Symmetry and transformation of waves in optics and acoustics of crystals

TL;DR

This paper explores the symmetry and transformation properties of electromagnetic and ultrasonic waves in crystals, revealing how crystal structure influences wave behavior and classification based on electromagnetic principles.

Contribution

It introduces a novel group representation approach using differential operators to analyze wave transformations and crystal classifications beyond traditional Maxwell equations.

Findings

Crystal symmetry affects wave transformation and caustic formation.

Crystals can be classified based on electromagnetic properties.

Wave processes in crystals share axiomatic foundations with other physics domains.

Abstract

It is show that in group representation by non-traditionally determining by the Maxwell equations, instead of wave, linear differential operator of momentous type from the common point of view the transformation of electromagnetic and ultrasonic radiation as well as the formation of caustics generation of solitons in crystals is represented. It is established that forming operator structural constants determine bias current with the connected charge and group velocity and also optical and acoustic axes of a crystal, which characterize its wave properties, moreover crystals are classified on common electromagnetic base. It is discovered that at change of crystal symmetry and representation of different wave process the problems also take place, which are similar to others spheres of physics and are constructed on the same aximatical base.