http://www.youtube.com/watch?v=87pPoGuLSuw start at 40 sec xxx http://en.wikipedia.org/wiki/Group_velocity http://www.youtube.com/watch?v=r_EdsNf-ljM&list=UUF4-Wvc9XiO9JF7794vscYw&feature=c4-overview Overview of Michelson interferometer http://www.youtube.com/watch?v=87pPoGuLSuw start at 40 sec

Suppose we put the thick piece of glass in one arm of the interferometer. What will happen? This is a different theory from what we’re developing today

Reading Quiz The output measured from the interferometer depends on the _______ that goes into it. amplitude and phase of light E(w) power spectrum of the light I(w)

Reading Quiz The interferometer studied was a) Michelson’s b) Fresnel’s c) Morley’s d) Young’s

Reading Quiz I am here yes no

Punchline: what can we learn from this interferometer? If you know the light’s wavelength….you can learn how far your mirror moved, and when the path lengths are the same. If you know how far the mirror moves….you can learn about the power spectrum of the light. …that’s it!

Can we see fringes coming from the interference of two lamps? …from the interference of two lasers?

You play an identical sine wave on the two speakers You play an identical sine wave on the two speakers. What do you hear as the distance is changed?

You play a song on two speakers (not stereo) You play a song on two speakers (not stereo). How far back can you place the 2nd speaker and still hear interference effects? (compensate for 1/r amplitude drop off...equal amplitudes reach the boy)

A simpler problem, clearly defined: You play the same song on two speakers. With a microphone you average the intensity over the entire song. How does Iavg(x) depend on the separation, and on the song?

A simpler problem, clearly defined: How does Iavg(x) depend on the separation, and on the song? Only on the power spectrum Iavg(w) of the song! No phase information matters. Iavg(x) will be greatest at x=0, will oscillate with period of lavg, and the oscillations die out in a distance (v/Dw)

What if I play identical random noise on both speakers? Iavg(x) still comes from Iavg(w) : will be greatest at x=0, will oscillate with period of lavg, and the oscillations die out in a distance (v/Dw). Noise might be random, but can be interfered with itself over a distance a distance (v/Dw).

What if I play two different songs (no “coherence”)? Iavg(x) will be constant =Iavg1 + Iavg2 …same as if I played independent noise on each speaker.

Temporal coherence and interference of light How thick can a piece of glass be to see interference fringes? …it depends on the coherence length of the light we use!

Coherence time and coherence. length “Longitudinal” coherence time tc, or length lc = ctc : time (distance) interval over which we can reasonably predict the phase of a wave at another time (or distance backward/forward in the wave), from a knowledge of the present phase

What’s similar about these waves? What’s different?

Beam diagnostic interferogram for light emitted by electron beam at Brookhaven This light has coherence length of 1-2 mm

Intensity measurements Let Io be the intensity in each arm of the interferometer. If t<< tc , we get typical interference, so at a bright fringe we should get ____ Io. At a dark fringe we should get ____ Io. If we move one arm so that t >> tc, there’s no interference (no fringes), and we should measure _____ Io. Why?

Single frequency case

Single frequency case Time averaged intensity in one arm Averaged intensity combined at detector Fringes keep going as t increases! So tc is infinite for single frequency

Many-frequency case Averaged over many periods, different frequencies can’t interfere. Interferogram of gaussian pulse.

Many-frequency case I(t) g(t) a dimensionless complex function to represent the oscillations in g(t) , the intensity in one arm

Suppose we have a short pulse, and put a thick piece of glass in the beam before the interferometer. The pulse after ___in time. a) narrows b) broadens c) chirps d) a & c e) b & c

We put the distorted pulse into our interferometer We put the distorted pulse into our interferometer. The interferogram _______ a) wiggles shift b) wiggles narrow c) envelope shifts d) envelope broadens e) pattern stays the same

Why a long, dispersed pulse will have the same I(t) as its original short one.

print transparencies

Suppose we put a thick piece of absorbing colored glass that absorbs the outer parts of the spectrum The ___ a) envelope shifts b) envelope narrows c) envelope broadens d) pattern stays the same

Summary What can we learn about a beam of light from Michaelson interferometry? Only things related to the power spectrum! No phase info. For estimates use this! We could also measure with a grating and detector, and get all the info from that.

If we FT-1 E(w), we get E(t) If we FT-1 I(w), we get ….. … g (t), something that gives us the coherence time of the beam E(t)! FT of

Suppose with filters we take sunlight and form I(w) as a rectangular function centered at wo. The envelope of the wiggles g(t) of the interferogram will be _____ sinc gaussian rectangular I w

If the width of the rectangle is wo /10 The coherence time will be about 10 wo 1 /(10wo) 10 /wo 100 wo I wo w How many oscillations will g(t) make before it dies down to about ½ or so of its peak amplitude?

time t (fs) E(t) is shown with time increments of femtoseconds (10-15 sec). The approx. frequency w=2p/T of the light is ______x1012 rad/sec a) 5 b) 15 c) 30 fs

time t (fs) t (fs) How many typical periods does it take for this light to get out of phase with previous part of the beam?

time t (fs) Sketch what the interferogram I(t) would look like, in femtoseconds of delay t. Mark the coherence time and the average period of light.

Actual unnormalized interferogram shape (half of it) Actual unnormalized interferogram shape (half of it). We know I(w) is “boxy” because of the ringing in g(t)! delay t (fs)