Related Experiment Video
Updated: May 7, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Coherent-form energy conservation relation for the elastic scattering of a guided mode in a symmetric scattering
Abstract:
We propose a coherent-form energy conservation relation (ECR) that is generally valid for the elastic transmission and reflection of a guided mode in a symmetric scattering system. In contrast with the classical incoherent-form ECR, |τ|2 + |ρ|2≤1 with τ and ρ denoting the elastic transmission and reflection coefficients of a guided mode, the coherent-form ECR is expressed as |τ + ρ|≤1, which imposes a constraint on a coherent superposition of the transmitted and reflected modes. The coherent-form ECR is rigorously demonstrated and is numerically tested by considering different types of modes in various scattering systems. Further discussions with the scattering matrix formalism indicate that two coherent-form ECRs, |τ + ρ|≤1 and |τ-ρ|≤1, along with the classical ECR |τ|2 + |ρ|2≤1 constitute a complete description of the energy conservation for the elastic scattering of a guided mode in a symmetric scattering system. The coherent-form ECR provides a common tool in terms of energy transfer for understanding and analyzing the scattering dynamics in currently interested scattering systems.
Related Concept Videos
Elastic Collisions: Introduction
Elastic Collisions: Case Study
Energy Carried By Electromagnetic Waves
Symmetry in Maxwell's Equations
Types Of Collisions - I
Conservation of Energy

