Graded Refractive Index Profile Research Articles

Stabilization of spatiotemporal dissipative solitons in multimode fiber lasers by external phase modulation

In this work, we introduce a method for the stabilization of spatiotemporal (ST) solitons. These solitons correspond to light bullets in multimode optical fiber lasers, energy-scalable waveguide oscillators and amplifiers, localized coherent patterns in Bose–Einstein condensates, etc. We show that a three-dimensional confinement potential, formed by a spatial transverse (radial) parabolic graded refractive index and dissipation profile, in combination with quadratic temporal phase modulation, may permit the generation of stable ST dissipative solitons. This corresponds to combining phase mode-locking with the distributed Kerr-lens mode-locking. Our study of the soliton characteristics and stability is based on analytical and numerical solutions of the generalized dissipative Gross–Pitaevskii equation. This approach could lead to higher energy (or condensate mass) harvesting in coherent spatio-temporal beam structures formed in multimode fiber lasers, waveguide oscillators, and weakly-dissipative Bose–Einstein condensates.

Design of diode laser using slab coupled optical waveguide with graded refractive index structure

Thickness and refractive index of slab layer have major effects in the electro-optical characteristics of slab coupled optical waveguide diode lasers. In this research, ordinary step refractive index profile was replaced by a broadened waveguide with linear graded refractive index profile and optimized doping. The results show such design can significantly improve the power conversion efficiency (PCE). According to these results, by using the asymmetric barrier in the sides of active region, the threshold current decreases and slop efficiency (SE) increases. The PCE and SE in the proposed structure are respectively 12% and 0.21 W/A higher than those in conventional step profile.

Precision of Silicon Oxynitride Refractive-Index Profile Retrieval Using Optical Characterization

Layers with gradient refractive-index profile are an attractive alternative to conventional homogeneous stack coatings. However, the optical characterization and monitoring of the graded refractive-index profile is a complex issue, which has been typically solved by using a simplified model of mixed materials. Although this approach provides a solution to the problem, the precision, which can be expected from optical characterization of the refractive index gradient, remains unclear. In this work, we study optical characterization of SiO_xN_y layers deposited via reactive dual ion beam sputtering. To characterize the deposited layers, we use several methods including reflectance, and transmittance spectra at a broad range of incident angles, together with spectral ellipsometry. All the data were simultaneously fitted with a general profile of refractive index. The expected profile used in our fit was based on characterization of SiO_xN_y layers with a varying stoichiometry. By altering of the profile, we discussed sensitivity of such alternation on fit quality and we studied ambiguity of merit-function minimization. We demonstrate that while the scanning of particular parameters of the profile can be seemingly very precise, we obtain a very good agreement between the experimental data and model for a broad range of gradient shapes, where the refractive-index value on major part of the profile can differ as much as 0.02 from the mean value.

An Efficient Semianalytical Modal Analysis of Rectangular Waveguides Containing Metamaterials with Graded Inhomogeneity

Rectangular waveguides containing inhomogeneous metamaterials with graded refractive-index profiles have potential applications in bending waveguides and radiation-enhanced antennas, and accurate eigenvalue solutions are prerequisite. Commonly used commercial electromagnetic solvers such as HFSS, COMSOL, and CST could not efficiently calculate the eigenvalues of waveguides containing graded refractive-index dielectrics. In this paper, an accurate and efficient semianalytical method based on the modal expansion has been proposed to solve these waveguides. The proposed method has been employed to calculate the eigenvalues, including the cutoff wavenumbers and dispersion relations, for metamaterials with various graded refractive-index profiles. Calculated results are then validated by comparison, using commercial solver HFSS, which indicates the superiority of the proposed method in accuracy and efficiency. Below-cutoff backward wave propagation is observed in waveguides filled with graded refractive-index metamaterials, which provides a new approach for waveguide miniaturization.

New Silica Laser-Optimized Multimode Optical Fibers with Extremely Enlarged 100-μm Core Diameter for Gigabit Onboard and Industrial Networks

We present new type of silica graded index laser-optimized multimode optical fibers (LOMF) with extremely enlarged core diameter up to 100 μm and “typical” “telecommunication” cladding diameter 125 μm. This optical fiber was designed for harsh environment Gigabit onboard cable systems and industrial networks. It differs by special optimized graded refractive index profile, providing low differential mode delay (DMD) for selected guided modes. We present some results of tests, performed for manufactured pilot 520 m length of described LOMF 100/125, concerned with its geometry properties as well as key transmission parameters—attenuation and DMD map.

Transmittance enhancement of micro-grating structure sapphire with high-refractive index Y2O3 layer

The theoretical analysis of micro-grating structure sapphire (sapphire MGS) with Y2O3 layer using the finite-difference time-domain method is presented. The results show that the total transmittance and reflectance of Y2O3/sapphire MGS have a close relationship with the thickness of Y2O3 layer, where about 300 nm is the ideal thickness. According to the simulant results, 300 and 600 nm of thicknesses of Y2O3 layer deposited onto sapphire MGS substrate by reactive magnetron sputtering method are studied experimentally. The experimental results agree well with the calculated data and further have better optical properties because of the rough surface of Y2O3 layer. It illustrates that the 300-nm Y2O3/sapphire MGS exhibits the best increase in the total transmittance and diffuse transmittance due to the greater graded refractive index profile than sapphire MGS. The results of this paper have potential applications in solar cells and diffraction grating.

Performance analysis of a highly nonlinear optical fiber with different graded refractive index profiles

In optical communication systems different types of fibers are employed for different applications. Particularly, highly nonlinear fibers are used for nonlinear signal processing such as wavelength conversion, optical switching, signal regeneration and demultiplexing. The performance parameters of these optical fibers can be altered through the refractive index (RI) profile modification during manufacturing. This paper explores the performance of a highly nonlinear fiber (HNLF) with parabolic, Gaussian and alpha power law functioned RI profile at the core instead of step index profile. The functional parameters are adjusted in order to obtain similar RI structure for these three functions. From the simulation analysis, it is concluded that HNLF with alpha power law RI profile reveals a better performance compared to the parabolic and Gaussian functions. Further by adjusting the alpha value in the design of alpha power law RI profile wide variety of dispersion curve and nonlinear coefficients are possible.

Interfacial structure designs with impedance-matching for ideal broadband antireflections

This work focuses on the ideal broadband antireflection structure designs based on the impedance-matching and the effective medium theory. Graded refractive index profiles that satisfy the impedance-matching condition between two media result in zero reflection over the entire wavelength range. Our studies found that both the thickness of the graded refractive index layer and the refractive indices of the adjacent two media determine the dispersion properties of the graded refractive index profiles. Specifically, we case-studied the dispersion properties of the gradient refractive index profiles for silicon, GaN, and glass substrates. The effective medium theory was utilized to design interface structures that match the ideal graded refractive index profiles. The accuracy of this design approach was assessed by comparing the filling factor as a function of thickness by using effective medium theory with zeroth-order and second-order approximations. A novel interface structure with concaved-dome geometrical shape was studied as a new type of impedance-matching antireflection structure (concaved-dome impedance-matching II), which has the advantage of reduced effective feature size and thus can better match the ideal graded refractive index profiles by applying the effective medium theory more accurately. The interface reflection properties of the impedance-matching II structure were computed via a three-dimensional finite difference time domain method. The interface reflections were compared with that of a conventional flat surface, a previously proposed micro-dome structure, and a traditional impedance-matching structure (impedance-matching I), which revealed that the concaved-dome impedance-matching II structure has the best antireflection performance over a broad wavelength range and wide incidence angles.

A simple and exact method to analyze optical waveguide with graded index profile

A simple analytical method is proposed to obtain the exact propagation constant and distribution of electric field intensity of optical waveguides with graded refractive index profile. The method is based on the Wenzel-Kramers-Brillouin (WKB) solution, variational method, modified eigen-equations and discretized scalar wave equation for planar optical waveguide. The expressions of the distribution of electric field intensity based on the conventional WKB method, which diverge around the turning point, have been demonstrated to be very exact in the region beyond the turning point where the refractive index profile varies slowly. The proposed method uses the conventional WKB method to calculate the values of electric field intensity at two adjacent positions beyond the turning point and then the electric field intensity profile for the whole region is obtained by making use of the two calculated values. Two simple and explicit formulas are deduced from the discretized scalar wave equation, which provide a relationship among the values of electric field intensity at three adjacent positions. If the effective refractive index of optical waveguide and the refractive index profile for the whole region are known, we can obtain the value of electric field intensity at any position according to the corresponding values at the adjacent positions by using the two formulas aforementioned. By using the two values calculated by WKB method, the electric field intensity profile for the whole region can be determined through the iterative use of the two formulas. The accuracy of the electric field intensity profile determined by the proposed method is greatly dependent on the accuracy of the applied value of the effective refractive index. To achieve exact propagation constant and distribution of electric field intensity, the variational method and modified eigen-equations are employed in the proposed method. Variational method is a very useful method to improve the accuracy of the propagation constant in the analysis of optical waveguide with step-asymmetrical graded refractive index profile. By combining the traditional variational method and calculation of electric field intensity profile by the proposed method, the improved variational method is presented to obtain the exact propagation constant of optical waveguide. The value of propagation constant calculated by WKB method and the corresponding electric intensity field profile determined by the proposed method are chosen as the initial trial value and trial function in the variational method. Propagation constant and the corresponding electric field intensity profile with better accuracy can be achieved by the variational calculation and then are regarded as the new trial value and trial function. By the iterative use of the variational method and calculation of electric field intensity profile by the proposed method at finite times, quite accurate results are obtained. The modified eigen-equations in combination with the proposed method is another approach to calculating accurate propagation constants of optical waveguides with both the step-asymmetrical and symmetrical graded index profile. In comparison with other published methods, the proposed method has the advantages of the simplicity and considerable accuracy.

Broadband and Crack-Free Antireflection Coatings by Self-Assembled Moth Eye Patterns

We report broadband and quasi-omnidirectional antireflective (AR) structures inspired to the nipple arrays of moth eyes. These nanocoatings, based on thin elastomeric films, are prepared by simple self-assembly processing of a co-polymer specifically designed to this purpose, and PDMS replica molding. Typically, their surface is covered by a compact distribution of hemispherical nanodomes of about 250 nm in diameter and about 100 nm in height. When these novel nanostructures are applied on a single glass surface, a maximum of 2% transmission enhancement (equivalent to a 50% reduction of the reflected component) towards wavelengths ranging from visible to near IR region is obtained. A considerable AR power is observed also at a wide range of incident angles ranging from normal to 50°. These properties could be attributed to an optimized graded refractive index profile resulting from the randomly distributed and close-packed nanodomes. Moreover, thanks to their elastomeric nature, these crack-free films can be easily applied on glass, as stickers, and periodically replaced, thus offering the possibility of easy dirt removal from an optical device.

Propagation of Electromagnetic Wave through Anisotropic Graded Refractive Index Profile

Propagation of electromagnetic wave (EW) through multilayer structure consisting anisotropic layers with gradient refractive index material is studied theoretically. Analytical solution for linear dependence of refractive index profile is examined. The structure consist the forbidden gaps, which are sensitive to parameters of refractive index profile.

Hydrophobic and antireflective characteristics of thermally oxidized periodic Si surface nanostructures

We reported the antireflective properties of periodic silicon (Si) subwavelength gratings and flat substrates in combination with thermal oxidation for an effective surface passivation. Moreover, theoretical calculations and analysis based on rigorous coupled-wave analysis simulation were performed. For thermally oxidized Si subwavelength grating structures, the reflectance was significantly reduced compared to that of the thermally oxidized flat Si substrates in wide ranges of wavelengths and angles of incidence. As the oxidation time increased, the reflectance became lower with increasing SiO x thickness on Si subwavelength gratings due to the more graded effective refractive index profile from air to the Si via the thermally oxidized Si subwavelength gratings with increased height. By incorporating a thermal oxidation process into the Si subwavelength gratings, a more hydrophobic surface with good surface passivation was obtained.

Self-cleaning, broadband and quasi-omnidirectional antireflective structures based on mesocrystalline rutile TiO2 nanorod arrays

We report excellent broadband and quasi-omnidirectional antireflective (AR) structures based on highly stable, self-cleaning, mesocrystalline rutile TiO2 nanorod arrays, which were grown by a facile hydrothermal synthesis directly on Ti foils. Typically, each hierarchical nanorod is a single-crystal-like rutile TiO2 mesocrystal comprising many [001]-oriented nanotips about 10–30 nm in diameter grown on the top of a [001]-oriented stem nanorod about 100–400 nm in diameter. These novel hierarchical mesostructures exhibit efficient suppression of reflection towards wavelengths ranging from visible to near infrared (NIR) region, with reflection <0.5% in the visible region and <2% in the NIR region, at a wide range of incident angles ranging from nearly normal to 45°. These excellent antireflection properties could be attributed to an optimized graded refractive index profile resulting from the hierarchical tips-on-rod structure of the mesocrystalline nanorods. The chemical and thermal stability of rutile TiO2 endows the prepared mesocrystalline TiO2 AR structures with high stability. Moreover, the AR structures exhibit useful self-cleaning properties either under UV irradiation or through fluorosilane-modification.

Highly transparent sapphire micro-grating structures with large diffuse light scattering

The highly transparent micro-grating structures (MGSs) of sapphire substrate with large diffuse light scattering were theoretically and experimentally studied. From the finite difference time domain simulation, it was found that the degree of diffuse light scattering is strongly dependent on the size of grating structures. For a highly transparent property, the sapphire MGSs were optimally designed by the theoretical calculations using the rigorous coupled wave analysis method. The order of taper, geometry (i.e., width and height), and pitch length of MGSs were optimized to maximize their average total transmittance over a wide wavelength range of 300-1800 nm. Additionally, the influence of the deposition of low-refractive index material such as SiO2 onto sapphire MGSs on the transmittance characteristics was investigated. To verify experimentally the feasibility, the sapphire MGSs were fabricated by the conventional lithography and dry etching processes. The SiO2 deposited sapphire MGS exhibited a further increase in the total transmittance due to its relatively more graded refractive index profile while maintaining a significantly enhanced diffuse light scattering. The experimental data were in a reasonable agreement with the theoretical results.

Photon management for photovoltaics

Abstract

Thin-film stack based integrated GRIN coupler with aberration-free focusing and super-high NA for efficient fiber-to-nanophotonic-chip coupling

Nanophotonic chip coupling using an optical thin-film stack forming a micro graded-refractive-index (GRIN) lens with a super-high numerical aperture (NA) that is highly compact (tens of micron long) and can be directly integrated is presented. We explore the lens' integration on the surface of Silicon-On-Insulator (SOI) platform with an asymmetric GRIN profile. We show that to achieve high efficiency for optical coupling between an optical fiber and a nanophotonic waveguide with a sub-wavelength (lambda/n) beam size, conventional asymmetric parabolic GRIN profile is no longer adequate due to the super-high NA needed (>3.1), which results in severe spatial beam aberration at the focal plane. We present an efficient algorithm to computationally generate the ideal GRIN profile that is completely aberration free even at super-high NA, which improves the coupling efficiency from ~66% (parabolic case) to ~95%. A design example involving an optical thin-film stack using an improved dual-material approach is given. The performance of the thin-film stack is analyzed. This thin-film stack based GRIN lens is shown to be high in coupling efficiency, wavelength insensitive and compatible with standard thin-film process.

Graded refractive-index SiOx infrared filters prepared by reactive magnetron sputtering

Dense, uniform SiOx (0⩽x⩽2) films were deposited by reactive magnetron sputtering. By controlling the oxygen flow rate and/or sputtering power during deposition, the refractive index of SiOx films can be continuously tuned from 1.44 to 3.69 at λ=1550nm. The authors fabricated an 11-layer bandpass filter of SiOx∕SiO2 with high refractive-index contrast (nH∕nL=1.91 at λ=1550nm) and a 35-layer SiOx optical filter with a graded refractive-index profile. The measured reflectance and transmittance spectra correlate well with the designed spectra. This work demonstrates that SiOx material can be used to make infrared optical filters with graded refractive index and high refractive-index contrast.

3D-soliton waveguides in lithium niobate for femtosecond light pulses

We show that efficient waveguides can be written by bright spatial solitons in the volume of lithium niobate photorefractive crystals by cw and pulsed laser beams. Using high-repetition-rate femtosecond laser pulses, an efficient formation of soliton waveguides (SWGs) is possible, after accumulating a large number of pulses, because the characteristic photorefractive build-up time is much longer than the pulse period and the efficient two-photon absorption may contribute to the solitonic confinement. These results open the possibility of writing reconfigurable single SWGs and SWG arrays (with any spatial orientation and large range of periods) and optimally guiding the femtosecond pulsed laser beams through them, creating a graded refractive-index profile matched to the spatial beam profile. Our experiments also show a small increase in pulse duration (small dispersion) in these waveguides.

Fabrication of single-mode waveguide structure in optical multimode fluoride fibers using self-channeled plasma filaments excited by a femtosecond laser

A permanent structure of a single-mode waveguide in optical multimode fluoride fibers was first fabricated using a self-channeled plasma filament excited by a femtosecond (110-fs) Ti:sapphire laser (λp=800 nm). The photoinduced refractive-index modification in a multimode step-index fluoride glass (ZBLAN) fiber with a 100/110-μm core/cladding diameter reached a length of approximately 12–15 mm from the input surface of the optical fiber, with the diameters ranging from 5 to 8 μm at input intensities more than 1.0×1012 W/cm2. The graded refractive-index profiles were fabricated to have a symmetric form from the center of a multimode fluoride fiber and a maximum value of the refractive-index change (Δn) was measured to be 1.3×10-2. The beam profile of the output beam transmitted through the modified multimode fibers showed that the photoinduced refractive-index modification produced a permanent structure of a single-mode waveguide.

Stepwise graded refractive-index profiles for design of a narrow-bandpass filter

A combination of stepwise graded refractive-index profiles and a cavity structure is used for designing narrow-bandpass filters of TiO(2)/SiO(2) multilayer films upon BK7 glass substrates. Symmetrical profiles of stepwise graded refractive indices result in high transmittance of passbands for the designed filters. The bandwidth of the narrow-bandpass filter is controlled by adjustment of parameters such as the thickness and the number of layers in the multilayer stack. This design is proposed as a new and simple method for coating synthesis of optical filters.