Lecture 21 Superposition and Coherence

Schedule WeekTopicChapters Apr 7InterferenceCh. 7 and 9 Apr 14DiffractionCh Apr 21Diffraction/Polarization ICh. 8, Apr 28Polarization IICh. 8 May 5EXAM II/Fourier May 12LasersCh. 13 May 19Clean UpFINAL MAY 23

Superposition recall

Recall wave addition

Interference When 2ABcos(  -  ) > 0 Constructive interference When 2ABcos(  -  ) < 0 Destructive interference If both A and B are positive then maximum constructive (destructive) interference occurs when  -  =2m  ((2m+1)  ) Example: Under what conditions does the amplitude of the sum equal zero?

Interference Measurements Typically when measuring electromagnetic waves, one measures The intensity of the light, rather than the amplitude. What is the intensity of a beam corresponding to 2 different waves

Spherical waves Intensity minima Are fringes…

Demo

Measuring Interference I xx xx Michelson Interferometer

Uses for interferometers Measuring index of refraction Measuring material thickness Measuring material flatness Gravitational waves Measuring Coherence….

Coherence If each wave has a definite phase relationship, then the wave is coherent Laser

Coherence length The “length” that a light source is coherent. xx

Characteristic Coherence Lengths 20cm - >10 7 m 0.3mm 900nm

Temporal Coherence 2tc2tc Sin(x)+sin(1.1x)

Beating

Y=sin(  t) Y=sin(  t)+sin(1.01  t)Y=sin(  t)+sin(1.01  t)+sin(1.02  t)Y=sin(  t)+sin(1.01  t)+sin(1.02  t)+…sin(1.5  t)

Fourier

Pulse Bandwidth Fourier Bandwidth Limit Equivalent to Heisenberg Uncertainty principle

Example If we have a pulse that has a frequency bandwidth of 40THz, What is the FWHM delay range in a Michelson interferometer that one could see fringes?

What happens to the beat in a dispersive medium?

Superluminal?

Group velocity vs. Phase Velocity