# Effective Light Dynamics in Perturbed Photonic Crystals

@article{DeNittis2013EffectiveLD, title={Effective Light Dynamics in Perturbed Photonic Crystals}, author={Giuseppe De Nittis and Max Lein}, journal={Communications in Mathematical Physics}, year={2013}, volume={332}, pages={221-260} }

In this work, we rigorously derive effective dynamics for light from within a limited frequency range propagating in a photonic crystal that is modulated on the macroscopic level; the perturbation parameter $${\lambda \ll 1}$$λ≪1 quantifies the separation of spatial scales.We do that by rewriting the dynamical Maxwell equations as a Schrödinger-type equation and adapting space-adiabatic perturbation theory. Just like in the case of the Bloch electron, we obtain a simpler, effective Maxwell…

## 18 Citations

### Derivation of Ray Optics Equations in Photonic Crystals via a Semiclassical Limit

- Physics
- 2015

In this work, we present a novel approach to the ray optics limit: we rewrite the dynamical Maxwell equations in Schrödinger form and prove Egorov-type theorems, a robust semiclassical technique. We…

### Derivation of Ray Optics Equations in Photonic Crystals via a Semiclassical Limit

- PhysicsAnnales Henri Poincaré
- 2017

In this work, we present a novel approach to the ray optics limit: we rewrite the dynamical Maxwell equations in Schrödinger form and prove Egorov-type theorems, a robust semiclassical technique. We…

### Wave packet dynamics in slowly modulated photonic graphene

- PhysicsJournal of Differential Equations
- 2019

### Symmetry classification of topological photonic crystals

- PhysicsAdvances in Theoretical and Mathematical Physics
- 2019

In a seminal paper Haldane conjectured that topological phenomena are not particular to quantum systems, and indeed experiments realized unidirectional, backscattering-free edge modes with…

### Taking Inspiration from Quantum-Wave Analogies --- Recent Results for Photonic Crystals

- Physics
- 2017

Similarities between quantum systems and analogous systems for classical waves have been used to great effect in the physics community, be it to gain an intuition for quantum systems or to anticipate…

### Wave dynamics in locally periodic structures by multiscale analysis

- Physics, Mathematics
- 2017

Wave dynamics in locally periodic structures by multiscale analysis Alexander B. Watson We study the propagation of waves in spatially non-homogeneous media, focusing on Schrödinger’s equation of…

### Equivalence of electric, magnetic, and electromagnetic Chern numbers for topological photonic crystals

- Physics
- 2018

Haldane predicted an analog of the Integer Quantum Hall Effect in gyrotropic photonic crystals, where the net number of electromagnetic edge modes moving left-to-right is given by a bulk Chern…

### The Schrödinger formalism of electromagnetism and other classical waves—How to make quantum-wave analogies rigorous

- PhysicsAnnals of Physics
- 2018

### The perturbed Maxwell operator as pseudodifferential operator

- Mathematics, PhysicsDocumenta Mathematica
- 2014

As a first step to deriving effective dynamics and ray optics, we prove that the perturbed periodic Maxwell operator in d = 3 can be seen as a pseudodifferential operator. This necessitates a better…

## References

SHOWING 1-10 OF 48 REFERENCES

### Topological aspects in the photonic-crystal analog of single-particle transport in quantum Hall systems

- Physics
- 2013

We present a perturbative approach to derive the semiclassical equations of motion for the two-dimensional electron dynamics under the simultaneous presence of static electric and magnetic fields,…

### Geometrical aspects in optical wave-packet dynamics.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

An application of the semiclassical theory for propagation of an optical wave packet in a nonconducting medium with a periodic structure of dielectric permittivity and magnetic permeability to a two-dimensional photonic crystal is shown, and an optimal design for the enhancement of the optical Hall effect in photonic crystals is proposed.

### Effective Dynamics for Particles Coupled to a Quantized Scalar Field

- Physics
- 2008

We consider a system of N non-relativistic spinless quantum particles (“electrons”) interacting with a quantized scalar Bose field (whose excitations we call “photons”). We examine the case when the…

### Photonic Crystals: Molding the Flow of Light

- Physics
- 1995

Since it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the…

### Effective Dynamics for Bloch Electrons: Peierls Substitution and Beyond

- Physics
- 2002

AbstractWe consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential, φ(ɛx), and vector potential A(ɛx), with xℝd and ɛ≪1. We…

### TOPOLOGICAL PHOTONIC STATES

- Physics
- 2014

As exotic phenomena in optics, topological states in photonic crystals have drawn much attention due to their fundamental significance and great potential applications. Because of the broken…

### The perturbed Maxwell operator as pseudodifferential operator

- Mathematics, PhysicsDocumenta Mathematica
- 2014

As a first step to deriving effective dynamics and ray optics, we prove that the perturbed periodic Maxwell operator in d = 3 can be seen as a pseudodifferential operator. This necessitates a better…

### APPLICATIONS OF MAGNETIC ΨDO TECHNIQUES TO SAPT

- Physics, Mathematics
- 2011

In this review, we show how advances in the theory of magnetic pseudodifferential operators (magnetic ΨDO) can be put to good use in space-adiabatic perturbation theory (SAPT). As a particular…

### Diffraction of Bloch Wave Packets for Maxwell's Equations

- Mathematics
- 2012

We study, for times of order 1/h, solutions of Maxwell's equations in an O(h^2) modulation of an h-periodic medium. The solutions are of slowly varying amplitude type built on Bloch plane waves with…