used to test the predictive power of our variational models by comparing them with direct numerical simulations, obtaining good agreement.

Highly Sensitive On-Chip Grating-Based Optical Sensor on Glass Substrate: Cost-Effective Design

This paper presents a novel on-chip optical sensing system using ion exchange technology and phase-shifted Bragg grating design. The sensor geometry has been optimized using a finite difference time domain (FDTD) solver to achieve maximum sensitivity and figure of merit (FOM). The proposed design offers high sensitivity to changes in refractive index and low fabrication costs. The ion exchange process used to create the sensor allows for precise refractive index control, optimizing the sensor’s sensitivity and FOM. A graded-index waveguide and a phase-shifted Bragg grating structure also contribute to the sensor’s high sensitivity. The proposed sensor design was tested for water-based sensing applications, achieving a FOM of 227.63 and a 343.1 nm/RIU sensitivity. These values are significantly higher than those reported for other Bragg grating sensors, highlighting the potential of the proposed design for high-performance sensing applications. The sensor’s high sensitivity and low fabrication costs make it a promising technology for future sensing and monitoring applications.

Asymmetries Caused by Nonparaxiality and Spin–Orbit Interaction during Light Propagation in a Graded-Index Medium

Spin–orbit coupling and nonparaxiality effects during the propagation of vortex vector light beams in a cylindrical graded-index waveguide are investigated by solving the full three-component field Maxwell’s equations. Symmetry-breaking effects for left- and right-handed circularly polarized vortex light beams propagating in a rotationally symmetric graded-index optical fiber are considered. The mode-group delay in a graded-index fiber due to spin–orbit interaction is demonstrated. A scheme for observing the temporal spin Hall effect is proposed. It is shown that the relative delay times between vortex pulses of opposite circular polarizations of the order of 10 ps/km can be observed in graded-index fibers for high-order topological charges.

Nonreciprocal Propagation of Nematicons

We model two-port nonlinear optical isolators based on solitary waveguides in planar cells with non-homogeneously oriented liquid crystals in the nematic phase. In a planar layout with molecular anchoring linearly changing along the sample length or across its width, we conduct numerical experiments on the excitation and propagation of reorientational solitons—“nematicons”—launched in opposite directions from the two ends of the cell. Specifically, in the Kerr-like diffractionless regime corresponding to graded-index waveguides for copolarized weak signals, we investigate the non-overlapping trajectories of forward and backward propagating wavepackets. The resulting non-specular transmission entails optical isolation and diode-like behavior as light propagating backwards does not reach the forward input. The response dependencies on input power, range of angular modulation, and one-photon losses are analyzed with reference to parameters of realistic soft matter.

Butterfly-shaped and dromion-like optical similaritons in an asymmetric twin-core fiber amplifier

Butterfly-shaped and dromion-like optical waves in a tapered graded-index waveguide (GRIN) with an external source are reported for the first time, to our knowledge. More pertinently, we obtain these waves both analytically and numerically in a generalized nonlinear Schrödinger equation (GNLSE), which describes self-similar wave propagation in GRIN with variable group-velocity dispersion (GVD), nonlinearity, gain, and source. The proposed GNLSE appertains to the study of similariton propagation through asymmetric twin-core fiber amplifiers. Dromion-like structures, which have generally been investigated in the (2+1) or higher dimensional systems, are reported in the (1+1) dimensional GNLSE with an external source. Herein, we introduce the concept of soliton management when the variable group-velocity dispersion and Kerr nonlinearity functions are suggested. For example, when the GVD parameter is perturbed, we observe the emergence of vibration of dromion-like structures. Then the dromion-like structure is transformed into oscillation by the modulation instability of the modified coefficient of the Gaussian GVD function, exhibiting interference based on two dromion-like structures. Additionally, the phenomenon of unbreakable PT symmetry of these nonlinear waves has been demonstrated for three explicit examples.

Modes of an exponentially graded-index waveguide with a light-induced change in Kerr nonlinearity signs in a nonlinear cladding

Modes of an exponentially graded-index waveguide with a light-induced change in Kerr nonlinearity signs in a nonlinear cladding

Models of waveguides combining gradient and nonlinear optical layers

Objectives. Theoretical studies of the waveguide properties of interfaces between nonlinear optical and graded-index media are important for application in optoelectronics. Waveguides combining layers with different optical properties seem to be the most promising, since they can be matched to optimal characteristics using a wide range of control parameters. The paper aims to develop a theory of composite optically nonlinear gradedindex waveguides with an arbitrary profile, within which it is possible to obtain exact analytical expressions for surface waves and waveguide modes in an explicit form. The main feature of the theory proposed in this paper is its applicability for describing surface waves and waveguide modes, in which the field is concentrated inside the gradient layer and does not exceed its boundary, avoiding contact with the nonlinear layer.Methods. Analytical methods of the theory of optical waveguides and nonlinear optics are used.Results. A theoretical description of the waveguide properties of the interface between two media having significantly different optical characteristics is carried out. The formulated model of a plane waveguide is applicable to media having an arbitrary spatial permittivity profile. An analytical expression describing a surface wave propagating along the interface between a medium having stepwise nonlinearity and a gradient layer with an arbitrary permittivity profile is obtained. Additionally, analytical expressions for surface waves propagating along the interface between a medium with Kerr nonlinearity (both self-focusing and defocusing), as well as graded-index media characterized by exponential and linear permittivity profiles, are obtained.Conclusions. The proposed theory supports a visual description in an explicit analytical form of a narrowly localized light beam within such waveguides. It is shown that by combining different semiconductor crystals in a composite waveguide, it is possible to obtain a nonlinear optical layer on one side of the waveguide interface and a layer with a graded-index dielectric permittivity profile on the other.

High-quality color image restoration from a disturbed graded-index imaging system by deep neural networks.

Imaging transmission plays an important role in endoscopic clinical diagnosis involved in modern medical treatment. However, image distortion due to various reasons has been a major obstacle to state-of-art endoscopic development. Here, as a preliminary study we demonstrate ultra-efficient recovery of exemplary 2D color images transmitted by a disturbed graded-index (GRIN) imaging system through the deep neural networks (DNNs). Indeed, the GRIN imaging system can preserve analog images through the GRIN waveguides with high quality, while the DNNs serve as an efficient tool for imaging distortion correction. Combining GRIN imaging systems and DNNs can greatly reduce the training process and achieve ideal imaging transmission. We consider imaging distortion under different realistic conditions and use both pix2pix and U-net type DNNs to restore the images, indicating the suitable network in each condition. This method can automatically cleanse the distorted images with superior robustness and accuracy, which can potentially be used in minimally invasive medical applications.

Using Hocker and Burns numerical method to analyze the dispersion properties of a planar waveguide with an exponentially graded-index core layer for s-polarized light

Although not realistic, the theory of step-index waveguide has been discussed in most published works. Electric and magnetic fields can be written as well-known functions such as exponential, sine and cosine functions. However, the index distribution of the most practical waveguides is better described as graded. Despite certain similarities, step-index and graded-index waveguide structures also have considerable differences. The characteristic equation of s-polarized wave propagating in a planar waveguide with an exponentially graded-index thin core layer is examined in this work using the Hocker and Burns numerical approach. This method utilizes the effective index method of analyzing waveguides with 2D confinement. It was efficiently applied to problems of channel waveguides formed by diffusion. The technique depends on finding the phase shift of the curved optical path in the graded index zone as stacked infinite thin layers. Three factors contribute to the total transverse phase shift: (1) film-cladding interface phase delay, (2) film-substrate interface phase delay, and (3) phase delay caused by the zigzag optical path of the guiding film. The findings revealed the following intriguing observations. The dispersion curves of the graded-index waveguide structure are in the normal shape in which the generalized guide index (GeGI) increases with the rise of the normalized frequency. At high values of the normalized frequency, the GeGI displays less dependence on it. The dispersion curves show cut-off thicknesses which increase for higher asymmetry measure values. A comparison between graded-index and step-index waveguide structures is carried out.

Nonlinear guided wave propagation along layers with the exponential index profile, constant index and the Kerr nonlinearity

Layered planar waveguide consisting of the layer with an exponential profile of the dielectric permittivity, optical linear layer, and nonlinear medium of Kerr-type is considered. Exact analytical solutions describing the nonlinear guided waves in such waveguide are found. The profiles of the waves in perpendicular to the layers direction are analyzed. The distinctions between layered waveguide structures with a linear optical substrate and a nonlinear one and the impact of dielectric interlayer separating the exponentially graded-index main waveguide layer and nonlinear material of Kerr-type are discussed. The presence of a dielectric interlayer leads to the possibility of the appearance of field oscillations inside it. The possibility of controlling the field localization length across the layers and its amplitude by changing the interlayer width is shown.

Modeling photocurrent spectra of high-indium-content InGaN disk-in-wire photodiode on silicon substrate

This work reports comprehensive theoretical modeling of photocurrent spectra generated by an In 0.91 Ga 0.09 N/ In 0.4 Ga 0.6 N disk-in-wire photodiode . The strain distribution is calculated by the valence-force-field model, while a realistic band structure of the In x Ga 1 − x N/In y Ga 1 − y N heterostructure is incorporated using an eight-band effective bond-orbital model with spin–orbit coupling neglected. The electrostatic potential is obtained from a self-consistent calculation employing the non-equilibrium Green’s function method. With the strain distribution and band profile determined, a multi-band transfer-matrix method is used to calculate the tunneling coefficients of optically-pumped carriers in the absorbing region. The photocurrent spectra contributed by both single-photon absorption and two-photon absorption (TPA) are calculated. The absorption coefficient is weighted by the carrier tunneling rate and the photon density-of-states (DOS) in the optical cavity formed in the nanowire region to produce the photocurrent. The calculated photocurrent spectra is in good agreement with experimental data, while physical mechanisms for the observed prominent peaks are identified and investigated. We found a dominant influence of the photon DOS near k | | = 0 , causing an enhancement of photocurrent at certain cut-off energies associated with resonance modes in the graded-index waveguide . The main features of photocurrent spectra are determined by the TPA absorption, while the peak positions depend heavily on the polarization of photon. • Modeling of photocurrent spectra in InGaN disk-in-wire with realistic band structure • The photocurrent is predominant by two-photon absorption in low photon energy region • Photocurrent peak positions are affected by resonance modes in waveguide structure

Implantable graded-index fibers for neural-dynamics-resolving brain imaging in awake mice on an air-lifted platform.

We demonstrate a versatile framework for cellular brain imaging in awake mice based on suitably tailored segments of graded-index (GRIN) fiber. Closed-form solutions to ray-path equations for graded-index waveguides are shown to offer important insights into image-transmission properties of GRIN fibers, suggesting useful recipes for optimized GRIN-fiber-based deep-brain imaging. We show that the lengths of GRIN imaging components intended for deep-brain studies in freely moving rodents need to be chosen as a tradeoff among the spatial resolution, the targeted imaging depth and the degree of fiber-probe invasiveness. In the experimental setting that we present in this paper, the head of an awake mouse with a GRIN-fiber implant is fixed under a microscope objective, but the mouse is free to move around an in-house-built flat-floored air-lifted platform, exploring a predesigned environment, configured as an arena for one of standard cognitive tests. We show that cellular-resolution deep-brain imaging can be integrated in this setting with robust cell-specific optical neural recording to enable in vivo studies with minimal physical restraints on animal models. The enhancement of the information capacity of the fluorescence signal, achieved via a suitable filtering of the GRIN-fiber readout, is shown to open routes toward practical imaging modalities whereby the deep-brain neuronal dynamics and axonal connections underpinning the integrative functions of essential brain structures can be studied in awake rodent models.

Dispersion properties of a slab waveguide with a graded-index core layer and a nonlinear cladding using the WKB approximation method

Graded-index waveguides deserve investigation because they are more practical than those of step-index profiles. In this communication, a three-layer slab waveguide in which the core film has an exponentially graded refractive index is assumed. In this case, the film and substrate layers merge smoothly to form one layer of refractive index n ( x ) which is equal to n f at the cladding–film boundary and n s deep in the substrate layer. The cladding layer is made of a Kerr-type nonlinear material. An exact solution to such a waveguide structure is not possible. Approximation techniques are usually used in these cases. We employ the WKB approximation method to find an approximate dispersion relation of the proposed waveguide in terms of the asymmetry parameters a , b , and V . The universal dispersion curves are studied in detail. A number of interesting features are observed, such as the lack of a cutoff thickness related to the symmetric waveguide structure of a = 0 . The b -values are all less than one, which corresponds to guided modes.

Mode Structure and the Envelope of a High-Power Pulse in a Nonsymmetric Graded-Index Waveguide Layer

Mode Structure and the Envelope of a High-Power Pulse in a Nonsymmetric Graded-Index Waveguide Layer

Distorted light bullet in a tapered graded-index waveguide with PT symmetric potentials

The light bullet is obtained in tapered graded-index waveguide with parity-time-symmetric potentials. Different kind of parity-time (PT) symmetric potentials admits different shape of light bullet. The result shows the light bullet may be distorted with Rosen Morse PT and sech-type PT-symmetrical potential. Moreover, the size and position of the light bullet can be controlled by changing some key parameters. These results are useful for the potential applications in the tapered graded-index waveguide amplifier with PT symmetric potentials and three-dimensional optical information storage.

Modulation instability in the presence of slowly varying saturable nonlinearity, dispersion and a PT-symmetric external potential over the length of waveguide

We study the modulation instability (MI) for optical wave propagation in the presence of slowly varying saturable nonlinearity, group velocity dispersion and a PT-symmetric external potential over the length of tapered graded-index waveguide. First we study the MI with space-dependent dispersion and saturated nonlinearity and then with constant dispersion and saturated nonlinearity. We analytically compute the growth rate and analyze the possibility of existence of MI for focussing and defocussing nonlinearities for different choices of group velocity dispersion terms and saturated nonlinearities. We observe that MI is independent of PT symmetric potential term and typically depends upon the choice of group velocity dispersion term, nonlinearity, saturated nonlinearity and wave amplitude. MI gain decreases with increase in cw amplitude however it increases with increase in saturated nonlinearity both for focussing and defocussing nonlinearities.

Non-isothermal phase-field simulations of laser-written in-plane SiGe heterostructures for photonic applications

Advanced solid-state devices, including lasers and modulators, require semiconductor heterostructures for nanoscale engineering of the electronic bandgap and refractive index. However, existing epitaxial growth methods are limited to fabrication of vertical heterostructures grown layer by layer. Here, we report the use of finite-element-method-based phase-field modelling with thermocapillary convection to investigate laser inscription of in-plane heterostructures within silicon-germanium films. The modelling is supported by experimental work using epitaxially-grown Si0.5Ge0.5 layers. The phase-field simulations reveal that various in-plane heterostructures with single or periodic interfaces can be fabricated by controlling phase segregation through modulation of the scan speed, power, and beam position. Optical simulations are used to demonstrate the potential for two devices: graded-index waveguides with Ge-rich (>70%) cores, and waveguide Bragg gratings with nanoscale periods (100–500 nm). Periodic heterostructure formation via sub-millisecond modulation of the laser parameters opens a route for post-growth fabrication of in-plane quantum wells and superlattices in semiconductor alloy films.