Importance of phase in f(  )…review 11 waves101 waves Linear phase dependence:  t  is the same. Pulse is shifted What phase function makes a shift? Why?

Importance of phase in f(  )… review 11 waves101 waves Quadratic dependence:  t  is bigger, lower frequencies are ahead

Plane waves and Fourier We’ve studied FT at one point in space (e.g. ) The pulse at all positions is (if it moves in z direction):

Assume  is large only near some  o (typical for a pulse)

Put into FT -1 : carrier wave moves the envelope rigidly broadens the envelope These products become convolutions in time

Pulse broadens and is “chirped”: lowest frequencies are ahead.

Output pulse duration versus initial pulse duration for dispersive pulse broadening with different levels of group delay dispersion (GDD). Note that shorter pulses are increasingly sensitive to dispersion. Substantial broadening occurs when the square of the pulse duration is smaller than the group delay dispersion.pulse duration Broadening of pulses, from a photonics website

Apparent faster-than-light pulses

If the pulse’s  band is in the box on the figure, the portions of light in the pulse moving fastest (highest group velocity) are :___ a)higher frequencies b)lower frequencies Group velocity changes with , so the pulse changes shape.

Apparent faster-than-light pulses The portion of the spectrum that is absorbed most is ______ frequencies a)higher b)lower

Apparent faster-than-light pulses In absorbing media: pulse if no material pulse if no absorption Peak has “moved” faster than speed of light simply because of absorption. But no information has traveled faster than c.

Apparent faster-than-light pulses Absorbing light from the middle of the spectrum can also reshape light pulse

Amplification of light due to stimulated emission If the pulse’s  band is in the box on the figure, the portions of light in the pulse moving fastest (highest group velocity) are :___ a)higher frequencies b)lower frequencies n flips about n=1;  simply becomes negative! What changed in the Lorenz model?

Can also get apparent faster-than light pulses with amplification from stimulated emission Peak can “move” faster than speed of light simply because of amplification. But no information has traveled faster than c.