Transcript Class07
So much to remember, so little space Diffraction Limits on Light What have we learned? • Any traveling sinusoidal wave may be described by y = ym sin(kx wt + f) • Light always reflects with an angle of reflection equal to the angle of incidence (angles are measured to the normal). • When light travels into a denser medium from a rarer medium, it slows down and bends toward the normal. • The Fourier spectrum of a wider pulse will be narrower than that of a narrow pulse, so it has a smaller bandwidth. • Your bandwidth B must be as large as the rate N at which you transfer different amplitudes. • The rise time of each pulse must be no more than 70% of the duration of the pulse What Else Have We Learned? • Can represent binary data with pulses in a variety of ways • 10110 could look like . . . Notice that the NRZ takes half the time of the others for the same pulse widths Non-return-to-zero (NRZ) Return-to-zero (RZ) Bipolar Coding Other schemes use tricks to reduce errors and BW requirements. Optical Waveguides Summary • Dispersion means spreading • Signals in a fiber will have several sources of dispersion: – Chromatic: • Material: index of refraction depends on wavelength (prism) • Waveguide: some of wave travels through cladding with different index of refraction (primarily single-mode) – leads to wavelength-dependent effects – Modal: different modes travel different paths and so require different amounts of time to travel down fiber (CUPS) • Also have attenuation/loss due to scattering/absorption by fiber material, which depends on wavelength/frequency Optical Waveguide Summary (cont.) • Modes in a fiber are specific field distributions that are independent of “z”, or length traveled down the fiber • Fields of modes look like harmonics of standing waves • Can make a single-mode fiber by: – reducing diameter of fiber so smaller cone of light enters – reducing NA of fiber so smaller cone of light is trapped What sets the limit on density of data stored? For a specific example, what determines the density of data on a CD ROM? Interference of Waves Amax If crests match crests, then waves Amax interfere constructively Crests will match 2Amax if waves are one wavelength, two wavelengths, … apart: path difference = ml wave 1 wave 2 sum Destructive Interference If crests match troughs Amax (180° out of phase), then waves interfere Amax destructively Crests will match troughs if waves are one/half wavelength, three/half wavelengths, … apart: path difference = (m+½)l wave 1 wave 2 sum What This Means for Light Light is electromagnetic radiation A light wave is oscillating electric and magnetic fields The amplitude of the oscillation represents the maximum electric (or magnetic) field and determines the intensity of light Intensity depends on the square of the maximum electric field: I = Emax2/(2cm0) Constructive interference produces brighter light; destructive interference produces dimmer light. Comparing Interference 2Emax Emax Medium amplitude of electric field yields medium intensity light Double amplitude of electric field yields quadruple intensity (very bright) light Zero amplitude of electric field yields zero intensity (no) light Coherent vs. Incoherent Light • “Everyday light” is incoherent • Laser light is an example of coherent light • Simple wave equation describes coherent waves y = ym sin(kx wt + f) Wavelet Approach to Interference and Diffraction Plane waves can be modeled as the interference of an array of point sources. l Direction of wave motion Wave Crest Wave Trough l = wavelength Wavelet Approach to Interference and Diffraction Any opening will cause plane wave to start spreading out. Direction of wave motion l a Wave Crest Wave Trough l = wavelength a = aperture width The Double Slit Experiment Waves spreading out from two points, such as waves passing through two slits, will interfere l d Wave crest Wave trough Spot of constructive interference Spot of destructive interference Diffraction Patterns Light traveling through a single slit also creates a pattern, due to interference between wavefronts passing through different regions of the slit l a Wave crest Wave trough Spot of constructive interference Spot of destructive interference Single Slit Math y b a q tan q = y/D D a/2 q b Path length difference = a/2 sin q Diffraction Math The locations of successive minima are given by a 1 sin q m l (m 0, 1, 2,...) 2 2 a sin q nl (n 1, 2, 3.....) tan q = y/D for small angles, sin q ~ q ~ tan q = y/D Diffraction by a circular aperture A circular aperture of diameter d l sin q 1.22 (1st minimum) d Single slit of width a sin q l a (1st minimum) Resolvability Two objects are just resolved when the central diffraction maximum of one object is at the first minimum of the other. (Rayleigh’s criterion) 1.22l 1.22l sin d d 1 R As before, q approximately y/L Comments on Resolvability y 1.22 l D d R If want to resolve objects closer to each other (smaller y), need smaller wavelength of light or larger aperature This is called the diffraction limit Why Do We Care? • CD-ROMS and other optical storage devices Do the Activity, Continuing through it After finishing Diffraction Pattern of a Red Laser, first two or three groups should jump to Green Laser part, then give green lasers to other groups when done Before the next class, . . . • Do Homework 8 • Read the handout about how CD ROMs work. • Do Activity 07 Evaluation by Midnight Tonight • Come with questions about the test material – Exam on Thursday, Feb. 14.