Foundations of Modern Optics

Syllabus

The syllabus covers the following topics organized in the following 4 units:

Introduction

Historical introduction, Waves: harmonic waves, longitudinal, transverse, complex description, phase velocity, wave front types.

Fundamentals

Electromagnetism, Maxwell’s equations: wave equation, velocity of wave propagation, Poynting vector, radiation intensity. Spectrum of electromagnetic radiation, refractive index, dispersion – absorption, classical dispersion theory.

Detection of radiation

The photoelectric effect, photomultipliers, photoresistors, photodiodes, phototransistors, CDD detectors, film Photometry – Radiometry.

Sources of radiation

Black body radiation, incandescent, arc, spectral gas, fluorescence lamps, LEDs, LASERs: basic principles, pumping – amplification of light, laser cavity, gas lasers, solid state lasers, diode lasers.

Polarization

Polarization state, degree of polarization, non polarized light. Linear, elliptical, circular polarization, Jones vectors and matrices, Stokes parameters and Mueller matrices, Linear polarizers, retardation plates. Birefringence: birefringent crystals, the dielectric tensor, refractive index ellipsoid, wavefront surface, eigen polarizations, optical activity, Polarization by scattering, Polarization by reflection, evanescent waves.

Interference

Group velocity, coherence, interference conditions, types and localization of interference fringes Two wave interference, multiple plane wave interference, Wavefront splitting interferometers: Young’s experiment, Amplitude splitting interferometers: Equal inclination fringes (thin film interference), Equal thickness fringes, interference under multiple reflections.

Imaging

Geometrical optics

Optical rays, the geometrical optics approximation,The concept of Imaging, stigmatic imaging, Reflection, Refraction (Snell equation), total internal reflection, Reflectivity (Fresnel coefficients), Fermat’s principle, application in reflection and refraction, Reflection prisms, Dispersion prisms: minimum deviation, monochromators.

Simple optical systems

Reflection from plane mirror, retro-reflectors. Refraction from a plane interface, propagation through a transparent plate, Spherical interfaces, Spherical lenses, Spherical mirrors. Paraxial approximation, Imaging with thin lenses and mirrors, the use of cardinal points, examples, 3D objects, Magnification.

The matrix method

The ray vector. Ray translation, refraction, reflection matrices, matrix of an optical system, estimation of cardinal points, imaging using matrices, optical system composition (equal subsystems, symmetrical systems, magnification, Basic principles of analysis and design of optical systems using ray matrices.

Image illumination

aperture stop, field stop, entrance-exit pupil, entrance-exit window, telecentric systems.

Optical Abberations

ray aberration, wavefront aberration, Monochromatic aberrations. Seidel primary aberrations: spherical, comma, astigmatism, field curvature, distortion. Chromatic aberrations: longitudinal -transverse, Sphero- chromatic. Achromatic lenses, apochromatic lenses, aspherical lenses.

Eikonal equation

Optical rays, Derivation of the eiconal equation, geometrical wave surfaces, ray equation, paraxial approximation Propagation in inhomogeneous media.

Wave propagation

Diffraction

Fresnel zones, Helmloltz-Kirchhoff integral theorem, Kirchhoff diffraction theory. Fraunhofer and Fresnel diffraction: slit, rectangular, circular opening. Resolution, diffraction limited systems. Array of diffracting openings: multiple slits

Gaussian beams

Propagation, beam waist, confocal parameter. Imaging of Gaussian beams, matrix description

Learning Outcomes

Upon successful completion of the course students will

• Be familiar with the basic principles of optics.
• Be familiar with the principles of electromagnetism with emphasis on their application to optics.
• Be familiar with the basic principles governing wave propagation, the description of transverse E/M waves in various media and the phenomena of contribution and diffraction.
• Be able to describe in detail the polarization of optical waves as they are imparted to complex optical devices.
• Know the principles of operation and design of imaging optical systems and to solve problems of designing optical light systems within complex optical systems.
• Be able to independently describe and solve optical design problems.

Recommended Bibliography

• Lecture notes
• “Optics”, E. Hecht, Addison-Wesley, (2001).
• “Principles of Optics”, M. Born, E. Wolf.
• “Introduction to Modern Optics”, G.R. Fowles, Dover, (1989).
• “Introduction to Fourier Optics”, J. W. Goodman, McGraw-Hill, (1996).

Bibliography: exercises with solutions

• “Solved exercises in Optics”, D. Papazoglou, UoC, (2022).