Problems And Solutions In Optics And Photonics

This book covers fundamental principles and wide array of numerical based problems, patterned as per FAQs in university exams. Answers follow the problems section by detailed conceptual explanations and student friendly step-wise solution. Cover 1 Contents 5 1. Matrix Method in Paraxial Optics 15 A Quick Review 15 1.1 Effect of Translation 15 1.2 Effect of Refraction 16 1.3 Unit Planes 18 Problems 20 Solutions 22 2. Fermat’s Principle, Snell’s Law and Ray Equation 32 A Quick Review 32 2.1 Fermat’s Principle 32 2.2 Ray Equations in Inhomogenous Media 33 Problems 33 Solutions 36 3. Optical Instruments 46 A Quick Review 46 3.1 The Eye 46 3.2 Magnifying Glass 46 3.3 Compound Microscope 46 3.4 Telescope 47 Problems 48 Solutions 49 4. Aberrations 52 A Quick Review 52 4.1 Chromatic Aberration 52 4.2 Spherical Aberration 52 Problems 56 Solutions 58 5. Huygens’ Principle and its Applications 68 A Quick Review 68 5.1 Introduction 68 Problems 69 Solutions 70 6. Interference—Division of Wavefront 78 A Quick Review 78 Problems 79 Solutions 84 7. Interference by Division of Amplitude 95 A Quick Review 95 Problems 97 Solutions 98 8. Multiple Beam Interferometry 102 A Quick Review 102 8.1 Multiple Reflections from a Plane Parallel Film 102 8.2 Modes of the Fabry-Perot Cavity 104 8.3 Resolving Power 104 Problems 104 Solutions 107 9. Fraunhofer Diffraction: I 113 A Quick Review 113 9.1 Fraunhofer Diffraction by a Single Slit 113 9.2 Fraunhofer Diffraction by Multiple Slits 115 9.3 Resolving Power of a Grating 116 9.4 Diffraction by a Circular Aperture 116 9.5 Limit of Resolution 119 Problems 120 Solutions 122 10. Fraunhofer Diffraction II: The Diffraction Integral 130 A Quick Review 130 Problems 131 Solutions 135 11. Fresnel Diffraction 145 A Quick Review 145 11.1 Fresnel Diffraction Integral 145 11.2 Diffraction of a Gaussian Beam 146 11.3 Fresnel Integrals 146 11.4 The Straight Edge Diffraction Pattern 147 Problems 149 Solutions 153 12. Fourier Optics and Holography 162 A Quick Review 162 12.1 Fourier Optics 162 12.2 Holography 162 Problems 163 Solutions 165 13. Polarisation I: Basics and Double Refraction 172 A Quick Review 172 13.1 Linearly Polarised Waves 172 13.2 Malus’ Law 173 13.3 Circularly Polarised Waves 173 13.4 Elliptically Polarised Waves 174 13.6 Anisotropic Media: Biaxial Media 175 13.7 Anisotropic Media: Uniaxial Media 176 13.8 Velocity of Ordinary and Extraordinary Waves 177 13.9 Velocity of Ordinary and Extraordinary Rays 178 Problems 178 Solutions 184 14. Polarisation II: Jones Vectors and Jones Matrices 201 A Quick Review 201 Problems 204 Solutions 208 15. Maxwell’s Equations and the Wave Equation 216 A Quick Review 216 Problems 219 Solutions 221 16. Group Velocity and Pulse Dispersion 226 A Quick Review 226 Problems 227 Solutions 229 17. Lasers 238 A Quick Review 238 17.1 Einstein Coefficients 238 17.2 Lineshape Functions 239 17.3 The Threshold Condition 240 17.4 Modes in a Cavity 241 Problems 242 Solutions 246 18. Fiber Optics I: Basic Concepts and Ray Optics 256 Considerations in Multimode Fibers A Quick Review 256 18.1 Step Index Fiber 256 18.2 Attenuation 257 18.3 Material Dispersion 258 18.4 Parabolic Index Fiber 259 Problems 261 Solutions 263 19. Basic Waveguide Theory and Concept of Modes 267 A Quick Review 267 19.1 Step Index Symmetric Profile 268 19.2 TE Modes of a Symmetric Step Index Planar Waveguide 269 19.3 TM Modes of a Symmetric Step Index Planar Waveguide 273 19.4 TE Modes in a Parabolic Index Medium 274 Problems 274 Solutions 276 20. Fiber Optics II: Single Mode Fibers 286 A Quick Review 286 20.1 Cut-off Frequencies and Number of Modes 289 20.2 Empirical Formula for the Normalised Propagation Constant 290 20.3 Spot Size of the Fundamental Mode 291 20.4 Splice Loss due to Transverse Misalignment 292 20.5 Pulse Dispersion in Single Mode Fibers 292 Problems 293 Solutions 295 21. Integrated Optics 302 A Quick Review 302 Problems 305 Solutions 309 22. Electro-Optic Effect 312 A Quick Review 312 Problems 315 Solutions 318 23. Acousto-Optic Effect 322 A Quick Review 322 Problems 324 Solutions 326 24. Nonlinear Optics 330 A Quick Review 330 Problems 332 Solutions 335 Appendix: Multiple Choice Questions 339 References and Suggested Readings 352