Oscillator Dispersion Research Articles

An investigation on structural, morphological, thermal, optical, and antibacterial properties of chitosan-oleic acid (CH-OA) composite thin films

Recent researches show an increasing interest in developing polymer composite films to improve their properties for use in biodegradable food packaging and optoelectronic applications. For this purpose, this study aims to fabricate and characterize chitosan-oleic acid (CH-OA) composite films for different optical applications. Solution casting process was used to prepare CH-OA composite films. XRD patterns of the films showed that the addition of OA up to 3.0 % (v/w) reduced their crystalline structure. The morphology of the composites was studied using SAED and SEM. SAED patterns indicated good mixing ability between OA and CH, while SEM analysis revealed the heterogeneous surface of the films and proved the incorporation of OA into the CH matrix. The thermal stability of the films was studied using DSC and TGA analyses of the composites, and their thermograms indicated the interactions between CH and OA which improved their thermal stability. The optical properties of the films were performed in the spectral region of 250–2500 nm. The near-infrared results showed that increasing the OA concentration can lead to strong local interactions between OA and other groups in the CH matrix. The transmittance spectra of CH-OA composites at UV wavelength ≤ 400 nm showed values ​​close to 0 %, indicating that all the films have UV-blocking features. Significant changes in color and opacity parameters were detected. In the visible range (400–700 nm), the absorption coefficients, absorption indices and refractive indices of the films were evaluated. The absorption edges, Urbach energies, direct and indirect energy band gaps were in the ranges of 2.491–1.849 eV, 0.591–2.008 eV, 2.698–2.578 eV and 2.167–1.422 eV, respectively, as well as the refractive index decreased from 1.837 to 1.735 to 1.149–1.119 by increasing the OA concentration to 3.0 % (v/w). The produced composites have high optical conductivities up to 1010S−1 indicating good photoresponse and enhanced electronic excitation due to increased absorption coefficient of the film. The Wemple-DiDomenico model was used to evaluate the dispersion energies and related parameters. The values ​​of dispersion energy and oscillator energy decreased from 12.388 to 1.327 eV and 6.7268 to 5.7525 eV, respectively, with the OA content increasing to 3.0 % (v/w). The swelling degree and degradation rate were also determined and the results showed an improvement in the swelling and degradation ability of the films. The composites showed the appearance of inhibition zones indicating antibacterial activity against Bacillus cereus, Staphylococcus aureus, and Escherichia coli. These obtained results indicate that CH-OA composite films exhibited better physico-chemical properties with significant improvement and thus can be used in biodegradable food packaging and optoelectronic devices.

Modulation of the morphological and optical properties of CVD grown non-Stochiometric [formula omitted] nanostructures by various substrate angles

Gallium oxide (Ga2O3) nanostructures (NSs) were synthesized via atmospheric pressure chemical vapor deposition (APCVD) technique assisted by hydrogen. The geometrical orientation in terms of the substrate angle was studied to investigate its influence on the morphological, compositional and optical properties of the material. The results revealed that the geometry, stoichiometry and optical parameters of Ga2O3 could be tuned by substrate angle variations during deposition. Tilting the substrate was found to enhance the step coverage of the substrate and the Ga/O atomic ratio above the stoichiometric value. Bandgap of the films was observed to vary inversely (ranged between 4.590 and 4.664eV) to the Ga/O atomic ratio. The refractive index at wavelength of 632.8 nm, dispersion and single oscillator energy of the prepared films were also evaluated, and were found to be in the range of 2.129–3.265, 20.952–56.520eV and 5.309–6.387eV, respectively, with the increase of substrate angle.

Optical, AC conductivity and antibacterial activity enhancement of chitosan-silver nanocomposites for optoelectronic and biomedical applications

This study is aimed to prepare and investigate the optical, electrical and antibacterial activity of the environmentally friendly (green) chitosan (Cs)/silver nanocomposites. TEM demonstrated that AgNPs have a spherical shape with particle size ranged from 3 nm to 25 nm. UV analysis spectra of Cs and Cs/Ag nanocomposites showed that, increasing the content of AgNPs led to a noticeable increase in the values of Urbach energy (E U ) and a dramatic decrease in both the indirect (E ig ) and direct (E dg ) optical bandgap energies. It is found that (E ig ) and (E dg ) are decreased from (4.72/5.31 eV) to (2.47/4.19 eV). The formation of the AgNPs is verified by the existence of surface plasmon resonance (SPR) peak at ∼ (421–450) nm. Wemple-DiDomenico and Sellmeier oscillator models are employed and displayed a clear enrichment in the dispersion energy (E d ) and oscillator energy (E 0) as well as the linear and nonlinear optical parameters of Cs. It is observed that the linear (χ(1)) and nonlinear (χ(3) and n2) parameters are enhanced from 0.083, 0.868 × 10−14 and 1.584 × 10−12 to 0.153, 9.762 × 10−14 and 4.088 × 10−12. The novel results in our study nominate Cs/Ag nanocomposites for applications in linear/nonlinear optical devices. AC conductivity behavior of Cs and Cs/Ag nanocomposites is analyzed based on Jonscher’s law and the analysis showed that the overlapping large polaron tunneling (OLPT) is the dominant conduction mechanism for our samples. It is clear that the values of dielectric constant (ε′) of Cs and Cs/Ag nanocomposites are higher confirming the presence of interface polarization (IP) relaxation. Moreover, it is found that the antibacterial activity of Cs against Gram-negative (P. aeruginosa) and Gram-positive (B. thuringiensis) bacteria is found to be enhanced with increasing the content of Ag NPs. These results suggested that Cs/Ag nanocomposites will be good source for preparing bio-nanocomposites for use in many biomedical and industrial applications.

Effect of daridorexant on sleep architecture in patients with chronic insomnia disorder: a pooled post hoc analysis of two randomized phase 3 clinical studies.

Post hoc analysis to evaluate the effect of daridorexant on sleep architecture in people with insomnia, focusing on features associated with hyperarousal. We studied sleep architecture in adults with chronic insomnia disorder from two randomized phase 3 clinical studies (Clinicaltrials.gov: NCT03545191 and NCT03575104) investigating 3 months of daridorexant treatment (placebo, daridorexant 25 mg, daridorexant 50 mg). We analyzed sleep-wake transition probabilities, EEG spectra, and sleep spindle properties including density, dispersion, and slow oscillation phase coupling. The wake EEG similarity index (WESI) was determined using a machine learning algorithm analyzing the spectral profile of the EEG. At month 3, daridorexant 50 mg decreased wake-to-wake transition probabilities (p < .05) and increased the probability of transitions from wake-to-N1 (p < .05), N2 (p < .05), and REM sleep (p < .05), as well as from N1-to-N2 (p < .05) compared to baseline and placebo. Daridorexant 50 mg decreased relative beta power during wake (p = .011) and N1 (p < .001) compared to baseline and placebo. During the wake, relative alpha power decreased (p < .001) and relative delta power increased (p < .001) compared to placebo. Daridorexant did not alter EEG spectra bands in N2, N3, and REM stages or in sleep spindle activity. Daridorexant decreased the WESI score during wake compared to baseline (p = .004). Effects with 50 mg were consistent between months 1 and 3 and less pronounced with 25 mg. Daridorexant reduced EEG features associated with hyperarousal as indicated by reduced wake-to-wake transition probabilities and enhanced spectral features associated with drowsiness and sleep during wake and N1. ClinicalTrials.gov NCT03545191: study to assess the efficacy and safety of ACT-541468 (daridorexant) in adult and elderly participants with insomnia disorder. URL: Study Details | study to assess the efficacy and safety of ACT-541468 (daridorexant) in adult and elderly participants with insomnia disorder | ClinicalTrials.gov ClinicalTrials.gov NCT03575104:study to assess the efficacy and safety of ACT-541468 (daridorexant) in adult and elderly participants who experience difficulties sleeping. URL: study details | study to assess the efficacy and safety of ACT-541468 (daridorexant) in adult and elderly participants who experience difficulties sleeping | ClinicalTrials.gov.

Defects assisted the enhancement of optical and ferromagnetism in Zn1-xCoxS quantum dots: Toward efficient optoelectronic and spintronic applications

Colloidal Co-doped ZnS Quantum dots (QDs) were successfully synthesized through a facile and effective chemical co-precipitation method using polyethylene glycol (PEG) as a capping agent. A comprehensive study on the structure, optoelectronic, and magnetic properties of ZnS: Co2+ QDs was thoroughly carried out using diverse characterization techniques. Transmission electron micrographs reveal spherical QDs with a mean particle size of 5 ± 0.5 nm, whereas the X-ray diffraction (XRD) analysis and Raman spectroscopy confirm the exclusive presence of cubic ZnS phase structure, without any signs of Co-related impurity phases. Energy-dispersive x-ray (EDX) analysis verifies the presence of only three elements: Zinc, Cobalt, and Sulphur, with nearly stoichiometric proportions. X-ray photoemission (XPS) analysis confirmed the presence of Co2+ ions in the divalent oxidation state as well as the fair existence of sulphur vacancies. Optical measurements demonstrate that Co-doping in ZnS leads to a decrease in the optical band gap owing to the presence of defects that create localized states within the band structure. In addition, the refractive index (n) is found to increase with Co-doping level due to the increase in the polarizability. The outcomes of optical properties reveal that the tunability of the optical band gap and dispersive oscillator parameters in Co-doped ZnS QDs results in an enhancement of the non-linear optical parameters, such as third-order non-linear optical susceptibility χ(3), and non-linear refractive index n2, rendering them well-suited for applications in optoelectronic devices. Furthermore, the room-temperature photoluminescence (PL) spectra revealed that the Co-doped ZnS QDs have two broad emission bands, including the blue emission, and the green emission. By varying the level of Co-doping, it becomes possible to effectively control the relative PL intensities of dual-color emissions, highlighting their potential for producing adjustable color outputs. The room temperature ferromagnetic behaviour of the QDs has been observed and analyzed in accordance with the bound magnetic polarons model. These findings suggest that Co-doped ZnS QDs can be utilized effectively in the design of spintronic devices.

Quantum correlation and squeezing in pulses propagating in dispersion oscillating fibers

We consider the squeezing and correlation of quantum fluctuations in pulse pairs arising due to soliton fission in dispersion oscillating fibers. The dispersion oscillation acts as a time-domain pulse splitter. After the split, the pulses interact via their tails and acquire nonzero correlations. We analyze the correlation pattern using Karhunen–Loève mode expansion. The regime of high intrapulse and interpulse correlations can be described using single Karhunen–Loève mode. The regime with partial pulse-to-pulse correlation requires to take into account at least two Karhunen–Loève modes. We found that the soliton fission in dispersion oscillating fibers allows to generate squeezed states with highly correlated fluctuations in the output pulses.

An upwind-mixed volume element method on changing meshes for compressible miscible displacement problem

Numerical simulation of oil-water miscible displacement is discussed in this paper, and a compressible problem of energy mathematics is solved potentially. The mathematical model defined by a nonlinear system includes mainly two partial differential equations (PDEs): a parabolic equation for the pressure and a convection-diffusion equation for the saturation. The pressure is obtained by a conservative mixed finite volume element method (MFVE). The computational accuracy is improved for Darcy velocity. A conservative upwind mixed finite volume element method (UMFVE) is applied to compute the saturation on changing meshes. The diffusion is discretized by a mixed finite volume element method, and the convection is computed by upwind differences. The upwind method can solve convection-dominated diffusion equations accurately and avoids numerical dispersion and nonphysical oscillation. The saturation and the adjoint vector function are obtained simultaneously. An optimal order error estimates is obtained. Finally, numerical examples are provided to show the accuracy, efficiency and possible applications.

GPU-accelerated full-field modelling of highly dispersive ultrafast optical parametric oscillators

We demonstrate GPU-accelerated modelling of ultrafast optical parametric oscillators (OPOs) via the χ(2) nonlinear envelope equation with 1265× improvement in execution time compared with a CPU-based approach. Incorporating an adaptive step-size algorithm and absorbing boundary conditions, our model is capable of simulating OPOs containing long (&gt;10 mm) nonlinear crystals or significant intracavity dispersion with outputs generated in less than 1 minute, allowing the investigation of systems that were previously computationally prohibitive to explore. We implement real-world parameters such as optical coatings, material absorption, and non-ideal poling domains within quasi-phase matched nonlinear crystals, producing excellent agreement with the spectral tuning behaviour and average power from a previously reported prism-based OPO. Our digital twinning approach provides a low-cost iterative development platform for ultrafast OPOs.

Optical, magneto-optical properties and fiber-drawing ability of tellurite glasses in the TeO2–ZnO–BaO ternary system

The presented work is focused on the optical and magneto-optical characterization of TeO2-ZnO-BaO (TZB) tellurite glasses. We investigated the refractive index and extinction coefficient dispersion by spectroscopic ellipsometry from ultraviolet, λ ≈ 0.193 μm, up to mid-infrared, λ ≈ 25 μm spectral region. Studied glasses exhibited large values of linear (n632 ≈ 1.91–2.09) and non-linear refractive index (n2 ≈ 1.20–2.67×10−11 esu), Verdet constant (V632 ≈ 22–33 radT−1m−1) and optical band gap energy (Eg ≈ 3.7–4.1 eV). The materials characterization revealed that BaO substitution by ZnO leads (at constant content of TeO2) to an increase in linear and nonlinear refractive index as well as Verdet constant while the optical band gap energy decreases. Fiber drawing ability of TeO2–ZnO–BaO glassy system has been demonstrated on 60TeO2–20ZnO–20BaO glass with presented mid-infrared attenuation coefficient. Specific parameters such as dispersion and single oscillator energy, Abbe number, and first-/third-order optical susceptibility are enclosed together with the values of magneto-optic anomaly derived from the calculation of measured dispersion of the refractive index.

Thermal annealing enhanced morphological, nonlinear characteristic, and optical features of Victoria blue nanofilms for photonic application

Victoria blue thin films (VB) were produced using the spin coating technique (SCT) and subsequently annealed at temperatures ranging from 293 K to 463 K. The chemical structure and surface topography of VB films have been described using the Fourier-transform infrared (FT-IR) method and Scanning electron microscope (SEM). The transmittance and reflectance data were immediately used to derive optical features from 190 to 2500 nm in the wavelength range. The single oscillator model of Wemple-DiDomenico was used for determining the dispersion characteristics of VB films. Some dispersion parameters, such as dispersion energy (Ed), oscillator energy (Eο), optical conductivity (σ1, σ2) and dielectric constants (ε1and ε2) have been determined and clearly described. The values of χ3, f,M−1, M−3, ε∞,εL, N/m* , E0, Ed, n2andηopt for as deposited film are calculated as: 6.10 × 10-14, 71.30 (eV)2, 0.31, 0.040, 2.72, 4.04, 3.06 × 1046 kg−1 m−3, 6.34, 11.09, 7.6 × 10-13and 1.98, respectively. Based on this study, thermal annealing changes the optical properties of VB thin film, making it a preferable option for some photonic applications. On the other hand, the high values of these nonlinear parameters are crucial for creating low-power electronics such as optical computers. As a result, we strongly advise employing thermal annealing to change the linear and nonlinear properties of VB films, which might be the ideal choice for many photonic applications And nonlinear devices.

MIXED VOLUME ELEMENT-CHARACTERISTIC MIXED VOLUME ELEMENT OF NUMERICAL SIMULATION OF NUCLEAR CONTAMINATION TREATMENT AND ITS CONVERGENCE ANALYSIS

We consider a nonlinear system with boundary-initial value conditions of convection-diffusion partial differential equations describing nuclear waste disposal contamination in porous media. The flow pressure is determined by an elliptic equation, the concentrations of brine and radionuclide are formulated by convection-diffusion equations, and the transport of temperature is defined by a heat equation. The transport pressure appears in the concentration equations and heat equation accompanying with Darcy velocity, and controls their processes. The flow equation is solved by the conservative method of mixed volume element and the accuracy of Darcy velocity is improved one order. The method of characteristic mixed volume element is applied to solve the concentrations and the heat, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm high computation stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. The scheme can adopt a large step while it has smaller time-truncation error and higher order of accuracy. The mixed volume element method has law of conservation on every element to treat the diffusion and it can obtain numerical solution is of the concentration and adjoint vectors. Using the theory and technique of priori estimate of differential equations, we derive an optimal second order estimate in l2 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool to solve such an international famous problem.

A double-layer scheme for extrapolating terahertz complex refractivity from reflectance of aerocraft materials

The complex refractive indexes of aero craft materials are seldom investigated. In this paper, we fabricate two aero craft materials: a white painted aluminum plate and a coated window glass, and measure the reflectance spectra in the region of 3–50 THz. Different from the acquainted metal materials, the reflectance spectra of the two materials have apparent peaks and valleys, which is known as the spectral fingerprint. With the preliminary analysis by using Lorentz-Drude/Lorentz dispersion oscillator models and Kramers-Kronig (KK) algorithm, we find that the errors of the extracted complex refractivity from the dispersion oscillator models are apparent at the abrupt regions, and the accuracy of the real refractive index n and extinction coefficient κ from KK algorithm differs dramatically. To reduce the inevitable errors, we design a double-layer extraction scheme to reestablish the oscillator models based on the KK relation. Compared with the inversed data from KK relation and dispersion oscillator models, the procedure assures the accuracy of the real refractive index and extinction coefficient concurrently, the error of n/κ values at the abrupt region is also improved significantly. The method is reliable and convenient to obtain the precise broadband refractive index from spectra with apparent spectral fingerprints. And the obtained complex refractivity can support the further THz scattering analysis for aero craft targets.

Numerical and experimental investigation of a dispersive optoelectronic oscillator for chaotic time-delay signature suppression.

Chaos generation from a novel single-loop dispersive optoelectronic oscillator (OEO) with a broadband chirped fiber Bragg grating (CFBG) is numerically and experimentally investigated. The CFBG has much broader bandwidth than the chaotic dynamics such that its dispersion effect rather than filtering effect dominates the reflection. The proposed dispersive OEO exhibits chaotic dynamics when sufficient feedback strength is guaranteed. Suppression of chaotic time-delay signature (TDS) is observed as the feedback strength increases. The TDS can be further suppressed as the amount of grating dispersion increases. Without compromising bandwidth performance, our proposed system extends the parameter space of chaos, enhances the robustness to modulator bias variation, and improves TDS suppression by at least five times comparing to the classical OEO. Experimental results qualitatively agree well with numerical simulations. In addition, the advantage of dispersive OEO is further verified by experimentally demonstrating random bit generation with tunable rate up to 160 Gbps.

An upwind-block-centered finite difference method for a semiconductor device of heat conduction and its numerical analysis

The mathematical model is formulated by a nonlinear system of initial–boundary problem including four partial differential equations: an elliptic equation for electrostatic potential, two convection–diffusion equations for electron concentration and hole concentration, a heat conduction equation for temperature. The electric field potential is solved by the conservative block-centered method, and the first order of the accuracy is improved. The concentrations and temperature are computed by the upwind-block-centered difference method. The block-centered method is used to discretize the diffusion terms. The upwind difference is applied to approximate the convection parts without numerical dispersion or nonphysical oscillation. The block-centered difference simulates the concentrations, temperature and their adjoint vector functions simultaneously. The local conservation of mass is preserved. An optimal order error estimates is obtained. Finally, numerical examples show the effectiveness and viability of this method.

Remark on the correlation between the refractive index and the optical band gap in some crystalline solids

The correlation between static refractive index (ns) and optical band gap (Eg) based on the Wemple-DiDomenico (WD) model and the empirical correlation between the energy of an effective dispersive oscillator and optical band gap is examined for 52 crystalline solids. A comparison with two recently published empirical relationships between ns and Eg indicates that the use of the WD model provides better results and, more importantly, connects the ns versus Eg dependence with some chemical characteristics of solids such as the coordination number of cation, the valence of anion, the effective number of valence electrons and ionicity.

Complementary dispersive mirror pair produced in one coating run based on desired non-uniformity.

We report a novel one-coating-run method for producing an octave-spanning complementary dispersive mirror (DM) pair. The anti-phase group delay dispersion (GDD) oscillations are realized by two mirrors of the DM pair due to the certain thickness difference. Both mirrors are deposited within a single coating run enabled by the non-uniformity of the ion beam sputtering coating plant, which is obtained by tuning the distance between the source target and coating substrates. Since the DM pair is produced in a single deposition run, the GDD performance is more robust against deposition errors than that of the conventional complementary DM pair, in which two separated coating runs are necessary. Moreover, the new DM pair is compatible for both laser polarizations under the same angle of incidence, which could effectively reduce the difficulties of alignment for their implementation in laser systems than the double angle DM pair. The new DM pair is successfully applied to compress pulses from a Ti: Sapphire laser system down to 4.26 fs in pulse duration.

Linear and nonlinear optical characteristics of Bi12SiO20 single crystals

Bi12SiO20 single crystals grown by Czochralski method were optically investigated in detail in the present paper. Transmission and reflection measurements were performed at room temperature in the 400–800 nm spectral range on the (111) plane. Linear and nonlinear optical characteristics of the Bi12SiO20 crystal were determined analyzing the transmission and reflection spectra. The spectral dependencies of absorption coefficient, skin depth, refractive index, optical and electrical conductivities, real and imaginary parts of dielectric function were plotted. Analyses of optical parameters presented the direct band gap and Urbach energies as 2.55 and 0.33 eV, respectively. Static refractive index and dielectric constant, oscillator strength, dispersion and single oscillator energies, nonlinear refractive index, first- and third-order nonlinear susceptibilities were revealed. Structural properties of the Bi12SiO20 crystal were investigated by x-ray diffraction and scanning electron microscopy measurements.

Energetic Electron Microinjections Observed by MMS in the Dusk Plasma Sheet and Drift Resonance Interpretation

AbstractMicroinjection phenomena, characterized by dispersive oscillations of electron fluxes at the Pc5 period and bi‐directional pitch angle anisotropy, are frequently observed by Magnetospheric Multiscale in the dusk to midnight plasma sheet. In this paper, two such events are analyzed and the features of toroidal mode drift resonance measured meanwhile are shown in detail. The prominent observation is that the fluctuations of the electron flux and the electric field have either −90° or +90° phase difference at the resonant energy, and the phase difference rises as the energy increases. We extend the present theory for drift resonance of toroidal mode wave with only the equatorial moving electrons in a dipole field to include bouncing electrons. The predicted phase differences based on the new theory are consistent well with the observations in the microinjection events. It is thus suggested that drift resonance may act as the forming mechanism for the observed microinjections.

A Mixed Volume Element Modified With Characteristic Fractional Step Difference Method for the Compressible Multicomponent Displacement and Its Numerical Analysis

A three-dimensional compressible problem with different components is fundamental in numerical simulation of enhanced oil recovery. The mathematical model consists of a parabolic equation for the pressure and a convection-diffusion system for the concentrations. The pressure determines Darcy velocity and plays an important role during the whole physical process. A conservative mixed volume element is used to discretize the flow equation, and improves the computational accuracy of Darcy. The concentrations are computed by the modified characteristic fractional step difference scheme, thus numerical dispersion and nonphysical oscillations are eliminated. The whole three-dimensional computation is accomplished effectively by solving three successive one-dimensional problems in parallel, where the speedup method is used and the work is decreased greatly. Based on the theory and special techniques of a priori estimates of partial differential equations, an optimal second error estimates in L^2-norm is concluded. This work concentrates on the model, numerical method and convergence analysis for modern oil recovery.

Structure Analysis, Photoluminescence, and Non-linear/Linear Optical Parameters of Li-=SUB=-2-=/SUB=-Ge-=SUB=-4-=/SUB=-O-=SUB=-9-=/SUB=- : Mn-=SUP=-4+-=/SUP=- Transparent Glass-Ceramic

In this study, Li2Ge4O9 : Mn4+ transparent glass-ceramic was prepared by conventional melt-quenching. The thermal treatment was used for the devitrification of the sample. The creation of a Li2Ge4O9 nanocrystalline precipitated through the glass matrix was verified by X-ray diffraction and HR-TEM. Electron paramagnetic resonance spectra were employed to confirm the oxidation of Mn2+ to Mn4+ in glass-ceramic after thermal treatment. The photoluminescence spectra displayed a narrow red band centered at 668 nm ascribed to the spin-forbidden 4Eg-&amp;gt;4A2g transition of Mn4+. To estimate the optical parameters, UV-Vis-IR absorption spectroscopies were measured. The red shift of the direct optical band gap Eoptg, from 3.81 to 2.55 eV, was observed by increasing the Mn4+ concentration. The dispersion parameters, refraction indices (n, nбесконечность), and oscillator wavelength (λ0) were examined by using Wemple--DiDomenico single-oscillator model. The relationship between the refractive index and the energy gap has been investigated using various models such as Moss, Herve--Vandamme, Ravindra, and Singh--Kumar. In addition, the linear and non-linear optical properties of Li2Ge4O9 : Mn4+ were mentioned. The temperature-dependent luminescence intensity measurement was also carried out. The method of preparation exposed herein for the synthesis of Mn4+-doped GCs might be prevailing to produce identical luminescent ceramics in accordance with the glass's devitrification. Keywords: glass-ceramics, photoluminescence, optical properties, non-linear/linear optical, dispersion parameters, energy gap