Optics.

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1 Optics

2 Course outline Light is a Ray (Geometrical Optics) 1. Nature of light 2. Production and measurement of light 3. Geometrical optics 4. Matrix methods in paraxial optics 5. Aberration theory 6. Optical instrumentation 27. optical properties of materials Light is a Wave (Physical Optics) 8. Wave equations 9. Superposition of waves 10. Interference of light 11. Optical interferometry 12. Coherence 13. Holography 14. Matrix treatment of polarization 15. Production of polarized light Light is a Wave (Physical Optics) 25. Fourier optics 16. Fraunhofer diffraction 17. The diffraction grating 18. Fresnel diffraction 19. Theory of multilayer films 20. Fresnel equations * Evanescent waves 26. Nonlinear optics Light is a Photon (Quantum Optics) 21. Laser basics 22. Characteristics of laser beams 23. Laser applications 24. Fiber optics

3 Radiometric and Photometric Definitions and Units radiometry photometry Radiant flux : Irradiance : Radiant intensity : Radiance : watt (W) W/m 2 W/sr W/(sr. m 2 ) lumen (lm) : Luminous flux lux (lx) : illuminance candela (cd): luminous intensity Cd/m 2 : luminance

4 Photometric Units 555 nm Radiant flux of 1 Watt at 555 nm is the luminous flux of 685 lm (lumen) Luminous efficiency V(λ) 610 nm Radiant flux of 1 Watt at 610 nm is the luminous flux of lm (lumen) Photometric unit = 685 x V(λ) x radiometric unit

$= nθ : Law of refraction i i t t in paraxial approx.$

5 Plane of incidence θ = θ : Law of reflection i r nθ = nθ : Law of refraction i i t t in paraxial approx.

6 Image Formation Summary Table

Matrix Method Matrix Method = 1 1 2 2 α α y D

7 Matrix Method Matrix Method = α α y D C B A y θ α θ D Cy B Ay y + = + =

8 D=0 A=0 B=0 C=0

9 Aberrations Chromatic Monochromatic n (λ)( Unclear image Deformation of image Spherical Coma astigmatism Distortion Curvature

10 Third-order (Seidel) aberrations Paraxial approximation

11 Third-Order Aberration Theory After some very complicated analysis the third-order aberration equation is obtained: 4 ( ) = a Q C r 0 40 Spherical Aberration θ Q + C h r cosθ Coma O r ρ + C h r 2 22 cos θ Astigmatism B + C h r Curvature of Field + 3 3C11h r cosθ Distortion

12 Stops, pupils and windows in an optical system α α E n P E n W AS FS E x P E x W

13 Camera: Brightness and f-number Brightness of image is determined by the amount of light falling on the film. Each point on the film subtends a solid angle dω = da 2 r πd = Define f-number, f 2 πd = 2 4s' 4 f A = Irradiance at any point on film is proportional to (D/f) 2 I p 1 A 2 This is a measure of the speed of the lens Small f# (big aperture) I large, t short Large f# (small aperture) I small, t long 2 2 f D D D s f

14 Numerical Aperture Measure of light gathering power N. A. = n sin α Lens Oil α g Air α g α o α a Cover Glass O n g

15 Microscopes In most microscopes, L = cm

16 Telescopes Astronomical telescope

17 Appendix : From Maxwell Equations to Wave Equations Professor Vladimir M. Shalaev, Univ of Purdue

19 Dispersion

20 One-dimensional Wave Equation v = 1 m/s, -z v = 2 m/s, +x

22 Poynting vector For an isotropic media energy flows in the direction of propagation, so both the magnitude and direction of this flow is given by, r r r S = E H Poynting Vector r 1 r r S= E B μ o The corresponding intensity or irradiance is then, r I = I r () t = S = E H

24 Phase velocity and Group velocity phase velocity : group velocity : v v g p ω ω + ω ω k k + k k p 1 2 = = p 1 2 ω ω ω dω k k k dk g 1 2 = = g 1 2 v g dω = dk d dv ( kv p) v k dk dk p = = p + d c c dn k dn = vp + k = vp + k v 1 2 = p + dk n n dk n dk λ dn = vp 1 + = 2 / n dλ ( k π λ)

25 The total irradiance is given by Two-Beam Interference There is a maximum in the interference pattern when This is referred to as constructive interference. There is a minimum in the interference pattern when This is referred to as destructive interference When

26 Visibility Visibility = fringe contrast V I I max max + I I min min { 0 V 1 } When Therefore, V = 1

27 Reflection and Interference in Thin Films 180 º Phase change of the reflected light by a media with a larger n No Phase change of the reflected light by a media with a smaller n

28 Interference Young s Double-Slit Experiment

29 The Michelson Interferometer Light source Beam splitter Bright fringe : Dark fringe :

30 Mach-Zehnder Interferometer Spatial filtering & collimation Laser Beam splitter PZT mirror monitor Test sample Imaging lens CCD mirror 2f 2f

31 Stokes Relations E i is the amplitude of the incident light. The amplitudes of the reflected and transmitted beams are given by From the principle of reversibility Stokes relations r = e iπ r

32 Multiple-Beam Interference in a Parallel Plate 2π δ = λ ( 2nt f cosθt )

33 The Fabry-Perot Interferometer

34 Coherence Coherence is a measure of the correlation between the phases measured at different (temporal and spatial) points on a wave Coherence theory is a study of the correlation properties of random light which is also known as the statistical optics. Δs 0 Δλ 0

35 Degree of of Coherence

PRINCIPLES OF PHYSICAL OPTICS

PRINCIPLES OF PHYSICAL OPTICS C. A. Bennett University of North Carolina At Asheville WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION CONTENTS Preface 1 The Physics of Waves 1 1.1 Introduction