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abstract: Topological protection for lasers Ideas based on topology, initially developed in mathematics to describe the properties of geometric space under deformations, are now finding application in materials, electronics, and optics. The main driver is topological protection, a property that provides stability to a system even in the presence of defects. Harari et al. outline a theoretical proposal that carries such ideas over to geometrically designed laser cavities. The lasing mode is confined to the topological edge state of the cavity structure. Bandres et al. implemented those ideas to fabricate a topological insulator laser with an array of ring resonators. The results demonstrate a powerful platform for developing new laser systems. Science, this issue p. eaar4003, p. eaar4005 Lasing is observed in an edge mode of a designed optical topological insulator. INTRODUCTION Topological insulators emerged in condensed matter physics and constitute a new phase of matter, with insulating bulk and robust edge conductance that is immune to imperfections and disorder. To date, topological protection is known to be a ubiquitous phenomenon, occurring in many physical settings, ranging from photonics and cold atoms to acoustic, mechanical, and elastic systems. So far, however, most of these studies were carried out in entirely passive, linear, and conservative settings. RATIONALE We propose topological insulator lasers: lasers whose lasing mode exhibits topologically protected transport without magnetic fields. Extending topological physics to lasers is far from natural. In fact, lasers are built on foundations that are seemingly inconsistent with the essence of topological insulators: They require gain (and thus are non Hermitian) they are nonlinear entities because the gain must be saturable, and they are open systems because they emit light. These properties, common to all lasers, cast major doubts on the possibility of harnessing topological features to make a topological insulator laser. Despite this common mindset, we show that the use of topological properties leads to highly efficient lasers, robust to defects and disorder, with single mode lasing even at conditions high above the laser threshold. RESULTS We demonstrate that topological insulator lasers are theoretically possible and experimentally feasible. We consider two configurations involving planar arrays of coupled active resonators. The first is based on the Haldane model, archetypical for topological systems. The second model, geared toward experiment, constitutes an aperiodic array architecture creating an artificial magnetic field. We show that by introducing saturable gain and loss, it is possible to make these systems lase in a topological edge state. In this way, the lasing mode exhibits topologically protected transport; the light propagates unidirectionally along the edges of the cavity, immune to scattering and disorder, unaffected by the shape of the edges. Moreover, we show that the underlying topological properties not only make the system robust to fabrication and operational disorder and defects, they also lead to a highly efficient single mode lasing that remains single mode even at gain values high above the laser threshold. The figure describes the geometry and features of a topological insulator laser based on the Haldane model while adding saturable gain, loss, and an output port. The cavity is a planar honeycomb lattice of coupled microring resonators, pumped at the perimeter with a lossy interior. We show that under these conditions, lasing occurs at the topological edge mode, which has unidirectional flux and is extended around the perimeter with almost uniform intensity. The topological cavities exhibit higher efficiency than the trivial cavity, even under strong disorder. For the topological laser with a small gap, the topological protection holds as long as the disorder level is smaller than the gap size. DISCUSSION The concept of the topological insulator laser alters current understanding of the interplay between disorder and lasing, and opens exciting possibilities at the interface of topological physics and laser science, such as topologically protected transport in systems with gain. We show here that the laser system based on the archetypal Haldane model exhibits topologically protected transport, with features similar to those of its passive counterpart. This behavior means that this system is likely to have topological invariants, despite the nonhermiticity. Technologically, the topological insulator laser offers an avenue to make many semiconductor lasers operate as one single mode high power laser. The topological insulator laser constructed from an aperiodic array of resonators was realized experimentally in an all dielectric platform, as described in the accompanying experimental paper by Bandres et al. Topological insulator laser based on the Haldane model and its efficiency. (A) Planar honeycomb lattice of coupled microring resonators pumped at the perimeter. The topological lasing mode has unidirectional flux with almost uniform intensity, which builds up as the mode circulates and drops when passing the output coupler. (B) Slope efficiency (in arbitrary units) versus disorder strength for three cases differing only in the Haldane phase (of the next to nearest neighbor coupling) a topological laser with the maximum gap (blue; Haldane phase of p/2) one with a small topological gap (red; Haldane phase of p/8) and a topologically trivial laser with no gap (black; Haldane phase of 0) Topological insulators are phases of matter characterized by topological edge states that propagate in a unidirectional manner that is robust to imperfections and disorder. These attributes make topological insulator systems ideal candidates for enabling applications in quantum computation and spintronics. We propose a concept that exploits topological effects in a unique way: the topological insulator laser. These are lasers whose lasing mode exhibits topologically protected transport without magnetic fields. The underlying topological properties lead to a highly efficient laser, robust to defects and disorder, with single mode lasing even at very high gain values. The topological insulator laser alters current understanding of the interplay between disorder and lasing, and at the same time opens exciting possibilities in topological physics, such as topologically protected transport in systems with gain. On the technological side, the topological insulator laser provides a route to arrays of semiconductor lasers that operate as one single mode high power laser coupled efficiently into an output port.
author_names: Gal Harari

Miguel A Bandres

Yaakov Lumer

Mikael C Rechtsman

Yidong Chong

Mercedeh Khajavikhan

Demetrios N Christodoulides

Mordechai Segev
title: Topological insulator laser: Theory
venue: Science
year: 2018

abstract: In the following, the first results on ultraviolet laser desorption (UVLD) of bioorganic compounds in the mass range above 10000 daltons are reported. Strong molecular ion signals were registered by use of an organic matrix with strong absorption at the wavelength used for controlled energy deposition and soft desorption (7)
author_names: Michael Karas

F Hillenkamp
title: Laser desorption ionization of proteins with molecular masses exceeding 10,000 daltons.
venue: Analytical chemistry
year: 1988

abstract: Random Processes and Random Fields Optical Turbulence in the Atmosphere Free Space Propagation of Gaussian Beam Waves Classical Theory of Optical Wave Propagation Line of Sight Propagation Weak Fluctuation Theory, Part 1 Line of Sight Propagation Weak Fluctuation Theory, Part 2 Propagation Through Random Phase Screens Laser Satellite Communication Systems Propagation Through Complex Paraxial ABCD Optical Systems Doublepassage Problems Laser Radar Systems Line of Sight Propagation Strong Fluctuation Theory Appendices Special Functions Integral Table Tables of Beam Statistics Mathematica Programmes.
author_names: Larry C Andrews

Ronald L Phillips
title: Laser Beam Propagation Through Random Media
year: 1998

abstract: Laser light with a Laguerre Gaussian amplitude distribution is found to have a well defined orbital angular momentum. An astigmatic optical system may be used to transform a high order Laguerre Gaussian mode into a high order Hermite Gaussian mode reversibly. An experiment is proposed to measure the mechanical torque induced by the transfer of orbital angular momentum associated with such a transformation.
title: Orbital angular momentum of light and the transformation of Laguerre Gaussian laser modes.
venue: Physical review. A, Atomic, molecular, and optical physics
year: 1992

abstract: Infrared Route to Graphene Electrodes Electrochemical capacitors can deliver large amounts of power quickly, but have limited energy storage because only the surface regions of electrodes can store charge. Graphene represents an alternative to activated carbon electrodes because of their high conductivity and surface area, but graphene sheets tend to reassociate and lose surface area. El Kady et al. (p. 1326; see the Perspective by Miller) show that graphite oxide sheets can be converted by infrared laser irradiation into porous graphene sheets that are flexible, robust, and highly conductive. Infrared laser reduction of graphene oxide creates a strong porous electrode with both high surface area and high conductivity. Although electrochemical capacitors (ECs) also known as supercapacitors or ultracapacitors, charge and discharge faster than batteries, they are still limited by low energy densities and slow rate capabilities. We used a standard LightScribe DVD optical drive to do the direct laser reduction of graphite oxide films to graphene. The produced films are mechanically robust, show high electrical conductivity (1738 siemens per meter) and specific surface area (1520 square meters per gram) and can thus be used directly as EC electrodes without the need for binders or current collectors, as is the case for conventional ECs. Devices made with these electrodes exhibit ultrahigh energy density values in different electrolytes while maintaining the high power density and excellent cycle stability of ECs. Moreover, these ECs maintain excellent electrochemical attributes under high mechanical stress and thus hold promise for high power, flexible electronics.
author_names: Maher F El-Kady

Veronica Strong

Sergey Dubin

Richard B Kaner
title: Laser Scribing of High Performance and Flexible Graphene Based Electrochemical Capacitors
venue: Science
year: 2012

abstract: Molecular excitation by the simultaneous absorption of two photons provides intrinsic three dimensional resolution in laser scanning fluorescence microscopy. The excitation of fluorophores having single photon absorption in the ultraviolet with a stream of strongly focused subpicosecond pulses of red laser light has made possible fluorescence images of living cells and other microscopic objects. The fluorescence emission increased quadratically with the excitation intensity so that fluorescence and photo bleaching were confined to the vicinity of the focal plane as expected for cooperative two photon excitation. This technique also provides unprecedented capabilities for three dimensional, spatially resolved photochemistry, particularly photolytic release of caged effector molecules.
author_names: Winfried Denk

James H Strickler

Watt W Webb
title: Two photon laser scanning fluorescence microscopy.
venue: Science
year: 1990

abstract: Solid State Laser Engineering is written from an industrialperspective and discusses in detail the characteristics, design, construction and practical problems of solid statelasers. Emphasis is placed on engineering and practicalconsiderations, with a phenomenological treatment usingmodelsbeing preferred to abstract mathematical derivations.This new edition has been updated and revised to includeimportant developments, concepts and technologies that haveemerged since the publication of the first edition.
author_names: Walter Koechner
title: Solid State Laser Engineering
year: 1976

abstract: Abstract This study demonstrates the significant effect of the recoil pressure and Marangoni convection in laser powder bed fusion (L PBF) of 316L stainless steel. A three dimensional high fidelity powder scale model reveals how the strong dynamical melt flow generates pore defects, material spattering (sparking) and denudation zones. The melt track is divided into three sections: a topological depression, a transition and a tail region, each being the location of specific physical effects. The inclusion of laser ray tracing energy deposition in the powder scale model improves over traditional volumetric energy deposition. It enables partial particle melting, which impacts pore defects in the denudation zone. Different pore formation mechanisms are observed at the edge of a scan track, at the melt pool bottom (during collapse of the pool depression) and at the end of the melt track (during laser power ramp down) Remedies to these undesirable pores are discussed. The results are validated against the experiments and the sensitivity to laser absorptivity is discussed.
author_names: Saad A Khairallah

Andrew T Anderson

Alexander M Rubenchik

Wayne E King
title: Laser powder bed fusion additive manufacturing: Physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones
year: 2016

abstract: The Linac Coherent Light Source free electron laser has now achieved coherent X ray generation down to a wavelength of 1.2 A and at a brightness that is nearly ten orders of magnitude higher than conventional synchrotrons. Researchers detail the first operation and beam characteristics of the system, which give hope for imaging at atomic spatial and temporal scales.
author_names: Paul J Emma

Ron Akre

John R Arthur

R M Bionta

Christoph Bostedt

John D Bozek

Axel Brachmann

Philip H Bucksbaum

Ryan N Coffee

Franz Josef Decker

Y Ding

David Harry Dowell

Steve Edstrom

A S Fisher

Josef C Frisch

Sasha Gilevich

Jerome B Hastings

Gregory Ross Hays

Ph Hering

Zhirong Huang

Richard H Iverson

Henrik Loos

Marc Messerschmidt

A A Miahnahri

Stefan Moeller

Heinz Dieter Nuhn

G Pile

Daniel Ratner

Jeffrey A Rzepiela

D C Schultz

Peter M Stefan

H Tompkins

J J Turner

James J Welch

William E White

Juhao Wu

Gerald Yocky

John N Galayda
title: First lasing and operation of an angstrom wavelength free electron laser
year: 2010

abstract: Processing of materials by ultrashort laser pulses has evolved significantly over the last decade and is starting to reveal its scientific, technological and industrial potential. In ultrafast laser manufacturing, optical energy of tightly focused femtosecond or picosecond laser pulses can be delivered to precisely defined positions in the bulk of materials via two /multi photon excitation on a timescale much faster than thermal energy exchange between photoexcited electrons and lattice ions. Control of photo ionization and thermal processes with the highest precision, inducing local photomodification in sub 100 nm sized regions has been achieved. State of the art ultrashort laser processing techniques exploit high 0.1 1 mm spatial resolution and almost unrestricted three dimensional structuring capability. Adjustable pulse duration, spatiotemporal chirp, phase front tilt and polarization allow control of photomodification via uniquely wide parameter space. Mature opto electrical/mechanical technologies have enabled laser processing speeds approaching meters per second, leading to a fast lab to fab transfer. The key aspects and latest achievements are reviewed with an emphasis on the fundamental relation between spatial resolution and total fabrication throughput. Emerging biomedical applications implementing micrometer feature precision over centimeter scale scaffolds and photonic wire bonding in telecommunications are highlighted.
author_names: Mangirdas Malinauskas

Albertas Zukauskas

Satoshi Hasegawa

Yoshio Hayasaki

Vygantas Mizeikis

Ricardas Buividas

Saulius Juodkazis
title: Ultrafast laser processing of materials: from science to industry
venue: Light, science applications
year: 2016