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Lecture16

# Lecture16 - absorption line Most pronounced in the region...

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Lecture 16 11. Superposition of waves We are at the point of no return • Complex Addition (same frequency) Complex amplitude Vector in the complex plane • Phasor Addition (same frequency) The whole phasor is rotating in time Example

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Standing waves Addition (same frequency) Two counter-propagating waves: Not of the form f(vt-x) Addition of waves (different frequencies) Beats For unequal amplitudes E 1 >E 2 : Beat amplitude only E 1 -E 2
Group velocity For nondispersive medium all waves move with the same phase velocity v= ! / k In the presence of dispersion the perturbation or beat pattern does not move with the phase velocity but with the group velocity because the phase relation between waves of different frequency is changing All kind of things can happen Let’s consider the beats and forget about the carrier For small changes around the carrier frequency = c n + kc d 1 n " # \$ % dk Group index of refraction " = v k Types of Dispersion normal dispersion Anormalous dispersion v>v g v<v g Superluminal light Less than 1 Possible in the region of anomalous dispersion close to a

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Unformatted text preview: absorption line Most pronounced in the region of gain Can become negative “Pulse appears behind the medium before it arrived at it ?????” Subluminal light No absorption at v o but strong dispersion Group velocity as low as 0.44m/s I can ran faster than that In a dense medium: B ose E instein C condensate Anharmonic periodic waves • Fourier Series Every period signal can be expressed as a Fourier series Example: Square wave "#\$ Nonperiodic waves • Fourier Integrals Pulses and Wave Packets • Fourier integrals give as a way to describe pulses • Case 1 (square pulse) Case 2: Monochromatic wave with beginning and end falls off fast The same for time and frequency " k " x " k = 2 # L " x = 2 L • For our pulse from before " x " k = 4 similarly "#" t = 4 \$ A short pulse has a wide spectrum Uncertainty principle Coherence Length " v # 1 " t " t c # 1 " v Coherence time " l c = c " t c # c " v Coherence length...
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