Topic 1: Models in Optics. Ray Optics

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1 V Topic 1: Models in ptics Aim: eview the of models used in optics, and the range of validity of each Contents: ffl ay ptics ffl ay Wave Theory ffl Vector ay Theory ffl calar Wave Theory ffl Vector Wave theory ffl Photon Models (Q) ay ptics Model: team of balls that obeys nell s Law of refraction at a surface. θ 1 n n 1 2 θ 2 n 1 sin(θ 1 )=n 2 sin(θ 2 ) s this simple model really useful? APPL PTC P PATMT of PYC Models in ptics -1- Autumn Term

2 V imple Lens f mage bject maging properties of Thin Lens u 1 u + 1 v = 1 f and v M = v u 1 2 The focal length is given by 1 f =(n 1)» These expressions will also appear in the more advanced theories. een in Physics 2 Lab and Physics 3 ptics. APPL PTC P PATMT of PYC Models in ptics -2- Autumn Term

3 V se of ay ptics Tracing rays through complex systems Principle Plane ay tracing to determine lens characteristics f ocal Length (f) Paraxial ocal Plane or ideal lens we get single point, but for aberrated lens we get indication of Point-pread-unction (P). ACT CT CL APPL PTC P PATMT of PYC Models in ptics -3- Autumn Term

4 V Typical systems: esign of Lens ystem ffl Camera Lens [4 to 20 lements] ffl Microscope bjective [3 to 10 lements] ffl Photocopier objective [6 to 8 lements] ffl Telescope [2 Mirrors plus 0 to 4 glass elements] Mostly complex system with multiple glass surfaces (almost always spherical). nitial esign Trace ays? Predict Performance ff 6 Modify esign Trace ays? ew esign - terative error reduction, (highly non-linear). deal Computer application, one of the first tasks ever transferred to computer [1956]. Look at this again in Lecture 9/10. APPL PTC P PATMT of PYC Models in ptics -4- Autumn Term

5 V ay Wave Theory Add wave nature of light by considering light to be rays that spread out and interfere to give node and anti-nodes. d θ Young s lits we get a bright fringe at: d sinθ = ±nλ This theory gives the correct resuults for: ffl iffraction ratings, so spectroscopy. ffl nterferometry: (Michelson, Twyman-reen, abre-perot, thin films.) This theory introduces wave properties to get interference, but still o iffraction Very useful theory, used in most of Physics 3 ptics. We will use this again for olography at end of this course. APPL PTC P PATMT of PYC Models in ptics -5- Autumn Term

6 V Vector ay Theory Add vector properties of light to ray model by assuming orthogonal and field. olve continuity equations at boundries. This gives Polarisation effects, for example, rewster s angle, resnel s qua- ffl Polarisation on reflection: tions. ffl Malus Law: transmission of polarisers, quarter/half wave plates. ffl irefrigence: Linear crystal optics, beam-splitters, icol prisms. ffl vanescent Waves: classical barrier penetration, skin depth, planar waveguides. This theory typically does not contain infererence or diffraction. een in Physics 3 lectromagnetism and Physics 3 ptics. imple polarisation problems can be formulated as Jones Matrices (very similar to spin operators), more complex, mixed polarisation, by tokes Matrices. APPL PTC P PATMT of PYC Models in ptics -6- Autumn Term

7 V calar Wave Theory lectro-magnetic theory with light field characterised by calar Potential. Valid for objects & apertures fl λ. ives diffraction as integral expression (mathematical version of ygen s econdary Waves) ses: Amplitude istribution Able to calculate analytic P of lens. Allows use of ourier Techniques to predict effect of diffraction. asis of mage ormation, olography, and ptical Processing. (This Course) Problems: 1. Monochromatic light assumed (developed to include Partial Coherence). 2. o polarisation effects, (added by Jone s matrices) 3. reaks down at wavelength structures 4. reaks down an very high & low intensities. APPL PTC P PATMT of PYC Models in ptics -7- Autumn Term

8 V Vector Theory Light is electro-magnetic wave with and vectors linked by Maxwell s quations. f we know boundary conditions, solved for and fields. xample: The Thick lit. λ >>λ ere calar iffraction not valid, due to Waveguide effects in the slit. n Practice only able to solve for very simple systems, 1. Thick lit 2. dge 3. nfinite metal grating 4. nfinite dielectric grating ven then with great difficulties. APPL PTC P PATMT of PYC Models in ptics -8- Autumn Term

9 V ibre ptics lass fibre withcoredownto1.5µm. Typical fibre, 5µm glass core and 125µm cladding. 125um Cladding Core 5um eeds vector treatment, but simple geometry. olutions identical to wave guide, including mode structure. Thinnest fibre s support only one mode, (mono-mode) ther Areas: ffl adar systems (λ ß 3cm) ffl adio transmissions (λ ß 3cm to km) ffl adio telescopes (λ ß 1cm to 1m). esign of these systems requires solution of the vector field problem. ither approximated by scalar field (with care), or solved by numerical simulation. APPL PTC P PATMT of PYC Models in ptics -9- Autumn Term

10 V Quantum Theories Light is really? and quantised vector field with light propagating as photons. Quantum effects at igh & Low ntensities igh ntensities At low intensities, elastic scattering of photons from material, but at high energies nelastic cattering. on-linear effect which are ntensity ependent. xamples ffl aman scattering (non-linear photon) ffl requency oubling (two photon processes) ffl our Wave mixing (intensity dependent refractive index) ffl ptical i-stability (intensity dependent refractive index) on-linear effects can be induced in any material, with enough power. ange of ptically Active materials, get non-linear effect at low(ish) powers 6 ati 4 aas Lib 3 LiquidCrystals ome discussion in Atomic and Molecular Physics and Laser Physics courses. APPL PTC P PATMT of PYC Models in ptics -10- Autumn Term

11 V Low ntensities: Linear interaction with materials, but detect a quantised intensity, (whole Photons). Measure a probability function, (approximate a probability function), but also quantum effects. ffects 1. oise in detected signal (fundamental problem at low light levels). 2. ntensity correlations (quantum effect used in radio interferometry). 3. quezzed tates: quantum states at low light levels, similar to low temperature statistical effects. Modern, specilised area of optics, not able to put much of this in an undergraduate physics course. APPL PTC P PATMT of PYC Models in ptics -11- Autumn Term

Topic 2: Scalar Diffraction

$Topic 2: Scalar Diffraction$ V Topic 2: calar iffraction Aim: Covers calar iffraction theory to derive ayleigh-ommerfled diffraction. Take approximations to get Kirchhoff and resnel approximations. Contents:. Preliminary Theory. 2.