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Eigenmode Sensitivity in Step-Index Fibers: A Sturm–Liouville Approach to Fabrication Tolerances

2025-12-04Mohammadmahdi Maharebi

A rigorous analysis of guided modes in optical fibers using Sturm–Liouville theory and first-order perturbation methods, with validated numerical solutions for index, radius, and absorption perturbations.

photonicsoptical fibersperturbation theory

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Why Linear Regression Is More Profound Than You Think: A Journey Through Estimation Theory

2025-11-27Mohammadmahdi Maharebi

An exploration of how geometry, probability, and sequential estimation converge on the elegant solution to linear regression, revealing deep connections across machine learning.

linear algebraestimation theoryregression

Simulating Electromagnetic Waves in a Cavity: FDTD Method for 2D PEC Resonators

2025-10-20Mohammadmahdi Maharebi

A complete implementation and validation of the Finite-Difference Time-Domain (FDTD) method for simulating electromagnetic wave propagation in a 2D Perfect Electric Conductor (PEC) cavity with sub-1% accuracy.

computational-physicselectromagneticsfdtd

From Ladder Operators to Photons: The Harmonic Oscillator → Quantum Optics Bridge

2025-10-19

How the algebra of the quantum harmonic oscillator becomes photon creation and annihilation operators in quantum optics.

quantum-mechanicsquantum-opticsharmonic-oscillator

Building a Modern Blog with MDX, KaTeX, and Custom Components

2024-01-15

A comprehensive tutorial on combining MDX, KaTeX, and React components to create rich, interactive technical content

mdxkatexreact