Skip to main content
SpringerLink
Log in

Localized Waves: Theory, Techniques and Applications

  • Living reference work entry
  • First Online:
Handbook of Antenna Technologies

  • 1176 Accesses

Abstract

In the first part of the chapter, an introduction to localized waves (LWs) is presented as polychromatic superposition of propagation-invariant beams (PIBs) with specific spatiotemporally coupled spectra. In the second part of the chapter, the focus is shifted towards some of the peculiar characteristics of electromagnetic LWs that distinguish them from other types of electromagnetic waves. In the last part, a presentation of the state-of-the-art techniques and experiments to generate electromagnetic PIBs is illustrated. Since PIBs are near-field phenomena, the electromagnetic structures that generate them differ significantly from conventional radiating antennas.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Similar content being viewed by others

References

  • Achouri K, Salem MA, Caloz C (2014) General metasurface synthesis based on susceptibility tensors. arXiv:1408.0273 [physics.optics]

    Google Scholar 

  • Arlt J, Hitomi T, Dholakia K (2000) Atom guiding along Laguerre-Gaussian and Bessel light beams. Appl Phys B 71(4):549–554

    Article  Google Scholar 

  • Arlt J, Garces-Chavez V, Sibbett W, Dholakia K (2001) Optical micromanipulation using a Bessel light beam. Opt Commun 197(46):239–245

    Article  Google Scholar 

  • Asadchy VS, Fanyaev IA (2011) Simulation of the electromagnetic properties of helices with optimal shape, which provides radiation of a circularly polarized wave. J Adv Res Phys 2(1):011107

    Google Scholar 

  • Asadchy VS, Faniayeu IA, Ra’di Y, Tretyakov SA (2014) Determining polarizability tensors for an arbitrary small electromagnetic scatterer. arXiv:1401.4930 [physics.optics]

    Google Scholar 

  • Balanis CA (2005) Antenna theory: analysis and design, 3rd edn. Wiley, Hoboken

    Google Scholar 

  • Bandres MA, Gutiérrez-Vega JC, Chávez-Cerda S (2004) Parabolic nondiffracting optical wave fields. Opt Lett 29(1):44–46

    Article  Google Scholar 

  • Bateman H (1915) Electrical and optical wave motion on the basis of Maxwell’s equations. Cambridge University, Cambridge, UK. Reprinted (Dover, New York, 1955)

    Google Scholar 

  • Besiries IM, Shaarawi AM, Ziolkowski RW (1989) A bidirectional traveling plane wave representation of exact solutions of the scalar wave equation. J Math Phys 30(6):1254–1269

    Article  MathSciNet  Google Scholar 

  • Brittingham JN (1983) Focus waves modes in homogeneous Maxwell’s equations: transverse electric mode. J Appl Phys 54(3):1179–1189

    Article  Google Scholar 

  • Caloz C, Itoh T (2005) Electromagnetic metamaterials: transmission line theory and microwave applications. Wiley, Hoboken

    Book  Google Scholar 

  • Capolino F (2009) Theory and phenomena of metamaterials. CRC Press, Boca Raton

    Book  Google Scholar 

  • Chattrapiban N, Rogers EA, Cofield D, Hill WD III, Roy R (2003) Generation of nondiffracting Bessel beams by use of a spatial light modulator. Opt Lett 28(22):2183–2185

    Google Scholar 

  • Cheng J, Lu J-Y (2006) Extended high-frame rate imaging method with limited-diffraction beams. IEEE Trans Ultrason Ferroelectr Freq Control 53(5):880–899

    Article  MathSciNet  Google Scholar 

  • Collin RE (1990) Field theory of guided waves, 2nd edn. Wiley-IEEE Press, New York

    Book  Google Scholar 

  • Courant R, Hilbert D (1966) Methods of mathematical physics, vol 2. Wiley, New York, p 760

    Google Scholar 

  • Cox AJ, Dibble DC (1992) Nondiffracting beam from a spatially filtered Fabry-Perot resonator. J Opt Soc Am A 9(2):282–286

    Article  Google Scholar 

  • Donnelly R, Ziolkowski RW (1993) Designing localized waves. Proc Royal Soc London A 440(1910):541–565

    Article  Google Scholar 

  • Durnin J (1987) Exact solutions for nondiffracting beams. I. the scalar theory. J Opt Soc Am A 4(4):651–654

    Article  Google Scholar 

  • Durnin J, Miceli JJ, Eberly JH (1987) Diffraction-free beams. Phys Rev Lett 58:1499–1501

    Article  Google Scholar 

  • Engheta N, Ziolkowski RW (2006) Metamaterials: physics and engineering explorations. Wiley, Hoboken

    Book  Google Scholar 

  • Erdélyi M, Horvàth ZL, Szabó G, Bor Z, Tittel FK, Cavallaro JR, Smayling MC (1997) Generation of diffraction-free beams for applications in optical microlithography. J Vac Sci Technol B 15(2):287–292

    Article  Google Scholar 

  • Ettorre M, Grbic A (2012) Generation of propagating Bessel beams using leaky-wave modes. IEEE Trans Antennas Propag 60(8):3605–3613

    Article  MathSciNet  Google Scholar 

  • Ettorre M, Rudolph S, Grbic A (2012) Generation of propagating Bessel beams using leaky-wave modes: experimental validation. IEEE Trans Antennas Propag 60(6):2645–2653

    Article  MathSciNet  Google Scholar 

  • Fan J, Parra E, Milchberg HM (2000) Resonant self-trapping and absorption of intense Bessel beams. Phys Rev Lett 84:3085–3088

    Article  Google Scholar 

  • Felsen LB, Marcuvitz N (1994) Radiation and scattering of waves. IEEE Press, Piscatawy

    Book  Google Scholar 

  • Garcés-Chávez V, McGloin D, Melville H, Sibbett W, Dholakia K (2002) Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam. Nature 419:145–147

    Article  Google Scholar 

  • Gutiérrez-Vega JC, Iturbe-Castillo MD, Chávez-Cerda S (2000) Alternative formulation for invariant optical fields: Mathieu beams. Opt Lett 25(20):1493–1495

    Article  Google Scholar 

  • Hecht E (1998) Optics, 4th edn. Addison-Wesley, Reading

    Google Scholar 

  • Herman RM, Wiggins TA (1991) Production and uses of diffraction less beams. J Opt Soc Am A 8(6):932–942

    Article  MathSciNet  Google Scholar 

  • Hernandez JE, Ziolkowski RW, Parker SR (1992) Synthesis of the driving functions of an array for propagating localized wave energy. J Acoust Soc Am 92(1):550–562

    Article  Google Scholar 

  • Hernández-Figueroa HE, Zamboni-Rached M, Recami E (eds) (2008) Localized waves. Wiley, Hoboken

    Google Scholar 

  • Hernández-Figueroa HE, Recami E, Zamboni-Rached M (eds) (2013) Non-diffracting waves. Wiley-VCH, Weinheim

    MATH  Google Scholar 

  • Holloway C, Mohamed M, Kuester EF, Dienstfrey A (2005) Reflection and transmission properties of a metafilm: with an application to a controllable surface composed of resonant particles. IEEE Trans Electromagn Compat 47(4):853–865

    Article  Google Scholar 

  • Holloway C, Dienstfrey A, Kuester EF, O’Hara JF, Azad AK, Taylor AJ (2009) A discussion on the interpretation and characterization of metafilms/metasurfaces: the two-dimensional equivalent of metamaterials. Metamaterials 3(2):100–112

    Article  Google Scholar 

  • Holloway C, Kuester EF, Gordon J, O’Hara J, Booth J, Smith D (2012) An overview of the theory and applications of metasurfaces: the two-dimensional equivalents of metamaterials. IEEE Antennas Propag Mag 54(2):10–35

    Article  Google Scholar 

  • Idemen MM (2011) Discontinuities in the electromagnetic field. Wiley, Hoboken

    Book  MATH  Google Scholar 

  • Indebetouw G (1989) Nondiffracting optical fields: some remarks on their analysis and synthesis. J Opt Soc Am A 6(1):150–152

    Article  Google Scholar 

  • Kong JA (1986) Electromagnetic wave theory. Wiley, New York

    Google Scholar 

  • Kuester EF, Mohamed M, Piket-May M, Holloway C (2003) Averaged transition conditions for electromagnetic fields at a metafilm. IEEE Trans Antennas Propag 51(10):2641–2651

    Article  Google Scholar 

  • Lemaître-Auger P, Abielmona S, Caloz C (2013) Generation of Bessel beams by two-dimensional antenna arrays using sub-sampled distributions. IEEE Trans Antennas Propag 61(4):1838–1849

    Article  Google Scholar 

  • Lindell IV (1994) Electromagnetic waves in chiral and bi-isotropic media. The Artech House Antenna Library. Artech House, Boston

    Google Scholar 

  • López-Mariscal C, Gutiérrez-Vega JC, Chávez-Cerda S (2004) Production of high-order Bessel beams with a Mach-Zehnder interferometer. Appl Opt 43(26):5060–5063

    Article  Google Scholar 

  • Lu J-Y (1997) 2D and 3D high frame rate imaging with limited diffraction beams. IEEE Trans Ultrason Ferroelectr Freq Control 44(4):839–856

    Article  Google Scholar 

  • Lu J-Y, Greenleaf JF (1992a) Experimental verification of nondiffracting X waves. IEEE Trans Ultrason Ferroelectr Freq Control 39(3):441–446

    Article  Google Scholar 

  • Lu J-Y, Greenleaf JF (1992b) Nondiffracting X waves-exact solutions to free-space scalar wave equation and their finite aperture realizations. IEEE Trans Ultrason Ferroelectr Freq Control 39(1):19–31

    Article  Google Scholar 

  • Lu J-Y, Zou H, Greenleaf JF (1994) Biomedical ultrasound beam forming. Ultrasound Med Biol 20(5):403–428

    Article  Google Scholar 

  • MacDonald MP, Paterson L, Volke-Sepulveda K, Arlt J, Sibbett W, Dholakia K (2002) Creation and manipulation of three-dimensional optically trapped structures. Science 296(5570):1101–1103

    Article  Google Scholar 

  • Mazzinghi A, Balma M, Devona D, Guarnieri G, Mauriello G, Albani M, Freni A (2014) Large depth of field pseudo-Bessel beam generation with a RLSA antenna. IEEE Trans Antennas Propag 62(8):3911–3919

    Article  Google Scholar 

  • McGloin D, Garcés-Chávez V, Dholakia K (2003) Interfering Bessel beams for optical micromanipulation. Opt Lett 28(8):657–659

    Article  Google Scholar 

  • Morse PM, Feshbach H (1953) Methods of theoretical physics, vol 1. McGraw-Hill, New York

    Google Scholar 

  • Moses HE, Prosser R (1986) Initial conditions, sources, and currents for prescribed time-dependent acoustic and electromagnetic fields in three dimensions, part I: the inverse initial value problem. Acoustic and electromagnetic “bullets,” expanding waves, and imploding waves. IEEE Trans Antennas Propag 34(2):188–196

    Article  MATH  MathSciNet  Google Scholar 

  • Moses HE, Prosser RT (1990) Acoustic and electromagnetic bullets: derivation of new exact solution of the acoustic and Maxwell’s equations. J Appl Math 50(5):1325–1340

    MATH  MathSciNet  Google Scholar 

  • Mugnai D, Ranfagni A, Ruggeri R (2000) Observation of superluminal behaviors in wave propagation. Phys Rev Lett 84:4830–4833

    Article  Google Scholar 

  • Munk BA (2000) Frequency selective surfaces: theory and design. Wiley, New York

    Book  MATH  Google Scholar 

  • Niemi T, Karilainen A, Tretyakov SA (2013) Synthesis of polarization transformers. IEEE Trans Antennas Propag 61(6):3102–3111

    Article  MathSciNet  Google Scholar 

  • Palma C, Cincotti G, Guattari G, Santarsiero M (1996) Imaging of generalized Bessel-gauss beams. J Mod Opt 43(11):2269–2277

    Article  Google Scholar 

  • Pfeiffer C, Grbic A (2013) Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets. Phys Rev Lett 110:197401

    Article  Google Scholar 

  • Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007) Numerical recipes: the art of scientific computing. Cambridge University Press, Cambridge, UK

    Google Scholar 

  • Ra’di Y, Asadchy V, Tretyakov S (2013) Total absorption of electromagnetic waves in ultimately thin layers. IEEE Trans Antennas Propag 61(9):4606–4614

    Article  MathSciNet  Google Scholar 

  • Rhodes DP, Lancaster GPT, Livesey J, McGloin D, Arlt J, Dholakia K (2002) Guiding a cold atomic beam along a co-propagating and oblique hollow light guide. Opt Commun 214(16):247–254

    Article  Google Scholar 

  • Saari P, Reivelt K (1997) Evidence of X-shaped propagation-invariant localized light waves. Phys Rev Lett 79:4135–4138

    Article  Google Scholar 

  • Salem MA, Bağci H (2010) On the propagation of truncated localized waves in dispersive silica. Opt Express 18(25):25482–25493

    Article  Google Scholar 

  • Salem MA, Bağci H (2011) Energy flow characteristics of vector X-waves. Opt Express 19(9):8526–8532

    Article  Google Scholar 

  • Salem MA, Bağci H (2012a) Modulation of propagation-invariant localized waves for FSO communication systems. Opt Express 20(14):15126–15138

    Article  Google Scholar 

  • Salem MA, Bağci H (2012b) Reflection and transmission of normally incident full-vector X waves on planar interfaces. J Opt Soc Am A 29(1):139–152

    Article  Google Scholar 

  • Salem MA, Caloz C (2014) Manipulating light at distance by a metasurface using momentum transformation. Opt Express 22(12):14530–14543

    Article  Google Scholar 

  • Salem MA, Kamel AH, Niver E (2011) Microwave Bessel beams generation using guided modes. IEEE Trans Antennas Propag 59(6):2241–2247

    Article  MathSciNet  Google Scholar 

  • Schelkunoff SA (1972) On teaching the undergraduate electromagnetic theory. IEEE Trans Educ 15(1):15–25

    Article  Google Scholar 

  • Sezginer A (1985) A general formulation of focus wave modes. J Appl Phys 57(3):678–683

    Article  Google Scholar 

  • Shaarawi AM, Besieris IM, Ziolkowski RW (1990) A novel approach to the synthesis of nondispersive wave packet solutions to the Klein-Gordon and Dirac equations. J Math Phys 31(10):2511–2519

    Article  MATH  MathSciNet  Google Scholar 

  • Shi H, Zhang A, Zheng S, Li J, Jiang Y (2014) Dual-band polarization angle independent 90° polarization rotator using twisted electric-field-coupled resonators. Appl Phys Lett 104(3):034102

    Article  Google Scholar 

  • Stratton J (1941) Electromagnetic theory. McGraw-Hill, New York

    MATH  Google Scholar 

  • Taflove A, Hagness SC (2005) Computational electrodynamics: the finite-difference time-domain method, 3rd edn. Artech House, Norwood

    Google Scholar 

  • Vasara A, Turunen J, Friberg AT (1989) Realization of general non-diffracting beams with computer-generated holograms. J Opt Soc Am A 6(11):1748–1754

    Article  Google Scholar 

  • Wu TT (1985) Electromagnetic missiles. J Appl Phys 57(7):2370–2373

    Article  Google Scholar 

  • Wu TT, Lehmann H (1985) Spreading of electromagnetic pulses. J Appl Phys 58(5):2064–2065

    Article  Google Scholar 

  • Yu Y-Y, Lin D-Z, Huang L-S, Lee C-K (2009) Effect of subwavelength annular aperture diameter on the nondiffracting region of generated Bessel beams. Opt Express 17(4):2707–2713

    Article  Google Scholar 

  • Yu N, Genevet P, Kats MA, Aieta F, Tetienne J-P, Capasso F, Gaburro Z (2011) Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334(6054):333–337

    Article  Google Scholar 

  • Zamboni-Rached M, Recami E, Hernndez-Figueroa H (2002) New localized superluminal solutions to the wave equations with finite total energies and arbitrary frequencies. Eur Phys J D 21(2):217–228

    Article  Google Scholar 

  • Zhang P, Phipps ME, Goodwin PM, Werner JH (2014) Confocal line scanning of a Bessel beam for fast 3D imaging. Opt Lett 39(12):3682–3685

    Article  Google Scholar 

  • Ziolkowski RW (1989) Localized transmission of electromagnetic energy. Phys Rev A 39:2005–2033

    Article  MathSciNet  Google Scholar 

  • Ziolkowski RW (1991) Localized wave physics and engineering. Phys Rev A 44:3960–3984

    Article  Google Scholar 

  • Ziolkowski R (1992) Properties of electromagnetic beams generated by ultra-wide bandwidth pulse-driven arrays. IEEE Trans Antennas Propag 40(8):888–905

    Article  Google Scholar 

  • Ziolkowski RW, Besieris IM, Shaarawi AM (1993) Aperture realizations of exact solutions to homogeneous-wave equations. J Opt Soc Am A 10(1):75–87

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Polytechnique Montreal, Montreal, QC, Canada

    Mohamed A. Salem & Christophe Caloz

Authors
  1. Mohamed A. Salem
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christophe Caloz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamed A. Salem .

Editor information

Editors and Affiliations

  1. Dept. Electrical and Computer Engin., National University of Singapore, Singapore, Singapore

    Zhi Ning Chen

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Her Majesty the Queen in Right of Canada

About this entry

Cite this entry

Salem, M.A., Caloz, C. (2015). Localized Waves: Theory, Techniques and Applications. In: Chen, Z. (eds) Handbook of Antenna Technologies. Springer, Singapore. https://doi.org/10.1007/978-981-4560-75-7_8-1

Download citation

  • DOI: https://doi.org/10.1007/978-981-4560-75-7_8-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Singapore

  • Online ISBN: 978-981-4560-75-7

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation