ISBN: 3540421254
TITLE: Gradient-Index Optics
AUTHOR: Gomez-Reino, Perez, Bao
TOC:

1 Light Propagation in GRIN Media 1
1.1 Introduction 1
1.2 Vector Wave Equations 1
1.3 Scalar Wave Equation 4
1.4 Parabolic Wave Equation 6
1.5 Ray Optics: Axial and Field Rays 9
2 Imaging and Transforming Transmission Through GRIN Media 25
2.1 Introduction 25
2.2 The Kernel Function 25
2.3 Imaging and Fourier Transforming Through GRIN Media 30
2.4 Fractional Fourier Transforming in GRIN Media 33
2.5 Modal Representation of the Kernel 37
3 GRIN Lenses for Uniform Illumination 43
3.1 Introduction 43
3.2 Transmittance Function of a GRIN Lens for Uniform Illumination 43
3.3 GRIN Lens Law: Imaging and Fourier Transforming by GRIN Lens 50
3.4 Geometrical Optics of GRIN Lenses 56
3.5 Effective Radius, Numerical Aperture, Aperture Stop, and Pupils 63
3.6 Diffraction-limited propagation of light in a GRIN lens 71
3.7 Effect of the Aperture on Image and Fourier Transform Formation 79
4 GRIN Lenses for Gaussian Illumination 87
4.1 Introduction 87
4.2 Propagation of Gaussian Beams in a GRIN Lens 87
4.3 GRIN Lens Law: Image and Focal Shifts 97
4.4 Effective Aperture 104
5 GRIN Media with Loss or Gain 109
5.1 Introduction 109
5.2 Active GRIN Materials: Complex Refractive Index 109
5.3 The Kernel Function 111
5.4 Focal Distance and Focal Shift for Uniform Illumination 113
5.5 Gaussian Illumination in an Active GRIN Medium: Beam Parameters 121
5.6 Transformation of a Gaussian Beam into a Uniform Beam 123
6 Planar GRIN Media with Hyperbolic Secant Refractive Index Profile 127
6.1 Introduction 127
6.2 Ray Equation and ABCD Law 128
6.3 Focusing and Collimation Properties 131
6.4 Numerical Aperture: On-Axis and Off-Axis Coupling 140
6.5 Mode Propagation 143
6.6 The Kernel Function 148
6.7 Diffraction-Free and Diffraction-Limited Propagation of Light 151
7 The Talbot Effect in GRIN Media 163
7.1 Introduction 163
7.2 Light Propagation and Imaging Condition 164
7.3 The Integer Talbot Effect 166
7.4 Self-Image Distances 170
7.5 Fractional Talbot Effect: Unit Cell 177
7.6 Effect of Off-Axis Source and Finite Object Dimension on Self-Images 182
8 GRIN Crystalline Lens 189
8.1 Introduction 189
8.2 The Optical Structure of the Human Eye 190
8.3 The GRIN Model of the Crystalline Lens 193
8.4 The Gradient Parameter: Axial and Field Rays in the Crystalline Lens 198
8.5 Refractive Power and Cardinal Points of the Crystalline Lens 203
9 Optical Connections by GRIN Lenses 209
9.1 Introduction 209
9.2 GRIN Fiber Lens 209
9.3 Anamorphic Selfoc Lens 212
9.4 Tapered GRIN Lens 218
9.5 Selfoc Lens 223
References 231
Index 239
END
