Gradient-Index Optics

1 Light Propagation in GRIN Media.- 1.1 Introduction.- 1.2 Vector Wave Equations.- 1.3 Scalar Wave Equation.- 1.4 Parabolic Wave Equation.- 1.5 Ray Optics: Axial and Field Rays.- 2 Imaging and Transforming Transmission Through GRIN Media.- 2.1 Introduction.- 2.2 The Kernel Function.- 2.3 Imaging and Fourier Transforming Through GRIN Media.- 2.4 Fractional Fourier Transforming in GRIN Media.- 2.5 Modal Representation of the Kernel.- 3 GRIN Lenses for Uniform Illumination.- 3.1 Introduction.- 3.2 Transmittance Function of a GRIN Lens for Uniform Illumination.- 3.3 GRIN Lens Law: Imaging and Fourier Transforming by GRIN Lens.- 3.4 Geometrical Optics of GRIN Lenses.- 3.5 Effective Radius, Numerical Aperture, Aperture Stop, and Pupils.- 3.6 Diffraction-Limited Propagation of Light in a GRIN lens.- 3.7 Effect of the Aperture on Image and Fourier Transform Formation.- 4 GRIN Lenses for Gaussian Illumination.- 4.1 Introduction.- 4.2 Propagation of Gaussian Beams in a GRIN Lens.- 4.3 GRIN Lens Law: Image and Focal Shifts.- 4.4 Effective Aperture.- 5 GRIN Media with Loss or Gain.- 5.1 Introduction.- 5.2 Active GRIN Materials: Complex Refractive Index.- 5.3 The Kernel Function.- 5.4 Focal Distance and Focal Shift for Uniform Illumination.- 5.5 Gaussian Illumination in an Active GRIN Medium: Beam Parameters.- 5.6 Transformation of a Gaussian Beam into a Uniform Beam.- 6 Planar GRIN Media with Hyperbolic Secant Refractive Index Profile.- 6.1 Introduction.- 6.2 Ray Equation and ABCD Law.- 6.3 Focusing and Collimation Properties.- 6.4 Numerical Aperture: On-Axis and Off-Axis Coupling.- 6.5 Mode Propagation.- 6.6 The Kernel Function.- 6.7 Diffraction-Free and Diffraction-Limited Propagation of Light.- 7 The Talbot Effect in GRIN Media.- 7.1 Introduction.- 7.2 Light Propagation and Imaging Condition.- 7.3 The Integer Talbot Effect.- 7.4 Self-Image Distances.- 7.5 Fractional Talbot Effect: Unit Cell.- 7.6 Effect of Off-Axis Source and Finite Object Dimension on Self-Images.- 8 GRIN Crystalline Lens.- 8.1 Introduction.- 8.2 The Optical Structure of the Human Eye.- 8.3 The GRIN Model of the Crystalline Lens.- 8.4 The Gradient Parameter: Axial and Field Rays in the Crystalline Lens.- 8.5 Refractive Power and Cardinal Points of the Crystalline Lens.- 9 Optical Connections by GRIN Lenses.- 9.1 Introduction.- 9.2 GRIN Fiber Lens.- 9.3 Anamorphic Selfoc Lens.- 9.4 Tapered GRIN Lens.- 9.5 Selfoc Lens.- References.