Related Experiment Video
Updated: Jun 17, 2026
07:16
Finite Element Analysis Model for Assessing Expansion Patterns from Surgically Assisted Rapid Palatal Expansion
Published on: October 20, 2023
Analysis of semi-infinite periodic structures using a domain reduction technique
Arya Fallahi1, Christian Hafner
1Laboratory of Electromagnetic Fields and Microwave Electronics, ETH Zürich, Zürich CH-8092, Switzerland. fallahia@ifh.ee.ethz.ch
Summary
A novel boundary condition simplifies calculating the effective impedance matrix for semi-infinite periodic structures like photonic crystals. This method efficiently determines reflection properties, reducing computational complexity.
Area of Science:
- Physics
- Materials Science
- Electromagnetics
Background:
- Semi-infinite periodic structures, including photonic crystals and metamaterials, are crucial in modern optics and electronics.
- Calculating their effective impedance matrix is essential for understanding wave reflection and transmission.
- Existing methods can be computationally intensive, especially for complex structures.
Purpose of the Study:
- To introduce a new boundary condition for calculating the effective impedance matrix of semi-infinite periodic structures.
- To reduce the computational solution space required for these calculations.
- To provide a method for relating the effective impedance matrix to the properties of photonic crystals (PCs) concerning interface reflection.
Main Methods:
- Development of a new boundary condition for effective impedance matrix calculation.
- Derivation of a closed-form equation for the effective impedance of 1D photonic crystals and multilayer films.
- Utilizing scattering matrices and solving a unilateral quadratic matrix equation for 2D photonic crystals.
Main Results:
- A reduced solution space for calculating the effective impedance matrix.
- The effective impedance matrix encapsulates all reflection properties of a periodic structure.
- Validated computational scheme through several examples focused on plane wave reflection from semi-infinite periodic structures.
Conclusions:
- The new boundary condition offers an efficient approach to characterizing wave reflection from semi-infinite periodic structures.
- The method is applicable to both 1D and 2D photonic crystals and metamaterials.
- The developed scheme provides accurate computation of reflection coefficients, crucial for device design.
Related Concept Videos
01:19Limits with Oscillating Discontinuities
An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the most...
01:17Trigonometric Fourier series
Fourier series is a foundational mathematical technique that decomposes periodic functions into an infinite series of sinusoidal harmonics. This method enables the representation of complex periodic signals as sums of simple sine and cosine functions, facilitating their analysis and interpretation in various fields, including signal processing, acoustics, and electrical engineering.
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
01:20Discrete-Time Fourier Series
The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
For a discrete-time periodic signal x[n]...
01:22Block Diagram Reduction
The process of deriving the transfer function of a control system often involves reducing its block diagram to a single block. This simplification can be achieved through a series of strategic operations, including relocating branch points and comparators. These operations preserve the overall function of the system while allowing for easier manipulation and combination of blocks.
The first step in this process is the identification and relocation of a branch point. A branch point, where a...
The first step in this process is the identification and relocation of a branch point. A branch point, where a...
01:16Properties of Laplace Transform-II
Time differentiation, convolution, integration, and periodicity are fundamental concepts in analyzing functions and signals over time. Each concept provides a unique perspective on how functions evolve, interact, and repeat, offering essential tools for various scientific and engineering applications.
Time differentiation involves analyzing the rate of change of a function over time. Mathematically, it is the derivative of a function with respect to time. This concept can be likened to tracking...
Time differentiation involves analyzing the rate of change of a function over time. Mathematically, it is the derivative of a function with respect to time. This concept can be likened to tracking...
01:26Linear Approximation in Frequency Domain
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.