Topological Photonics

 

 

weber beam

Topological Photonic Quasicrystals:

Fractal Topological Spectrum and Protected Transport

M.A. Bandres, M.C. Rechtsman, M. Segev

 

Phys. Rev. X, 6 (2016)

 

 

Abstract: We show that it is possible to have a topological phase in two-dimensional quasicrystals without any magnetic field applied, but instead introducing an artificial gauge field via dynamic modulation. This topological quasicrystal exhibits scatter-free unidirectional edge states that are extended along the system’s perimeter, contrary to the states of an ordinary quasicrystal system, which are characterized by power-law decay. We find that the spectrum of this Floquet topological quasicrystal exhibits a rich fractal (self-similar) structure of topological “minigaps,” manifesting an entirely new phenomenon: fractal topological systems. These topological minigaps form only when the system size is sufficiently large because their gapless edge states penetrate deep into the bulk. Hence, the topological structure emerges as a function of the system size, contrary to periodic systems where the topological phase can be completely characterized by the unit cell. We demonstrate the existence of this topological phase both by using a topological index (Bott index) and by studying the unidirectional transport of the gapless edge states and its robustness in the presence of defects. Our specific model is a Penrose lattice of helical optical waveguides—a photonic Floquet quasicrystal; however, we expect this new topological quasicrystal phase to be universal..

Photonic Lattices

 

 

weber beam

Experimental observation of bulk and edge transport in photonic Lieb lattices

D. Guzman-Silva, C. Mejia-Cortes, M.A. Bandres, M.C. Rechtsman, S. Weimann, S. Nolte, M. Segev, A. Szameit and R.A. Vicencio

 

New Journal of Physics, 16(063061) (2014)

 

 

Abstract: We analyze the transport of light in the bulk and at the edge of photonic Lieb lattices, whose unique feature is the existence of a flat band representing stationary states in the middle of the band structure that can form localized bulk states. We find that transport in bulk Lieb lattices is significantly affected by the particular excitation site within the unit cell, due to overlap with the flat band states. Additionally, we demonstrate the existence of new edge states in anisotropic Lieb lattices. These states arise due to a virtual defect at the lattice edges and are not described by the standard tight-binding model.

Accelerating beams and waves

 

 

weber beam

Generation of nonparaxial accelerating fields through mirros.

II: Three dimensions

Miguel A. Alonso and Miguel A. Bandres

 

Optics Express, Vol. 22, Issue 12, pp. 14738-14749 (2014)

 

 

Abstract: Accelerating beams are wave packets that preserve their shape while propagating along curved trajectories. In this article, we extend the ray-based treatment in Part I of this series to nonparaxial accelerating fields in three dimensions, whose intensity maxima trace circular or helical paths. We also describe a simple procedure for finding mirror shapes that convert collimated beams into fields whose intensity features trace arcs that can extend well beyond 180 degrees.

weber beam

Generation of nonparaxial accelerating fields through mirros.

I: Two dimensions

Miguel A. Alonso and Miguel A. Bandres

 

Optics Express, Vol. 22, Issue 6, pp. 7124-7132 (2014)

 

 

Abstract: Accelerating beams are wave packets that preserve their shape while propagating along curved trajectories. Recent constructions of nonparaxial accelerating beams cannot span more than a semicircle. Here, we present a ray based analysis for nonparaxial accelerating fields and pulses in two dimensions. We also develop a simple geometric procedure for finding mirror shapes that convert collimated fields or fields emanating from a point source into accelerating fields tracing circular caustics that extend well beyond a semicircle.

 

weber beam

Accelerating light beams with arbitrarily transverse shapes

Adrian Ruelas, Jeffrey A. Davis, Ignacio Moreno, Don M. Contrell and Miguel A. Bandres

 

Optics Express, Vol. 22, Issue 3, pp. 3490 (2014)

 

 

Abstract: Accelerating beams are wave packets that preserve their shape while propagating along curved trajectories. Their unique characteristics have opened the door to applications that range from optical micromanipulation and plasma-channel generation to laser micromachining. Here, we demonstrate, theoretically and experimentally, that accelerating beams can be generated with a variety of arbitrarily chosen transverse shapes. We present a general method to construct such beams in the paraxial and nonparaxial regime and demonstrate experimentally their propagation in the paraxial case. The key ingredient of our method is the use of the spectral representation of the accelerating beams, which offers a unique and compact description of these beams. The on-demand accelerating light patterns described here are likely to give rise to new applications and add versatility to the current ones.

 

  

weber beam

Accelerating Optical Beams (REVIEW)

Miguel A. Bandres, Ido Kaminer, Matthew Mills, B. M. Rodriguez-Lara, Elad Greenfield, Morderchai Segev and Demitrios N. Christodoulides

 

Optics and Photonic News, Vol. 24, Issue 6, pp. 30-37 (2013)

 

 

Abstract: Thanks to their unique interference, accelerating beams appear to curve as they travel. They require no waveguiding structures or external potentials and appear even in free space. This beautiful phenomenon has led to many intriguing ideas and exciting new applications.

  

weber beam

Three-dimensional Accelerating Electromagnetic Waves

Miguel A. Bandres, Miguel A. Alonso, Ido Kaminer and Mordechai Segev

 

Optics Express, Vol. 21, Issue 12, pp. 13917-13929 (2013)

 

 

Abstract: We present a general theory of three-dimensional non-paraxial spatially-accelerating waves of the Maxwell equations. These waves constitute a two-dimensional structure exhibiting shape-invariant propagation along semicircular trajectories. We provide classification and characterization of possible shapes of such beams, expressed through the angular spectra of parabolic, oblate and prolate spheroidal fields. Our results facilitate the design of accelerating beams with novel structures, broadening scope and potential applications of accelerating beams.

 

 

weber beam

Nondiffracting accelerating waves:

Weber waves and parabolic momentum

Miguel A. Bandres and B.M. Rodriguez-Lara

 

New Journal of Physics, 15(013054) (2013)

 

Abstract: Diffraction is one of the universal phenomena of physics, and a way to overcome it has always represented a challenge for physicists. In order to control diffraction, the study of structured waves has become decisive. Here, we present a specific class of nondiffracting spatially accelerating solutions of the Maxwell equations: the Weber waves. These nonparaxial waves propagate along parabolic trajectories while approximately preserving their shape. They are expressed in an analytic closed form and naturally separate in forward and backward propagation. We show that the Weber waves are self-healing, can form periodic breather waves and have a well-defined conserved quantity: the parabolic momentum. We find that our Weber waves for moderate to large values of the parabolic momenta can be described by a modulated Airy function. Because the Weber waves are exact time-harmonic solutions of the wave equation, they have implications for many linear wave systems in nature, ranging from acoustic, electromagnetic and elastic waves to surface waves in fluids and membranes.

 

spherical accelerating beam

Spherical fields as nonparaxial accelerating waves

M.A. Alonso and Miguel A. Bandres

 

Optics Letters, 37(24) 5175-5177 (2012)

 

 

 

Abstract: We introduce nonparaxial spatially accelerating waves whose two-dimensional transverse profiles propagate along semicircular trajectories while approximately preserving their shape. We derive these waves by considering imaginary displacements on spherical fields, leading to simple closed-form expressions. The structure of these waves also allows the closed-form description of pulses.

 

accelerating beam

Accelerating Beams

Miguel A. Bandres

 

Optics Letters, 34(24), 3791-3793 (2009) (Times Cited: 19)

 

 

Abstract: We demonstrate that any two-dimensional accelerating beam can be described in a canonical form in Fourier space. In particular, we demonstrate that there is a one-to-one correspondence between complex functions in the real line (the line spectrum) and accelerating beams. An arbitrary line spectrum can be used to generate novel accelerating beams with diverse transverse shapes. The line spectra for the special cases of the families of Airy and accelerating parabolic beams are provided.

 

2d Airy experimental

Generation of accelerating Airy and accelerating parabolic beams using phase-only patterns

J.A. Davis, M.J. Mitry, Miguel A. Bandres, I. Ruiz, KP. McAuley, and D.M. Cottrell

 

Appl. Opt., 48(17), 3170-3176 (2009) (Times Cited: 11)

 

Abstract: We generate both accelerated Airy and accelerated parabolic beams using phase-only patterns encoded onto a liquid crystal display (LCD). The usual system length is 2f, where f is the focal length of the Fourier transform lens. We develop a compact optical system having a total system length of f. However, the mask must now incorporate the Fresnel diffraction that is not provided by the reduced optical system length. Finally we incorporate the Fourier transform lens onto the mask. We obtain excellent experimental results with a phase-only pattern and a shorter optical system. This approach makes these beams much easier to implement.

 

parabolic accelerating experimental

Observation of accelerating parabolic beams

Jeffrey A. Davis, Mark J. Mitry, Miguel A. Bandres, and Don M. Cottrell

 

Optics Express, 16(17), 12866-12871 (2008) (Times Cited: 16)

 

 

Abstract: We report the first observation of accelerating parabolic beams. These accelerating parabolic beams are similar to the Airy beams because they exhibit the unusual ability to remain diffraction-free while having a quadratic transverse shift during propagation. The amplitude and phase masks required to generate these beams are encoded onto a single liquid crystal display. Experimental results agree well with theory.

 

accelerating parabolic

Accelerating parabolic beams

Miguel A. Bandres

 

Optics Letters, 33(15), 1678-1680 (2008) (Times Cited: 26)

 

 

 

Abstract: We demonstrate the existence of accelerating parabolic beams that constitute, together with the Airy beams, the only orthogonal and complete families of solutions of the two-dimensional paraxial wave equation that exhibit the unusual ability to remain diffraction-free and freely accelerate during propagation. Since the accelerating parabolic beams, like the Airy beams, carry infinite energy, we present exact finite-energy accelerating parabolic beams that still retain their unusual features over several diffraction lengths.

 

Airy function

Airy-Gauss beams and their transformation by paraxial optical systems

Miguel A. Bandres and J. C. Gutiérrez-Vega

Optics Express, 15 (25), 16719-16728 (2007) (Times Cited: 46)

 

 

 

Abstract: We introduce the generalized Airy-Gauss (AiG) beams and analyze their propagation through optical systems described by ABCD matrices with complex elements in general. The transverse mathematical structure of the AiG beams is form-invariant under paraxial transformations. The conditions for square integrability of the beams are studied in detail. The AiG beam describes in a more realistic way the propagation of the Airy wave packets because AiG beams carry finite power, retain the nondiffracting propagation properties within a finite propagation distance, and can be realized experimentally to a very good approximation.

 

Paraxial Beams

 

paraxial propagation

Paraxial group

Miguel A. Bandres and Manuel Guizar-Sicairos

 

Optics Letters, 34(1), 13-15 (2009) (Times Cited:  7)

 

 

Abstract: We introduce the paraxial group, the group of symmetries of the paraxial-wave equation and its action on paraxial beams. The transformations, elements of the group, are used to obtain closed-form expressions for the propagation of any paraxial beam through misaligned ABCD optical systems. We prove that any paraxial beam is form-invariant under these transformations.

 

Ellical beams

Elliptical beams

Miguel A. Bandres and J. C. Gutiérrez-Vega

 

Optics Express, 16(25), 21087-21092 (2008) (Times Cited: 16)

 

 

 

Abstract: A very general beam solution of the paraxial wave equation in elliptic cylindrical coordinates is presented. We call such a field an elliptic beam (EB). The complex amplitude of the EB is described by either the generalized Ince functions or the Whittaker-Hill functions and is characterized by four parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integrability are studied in detail. Special cases of the EB are the standard, elegant, and generalized Ince-Gauss beams, Mathieu-Gauss beams, among others.

 

Circular Beams

Miguel A. Bandres and J. C. Gutiérrez-Vega

 

Optics Letters, 33(2), 177-179 (2008) (Times Cited: 33)

 

 

Abstract: A very general beam solution of the paraxial wave equation in circular cylindrical coordinates is presented. We call such a field a circular beam (CiB). The complex amplitude of the CiB is described by either the Whittaker functions or the confluent hypergeometric functions and is characterized by three parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integrability are studied in detail. Special cases of the CiB are the standard, elegant, and generalized Laguerre-Gauss beams, Bessel-Gauss beams, hypergeometric beams, hypergeometric-Gaussian beams, fractional order elegant Laguerre-Gauss beams, quadratic Bessel-Gauss beams, and optical vortex beams.

 

 

momentas of rotational beams

Higher-order moments and overlaps of rotationally symmetric beams

Miguel A. Bandres, Dorilian López-Mago, and Julio C. Gutiérrez-Vega

 

Journal of Optics, 12, 015706(10pp) (2010) (Times Cited:  4)

 

 

Abstract: We introduce a closed-form expression for the overlap between two different circular beams (CiBs) with azimuthal symmetry. A full description of the propagation of the higher-order moments of the CiBs through paraxial ABCD systems is presented. Our formalism can be easily applied to calculate relevant beam parameters such as the normalization constants, the M2 factors, the kurtosis parameters, the expansion coefficients of the CiBs, and therefore of all its relevant special cases, including the standard, elegant, and generalized Laguerre-Gaussian beams, Bessel-Gaussian beams, hypergeometric-Gaussian beams, quadratic Bessel-Gaussian beams, and optical vortex beams, among others.

 

Cartesian beams

Cartesian Beams

Miguel A. Bandres and J. C. Gutiérrez-Vega

 

Optics Letters, 32(23), 3459-3461 (2007) (Times Cited: 25)

 

 

Abstract: A new and very general beam solution of the paraxial wave equation in Cartesian coordinates is presented. We call such a field a Cartesian beam. The complex amplitude of the Cartesian beams is described by either the parabolic cylinder functions or the confluent hypergeometric functions, and the beams are characterized by three parameters that are complex in the most general situation. The propagation through complex ABCD optical systems and the conditions for square integrability are studied in detail. Applying the general expression of the Cartesian beams, we also derive two new and meaningful beam structures that, to our knowledge, have not yet been reported in the literature. Special cases of the Cartesian beams are the standard, elegant, and generalized Hermite-Gauss beams, the cosine-Gauss beams, the Lorentz beams, and the fractional order beams.

 

Moments Cartesian beams

Higher-order moments and overlaps of Cartesian beams

Miguel A. Bandres, Dorilian López-Mago, and Julio C. Gutiérrez-Vega

Journal of Optics, 12(6), 065702(9pp) (2010) (Times Cited:  2)

 

 

Abstract: We introduce a closed-form expression for the overlap between two different Cartesian beams. In the course of obtaining this expression, we establish a linear relation between the overlap of circular beams with azimuthal symmetry and the overlap of Cartesian beams such that the knowledge of the former allows the latter to be calculated very easily. Our formalism can be easily applied to calculate relevant beam parameters such as the normalization constants, the M2 factors, the kurtosis parameters, the expansion coefficients of Cartesian beams, and therefore of all their relevant special cases, including the standard, elegant, and generalized Hermite-Gaussian beams, cosh-Gaussian beams, Lorentz beams, and Airy beams, among others.

 

Complex Source

Higher-order complex source for elegant Laguerre-Gaussian waves

Miguel A. Bandres and Julio C. Gutiérrez-Vega

 

Optics Letters, 29(19), 2213-2215 (2004) (Times Cited: 27)

 

 

Abstract: We introduce a higher-order complex source that generates elegant Laguerre-Gaussian waves with radial mode number n and angular mode number m. We derive the integral and differential representations for the elegant Laguerre-Gaussian wave that in the appropriate limit yields the corresponding elegant Laguerre-Gaussian beam. From the spectral representation of the elegant Lauguerre-Gaussian wave we determine the first three orders of nonparaxial corrections for the corresponding paraxial elegant Laguerre-Gaussian beam.

 

Nondiffractive beams

 

Parabolic nondiffracting

Parabolic nondiffracting optical wavefields

Miguel A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda

 

Optics Letters, 29(1), 44-46 (2004) (Times Cited: 69)

 

 

Abstract: We demonstrate the existence of parabolic beams that constitute the last member of the family of fundamental nondiffracting wave fields and determine their associated angular spectrum. Their transverse structure is described by parabolic cylinder functions, and contrary to Bessel or Mathieu beams their eigenvalue spectrum is continuous. Any nondiffracting beam can be constructed as a superposition of parabolic beams, since they form a complete orthogonal set of solutions of the Helmholtz equation. A novel class of traveling parabolic waves is also introduced for the first time.

 

Parabolic nondiffracting experiment

Observation of Parabolic nondiffracting optical fields

Carlos López-Mariscal, Miguel A. Bandres, S. Chávez-Cerda, and J. C. Gutiérrez-Vega

 

Optics Express, 13(7), 2364-2369 (2005) (Times Cited: 25)

 

 

 

Abstract:

 

 

 

parabolic beam

Helmholtz-Gauss waves

Julio C. Gutiérrez-Vega and Miguel A. Bandres

 

Journal of the Optical Society of America A, 22(2), 289-298 (2005) (Times Cited: 70)

 

 

 

Abstract:

 

 

 

Mathieu Gauss

Observation of the experimental propagation properties of Helmholtz-Gauss beams

Carlos López-Mariscal, Miguel A. Bandres, and J. C. Gutiérrez-Vega

 

Opt. Eng., 45(6), 068001(8pp) (2006) (Times Cited: 19)

 

 

 

Abstract:

 

 

 

Vector Helmholtz Gauss

Vector Helmholtz-Gauss and vector Laplace-Gauss beams

Miguel A. Bandres and J. C. Gutiérrez-Vega

 

Optics Letters, 30(16), 2155-2157 (2005) (Times Cited: 15)

 

 

 

Abstract:

 

 

 

 

Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems

RI. Hernandez-Aranda, JC. Gutiérrez-Vega, M. Guizar-Sicairos, and Miguel A. Bandres

 

Optics Express, 14(20), 8974-8988 (2006) (Times Cited: 13)

 

 

 

Abstract:

 

 

 

Mathieu Gauss

Normalization of the Mathieu-Gauss optical beams

J. C. Gutiérrez-Vega and Miguel A. Bandres

 

Journal of the Optical Society of America A, 24(1), 215-220 (2007) (Times Cited: 11)

 

 

 

 

Abstract:

 

 

 

Ince Gaussian Beams

 

Ince Gaussian beam

Ince-Gaussian beams

Miguel A. Bandres and J. C. Gutiérrez-Vega

 

Optics Letters, 29(2), 144-146 (2004) (Times Cited: 73)

 

 

 

Abstract:

 

 

 

Ince Gaussian beam

Ince-Gaussian modes of the paraxial wave equation and stable resonators

Miguel A. Bandres and Julio C. Gutiérrez-Vega

 

Journal of the Optical Society of America A, 21(5), 873-880 (2004) (Times Cited: 55)

 

 

 

Abstract:

 

 

 

Stable resonator

Observation of Ince-Gaussian modes in stable resonators

Ulrich T. Schwarz, Miguel A. Bandres and Julio C. Gutiérrez-Vega

 

Optics Letters, 29(16), 1870-1872 (2004) (Times Cited: 45)

 

 

 

Abstract:

 

 

 

Helical Ince gaussian beam

Generation of helical Ince-Gaussian beams with a liquid crystal display

Joel B. Bentley, Jeffrey A. Davis, Miguel A. Bandres and J. C. Gutiérrez-Vega

 

Optics Letters, 31(5), 649-651 (2006) (Times Cited: 46)

 

 

 

Abstract:

 

 

 

Elegant Ince gaussian beam

Elegant Ince-Gaussian beams

Miguel A. Bandres

 

Optics Letters, 29(15), 1724-1726 (2004) (Times Cited: 27)

 

 

 

Abstract:

 

 

 

Ince Gaussian beam

Ince-Gaussian series representation of the two–dimensional fractional Fourier transform

Miguel A. Bandres and J. C. Gutiérrez-Vega

 

Optics Letters, 30(5), 540-542 (2005) (Times Cited: 14)

 

 

 

Abstract:

 

 

 

GRIN medium

Ince-Gaussian beam in quadratic index medium

Julio C. Gutiérrez-Vega and Miguel A. Bandres

 

Journal of the Optical Society of America A, 22(2), 306-309 (2005) (Times Cited: 14)

 

 

 

Abstract:

 

 

 

String Theory

 

Algebraic curve

One-Loop Corrections to Type IIA String Theory in AdS4 xCP3

Miguel A. Bandres, Arthur E. Lipstein

 

Journal of High Energy Physics, 2010(4), 59(43pp) (2010) (Times Cited: 20)

 

 

 

Abstract:

 

 

 

Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry

Miguel A. Bandres, Arthur E. Lipstein, and John H. Schwarz

 

Journal of High Energy Physics, 2008(9), 27(16pp) (2008) (Times Cited: 76)

 

 

 

Abstract:

 

 

 

Ghost-Free Superconformal Action for Multiple M2-Branes

Miguel A. Bandres, Arthur E. Lipstein, and John H. Schwarz

 

Journal of High Energy Physics, 2008(7), 117(9pp) (2008)  (Times Cited: 104)

 

 

 

Abstract:

 

 

 

N = 8 Superconformal Chern-Simons Theories

Miguel A. Bandres, Arthur E. Lipstein, and John H. Schwarz

 

Journal of High Energy Physics, 2008(5), 25(11pp) (2008) (Times Cited: 122)

 

 

 

Abstract:

 

 

 

 

General Physics

 

Elliptical Billiard

Classical Solutions for a free Particle in a Confocal Elliptic Billiard

Miguel A. Bandres and Julio C. Gutiérrez-Vega

 

American Journal of Physics, 72(6), 810-817 (2004) (Times Cited: 2)

 

 

 

Abstract:

 

 

 

Integrated predictive modeling of high-mode tokamakplasmas using a combination of core and pedestal models

G. Bateman, Miguel A. Bandres, T. Onjun, AH. Kritz, and A. Pankin

 

Physics of Plasmas, 10(11), 4358-4370 (2003) (Times Cited: 10)

 

 

 

Abstract:

 

 

 

Thesis

 

Superconformal Chern-Simons theories and their string theory duals

Miguel A. Bandres

Ph.D. Thesis, California Institute of Technology, Pasadena, California, (2011)

 

Other Publications (Comments, news magazines, etc.)

 

Ince-Gaussian beams: the third family of eigenmodes of stable laser resonators

Miguel A. Bandres, Ulrich T. Schwarz, and J. C. Gutiérrez-Vega

Optics and Photonics News, Special Issue: Optics in 2004, 15(12), 36 (2004)

 

Comment on Exact solution of resonant modes in a rectangular resonator

J. C. Gutiérrez-Vega and Miguel A. Bandres

Optics Letters, 31(16), 2468-2469 (2006)