Front Matter

Example

<front-matter id="bk978-0-7503-3579-9ch0">
  <front-matter-part>
    <book-part-meta>                       
      <title-group>
        <title>Front matter</title>
      </title-group>
<contrib-group>
        <contrib contrib-type="author" xlink:type="simple">
          <name name-style="western">
            <surname>McGurn</surname>
            <given-names>Arthur R</given-names>
          </name>
          <xref ref-type="aff" rid="aff1_0"/>
        </contrib>
        <aff id="aff1_0">Department of Physics, <institution xlink:type="simple">Western Michigan University</institution>,
        Kalamazoo, MI, <country>USA</country>
      </aff>
      </contrib-group>
<fpage>i</fpage>
      <lpage>xv</lpage>
      <self-uri content-type="pdf" xlink:href="bk978-0-7503-3579-9ch0.pdf"/>
      <self-uri content-type="epub" xlink:href="bk978-0-7503-3579-9ch0.epub"/>
</book-part-meta>
  </front-matter-part>
<dedication id="bk978-0-7503-3579-9ch0s1">
    <named-book-part-body>
      <p>To my wife, Maria</p>
    </named-book-part-body>
  </dedication>
<preface id="bk978-0-7503-3579-9ch0s2">
    <named-book-part-body>
      <p>This book is pedagogical. It is meant as an introduction to the ideas and
    phenomena that occur in the nonlinear optics of photonic crystals and
    metamaterials. At the same time it also provides the student with a basic
    introduction to the general ideas of nonlinear optics. The book should
    not, however, be viewed as a comprehensive review of the topics of
    photonic crystals and metamaterials and their nonlinear properties but
    rather as a survey of some of the most important fundamentals of the
    field. In this regard, it provides a strong background to a student new
    to the field. The phenomena discussed are illustrated within the context
    of simple models, offering an easy understanding of the physical
    phenomena that are important in these two rapidly developing areas of
    nanophotonic technology.</p>
      <p>The book first deals with nonlinear dielectric properties. A model based
    on classical physics is used to develop some of the ideas of the Kerr
    nonlinear dielectric and the generation of second and higher harmonics of
    radiation in a semi-quantitative way. The treatment is similar to that
    used in basic electrodynamics texts to provide an understanding of the
    dielectric properties of linear dielectric materials. An emphasis is on
    nonlinear effects as being small and on their treatment within the
    context of them entering the considerations as perturbations of otherwise
    linear systems. Consequently, along with the development of the
    dielectric properties, the theory of multiple scale perturbation theory
    is simultaneously formulated as an important technique in correctly
    dealing with the physics of systems with small nonlinearities. The
    reasons why multiple scale perturbation techniques are needed and a
    number of examples of the multiple scale treatment of nonlinear systems
    are given.</p>
      <p>The distinctions between the ideas of photonic crystals and metamaterials
    and the different types of applications they address are discussed with
    emphasis on their elementary properties. Photonic crystals have
    dielectric properties which exhibit periodicity in space. Due to their
    spatial periodicity the dispersion relation of light within the photonic
    crystal exhibits a sequence of frequency pass bands and stop bands. Light
    at pass band frequencies propagates in the photonic crystal and light at
    stop band frequencies does not propagate through the photonic crystal. On
    the other hand, metamaterials are composed as arrays of nanoscopic
    electromagnetic resonator units. They are engineered to appear to be
    homogeneous media on the scale of the wavelengths of light with which
    they are designed to interact. The frequency dependence of the resonators
    allow metamaterials to exhibit frequency dependent refractive indices not
    otherwise observed in nature. Of particular importance is their ability
    to display negative index of refraction.</p>
      <p>The theory of photonic crystals is greatly influenced by their spatial
    periodicity. In this regard, basic discussions of the dynamics of systems
    defined on a periodic lattice are made with a focus on the Maxwell
    equations expressed for periodic media. The direct and reciprocal
    lattices, Brillouin zones, Block functions, and the properties of stop
    and pass bands are introduced at an elementary level. Waveguides and
    single site impurities introduced into otherwise periodic bulk photonic
    crystal systems also are discussed at an introductory level, as are the
    techniques of Wannier functions and computer simulation treatments
    applied to these types of problems.</p>
      <p>The discussions of periodic systems are also extended to considerations
    of the basic theory of surface gratings and applications of Bragg
    gratings within fiber optics and general optical waveguides. The use of
    photonic crystal technology in the design of optical fibers is an
    additional consideration of new designs based on the ideas of periodic
    media. In this regard, periodicity is introduced both as a novel means of
    making fiber claddings and as a confining mechanism based on stop bands.
    In addition, discussions of soliton modes within optical fibers formed of
    nonlinear optical media is briefly presented, offering a comparison with
    the soliton-like intrinsic localized modes present in photonic crystal
    waveguides formed of nonlinear optical media.</p>
      <p>The application of metamaterials in the design of media with unusual
    refractive properties is discussed, with a particular focus on the
    development of materials exhibiting a negative refractive index.
    Metamaterials are typically designed as arrays of electromagnetic
    nanoresonators, and a commonly used resonator form is that of a split
    ring resonator (SRRs). In this regard, an understanding of the resonant
    properties of SRRs is developed in a detailed but elementary treatment.
    How these resonant properties are then employed to engineer a material
    exhibiting negative refraction is then explained in detailed.</p>
      <p>The refractive properties of plane waves traveling between semi-infinite
    media of positive and negative refractive index media are studied
    comprehensively. Differences in the radiative properties of antennas and
    radiating charges within both positive and negative index media are
    compared. The essential operating principles of perfect lenses are
    explained and a comparison is made with the properties of lenses formed
    only of positive refractive index materials. In addition, the application
    of metamaterials in the formulation of the ideas of optical cloaking
    mechanisms are developed.</p>
      <p>Both analytic and computer simulation methods are introduced at an
    elementary level for the treatment of basic problems in photonic crystals
    and metamaterials. In terms of computer solutions, the plane wave method,
    the finite difference time domain method, the method of moments, the
    conjugate gradient method, and the finite element method of computer
    simulation techniques are formulated and discussed in elementary and
    detailed manners. Various formulations for the boundary conditions of
    computer simulation studies needed to accurately approximate the
    interaction of radiation with dielectric features in infinite systems are
    presented.</p>
      <p>On the side of analytic models, a number of difference equation
    formulations are given for photonic crystal and metamaterial waveguides.
    These difference equation models are used to facilitate the understanding
    of the basic physics of photonic crystals and metamaterials. The
    difference equation models are also realizable in many experimentally
    accessible cases. They often provide simple exactly solvable models whose
    properties are easily made transparent and are also representative of
    more complex general systems studied using computer simulations. Analytic
    techniques for the solution of difference equation formulations are
    discussed and are related to the physics of many different types of
    physical systems that occur in physics and technology.</p>
      <p>The properties of photonic crystal and metamaterial systems with Kerr
    nonlinearity are discussed in terms of formulations based on difference
    equation models. Properties of optical bistability and resonant
    transmission anomalies are explained in detail based on elementary
    treatments in the difference equation formulations. The various
    properties are treated with discussions for their applications in devices
    and examples given in the context of the simple models.</p>
      <p>A chapter is dedicated to discussions of computer simulation studies of
    nonlinear properties of some recently considered systems and the
    properties with which these have dealt. One-dimensional photonic crystals
    formed of a periodic layering of Kerr slabs are discussed along with the
    properties of Kerr impurities in higher-dimensional photonic crystals. In
    another important treatment, studies of the applications of photonic
    crystals to enhance the generation of second harmonics are outlined as
    another application of the use of photonic crystals. Some recent computer
    simulation studies of nonlinear metamaterials and the properties these
    studies have treated are also summarized. In these discussions only some
    of the important basic results from computer simulations are presented,
    and the discussions are not meant to be a comprehensive review of the
    field of computer simulation applied to nonlinear systems.</p>
      <p>In the last chapter of the book a treatment is given of the effects of
    impurities and disorder introduced into photonic crystals and
    metamaterials. Single site impurities and finite clusters of impurities
    are discussed in the context of Green’s functions theories and with the
    applications of ideas of group theory. General random disorder is treated
    through the application of the coherent potentional approximation, and
    the theory of this methodology is explained in detail. The general theory
    of Anderson localization in random disordered optical media is discussed
    along with the ideas of a scaling theory approach to the effects of
    disorder on the transport properties of disordered systems. In this
    regard, optical systems have provided important systems for the
    discussion of the ideas of so-called strong and weak localization. As a
    final treatment of localization, a focus is given on the effects of weak
    localization observed in the general diffuse elastic scattering of light
    and the general diffusely generated second harmonics of light from a
    randomly rough surface which supports surface electromagnetic waves. In
    this context, an introductory treatment is presented to the theory of
    surface electromagnetic waves and the requirements for their existence on
    a rough interface.</p>
      <p>As a final note: both the Gaussian and Standard International Units
    formulations of the Maxwell equations are used at different points in the
    text. This is done as many of the results referenced from the literature
    occur in these sets of units, as will be indicated in the text. In
    addition, the author would like to thank the Department of Physics,
    University of California, Riverside, for allowing me the use of the
    University Library during the course of this project.</p>
      <p>Arthur R McGurn</p>
      <p>Rancho Mirage, California</p>
      <p>May, 2021</p>
    </named-book-part-body>
  </preface>
<ack>
    <title>Acknowledgements</title>
    <p>The author wishes to thank Western Michigan University for the opportunity
  to write this book and the Department of Physics and Astronomy, University
  of California, Riverside, for the extension of library privileges at the UCR
  Library. The author also expresses his appreciation for former students, all
  of whom have pursued successful careers in physics and engineering.</p>
  </ack>
<bio content-type="full-bio">
    <title>Author biography</title>
    <sec id="bk978-0-7503-3579-9ch0s5">
      <title>Arthur R McGurn</title>
      <p>
      <fig id="bk978-0-7503-3579-9ch0ufig1" position="float" orientation="portrait">
        <graphic id="bk978-0-7503-3579-9ch0f1_eps" content-type="print" xlink:href="bk978-0-7503-3579-9ch0f1_pr.eps" position="float" orientation="portrait" xlink:type="simple"/>
        <graphic id="bk978-0-7503-3579-9ch0f1_online" content-type="online" xlink:href="bk978-0-7503-3579-9ch0f1_online.jpg" position="float" orientation="portrait" xlink:type="simple"/>
        <graphic id="bk978-0-7503-3579-9ch0f1_hr" content-type="high" xlink:href="bk978-0-7503-3579-9ch0f1_hr.jpg" position="float" orientation="portrait" xlink:type="simple"/>
      </fig>Professor Emeritus Arthur R McGurn, CPhys, FInstP, is a Fellow of
    the Institute of Physics, a Fellow of the American Physical Society, a
    Fellow of the Optical Society of America, a Fellow of the
    Electromagnetics Academy, and an Outstanding Referee for the journals of
    the American Physical Society. He received the PhD in Physics in 1975
    from the University of California, Santa Barbara, followed by
    postdoctoral studies at Temple University, Michigan State University, and
    George Washington University (NASA Langley Research Center). The research
    interests of Professor McGurn have included works in the theory of:
    magnetism in disorder materials, electron conductivity, the properties of
    phonons, ferroelectrics and their nonlinear dynamics, Anderson
    localization, amorphous materials, the scattering of light from
    disordered media and rough surfaces, the properties of speckle
    correlations of light, quantum optics, nonlinear optics, the dynamical
    properties of nonlinear systems, photonic crystals, and metamaterials. He
    has over 150 publications spread amongst these various topics. Since
    1981, he has taught physics at Western Michigan University, where he is
    currently a Professor of Physics and a WMU Distinguished Faculty Scholar.
    A number of PhD students have graduated from Western Michigan University
    under his supervision.</p>
    </sec>
  </bio>
<glossary id="bk978-0-7503-3579-9ch0s10">
    <title>Symbols</title>
    <def-list list-content="abbreviations">
      <def-item>
        <term>ε</term>
        <def>
          <p>Electric permittivity</p>
        </def>
      </def-item>
      <def-item>
        <term>
          <inline-formula>
            <tex-math><?CDATA $\mu $?></tex-math>
            <mml:math overflow="scroll">
              <mml:mi>μ</mml:mi>
            </mml:math>
            <inline-graphic xlink:href="bk978-0-7503-3579-9ch0ieqn1.gif" xlink:type="simple"/>
          </inline-formula>
        </term>
        <def>
          <p>Magnetic permeability</p>
        </def>
      </def-item>
      <def-item>
        <term>
          <italic>λ</italic>
        </term>
        <def>
          <p>Wavelength (m)</p>
        </def>
      </def-item>
      <def-item>
        <term>
          <inline-formula>
            <tex-math><?CDATA $k$?></tex-math>
            <mml:math overflow="scroll">
              <mml:mi>k</mml:mi>
            </mml:math>
            <inline-graphic xlink:href="bk978-0-7503-3579-9ch0ieqn2.gif" xlink:type="simple"/>
          </inline-formula>
        </term>
        <def>
          <p>Wavevector</p>
        </def>
      </def-item>
      <def-item>
        <term>
          <italic>Ρ</italic>
        </term>
        <def>
          <p>Charge density</p>
        </def>
      </def-item>
      <def-item>
        <term>
          <inline-formula>
            <tex-math><?CDATA $B$?></tex-math>
            <mml:math overflow="scroll">
              <mml:mi>B</mml:mi>
            </mml:math>
            <inline-graphic xlink:href="bk978-0-7503-3579-9ch0ieqn3.gif" xlink:type="simple"/>
          </inline-formula>
        </term>
        <def>
          <p>Magnetic induction</p>
        </def>
      </def-item>
      <def-item>
        <term>
          <inline-formula>
            <tex-math><?CDATA $H$?></tex-math>
            <mml:math overflow="scroll">
              <mml:mi>H</mml:mi>
            </mml:math>
            <inline-graphic xlink:href="bk978-0-7503-3579-9ch0ieqn4.gif" xlink:type="simple"/>
          </inline-formula>
        </term>
        <def>
          <p>Magnetic field</p>
        </def>
      </def-item>
      <def-item>
        <term>
          <inline-formula>
            <tex-math><?CDATA $E$?></tex-math>
            <mml:math overflow="scroll">
              <mml:mi>E</mml:mi>
            </mml:math>
            <inline-graphic xlink:href="bk978-0-7503-3579-9ch0ieqn5.gif" xlink:type="simple"/>
          </inline-formula>
        </term>
        <def>
          <p>Electric field</p>
        </def>
      </def-item>
      <def-item>
        <term>
          <inline-formula>
            <tex-math><?CDATA $D$?></tex-math>
            <mml:math overflow="scroll">
              <mml:mi>D</mml:mi>
            </mml:math>
            <inline-graphic xlink:href="bk978-0-7503-3579-9ch0ieqn6.gif" xlink:type="simple"/>
          </inline-formula>
        </term>
        <def>
          <p>Electric displacement</p>
        </def>
      </def-item>
      <def-item>
        <term>
          <inline-formula>
            <tex-math><?CDATA $n$?></tex-math>
            <mml:math overflow="scroll">
              <mml:mi>n</mml:mi>
            </mml:math>
            <inline-graphic xlink:href="bk978-0-7503-3579-9ch0ieqn7.gif" xlink:type="simple"/>
          </inline-formula>
        </term>
        <def>
          <p>Index of refraction</p>
        </def>
      </def-item>
      <def-item>
        <term>
          <inline-formula>
            <tex-math><?CDATA $L$?></tex-math>
            <mml:math overflow="scroll">
              <mml:mi>L</mml:mi>
            </mml:math>
            <inline-graphic xlink:href="bk978-0-7503-3579-9ch0ieqn8.gif" xlink:type="simple"/>
          </inline-formula>
        </term>
        <def>
          <p>Inductance</p>
        </def>
      </def-item>
      <def-item>
        <term>
          <inline-formula>
            <tex-math><?CDATA $C$?></tex-math>
            <mml:math overflow="scroll">
              <mml:mi>C</mml:mi>
            </mml:math>
            <inline-graphic xlink:href="bk978-0-7503-3579-9ch0ieqn9.gif" xlink:type="simple"/>
          </inline-formula>
        </term>
        <def>
          <p>Capacitance</p>
        </def>
      </def-item>
      <def-item>
        <term>
          <inline-formula>
            <tex-math><?CDATA $\omega $?></tex-math>
            <mml:math overflow="scroll">
              <mml:mi>ω</mml:mi>
            </mml:math>
            <inline-graphic xlink:href="bk978-0-7503-3579-9ch0ieqn10.gif" xlink:type="simple"/>
          </inline-formula>
        </term>
        <def>
          <p>Angular frequency</p>
        </def>
      </def-item>
      <def-item>
        <term>
          <inline-formula>
            <tex-math><?CDATA $\upsilon $?></tex-math>
            <mml:math overflow="scroll">
              <mml:mi>υ</mml:mi>
            </mml:math>
            <inline-graphic xlink:href="bk978-0-7503-3579-9ch0ieqn11.gif" xlink:type="simple"/>
          </inline-formula>
        </term>
        <def>
          <p>Frequency</p>
        </def>
      </def-item>
      <def-item>
        <term>
          <inline-formula>
            <tex-math><?CDATA $S$?></tex-math>
            <mml:math overflow="scroll">
              <mml:mi>S</mml:mi>
            </mml:math>
            <inline-graphic xlink:href="bk978-0-7503-3579-9ch0ieqn12.gif" xlink:type="simple"/>
          </inline-formula>
        </term>
        <def>
          <p>Poynting vector</p>
        </def>
      </def-item>
    </def-list>
  </glossary>
</front-matter>