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Principles of Optics for Engineers

Book Description

Uniting classical and modern photonics approaches by presenting optical analyses as solutions of Maxwell's equations, this unique book enables students and practising engineers to fully understand the similarities and differences between the different methods. The book begins with a thorough discussion of plane wave analysis, which provides a clear understanding of optics without considering boundary condition or device configuration. It then goes on to cover diffraction analysis of many applications, including a rigorous analysis of TEM waves using Maxwell's equations with boundaries. Laser cavity modes and Gaussian beams are presented, modal analysis is covered, and approximation methods are discussed (including the perturbation technique, coupled mode analysis, and super mode analysis). With theory linked to practical examples throughout, it provides a clear understanding of the interplay between plane wave, diffraction and modal analysis, and how the different techniques can be applied to various areas including imaging, signal processing, and optoelectronic devices.

Table of Contents

  1. Cover
  2. Half title
  3. Title page
  4. Imprints page
  5. Contents
  6. Introduction
  7. 1 Optical plane waves in an unbounded medium
    1. 1.1 Introduction to optical plane waves
      1. 1.1.1 Plane waves and Maxwell’s equations
        1. (a) The y-polarized plane wave
        2. (b) The x-polarized plane wave
      2. 1.1.2 Plane waves in an arbitrary direction
      3. 1.1.3 Evanescent plane waves
      4. 1.1.4 Intensity and power
      5. 1.1.5 Superposition and plane wave modes
        1. (a) Plane waves with circular polarization
        2. (b) Interference of coherent plane waves
        3. (c) Representation by summation of plane waves
      6. 1.1.6 Representation of plane wave as optical rays
    2. 1.2 Mirror reflection of plane waves
      1. 1.2.1 Plane waves polarized perpendicular to the plane of incidence
      2. 1.2.2 Plane waves polarized in the plane of incidence
      3. 1.2.3 Plane waves with arbitrary polarization
      4. 1.2.4 The intensity
      5. 1.2.5 Ray representation of reflection
      6. 1.2.6 Reflection from a spherical mirror
    3. 1.3 Refraction of plane waves
      1. 1.3.1 Plane waves polarized perpendicular to the plane of incidence
      2. 1.3.2 Plane waves polarized in the plane of incidence
      3. 1.3.3 Properties of refracted and transmitted waves
        1. (a) Transmission and reflection at different incident angles
        2. (b) Total internal reflection
        3. (c) Refraction and reflection of arbitrary polarized waves
        4. (d) Ray representation of refraction
      4. 1.3.4 Refraction and dispersion in prisms
        1. (a) Plane wave analysis of prisms
        2. (b) Ray analysis of prisms
        3. (c) Thin prism represented as a transparent layer with a varying index
      5. 1.3.5 Refraction in a lens
        1. (a) Ray analysis of a thin lens
        2. (b) Thin lens represented as a transparency with varying index
    4. 1.4 Geometrical relations in image formation
    5. 1.5 Reflection and transmission at a grating
    6. 1.6 Pulse propagation of plane waves
    7. Chapter summary
  8. 2 Superposition of plane waves and applications
    1. 2.1 Reflection and anti-reflection coatings
    2. 2.2 Fabry–Perot resonance
      1. 2.2.1 Multiple reflections and Fabry–Perot resonance
      2. 2.2.2 Properties of Fabry–Perot resonance
      3. 2.2.3 Applications of the Fabry–Perot resonance
        1. (a) The Fabry–Perot scanning interferometer
        2. (b) Measurement of refractive properties of materials
        3. (c) Resonators for filtering and time delay of signals
    3. 2.3 Reconstruction of propagating waves
    4. 2.4 Planar waveguide modes viewed as internal reflected plane waves
      1. 2.4.1 Plane waves incident from the cladding
      2. 2.4.2 Plane waves incident from the substrate
        1. (a) Incident plane waves with sin(n /n) < < /2
        2. (b) Incident plane waves with 0 < < sin(n /n)
      3. 2.4.3 Plane waves incident within the waveguide: the planar waveguide modes
      4. 2.4.4 The hollow dielectric waveguide mode
    5. Chapter summary
  9. 3 Scalar wave equation and diffraction of optical radiation
    1. 3.1 The scalar wave equation
    2. 3.2 The solution of the scalar wave equation: Kirchhoff’s diffraction integral
      1. 3.2.1 Kirchhoff’s integral and the unit impulse response
      2. 3.2.2 Fresnel and Fraunhofer diffractions
      3. 3.2.3 Applications of diffraction integrals
        1. (a) Far field diffraction pattern of an aperture
        2. (b) Far field radiation intensity pattern of a lens
        3. (c) Fraunhofer diffraction in the focal plane of a lens
        4. (d) The lens viewed as a transformation element
      4. 3.2.4 Convolution theory and other mathematical techniques
        1. (a) The convolution relation
        2. (b) Double slit diffraction
        3. (c) Diffraction by an opaque disk
        4. (d) The Fresnel lens
        5. (e) Spatial filtering
    3. Chapter summary
  10. 4 Optical resonators and Gaussian beams
    1. 4.1 Integral equations for laser cavities
    2. 4.2 Modes of confocal cavities
      1. 4.2.1 The simplified integral equation for confocal cavities
      2. 4.2.2 Analytical solutions of the modes in confocal cavities
      3. 4.2.3 Properties of resonant modes in confocal cavities
        1. (a) The transverse field pattern
        2. (b) The resonance frequency
        3. (c) The orthogonality of the modes
        4. (d) A simplified analytical expression of the field
        5. (e) The spot size
        6. (f) The diffraction loss
        7. (g) The line width of resonances
      4. 4.2.4 Radiation fields inside and outside the cavity
        1. (a) The far field pattern of the TEM modes
        2. (b) A general expression for the TEM Gaussian modes
        3. (c) An example to illustrate confocal cavity modes
    3. 4.3 Modes of non-confocal cavities
      1. 4.3.1 Formation of a new cavity for known modes of confocal resonator
      2. 4.3.2 Finding the virtual equivalent confocal resonator for a given set of reflectors
      3. 4.3.3 A formal procedure to find the resonant modes in non-confocal cavities
      4. 4.3.4 An example of resonant modes in a non-confocal cavity
    4. 4.4 The propagation and the transformation of Gaussian beams (the ABCD matrix)
      1. 4.4.1 A Gaussian mode as a solution of Maxwell’s equation
      2. 4.4.2 The physical meaning of the terms in the Gaussian beam expression
      3. 4.4.3 The analysis of Gaussian beam propagation by matrix transformation
      4. 4.4.4 Gaussian beam passing through a lens
      5. 4.4.5 Gaussian beam passing through a spatial filter
      6. 4.4.6 Gaussian beam passing through a prism
      7. 4.4.7 Diffraction of a Gaussian beam by a grating
      8. 4.4.8 Focusing a Gaussian beam
      9. 4.4.9 An example of Gaussian mode matching
      10. 4.4.10 Modes in complex cavities
      11. 4.4.11 An example of the resonance mode in a ring cavity
    5. Chapter summary
  11. 5 Optical waveguides and fibers
    1. 5.1 Introduction to optical waveguides and fibers
    2. 5.2 Electromagnetic analysis of modes in planar optical waveguides
      1. 5.2.1 The asymmetric planar waveguide
      2. 5.2.2 Equations for TE and TM modes
    3. 5.3 TE modes of planar waveguides
      1. 5.3.1 TE planar guided-wave modes
      2. 5.3.2 TE planar guided-wave modes in a symmetrical waveguide
      3. 5.3.3 The cut-off condition of TE planar guided-wave modes
      4. 5.3.4 An example of TE planar guided-wave modes
      5. 5.3.5 TE planar substrate modes
      6. 5.3.6 TE planar air modes
    4. 5.4 TM modes of planar waveguides
      1. 5.4.1 TM planar guided-wave modes
      2. 5.4.2 TM planar guided-wave modes in a symmetrical waveguide
      3. 5.4.3 The cut-off condition of TM planar guided-wave modes
      4. 5.4.4 An example of TM planar guided-wave modes
      5. 5.4.5 TM planar substrate modes
      6. 5.4.6 TM planar air modes
      7. 5.4.7 Two practical considerations for TM modes
    5. 5.5 Guided waves in planar waveguides
      1. 5.5.1 The orthogonality of modes
      2. 5.5.2 Guided waves propagating in the y–z plane
      3. 5.5.3 Convergent and divergent guided waves
      4. 5.5.4 Refraction of a planar guided wave
      5. 5.5.5 Focusing and collimation of planar waveguide modes
        1. (a) The Luneberg lens
        2. (b) The geodesic lens
        3. (c) The Fresnel diffraction lens
      6. 5.5.6 Grating diffraction of planar guided waves
      7. 5.5.7 Excitation of planar guided-wave modes
      8. 5.5.8 Multi-layer planar waveguides
    6. 5.6 Channel waveguides
      1. 5.6.1 The effective index analysis
      2. 5.6.2 An example of the effective index method
      3. 5.6.3 Channel waveguide modes of complex structures
    7. 5.7 Guided-wave modes in optical fibers
      1. 5.7.1 Guided-wave solutions of Maxwell’s equations
      2. 5.7.2 Properties of the modes in fibers
      3. 5.7.3 Properties of optical fibers in applications
      4. 5.7.4 The cladding modes
    8. Chapter summary
  12. 6 Guided-wave interactions
    1. 6.1 Review of properties of the modes in a waveguide
    2. 6.2 Perturbation analysis
      1. 6.2.1 Derivation of perturbation analysis
      2. 6.2.2 A simple application of perturbation analysis:perturbation by a nearby dielectric
    3. 6.3 Coupled mode analysis
      1. 6.3.1 Modes of two uncoupled parallel waveguides
      2. 6.3.2 Modes of two coupled waveguides
      3. 6.3.3 An example of coupled mode analysis: the grating reflection filter
      4. 6.3.4 Another example of coupled mode analysis: the directional coupler
    4. 6.4 Super mode analysis
    5. 6.5 Super modes of two parallel waveguides
      1. 6.5.1 Super modes of two well-separated waveguides
      2. 6.5.2 Super modes of two coupled waveguides
      3. 6.5.3 Super modes of two coupled identical waveguides
        1. (a) Super modes obtained from the effective index method
        2. (b) Super modes obtained from coupled mode analysis
    6. 6.6 Directional coupling of two identical waveguides viewed as super modes
    7. 6.7 Super mode analysis of the adiabatic Y-branch and Mach–Zehnder interferometer
      1. 6.7.1 The adiabatic horn
      2. 6.7.2 Super mode analysis of a symmetric Y-branch
        1. (a) A single-mode Y-branch
        2. (b) A double-mode Y-branch
      3. 6.7.3 Super mode analysis of the Mach–Zehnder interferometer
    8. Chapter summary
  13. 7 Passive waveguide devices
    1. 7.1 Waveguide and fiber tapers
    2. 7.2 Power dividers
      1. 7.2.1 The Y-branch equal-power splitter
      2. 7.2.2 The directional coupler
      3. 7.2.3 The multi-mode interference coupler
      4. 7.2.4 The Star coupler
    3. 7.3 The phased array channel waveguide frequency demultiplexer
    4. 7.4 Wavelength filters and resonators
      1. 7.4.1 Grating filters
      2. 7.4.2 DBR resonators
      3. 7.4.3 The ring resonator wavelength filter
        1. (a) Variable-gap directional coupling
        2. (b) The resonance condition of the coupled ring
        3. (c) Power transfer
        4. (d) The free spectral range and the Q-factor
          1. The radiation loss of a curved waveguide
          2. The propagation loss
      4. 7.4.4 The ring resonator delay line
    5. Chapter summary
  14. 8 Active opto-electronic guided-wave components
    1. 8.1 The effect of electro-optical
      1. 8.1.1 Electro-optic effects in plane waves
      2. 8.1.2 Electro-optic effects in waveguides at low frequencies
        1. (a) Effect of ′
        2. (b) Effect of ′′
    2. 8.2 The physical mechanisms to create
      1. 8.2.1 ′
        1. (a) The LiNbO waveguide
        2. (b) The polymer waveguide
        3. (c) The III–V compound semiconductor waveguide
      2. 8.2.2 ′′ in semiconductors
        1. (a) Stimulated absorption and the bandgap
        2. (b) The quantum-confined Stark effect, QCSE
          1. Energy levels in quantum wells
          2. Exciton transitions and absorption
          3. The quantum-confined Stark effect (QCSE)
    3. 8.3 Active opto-electronic devices
      1. 8.3.1 The phase modulator
      2. 8.3.2 The Mach–Zhender modulator
      3. 8.3.3 The directional coupler modulator/switch
      4. 8.3.4 The electro-absorption modulator
    4. 8.4 The traveling wave modulator
    5. Chapter summary
  15. Appendices
    1. Section
    2. The equation for Green’s function
    3. Finding U from Green’s function, G
    4. A general Green’s function, G
    5. Green’s function for known U in a planar aperture
  16. Index