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A theoretical investigation of coupling optics is presented in this paper based on ABCD matrix formulation in order to predict the coupling efficiency involving a laser diode (LD) and some identical single-mode circular core dispersion-shifted fiber (DSF) and dispersion-flattened fiber (DFF) with a cylindrical microlens (CML) in its tip. The authors derive analytical equations for the relevant coupling efficiency by assuming Gaussian distributions of the fields for both the source and the fiber under paraxial approximation. Further, in order to consider the non-Gaussian nature of the field of dispersion managed fibers, we employ spot size of Petermann II in our investigation. The investigations are made for two commonly used wavelengths, namely 1.3 and 1.5 μm. Our suggested technique demands extremely little computing for execution. For stimulation by a LD generating light of wavelength 1.3 μm, the maximum coupling efficiency ( η ) goes up to 94.41 percent. The proposed formulation also accounts for the limited aperture permitted by the CML. Thus, the analysis should find wide use in the design of CML on the single-mode circular core dispersion-controlled fibers tip to achieve large propagation distance.

We report the theoretical prediction of the coupling optics involving a laser diode and photonic crystal fiber which contains on its tip cylindrical microlens. The analysis is based on relevant ABCD matrix formalism. Though photonic crystal fiber has very large single-mode region, we carry on the investigation for two commonly used wavelengths such as 1.3 µm and 1.5 µm. For the particular kind of photonic crystal having specific value of air filling ratio and hole pitch, we have optimized the distance of laser diode from the microlens in order to get maximum value of coupling efficiency for each value of radius of cylindrical microlens. Incidentally, we have got here maximum coupling efficiency to the extent of 86.99 % at the wavelength 1.3 µm when the radius of the cylindrical microlens is 8.5 µm and effective spot size of the fiber is 4.433909 µm. Further, the maximum efficiency becomes 91.78 % at 1.3 µm when the radius of the cylindrical microlens is 4.0 µm and effective spot size of the fiber is 1.859907 µm. It has been shown that wavelength 1.5 µm is not so coupling efficient like 1.3 µm. Moreover, it has been shown that with same set of relevant parameters, PCF is more coupling efficient compared to ordinary graded index fiber. Thus the present work generates scope for varying different photonic crystal fiber parameters and the wavelengths of source as well for enhancing the coupling efficiency. Accordingly, the present analysis will be extremely helpful for design of efficient coupler of this kind.

The synthesis and characterization of novel p-type copper delafossite CuBO 2 microstructures were performed using an eco-friendly and cost-effective hydrothermal process. This study aims to explore the potential of these microstructures for environmental applications, specifically in the photo-induced degradation of hazardous dyes in wastewater. Various growth times were investigated to determine their influence on the morphology and photocatalytic performance of the synthesized microstructures. The characterization was carried out using X-ray diffractometer (XRD), field emission scanning electron microscope (FESEM), and transmission electron microscope (TEM). The energy dispersive X-ray (EDX) studies and UV-Vis spectrophotometer were used to analyze the optical properties and compositional purity. The synthesized CuBO 2 microstructures demonstrated significant photocatalytic activity, with the optimal sample synthesized in 2 h exhibiting a high degradation rate constant of 0.263 min −1 , it was found that the materials synthesized for the ideal 2 h exhibited good photocatalytic activity. The results indicated that the photocatalytic activity of the CuBO₂ samples improved with increasing growth time, attributed to the enhanced crystallinity and larger surface area of the microstructures. Moreover, The findings suggest that these hierarchical microstructures have a strong potential for use in wastewater treatment applications. This work indicates that CuBO 2 can be a versatile and effective material for environmental remediation, highlighting its importance in developing sustainable solutions for pollution control. Graphical Abstract Highlights Synthesized CuBO₂ microstructures for photocatalytic degradation of hazardous Rhodamine B dye in wastewater. Conducted eco-friendly hydrothermal synthesis at different times (1, 2, 4 h), with characterization by XRD, FESEM, and EDX. Sample synthesized at 2 h showed the highest degradation rate (0.263 min⁻¹), attributed to superior crystallinity and morphology. Hydroxyl radicals (OH•) were identified as key active species in dye degradation under UV irradiation. CuBO₂ microstructures offer a promising, sustainable solution for water purification and pollution control.

This paper estimates transmission coefficient at the splice of single-mode dispersion shifted trapezoidal and dispersion flattened graded and step W fibers in presence as well as in absence of Kerr nonlinearity. We restrict our analysis for both angular and transverse offsets only since splices are highly tolerant in respect of longitudinal mismatch. Here, we apply method of iteration involving Chebyshev formalism in order to take care of Kerr nonlinearity. The concerned investigation requires very little computation. It has been shown that our results match excellently with the exact results both in absence as well as in presence of Kerr nonlinearity. Considering that prediction of exact results in presence of Kerr nonlinearity requires application of rigorous finite element technique, our formalism in this context can be treated as a simple alternative to the existing method. Thus, this user friendly method generates ample scope for many useful applications in the field of nonlinear photonics involving such kinds of fiber.

A new technique is presented for computing very useful propagation parameters like effective core area and effective index of refraction of mono-mode dispersion shifted and dispersion flattened fibers both in the presence and in the absence of Kerr nonlinearity. The technique involves application of accurate but simple expressions for modal fields developed by Chebyshev formalism. The study of the influence of Kerr nonlinearity on the aforementioned parameters, however, requires the application of the method of iteration. For the purpose of such investigation, in linear as well as nonlinear region, we take some typically used dispersion shifted and dispersion flattened fibers and we show that the results found by our simple formalism are in excellent agreement with those obtained by using complex finite element method. Further, the necessary evaluation by our simple method needs very less computations. Thus, our formalism generates ample opportunity for applications in many areas in the field of nonlinear optics.

The coupling reliability of laser-to-fiber coupling has become a significant concern in optical communication technologies. However, it appears that different categories of misalignment degrade the coupling efficiency (CE) when it comes to fiber-to-lens coupling. Unexpected noise gets generated by the lateral asymmetry because of back-reflection from the fiber endpoint to the laser diode (LD). In this article, we present an easily understood theoretical approach for determining the reflected intensity noise (RIN) when an LD is coupled to a graded index fiber (GIF) with an upside-down tapering parabolic microlens (UDTPML) on the fiber tip. We exhibit the RIN values concerning probable lateral alignment errors. The pertinent ABCD matrix has been applied to derive the relevant CE in the context of lateral misalignment. The findings will provide significant guidance for minimizing such noise in optical fiber couplers, leading to more efficient and reliable optical technology. Further, the study not only meets the current demands of high-speed data transmission but also paves the way for future advancements in optical technology.

This paper reports simple but accurate analytical expressions of group delay and modal dispersion parameters for single-mode graded index fibers over a wide range of numbers. The formulation employs power series expression for the fundamental modal field of graded index fiber derived by Chebyshev formalism. Choosing some typical step, parabolic and triangular index fibers as examples in our present study, we use the prescribed formulations to estimate group delay and modal dispersion parameters of those fibers both in presence and absence of Kerr nonlinearity. Iterative technique is applied for prediction of concerned propagation parameters in presence of Kerr nonlinearity. Our results show excellent agreement with the numerical exact ones both in absence and presence of Kerr nonlinearity. The exact results in case of Kerr nonlinearity are obtained using cumbersome finite element method. The execution of our accurate formalism involves little computation and is thus user friendly for technologists and researchers working in the field of nonlinear optical engineering.

In an all-optical communication system, an erbium-doped fiber amplifier performs a very significant role. The effectiveness of the operation of this kind of amplifier depends on different parameters of the amplifier. Variation of the intensities of pump and signal with distance along the radius of the fiber from the core axis is one such significant parameter. In our present case, we have studied the distribution of the intensities of both the pump and signal along the radius of the fiber in an erbium-doped dual-mode fiber amplifier for the LP 11 mode. In the present case, some step-index fibers of different normalized frequencies have opted. Our study is an application of the Chebyshev technique expressing the LP 11 modal field in the form of a power series. A little computation is required for the prediction of the concerned results by this technique. Results obtained from this study show an excellent match with those found by the rigorous finite element method establishing its accuracy. This study using such a user-friendly and accurate technique will be helpful to the optical engineers involved in this domain.

In an all-optical communication system, an erbium-doped fiber amplifier performs a very significant role. The effectiveness of the operation of this kind of amplifier depends on different parameters of the amplifier. Variation of the intensities of pump and signal with distance along the radius of the fiber from the core axis is one such significant parameter. In our present case, we have studied the distribution of the intensities of both the pump and signal along the radius of the fiber in an erbium-doped dual-mode fiber amplifier for the LP mode. In the present case, some step-index fibers of different normalized frequencies have opted. Our study is an application of the Chebyshev technique expressing the LP modal field in the form of a power series. A little computation is required for the prediction of the concerned results by this technique. Results obtained from this study show an excellent match with those found by the rigorous finite element method establishing its accuracy. This study using such a user-friendly and accurate technique will be helpful to the optical engineers involved in this domain.