Floquet Chern insulators of light

He, Li; Addison, Zachariah; Jin, Jicheng; Mele, Eugene J.; Johnson, Steven G.; Zhen, Bo

doi:10.1038/s41467-019-12231-4

Title: Floquet Chern insulators of light

Abstract

Achieving topologically-protected robust transport in optical systems has recently been of great interest. Most studied topological photonic structures can be understood by solving the eigenvalue problem of Maxwell’s equations for static linear systems. Here, we extend topological phases into dynamically driven systems and achieve a Floquet Chern insulator of light in nonlinear photonic crystals (PhCs). Specifically, we start by presenting the Floquet eigenvalue problem in driven two-dimensional PhCs. We then define topological invariant associated with Floquet bands, and show that topological band gaps with non-zero Chern number can be opened by breaking time-reversal symmetry through the driving field. Finally, we numerically demonstrate the existence of chiral edge states at the interfaces between a Floquet Chern insulator and normal insulators, where the transport is non-reciprocal and uni-directional. Our work paves the way to further exploring topological phases in driven optical systems and their optoelectronic applications.

Authors:

He, Li ^[1]; Addison, Zachariah ^[1]; Jin, Jicheng ^[1]; Mele, Eugene J. ^[1]; Johnson, Steven G. ^[2]; Zhen, Bo ^[1]

Pennsylvania State Univ., University Park, PA (United States). Dept. of Physics and Astronomy
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Mathematics

Publication Date:: Fri Sep 13 00:00:00 EDT 2019

Research Org.:: Pennsylvania State Univ., University Park, PA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1624194

Grant/Contract Number:: FG02-00ER41132

Resource Type:: Accepted Manuscript

Journal Name:: Nature Communications

Additional Journal Information:: Journal Volume: 10; Journal Issue: 1; Journal ID: ISSN 2041-1723

Publisher:: Nature Publishing Group

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Science & Technology - Other Topics

Citation Formats


                    He, Li, Addison, Zachariah, Jin, Jicheng, Mele, Eugene J., Johnson, Steven G., and Zhen, Bo. Floquet Chern insulators of light.  United States: N. p., 2019. 
Web.  doi:10.1038/s41467-019-12231-4.

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                    He, Li, Addison, Zachariah, Jin, Jicheng, Mele, Eugene J., Johnson, Steven G., & Zhen, Bo. Floquet Chern insulators of light.  United States.  https://doi.org/10.1038/s41467-019-12231-4

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                    He, Li, Addison, Zachariah, Jin, Jicheng, Mele, Eugene J., Johnson, Steven G., and Zhen, Bo. Fri .  
"Floquet Chern insulators of light".  United States.  https://doi.org/10.1038/s41467-019-12231-4.  https://www.osti.gov/servlets/purl/1624194.

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@article{osti_1624194,

  title        = {Floquet Chern insulators of light},

  author       = {He, Li and Addison, Zachariah and Jin, Jicheng and Mele, Eugene J. and Johnson, Steven G. and Zhen, Bo},

  abstractNote = {Achieving topologically-protected robust transport in optical systems has recently been of great interest. Most studied topological photonic structures can be understood by solving the eigenvalue problem of Maxwell’s equations for static linear systems. Here, we extend topological phases into dynamically driven systems and achieve a Floquet Chern insulator of light in nonlinear photonic crystals (PhCs). Specifically, we start by presenting the Floquet eigenvalue problem in driven two-dimensional PhCs. We then define topological invariant associated with Floquet bands, and show that topological band gaps with non-zero Chern number can be opened by breaking time-reversal symmetry through the driving field. Finally, we numerically demonstrate the existence of chiral edge states at the interfaces between a Floquet Chern insulator and normal insulators, where the transport is non-reciprocal and uni-directional. Our work paves the way to further exploring topological phases in driven optical systems and their optoelectronic applications.},

  doi          = {10.1038/s41467-019-12231-4},

  journal      = {Nature Communications},

  number       = 1,

  volume       = 10,

  place        = {United States},

  year         = {Fri Sep 13 00:00:00 EDT 2019},

  month        = {Fri Sep 13 00:00:00 EDT 2019}

}

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Journal Article:

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https://doi.org/10.1038/s41467-019-12231-4

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Figures / Tables:

Fig. 1: Floquet bands and gaps in a periodically driven nonlinear photonic crystal. a Schematic of a nonlinear photonic crystal (PhC) placed in a monochromatic driving field E^d at frequency Ω. b Due to the periodic drive, static bands of the PhC (solid lines) create copies of themselves—Floquet bands (dashedmore »

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Similar Records

Title: Floquet Chern insulators of light

Abstract

Citation Formats

Figures / Tables:

The topological theory of defects in ordered media journal, July 1979

Weyl and Dirac semimetals in three-dimensional solids journal, January 2018

Experimental Observation of Large Chern Numbers in Photonic Crystals journal, December 2015

Topological photonics journal, March 2019

Topological phases and nonreciprocal edge states in non-Hermitian Floquet insulators journal, July 2019

Observation of bulk Fermi arc and polarization half charge from paired exceptional points journal, January 2018

Floquet topological insulator in semiconductor quantum wells journal, March 2011

Bloch oscillation and unidirectional translation of frequency in a dynamically modulated ring resonator journal, January 2016

Photonic Floquet topological insulators journal, April 2013

Experimental observation of Weyl points journal, July 2015

Analogue of Rashba pseudo-spin-orbit coupling in photonic lattices by gauge field engineering journal, July 2016

Topological phase transitions and chiral inelastic transport induced by the squeezing of light journal, March 2016

Dynamical preparation of Floquet Chern insulators journal, October 2015

Nonreciprocal lasing in topological cavities of arbitrary geometries journal, October 2017

Topological insulator laser: Experiments journal, February 2018

Anomalous Quantum Hall Effect of Light in Bloch-Wave Modulated Photonic Crystals journal, June 2019

Topological photonics journal, October 2014

Two-dimensional topological photonics journal, November 2017

A three-dimensional photonic topological insulator using a two-dimensional ring resonator lattice with a synthetic frequency dimension journal, October 2018

Observation of photonic anomalous Floquet topological insulators journal, January 2017

Observation of unidirectional backscattering-immune topological electromagnetic states journal, October 2009

Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension journal, December 2016

What is — and what is not — an optical isolator journal, July 2013

Observation of unidirectional backscattering-immune topological electromagnetic states journal, October 2009

Photonic Floquet topological insulators journal, April 2013

Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension journal, December 2016

Observation of photonic anomalous Floquet topological insulators journal, January 2017

Topological photonics journal, October 2014

Two-dimensional topological photonics journal, November 2017

Interband transitions in photonic crystals journal, January 1999

Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry journal, January 2008

Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal journal, January 2008

Photonic Band Structure of Dispersive Metamaterials Formulated as a Hermitian Eigenvalue Problem journal, February 2010

Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators journal, June 2016

A three-dimensional photonic topological insulator using a two-dimensional ring resonator lattice with a synthetic frequency dimension journal, October 2018

Nonreciprocal lasing in topological cavities of arbitrary geometries journal, October 2017

Observation of bulk Fermi arc and polarization half charge from paired exceptional points journal, January 2018

Topological insulator laser: Experiments journal, February 2018

Topological aspects of photonic time crystals journal, January 2018

Dynamical preparation of Floquet Chern insulators text, January 2014

Experimental observation of Weyl points text, January 2015

Experimental Observation of Large Chern numbers in Photonic Crystals text, January 2015

Topological quantum fluctuations and travelling wave amplifiers text, January 2016

Broadband Nonreciprocal Amplification in Luminal Metamaterials journal, November 2019

Fresnel drag in space–time-modulated metamaterials journal, November 2019

Broadband Nonreciprocal Amplification in Luminal Metamaterials text, January 2019

Fresnel drag in space-time modulated metamaterials text, January 2019

Non-Hermitian Bulk-Boundary Correspondence in Periodically Driven System text, January 2020

The topological theory of defects in ordered media
journal, July 1979

Weyl and Dirac semimetals in three-dimensional solids
journal, January 2018

Experimental Observation of Large Chern Numbers in Photonic Crystals
journal, December 2015

Topological photonics
journal, March 2019

Topological phases and nonreciprocal edge states in non-Hermitian Floquet insulators
journal, July 2019

Observation of bulk Fermi arc and polarization half charge from paired exceptional points
journal, January 2018

Floquet topological insulator in semiconductor quantum wells
journal, March 2011

Bloch oscillation and unidirectional translation of frequency in a dynamically modulated ring resonator
journal, January 2016

Photonic Floquet topological insulators
journal, April 2013

Experimental observation of Weyl points
journal, July 2015

Analogue of Rashba pseudo-spin-orbit coupling in photonic lattices by gauge field engineering
journal, July 2016

Topological phase transitions and chiral inelastic transport induced by the squeezing of light
journal, March 2016

Dynamical preparation of Floquet Chern insulators
journal, October 2015

Nonreciprocal lasing in topological cavities of arbitrary geometries
journal, October 2017

Topological insulator laser: Experiments
journal, February 2018

Anomalous Quantum Hall Effect of Light in Bloch-Wave Modulated Photonic Crystals
journal, June 2019

Topological photonics
journal, October 2014

Two-dimensional topological photonics
journal, November 2017

A three-dimensional photonic topological insulator using a two-dimensional ring resonator lattice with a synthetic frequency dimension
journal, October 2018

Observation of photonic anomalous Floquet topological insulators
journal, January 2017

Observation of unidirectional backscattering-immune topological electromagnetic states
journal, October 2009

Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension
journal, December 2016

What is — and what is not — an optical isolator
journal, July 2013

Observation of unidirectional backscattering-immune topological electromagnetic states
journal, October 2009

Photonic Floquet topological insulators
journal, April 2013

Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension
journal, December 2016

Observation of photonic anomalous Floquet topological insulators
journal, January 2017

Topological photonics
journal, October 2014

Two-dimensional topological photonics
journal, November 2017

Interband transitions in photonic crystals
journal, January 1999

Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
journal, January 2008

Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
journal, January 2008

Photonic Band Structure of Dispersive Metamaterials Formulated as a Hermitian Eigenvalue Problem
journal, February 2010

Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators
journal, June 2016

A three-dimensional photonic topological insulator using a two-dimensional ring resonator lattice with a synthetic frequency dimension
journal, October 2018

Nonreciprocal lasing in topological cavities of arbitrary geometries
journal, October 2017

Observation of bulk Fermi arc and polarization half charge from paired exceptional points
journal, January 2018

Topological insulator laser: Experiments
journal, February 2018

Topological aspects of photonic time crystals
journal, January 2018

Dynamical preparation of Floquet Chern insulators
text, January 2014

Experimental observation of Weyl points
text, January 2015

Experimental Observation of Large Chern numbers in Photonic Crystals
text, January 2015

Topological quantum fluctuations and travelling wave amplifiers
text, January 2016

Broadband Nonreciprocal Amplification in Luminal Metamaterials
journal, November 2019

Fresnel drag in space–time-modulated metamaterials
journal, November 2019

Broadband Nonreciprocal Amplification in Luminal Metamaterials
text, January 2019

Fresnel drag in space-time modulated metamaterials
text, January 2019

Non-Hermitian Bulk-Boundary Correspondence in Periodically Driven System
text, January 2020