Arbitrary Refractive Index Research Articles

Ray-transfer matrix for GRIN lenses: application to the crystalline lens

We present a Hamiltonian optics approach to determine the paraxial propagation of rays in gradient-index (GRIN) media. A derivation of the evolution equation for the corresponding ray-transfer matrix is given. An analytical solution can be found for a certain class of GRIN media. The proposed matrix is shown to be a generalization of the well-known matrices for planar and cylindrical GRIN lenses. We provide the accuracy results when applying our analytical method to arbitrary refractive indices and verify its validity by comparing it to other matrices in the literature with satisfactory results.

Two distinct algorithms for conformable time-fractional nonlinear Schrödinger equations with Kudryashov’s generalized non-local nonlinearity and arbitrary refractive index

Two distinct algorithms for conformable time-fractional nonlinear Schrödinger equations with Kudryashov’s generalized non-local nonlinearity and arbitrary refractive index

Optical solitons for twin-core couplers in optical metamaterials with Kudryashov’s sextic power law of arbitrary refractive index

Optical solitons for twin-core couplers in optical metamaterials with Kudryashov’s sextic power law of arbitrary refractive index

Tackling the inverse problem in ellipsometry: analytic expressions for supported coatings with nonuniform refractive index profiles in the thin film and weak contrast limits

Ellipsometry is a powerful tool for the evaluation of the refractive index profile of a film or coating supported on a solid substrate. A well-acknowledged problem, however, is the inverse problem: Given a set of data, under what conditions can a refractive index profile be determined unambiguously? To this end, a series expansion of the Abeles matrix method has been applied to an arbitrary refractive index profile to determine analytic expressions of the ellipsometric ratio ρ. Two types of expressions are found: The thin film limit in which the film thickness L is much less than the wavelength of the incident light beam ( L≪λ ) and the weak contrast limit in which the refractive index of the coating is very near the refractive index of the supporting substrate. In the thin film limit, the first two terms in the series expansion are relatively straight-forward, and they depend on two types of integrals involving the difference between the dielectric profile of the coating and the dielectric constant of the substrate. While higher order terms are possible, they are quite convoluted and do not assist in the inverse problem. In the weak contrast limit, however, the series expansion of ρ depends on the moments of the difference between the dielectric profile of the coating and the dielectric constant of the substrate, allowing an analytic expression that applies to coatings that are even much larger than the incident light beam. The expressions associated with both limits are verified through comparison to the numerical evaluation of ρ with the Abeles matrix method. The results demonstrate that through judicious selection of the substrate refractive index and incident wavelength, conditions can be created that permit critical insights into the inverse problem for either thin coatings or for coatings that are very near the refractive index of the substrate.

Quantum electrodynamics with a nonmoving dielectric sphere: quantizing Lorenz–Mie scattering

We quantize the electromagnetic field in the presence of a nonmoving dielectric sphere in vacuum. The sphere is assumed to be lossless, dispersionless, isotropic, and homogeneous. The quantization is performed using normalized eigenmodes as well as plane-wave modes. We specify two useful alternative bases of normalized eigenmodes: spherical eigenmodes and scattering eigenmodes. A canonical transformation between plane-wave modes and normalized eigenmodes is derived. This formalism is employed to study the scattering of a single photon, coherent squeezed light, and two-photon states off a dielectric sphere. In the latter case, we calculate the second-order correlation function of the scattered field, thereby unveiling the angular distribution of the Hong–Ou–Mandel interference for a dielectric sphere acting as a three-dimensional beam splitter. Our results are analytically derived for a dielectric sphere of arbitrary refractive index and size with a particular emphasis on the small-particle limit. As shown in Phys. Rev. A 108, 033714 (2023)PLRAAN1050-294710.1103/PhysRevA.108.033714, this work sets the theoretical foundation for describing the quantum interaction between light and the motional, rotational, and vibrational degrees of freedom of a dielectric sphere.

Retrieval of optical solitons in fiber Bragg gratings for high-order coupled system with arbitrary refractive index

With the rapid development of communication technology, fiber Bragg gratings are used in all optical communication systems. Bragg gratings are a technological spectacle that sustained balance between dispersion and nonlinear effects that leads to a stable transmission of solitons over huge distances. In this paper, the extended F-expansion technique is used for determining the solitons and other invariant solutions to the higher-order coupled system of nonlinear partial differential equations (NLPDEs) with arbitrary refractive index in fiber Bragg gratings. Various solutions, such as bright solitons, dark solitons, hyperbolic solutions, periodic solutions, Jacobi elliptic functions solutions, and rational solutions are extracted. The extracted solutions confirmed the efficacy and strength of the current technique. Moreover, the graphs for some solutions are presented to demonstrate their physical nature.

Conservation laws and Hamiltonian of the nonlinear Schrödinger equation of the fourth order with arbitrary refractive index

Objective:Conservation laws of the generalized nonlinear Schrödinger equation with arbitrary refractive index of the fourth order are found. Conservative quantities corresponding to the bright optical soliton are calculated. Method:Direct calculations of three conservation laws for the considered equation are used. This approach allows us to obtain the conservative densities and fluxes of the equation. Results:It is shown that there exist three conservation laws corresponding to the studied equation. The bright optical solitons of the equation are obtained. Using these solutions, conservative quantities of the soliton for the equation are calculated by means of integration. Some properties of conservation laws are discussed.

An Ab Initio, Fully Coherent, Semi-Analytical Model of Surface-Roughness-Induced Scattering

Integrated optics and silicon photonics is a rapidly maturing technology and is progressing in telecom, computation, and sensing. Surface-roughness-induced scattering is the primary source of optical loss in most photonic integrated circuits, and as such, ultimately limits the performance of their applications. However, a closed-form description for arbitrary refractive index profiles remains lacking, even though such a one is essential to enable an objective-oriented design of the waveguide platform. We present an ab initio, fully coherent, analytical model based on the volume current method that uses the surface roughness' autocorrelation function and the unperturbed mode's electromagnetic fields to predict the loss coefficient in closed form. An improved expression for the perturbation facilitates the application also to high-index-contrast systems. Hence, it is flexible concerning wavelength, materials, fabrication process, geometry and mode. Consequently, our model may be seamlessly integrated into electromagnetic simulation software suites, once the surface roughness is known for the utilized fabrication process. To verify our model, we compare the calculated scattering losses to measured propagation losses and established models for a wide range of waveguide systems in literature. We find that the previously neglected correlation along the waveguide height significantly impacts the scattering, which necessitates the holistic statistical analysis of the surface roughness. We believe these comprehensive prediction capabilities to be a useful tool for the optimization of silicon photonics design and fabrication, especially for low-confinement applications like sensors.

Optical wave propagation for the resonant nonlinear Schrödinger equation with arbitrary refractive index in optical fiber

In this paper, we study the resonant nonlinear Schrödinger equation which describes the propagation of optical solitons in optical fibers. Through the trial equation method and the complete discrimination system for polynomial we obtain abundant optical wave propagation patterns for the model and divide them into three categories. Besides, we analyze the topological stability of these patterns. Ultimately, we give physical representations of optical wave patterns and draw some figures to show their temporal-space structures.

Digital and Gradient Refractive Index Planar Optics by Nanoimprinting Mesoporous Silicon

AbstractWe report the realization of digital and gradient index flat‐optics and planar waveguides using the ‘nanoimprinting refractive index’ (NIRI) technique applied to mesoporous silicon. This technique combines the distinct optical and mechanical metamaterial qualities of mesoporous silicon, including its widely tunable effective refractive index and ability to undergo plastic deformation with a near zero Poisson ratio. Nanoimprinting with premastered and reusable stamps containing analog or digital features enables the continuous or discontinuous patterning of refractive index with high contrast Δn ≥ 0.8 and subwavelength resolution. Using NIRI we experimentally demonstrate a wavefront shaping flat microlens array operating in the visible (405–635 nm) and mesoporous silicon and silica waveguides operating near 1310 nm. This study demonstrates the viability of patterning arbitrary refractive index distributions, n(x,y), on the surface of a chip while circumventing the challenges and limitations of top‐down lithographic techniques – thus opening a low‐cost and scalable approach for the realization of advanced planar optical technologies.

Bright solitons of the model with arbitrary refractive index and unrestricted dispersion

Objective:The generalized Schrödinger equation with arbitrary refractive index and unrestricted order is considered. The objective of this paper is to demonstrate the bright solitons of this mathematical model can be found by the same formula taking into account the order of nonlinear differential equation. Method:The algorithm of constructing optical solitons of the generalized nonlinear Schrödinger equation with unrestricted dispersion using the simplest equation method is presented and applied for finding of optical solitons. Results:The optical solitons of the generalized nonlinear Schrödinger equation of the twelfth order are found at three powers on nonlinearity. The application of the method for finding solution of the generalized Korteweg–de Vries equation with arbitrary power of nonlinearity and unrestricted dispersion is discussed.

Exploring the solitons for multiple-core couplers having optical metamaterials using the modified extended direct algebraic method

This paper investigates the optical solitons for the cubic–quartic (CQ) multiple-core couplers with optical metamaterials having Kudryashov’s sextic power law of arbitrary refractive index. With the aid of the modified extended direct algebraic method, various types of solutions are raised. The obtained solutions include bright soliton solutions, dark soliton solutions, singular soliton solutions, singular periodic solutions, hyperbolic-type solutions, rational-type solutions, and exponential-type solutions. Moreover, for the physical illustration of the obtained solutions 2D, 3D, and contour graphs are presented.

Cubic–quartic solitons in twin-core couplers with optical metamaterials having Kudryashov’s sextic power law of arbitrary refractive index by using improved modified extended tanh-function method

In this article, the improved modified extended tanh-function method is applied to obtain optical solitons for the cubic–quartic (CQ) twin-core couplers in optical metamaterials having Kudryashov’s sextic power law of arbitrary refractive index. Various types of solutions are raised such as bright solitons, dark solitons, singular solitons, periodic solutions, singular periodic solutions, hyperbolic-type solutions, rational-type solution, Jacobi elliptic wave solutions, exponential wave solutions and Weierstrass elliptic doubly periodic-type solutions. Moreover, for the physical illustration of the obtained solutions 2D, 3D and contour graphs are presented.

Towards photophoresis with the generalized Lorenz-Mie theory

Based on the adjoint boundary value problem proposed decades ago by Zulehner and Rohatschek [1], analytic and closed-form expressions for the photophoretic forces exerted by arbitrary-shaped beams on homogeneous and low-loss spherical particles is derived in both the free molecular and slip flow regimes. To do so, the asymmetry vector for arbitrary refractive index particles is explicitly calculated by expanding the internal electromagnetic fields with the aid of the generalized Lorenz-Mie theory (GLMT). The approach here proposed is, to the best of the authors’ knowledge, the first systematic attempt to incorporate the GLMT stricto sensu into the field of photophoresis and might as well be extended, e.g. to spheroids and find important applications, among others, in optical trapping and manipulation of microparticles, in geoengineering, particle levitation, optical trap displays and so on.

Cubic–quartic optical solitons in magneto-optic waveguides for NLSE with Kudryashov’s law arbitrary refractive index and generalized non-local laws of nonlinearity

The present work addresses, for the first time, the cubic–quartic optical solitons in magneto-optic waveguides (MOW) for NLSE with Kudryashov’s law (KL) arbitrary refractive index and generalized non-local laws of nonlinearity. Two integrative methods, namely, the modified Kudryashov’s (MK’s) methodology and the addendum to Kudryashov’s (AK’s) methodology are utilized. Many different pattern of soliton solutions are deduced such as dark, bright optical solutions, candid solutions and combo bright-singular (CBS) solutions.

Highly dispersive optical solitons of the sixth-order differential equation with arbitrary refractive index

Partial differential equation of the sixth order for description of the propagation impulse in nonlinear optics is considered at arbitrary refractive index. Exact solution of differential equation is looked for using the traveling wave reductions. The first integral of nonlinear differential equation is presented. Highly dispersive optical solitons of the equation with arbitrary refractive index is found.

Cubic–quartic optical solitons in magneto-optic waveguides for Biswas–Milovic equation with Kudryashov’s law of arbitrary refractive index

This article reports cubic–quartic optical solitons in magneto-optic waveguides with Biswas–Milovic equation having Kudryashov’s nonlinear form for the first time. Bright, dark, singular and bright–singular solitons are retrieved via two integration methods.

Stationary solitons of the model with nonlinear chromatic dispersion and arbitrary refractive index

The generalized nonlinear Schrödinger equation with nonlinear chromatic dispersion and polynomial of powers with arbitrary refractive index is considered. The first integral of the nonlinear ordinary differential equation corresponding to the stationary solution of equation is presented. Analytical solutions for bright and dark stationary optical solitons described by the generalized mathematical model are found using transformations of variables.

Optical solutions and conservation laws of the Chen–Lee–Liu equation with Kudryashov's refractive index via two integrable techniques

The fundamental objective of this study is to find optical solutions to the perturbed Chen–Lee–Liu equation with Kudryashov's arbitrary refractive index model. Therefore, we applied the enhanced Kudryashov's and improved extended tanh-function techniques to the model. We obtained bright soliton, singular soliton, singular periodic wave, Jacobi elliptic function, exponential function, Weierstrass function, and dark soliton solutions. The obtained results are different from the other solutions available in the literature. As a result of the study, we can say that the proposed methods are effective and powerful for securing exact solutions of the nonlinear partial differential equations. Finally, using a new conservation theorem, we were able to establish the conservation laws for the current model.

Optical solitons of the model with generalized anti-cubic nonlinearity

The mathematical model for description of pulse propagation in optical fiber for the generalized anti-cubic nonlinearity with arbitrary refractive index is considered. The Cauchy problem for this partial differential equation cannot be solved by the inverse scattering transform and the analytical solutions of this mathematical model are found taking into account the traveling wave reduction. First integral of nonlinear ordinary differential equation is presented. Analytical solutions in the form of periodic and solitary waves are found using some transformations. Partial cases of the mathematical model for the generalized anti-cubic nonlinearity are studied.