EE 231 Optics, Fall



Prof. Andrea Fratalocchi

Update Syllabi here.


Class Notes

Last Update Topics Notes and References
2-Sep-2018 Maxwell’s equations in isotropic media. Poynting theorem. Definition and physical meaning of the Poynting vector and the energy density of the electromagnetic wave. Complex formalism. Time average of products of sinusoidal functions. Definition of optical intensity. Plane wave solutions of Maxwell’s equations. lesson 1
02-Oct-2017 The scalar theory of diffraction. Sommerfield definition of diffraction. Discussion and theoretical justification of the scalar approximation. Helmholtz equation for the disturbance field. Intensity observable in the scalar approximation. Classical approach to the diffraction problem: definition of propagation and interaction problems.

lesson 2

19-Sep-2017 A first example of propagation problem: interference of two non collinear plane waves. Analysis of intensity distribution. Definition of interference fringes and discussion on possible applications. Spherical waves.

lesson 3

21-Sep-2017 Brief introduction to coherence and interference effects in coherent fields. Discussion of applications of Newtons rings. Interference between spherical waves and plane waves. lesson 4
02-Oct-2017 Bessel beam solution of the Helmholtz equations. Field distribution and dispersionless propagation. Discussion and experimental generation of Bessel beams.

lesson 5

02-Oct-2017 Experimental generation of Bessel beam; discussion on possible applications of Bessel beams; Elements of linear system theory and Fourier analysis. Exercises set before the midterm evaluation.

lesson 6

05-Oct-2017 The propagation problem. General solution through Fourier modal decomposition. Plane-wave propagator. Linear system representation. Evanescent waves and their physical implications.

lesson 7

27-Oct-2016 First formula of Rayleigh-Sommerfield. Huygens principle. Fresnel diffraction integral. Far-Field diffraction formula. Optical resolution limits from wave propagation. Exercise set on far-field diffraction from slit and simple optical apertures.

lesson 8

27-Nov-2017 Modeling of laser light beams. General considerations on laser light properties. Derivation of Paraxial wave equation.

lesson 9

9-nov-2016 Spherical waves and Gaussian beam solutions of the paraxial wave equation. Curvature, waist and general properties of Gaussian beams.

lesson 10

27-nov-2017 Direct and Inverse problem of Gaussian beams. Physical explanation of the diffraction of Gaussian beam in terms of dispersion relation. ABCD Law of Gaussian beams. Free space propagation ABCD matrix. The interaction problem: general approach through the transfer function. Exact solution of the interaction with a semi-infinite metallic plane; comparison with the transfer function method; discussion. .

lesson 11

17-nov-2016  The thin lens. Transfer function of the thin lens. Application of the thin lens to visualize the far fieldPart II) Action of a thin lens on a Gaussian Beam. Collimation and Focusing problem. Beam Expander. ABCD matrix of a thin lens.  lesson 12
21-nov-2016 Hands on real cases: experiments on diffraction theory.

lesson 13

24-Nov-2016 Gratings. General properties and different examples of applications

lesson 14

Not covered this year Analysis of dispersion relation of symmetric waveguide. TE and TM modes. Number of modes for a given geometry. Asymetric waveguides: study of the general case. Modal profile of guided modes.

lesson 14

Yariv: Chapter 3

Not covered this year The Fabry-Perot interferometer. Reflection and Transmission from multiple rays. Airy’s Formulae. Finesse. Interferometer resolving power.

lesson 15

Wolf: Chapter 7

Not covered this year Optical cavities. ABCD transfer matrix approach. Stability analysis. Gaussian mode solution of cavities made by spherical mirrors. Phase and amplitude self-consistent equations.

lesson 16

lesson 17

Verdeyen: Chapters 2,5


Lab Lessons 1: Imaging and microscope theory

05-Oct-2017 Introduction to geometrical optics and the concept of rays. Optical path. Fermat Principle of least time: variations formulation. Fermat principle from Maxwell Equations: limits of geometrical optics. The propagation of rays. Examples of Ray Tracing. Imaging 1

9-Nov-2017 Introduction to Matrix optics. ABCD matrix. Refraction matrix, propagation matrix and reflection matrix. Significance of matrix elements. Lenses. Thick and thin lenses. Imaging formation by thin lenses. The human eye. Brief discussion of chromatic and spherical aberrations of lenses. Elements of microscope theory: infinity corrected systems. Microscope resolution. Microscope objectives. Gallery of microscopes techniques. Imaging 2

EE231 Final results

ID            Midterm    Final   Average

160159           57/60      55/60               A (this is final grade)

165725           56/60      35/60              46/60       A- (oral optional)

162830           50/60      55/60              53/60      A (this is final grade)

162446           50/60       45/60              48/60     A- (oral optional)

159706          50/60        40/60             45/60

159663          49/60       44/60               47/60

160310           46/60       55/60               51/60     A- (oral optional)

159450           41/60        31/60               36/60

158163           40/60      55/60               48/60      A- (oral optional)

159670           38/60       40/60               39/60

157171          37/60         45/60                41/60

165019            36/60         35/60                36/60

157640           35/60         40/60              37/60

166129           26/60        35/60                31/60

134160           25/60        43/60               34/60

152367          24/60         50/60              38/60

158084           23/60          28/60              26/60

162724           9/60           25/60                 17/60

Grade A is final, no need for oral

Grade A- is optional oral

All others are required to come for the oral, revise everything, especially imaging + Gaussian beams


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