Related Experiment Video
Updated: Aug 15, 2026

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
Published on: September 17, 2021
Numerical simulation for SNAP based on the Numerov method
Abstract:
Surface nanoscale axial photonics (SNAP) microresonators are optical resonators characterized by nanoscale effective radius variations (ERV). In this work, we developed a numerical framework based on the Numerov method for modeling SNAP microresonators. The accuracy of the approach is validated by comparison with analytical solutions for specified ERV profiles. We further apply the method to a long semiparabolic ERV structure designed for advanced group delay applications, for which no analytical solution exists. The results demonstrate high accuracy and at least a twenty-fold improvement in computational efficiency. This work provides an efficient and reliable approach for modeling SNAP devices with arbitrary ERV profiles.
Related Concept Videos
Numerical Calculations
The solution to a problem is obtained using different methods. While manually solving algebraic symbols is one of the most common methods, the graphical method is often preferred. Computers...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Basic Discrete Time Signals
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
Critical Numbers and the Closed Interval Method
Newton’s Method
Downsampling
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
