Graded index profiles and loss-induced single-mode characteristics in vertical-cavity surface-emitting lasers with petal-shape holey structure

The 850-nm oxide-confined vertical-cavity surface-emitting lasers with petal-shape holey structures are presented. An area-weighted average refractive index model is given to analyse their effective index profiles, and the graded index distribution in the holey region is demonstrated. The index step between the optical aperture and the holey region is obtained which is related merely to the etching depth. Four types of holey vertical-cavity surface-emitting lasers with different parameters are fabricated as well as the conventional oxide-confined vertical-cavity surface-emitting laser. Compared with the conventional oxide-confined vertical-cavity surface-emitting laser without etched holes, the holey vertical-cavity surface-emitting laser possesses an improved beam quality due to its graded index distribution, but has a lower output power, higher threshold current and lower slope efficiency. With the hole number increased, the holey vertical-cavity surface-emitting laser can realize the single-mode operation throughout the entire current range, and reduces the beam divergence further. The loss mechanism is used to explain the single-mode characteristic, and the reduced beam divergence is attributed to the shallow etching. High coupling efficiency of 86% to a multi-mode fibre is achieved for the single-mode device in the experiment.

Near-stoichiometric Ti:LiNbO3 strip waveguide with varied substrate refractive index in waveguide layer

We report the near-stoichiometric Ti：LiNbO3 strip waveguides fabricated by vapour transport equilibration （VTE） at 1060~^{／circ}C for 12 h and co-diffusion of 4--8~／mu m wide, 115-nm thick Ti-strips. Optical studies show that these waveguides are monomode at 1.5~／mu m and have losses of 1.3 and 1.1~dB/cm for the TM and TE modes, respectively. In the waveguide width/depth direction, the mode field follows a Gauss/Hermite--Gauss profile. A secondary ion mass spectrometry study reveals that the Ti profile follows a sum of two error functions along the width direction and a complementary error function in the depth direction. Micro-Raman analysis shows that the Li-composition in the depth direction also follows a complementary error function. The mean Li/Nb ratio in the waveguide layer is about 0.98. The inhomogeneous Li-composition profile results in a varied substrate index in the guiding layer, and the refractive index profile in the guiding layer is given.

Parameter analysis of a photonic crystal fiber with raised-core index profile based on effective index method

Photonic crystal fibers （PCFs） with a stepped raised-core profile and one layer equally spaced holes in the cladding are analyzed. Using effective index method and considering a raised step refractive index difference between the index of the core and the effective index of the cladding, we improve the characteristic parameters such as numerical aperture and V-parameter, and reduce its bending loss to about one tenth of a conventional PCF. Implementing such a structure in PCFs may be one step forward to achieve low loss PCFs for communication applications.

Modelling of Energy Storage Photonic Medium by Wavelength-Based Multivariable Second-Order Differential Equation

Wavelength-dependent mathematical modelling of the differential energy change of a photon has been performed inside a proposed hypothetical optical medium.The existence of this medium demands certain mathematical constraints,which have been derived in detail.Using reverse modelling,a medium satisfying the derived conditions is proven to store energy as the photon propagates from the entry to exit point.A single photon with a given intensity is considered in the analysis and hypothesized to possess a definite non-zero probability of maintaining its energy and velocity functions analytic inside the proposed optical medium,despite scattering,absorption,fluorescence,heat generation,and other nonlinear mechanisms.The energy and velocity functions are thus singly and doubly differentiable with respect to wavelength.The solution of the resulting second-order differential equation in two variables proves that energy storage or energy flotation occurs inside a medium with a refractive index satisfying the described mathematical constraints.The minimum-value-normalized refractive index profiles of the modelled optical medium for transformed wavelengths both inside the medium and for vacuum have been derived.Mathematical proofs,design equations,and detailed numerical analyses are presented in the paper.

Fabrication and Determination of Refractive Index Profile of the Planar Waveguides by Wedge Technique

Several planar waveguides have been fabricated. The waveguides have been polished for determination of their refractive index profiles (RIP) by wedge method. The RIP determined by inserting the sample in a Mach-Zehnder interferometer and applying fringe analysis methods.

Optimization of the Placement and Size of Photovoltaic Source

This paper presents a new optimization study of the placement and size of a photovoltaic source(PVS)in a distribution grid,based on annual records of meteorological parameters(irradiance,temperature).Based on the recorded data,the production output as well as the daily average power(24-h vector)of the PVS is extracted over the year.When a power vector is available,it can be used as an input when searching for the optimal size of the PVS.This allows to take into account the constraint of the variation of the power generated by this source considering the variation of the power consumed by the electrical loads during the whole day.A multi-objective fitness function has been considered.The latter minimizes the active losses and maximizes the voltage stability index during the day,while considering the constraints of the system,that is,the security,technical,geographical,and meteorological constraints.This problem was solved using the Non-dominated Sorting Genetic Algorithm NSGA-II optimization technique under MATLAB 2021.It was applied to the distribution network of Ghardaïa of 59 nodes.

Capillary bridges and capillary forces between two axisymmetric power-law particles

Capillary interactions are fundamentally important in many scientific and industrial fields. However, most existing models of the capillary bridges and capillary forces between two solids with a mediated liquid, are based on extremely simple geometrical configurations, such as sphere-plate, sphere-sphere, and plate-plate. The capillary bridge and capillary force between two axisymmetric power-law profile particles with a mediated constant-volume liquid are investigated in this study. A dimensionless method is adopted to calculate the capillary bridge shape between two power-law profile particles based on the Young-Laplace equation. The critical rupture criterion of the liquid bridge is shown in four forms that produce consistent results. It was found that the dimensionless rupture distance changes little when the shape index is larger than 2. The results show that the power-law index has a significant influence on the capillary force between two power-law particles. This is directly attributed to the different shape profiles of power-law particles with different indices. Effects of various other parameters such as ratio of the particle equivalent radii, liquid contact angle, liquid volume, and interparticle distance on the capillary force between two power-law particles are also examined.

Dynamical Behavior of Solution in Integrable Nonlocal Lakshmanan–Porsezian–Daniel Equation

The integrable nonlocal Lakshmanan–Porsezian–Daniel(LPD) equation which has the higher-order terms(dispersions and nonlinear effects) is first introduced. We demonstrate the integrability of the nonlocal LPD equation,provide its Lax pair, and present its rational soliton solutions and self-potential function by using the degenerate Darboux transformation. From the numerical plots of solutions, the compression effects of the real refractive index profile and the gain-or-loss distribution produced by δ are discussed.